Talk:A text-book of experimental cytology (1931) 9
CHAPTER NINE Cell Division
A cleavage of the whole cell is the natural sequence to the dhision of the nucleus and the two phenomena are usually part of one complete cycle of cellular activity. During this cycle, the cell undergoes more drastic changes in its internal architecture and in its external form than at any other stage of its existence; nevertheless, the mechanism of cleavage is still the subject of acute controversy.
Since a dividing cell undergoes a spontaneous change in form, there are two possible ways whereby its actmties might be analysed. Firstly, the cell may be regarded as a small elastic sphere which can only be divided into two parts by an expenditure of sufficient energ}' to overcome the natural t^idency of the cell to resist deformation of form. On the analogy of other types of cell movement, such a mobilisation of energy might be expected to show itself by an alteration in the rate at which the cell evolves heat or absorbs oxygen . Observations of this nature are of peculiar importance, since they should give a measure of the forces involved during cleavage even when the actual mechanical causes of the phenomenon are imisible under the microscope. Failure to obtain an insight into the energy changes involved would, on the other hand, restrict the analysis of cleavage to the visual observation of cell structures and to the response made by these to a variable environment. Oiu knowledge of the energetics of cell division is, unfortunately, very slight and most of the data are of a negative character. For this reason it is convenient first to consider the visual phenomena of cleavage.
The visual 'phenomena of cell division
In selecting material for a study of the visual phenomena of cleavage it is important to remember that the form of any given tissue cell is almost always determined by or affected by the presence of its neighbours, and that this disturbing effect wiU operate during
190 CELL DIVISION
the actual process of division. Such a factor is absent in the case of ceUs which, after cleavage, live isolated from each other. It is very unfortunate that cells of this latter type (e.g. leucocjdes or fibroblasts) exhibit during diA-ision a highly irregular form which i. exceedincrlv difficult if not impossible to resolve into simpler components.'’ Dh-ision of this type is brought about by a slow and disiointed process of separation into two daughter cells, and wliilst this is aoing on little or no change is visible in the interior of the cell The cleavaae of a living fibroblast has been observed on many occasions and by many authors: the following description is largely based on the account given by Strangeways (1922).
Durim^ the earlv stages of mitotic activity all isolated cells, however^irregular their original outline, withdraw their pseudopodial projections and assume a spherical or ellipsoidal form (fig. 77, 1-5). Soon after the anaphasic movement of the chromosomes, the cell begins to elongate along the mitotic axis. This elongation is accompanied bv two sets of visual phenomena at the surface of the cell Firstly, the elongation of the mitotic axis involves a diminution in lencrth of the equatorial axis of the cell, except in the regions of the poles, where the diameter of the cell remains practically unelianced. Secondlv, there appears at the poles a series of blunted nroiectioiis or ‘blikers’ wliich slowly develop and slowly disappear bv reincorporation into the body' of the cell (fig. 77, 7-10). This curious actimty at the poles of the cell lasts, as a rule, for about three or four minutes, and during the whole of this time the equatorial constriction gradually becomes more obvious. Eventually the two poles of the cell appear to attach themselves to the substratum by the formation of fine pseudopodia very similar to those characteristic of non-dividing ceUs . From this point onwards the two halves of the cell separate from each other by a disjointed but active process of mutual separation— until, with increasing velocity, the two daughter cells move away from each other leaving until the last moment fine strands of hyaline material which connect one daughter cell to the other. The whole process of dmsion occupies at 37° C. from 30 to 45 minutes. Owing to its low velocity, disjunctive cleavage is not readilv followed as a series of successive events which are clearly marked out as such to the eye of the observer. For this reason the artificial acceleration made possible by the process of cinematography affords considerable assistance in establishing an adequate time relationship between the different phases of the whole process. Films ot
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iQa.m.
70.5
2
70.10
3
70.75
4
70.17
5
70.21
10.18
70.79
70.52
10
70.30
70.20
s
70. 23
11
70.50
77 a.m.
Pig. 77. Cleavage of a living cell from the choroid ^
The whole cycle occupied about fifty minutes. Note the buhbhn^ the cell which accompanies the formation of the polar furrow.
(Strangeways).
at the poles of
192 CELL DIVISION
this nature (e.g. those of Dr Carrel, and those of Dr Caiiti) show very clearly the polar activities of the dividing cell, and the curious pulling effect of one daughter cell against the other. At the same time, the interpretation of accelerated films demands some degree of caution if they are used as a basis for understanding the underhung processes
of di\usion. , • • •
INo coiiiprciicnsivc tlicory of disjuncti^ 6 cell cli^ ision ii8,s ^ et been put forward. There are, however, two features which seem worthy of comment. Firstly, the so-called bubbling aethuty at the poles of the cell. This process is not restricted to dividing cells, it occurs over the whole surface of the cell when the latter becomes moribund and is about to die; it can also be induced to occur in other types of cell
Fi'> TS Pour obseri-ations at 5-minute intervals of the cleavage of a connective tissue eelTof a rat Note the elliptical form of the cell immediately before the development of the cleavage furrow. During the later stages the spherical form of the daughter cells is well marked. (Lambert and Hanes.)
(e.g. eggs of molluscs and echinoderms) by a weakening of the
hyaline layer with resultant protrusion of temporary exovate processes. When illustrated by an accelerated cinematograph film
both eggs and moribund fibroblasts give the same impression of
active ^bubbling’ as the poles of a normally dividing cell. One gets
the impression that bubbling is invariably associated with a weakening of the hyaline layer of the cell. The second point of interest
involves the drawing apart of the two daughter cells. It is more
than probable that the active organs of movement are located in
the pseudopodial processes (as in normal cell movement), and it is
significant that the pseudopodia make their appearance in the regions
where the ‘blisters’ have recently been forming; it is conceivable
that the pseudopodia, like the blisters, possess a thinner and less
well-defined surface layer than does the rest of the cell.
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193
Cell cleavage of the disjunctive type clearly involves three factors :
si) the organisation of the cell into an ellipsoid mass followed by the
development of an equatorial furrow, (ii) a weakening of the hyaline
surface at the poles of the long axis, and (iii) an active drawing apart
of the two halves by pseudopodial movement. The possible significance of this interpretation must be deferred to a later paragraph.
Fig. 79. Cells form a culture of the heart of a chick. A, Vegetative cell before the withdrawal of the large pseudopodium seen at the top left corner ; B, same cell after withdrawal of the pseudopodium, note the long protoplasmic filaments ; C, a vegetative cell withdrawing pseudopodia; Z), two daughter cells moving apart after division. Note the protoplasmic junctions: these are eventually ruptured. (From Seifriz.)
Astral cleavage
In contrast with the disjunctive cleavage, so typical of leucoc^-tes and other isolated cells, are the orderly and geometrical changes in form which characterise the division of a spherical egg cell into two contiguous blastomeres. Not only are the changes in form of a comparatively simple nature, but during cleavage the internal architecture of the cell is of a type which exists at no other phase of actmty. It is not surprising, therefore, that marine eggs provide the favourite material for the investigation of cell division. At the same time they introduce a complication. When an echinoderm egg dmdes into two blastomeres, each of the latter remains adherent to its neighbour, and neither of them (in nature) ever regains the spherical form of the undivided egg. A considerable body of e\ddence
GC _ 13
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CELL DIVISION
shows that the precise form of the cleavage furrow is the result, not only of the cleavage mechanism, but also of the mechanism which keeps the two daughter cells in contact with each other when the cleavage itself has been completed (Gray, 1924).
Before proceeding to aspects of astral cell division, which are either speculative or controversial, it is useful to consider those facts which are generally accepted as true. As pointed out elsewhere (Chapter VI) the fertilised egg of a sea urchin {Echinus esculenius in Urticular) no-v•^>cs a well-defined hyaline layer at the surface of the cell (fi<^ 3-’ ) Until the process of cleavage begins, this peripheral or hvaloplasmic laver is uniformly distributed over the egg surface and fine protoplasmic strands pass across it between the c}i:oplasm of the cell mid the external boundary of the layer itself (Gray, 1924). Tlus external boundarv undoubtedly consists of a solid membrane whose properties are quite well defined. It is imperfectly elastic; it can be iawn into fine threads which, on release, recover to some extent their original form, leaving distinct although sometimes transitory traces of disturbance. The chemical nature of the membiane is unknown, but it has two important reactions; firstly, it is soluble in sea water if the latter contains no calcium ; secondly, m the presence of dilute acid it contracts and becomes tightly compressed to the surface of the cvtoplasm. The existence of this hyaline membrane has been clearly demonstrated in a considerable variety of material, but it is much more clearlv defined in the eggs of E. esculentus than in E miliaris, Arbacia, or Echinarachius. Just as in the case of disiunctive cleavage, so the onset of astral cleavage is marked by an eloimation of the egg axis which is at right angles to the plane ot the future cleavage furrow. Until this polar elongation begins, the hvaloplasmic laver is uniformly distributed over the surface of the eaa ; as soon as the egg elongates, the hyaline material begins to flow from the poles of the cell to the equatorial furrow. As the furrow deepens, so the hyalme material becomes more and more aggregated into the equatorial region of the egg until, with completion of cleavage, a well defined intercellular plate of hyaloplasm separates each cell from its mate, whilst the intercellular plate is contmuous with a verv thin laver of similar hyaline substance which still covers the polar regions of each cell (fig. 80). The protoplasmic processes, which, prior to cleavage, traverse the hyaloplasm, are withdrawn during dmsion, only to be reformed after this process is complete The more pertinent of these facts have not been questioned, bu
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195
are accepted with one important proviso by three recent investigators whose interpretations differ Avidely from each other (Just, 1922 ;
CliaDihers, 1919, 1924 ; Gray, 1924). The main point at issue inA’olves
the precise moment at which the hyaloplasm begins to flow from the
poles of the cell to the equator. According to Just (1922), this
redistribution proceeds to an appreciable extent before the cj-toplasm
Fig. 80 . a-g, Normal cleavage of the egg of Echinus esculentus. Note the gradual flow of hyaloplasm (’white) from the poles of cell to the equator. Inf note tliat the cytoplasm is almost completely divided. In g the hyaloplasm has joined in the centre and the two masses of cytoplasm are completely divided off from each other but are complete!}' surrounded by hyaloplasm.
of the egg begins to lose its spherical form, whereas other obserTations (Gray, 1924) lead to the belief that these two processes begin simultaneously. As will be obvious later, this point is of fundamental importance.
In discussing the process of mitotic division, it was pointed out that the period between the fusion of the two pronuclei and the anaphase of the first division is marked by a gradual increase in the size of the two mitotic asters. As this increase in size takes place, it
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CELL DIVISION
can be seen that each aster is an almost perfect sphere, but as the
spheres increase in volume the individual rays tend to become less
distinct. This phase of increase in size of the two asters is illustrated
by fig. 81 . At the anaphase (see fig. 81, 8) the form of the asters begins
to change. They continue to enlarge in volume but they are no
longer spherical, for they flatten against each other in the median line
(figs. 58 a and 81, 4-T). As soon as the two daughter nuclei are formed,
practically the whole of the cjToplasm of the egg is occupied by the
two asters whose rays extend almost to the periphery of the cytoplasm. So far, the cell has retained its spherical outline, but at this
moment there is a visible change in the shape of the whole egg. The
polar elongation begins.
The changes in the size and in the form of the asters are admittedly not so clear in the living egg as they are in preserved material (see, however, fig. 58), and some difference of opinion exists, concerning the precise moment at which the asters reach their maximal development. Just (1922) concludes that the astral rays, in Arbacia eggs, fade away before cleavage of the cytoplasm begins: this is not the ease in E, esculentus^ for a well-defined aster can be seen after the completion of cleavage, both in preserved and in living material; during the actual process of division almost the entire volume of the egg is occupied by the astral rays, only the region of the equatorial furrow is exempt. This uncertainty concerning tlie time relationship of cleavage to astral development is of importance, although not decisive from a theoretical standpoint.
In some cells the development of the cleavage furrow is accompanied by a visible streaming of peripheral cytoplasm towards the equatorial furrow. This has been described by Erlanger (1897), Loeb (1895), and more recently by Spek (1918).
So much for the facts. All recent theories of cell cleavage hinge on three points. Firstly, what role, if any, is played by the hyaloplasm? Secondly, Tvhat rdle, if any, is played by the mitotic asters? Thirdly, what part is played by the peripheral streaming of the cytoplasm?
It is convenient to consider the hyaloplasm first. Just believes that this layer is the active mechanism of cleavage. In Arbacia eggs he has observed in this layer some degree of amoeboid movement which he regards as an indication of sufficient power to move to the equator of the ceil and, by a process of active constriction, divide the cell into two halves. Obviously, on this interpretation, there is no
2
Pig. 81. Camera lueida drawings of developing asters from sMtions of B^inus eggs
fixli in corrosive sublimate. Note change in shape of the asters after the a^phase
stage is reached : also note loss of definition of astral rays with increase in
the asters.
19S CELL DIVISION
reason ^vhv an equatorial accumulation of hyaloplasm should not occur before the actual process of cytoplasmic cleavage begins, since the polar elongation of the cell ivould be the natural result of equatorial compression. A direct test of Just’s interpretation is available bv removing the hvaloplasmic layer from the egg either before or during cleavage. already mentioned, the hyaloplasmic membrane is soluble in calcium-free sea vater, and it is for this reason that secmiented eggs disintegrate into their constituent cells when in such a medium (see Chapter VI). If eggs of Echinus escu entus are reared in normal sea water until 10-15 minutes before cleavage, and are then placed in calcium-free sea water, they soon reveal two significant facts Firstlv the hyaline layer has been dissolved. Secondly, the
Pi« 8-> Cleavage of the eag of Echinus in calcium-free sea water Note that the K nV ute hvahne layer causes a marked increase of the elongation of the polar Ss S the cili "and that the latter is eventually resolved into Pvo spherical
blastomeres.
polar elongation of the cells, far from being decreased, is actually
increased (see fig. 82). It is extremely difficult to harmonise these
facts with Just’s hypothesis. That the presence of the hyaline layer
tends to reduce rather than increase the polar elongation of the
dmding cell is strongly supported not only by the effect of its
removal during (or after) cleavage by calcium-free sea water but also
bv the action of twm entirely independent pieces of evidence.
By a fortunate coincidence there is a marked difference in t e osmotic properties of the hyaline membrane and of the egg cytoplasm The former is freely permeable to electrolytes, whereas the latter is not: consequently when the eggs of Echinus esculentus are placed in hypertonic sea water the volume of the cytoplasm is
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decreased, whilst the volume contained within the hyaline membrane
is. if anything, increased. Under such conditions the compression
normally exerted by the hyaloplasm on the cytoplasm is relieved
and the relative length of the polar axis of the cell is definitely
increased (fig- 83). The form of the dividing cell under such circiiiiistances is similar to that of eggs exposed to calcium-free sea water,
although of course the cell volume is less. Just as the compression
exerted by the hyaloplasmic layer on the cytoplasm can be relieved
Fig. 83. Effect of hypertonic sea water on the form of the cleaving eggs, a-g show the
effect of transferring the normal eggs shown in fig. 80 a-g to Iiv’pertonic sea water.
Note change in form of cytoplasm, with increased elongation of the polar axis.
by hypertonic sea water, so it can be reinstituted by returning the
egg to normal sea water, or better still by exposing the egg to acid
sea water. Under such circumstances the dividing cell in\ariably
responds by shortening its polar axis. Since the hyaloplasm is
bounded by a solid extensible membrane which w’^ill only change
in form if we exert on it a definite force, and since it is undoubtedly
the agent whereby the fully divided cells adhere to each other in
their naturally compressed form, we are driven to conclude from the
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CELL DIVISION
aboTe evidence that the r5Ie of the hyaloplasm during cleavage is
the same as after cleavage ; in both cases it tends to reduce the polar
axis of the cell when the latter tends to elongate under the influence
of other forces. We cannot regard the hyaloplasm as the active
cause of polar elongation or of cell division: it affects the form of the
cleaving cell, but is not part of the active cleavage mechanism.
Pig. 84 . Effect of acid on the form of contiguous blastomeres of Echinm. a> Normal egg; b, same egg in acid sea water; c, egg with hyaloplasm partially removed by calcium-free sea water; d, same egg in calcium-free sea water + acid. Note that the compression of blastomeres is restricted to the area over which hyaloplasm is still present.
'When a dividing cell is denuded of hyaloplasm (see fig. 82), its form suggests quite clearly that division into two daughter cells is being effected by the resolution of the cytoplasm into two spherical regions, each of which when surrounded by its normal hyaloplasm responds as though it were an elastic shell. The suggestion at once
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— can each of these spherical regions be correlated with the
regions occupied by each of the two mitotic asters?
The rdle of the asters during cleavage
The most direct proof that the asters form an active part of the cleavage mechanism is provided by the fact that any irregularity in the size or position of these structures is invariably accompanied by an irregularity in the form and position of the cleavage furrow.
In order that cleavage should occur in echinoderm eggs it is essential that there should be two asters each of which must be located within a short distance of the cytoplasmic periphery.
Fig. 85. Fertilised egg of Toxo'pnemtes after exposure to ether, a. Before cleavage:
b, after cleavage. Note that the male amphiaster has divided the ceil into two
blastomeres A and B, whilst the female monaster has deformed the surface of the
cell at C. (From Wilson.)
A single aster near the periphery will deform the surface of the cell but it will not produce a cleavage furrow; this can be observed in the case of the large monaster typical of the period prior to fusion of the two pronuelei (Gray, 1924): it is also illustrated by the observations of Wilson (1901) (fig. 85). Whenever there are two asters present which are equal in size and whose rays extend to the periphery of the cell, a cleavage furrow will form between them ; if there are three asters, there will be three cleavage furrows ; if there are four asters, there will be four cleavage furrows. Similarly if two asters (of adequate size) are present — but one is larger than its mate —then unequal cleavage results. If the line joining the centre of the two asters does not pass through a diameter of the egg by the time
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CELL DIVISION
the astral rays reach one side of the egg, then the cleavage furrow
develops first on that side, and only later (as the raj^s reach tiif^
opposite side of the equator) does the furrow develop on the other
side. All these phenomena can be observed in the natural cleava<ye>
of various types of cell. That the irregularity of form and positLn
of the asters is the cause and not the result of irregular cleavage is
suggested by the fact that similarly irregular cleavages can be
induced to occur in Echinus eggs by experimental means (Grav
1924).
E. B. Wilson (1901 b) showed that the normal astral radiations disappear if the eggs of Sphaerechmus are exposed to sea water containing ether (see p. 159). On replacing the eggs in normal sea water the radiations reappear: they do not, however, reach their normal size before again fading away. The result is that the egg niav subsequently form a cleavage furrow which fails to cleave the eg(y As soon as the asters fade away all development of a cleavage furrow ceases. This experiment has been repeated, and Wilson’s results have been confirmed.
If eggs of £. esculentus are allowed to develop in normal sea water until the anaphase of the first division and are then transferred to 3 per cent, solution of ether in sea water, the astral rays very rapidlv (2-3 minutes) disappear, and a clear irregular space appears in the centre of each of the original asters (fig. 58 b). If these eggs are now returned to normal sea ^vater, the astral rays reappear within about 15 minutes. In some of these eggs the rays rapidly extend to the periphery of the cell, and the latter cleaves normally into two cells. In other eggs, ho^vever, the reformed rays do not reach the periphery of the c^oplasm before fading a^vay . In such eggs no cleavage occurs until the second nuclear division.
If eggs are allowed to develop in normal sea water until the telophase stage is reached, and are then etherised and returned to normal sea ivater again, it is found that -whereas two large asters existed at the beginning of the treatment, yet w^hen the asters reform in sea water, they appear not as tvro large asters, but as four asters much smaller ill size. The two original daughter nuclei divide in conjunction -with the four new asters and the cell divides into four normal blastomeres. In other words, the first cleavage has been entirely omitted (see also fig. 94).
Finally, if eggs are etherised in 2-5 per cent, ether solution, and are then transferred to sea w-ater containing a very small concentra
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tioa of ether, e.g. 0-05 per cent., the asters -n^hich reform in the sea
water always remain small. Nuclear division occurs normally but,
oving to the small size of the spindle and of the asters, the nuclei
remain close together and no cleavage occurs. The cell thus becomes
a well-marked syncytium (fig. 86 a). Eventually, however, the small
asters become sufficiently numerous to extend throughout the whole
ess, and at this moment multiple cleavage occurs. In some eggs
there appears to be a tendency for the nuclei with their asters to
collect at the surface of the egg (see fig. 86 b), and when the astral
rays of these nuclei extend to the egg surface there is a distinct
tendency for segmentation furrows to appear between them, although
these furrows are never complete.
Fig. S6. Echinus eggs segmenting in the presence of 0-05 per cent, ether, a, Xote numerous nuclei forming a syncytium ; 5, note peripheral arrangement of nuclei and incomplete cleavage planes.
There can be very little doubt, therefore, that the nature and
extent of the cleavage furrow are very closely associated with the
position and the size of the asters. If, then, the appearance of a
cleavage furrow is the direct mechanical effect of asters whose rays
extend to within a critical distance of the periphery of the cytoplasm,
and these asters are made to disappear before the cleavage furrow
is actually completed, further cleavage should cease and. the egg
should tend to resume its spherical form. This is the case. If eggs
are allowed to develop in normal sea water until the cleavage furrow
is just beginning and are then etherised in 2-5 per cent, ether, the
condition shown in fig. 87 can be obtained. In these eggs a welldefined cleavage furrow exists but there are no asters. On transferring such eggs to sea water the cleavage plane is gradually lost.
If the original cleavage furrow was shallow, then on transference to
normal sea water after etherisation, the egg gradually becomes completely spherical, at the same time the surface of the hyaloplasm is
thrown into distinct folds. If, however, the original furrow was
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CELL DIVISION
Fig. 87. Eg" of Echmus vdth normal cleavage furrow placed in 2*5 per cent, ether solution for 20 minutes, then transferred to normal sea water. Note absence of asters and gradual loss of cleavage furrow; also the crinkled hyaline membrane in d.
Pig. 88. Egg of Echinus transferred from 2 per cent, ether to normal sea water. Note asymmetrical astrospheres without astral rays, also cleavage furrow, gradual obliteration of cleavage furrow, and displacement of hyaloplasm. Note subsequent division of astrospheres and development of astral rays.
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CELL DITISION
well developed, then on return to sea water the egg tends to retaip
an elongated form, although the furrow itself disappears. At the
same time the vTinkliiig of the hyaloplasm is extremely obvious ir
the equatorial region. The elongated form of these eggs is, however
rapidly lost as soon as the astral rays of the next nuclear divisior
begin to approach the periphery of the cytoplasm.
Besides ether, many otiier reagents tend to inhibit the iiomiai develo]}. iiient of the asters, and yet allow the nucleus to divide normally. Aniori'. such reagents is siiglitly hyperaikaline sea water. The asters*" are sniaH a Lid asYiiimetrieally bitiiated and produce a cleavage furrow on om side of tlie egg only. The same thing occurs in hypertonic sea water A delieiency of calcium or potassium has the same effect.
I’he form of the cleavage furrows in many of these reagents is extremely irregular. It is difficult to see how such furrows could be the result of a differential iiiterfacial tension at the poles and at the equator oi tlie cell; they are, however, explicable on the assumption that the furrow is being brought about by a redistribution of the different phases of the egg.
The close relationship which exists between the position and form of the asters with the position and form of the cleavage furrow is readily understood if we assmne that the asters are an essential part of the active cleavage mechanism, and this view provides areasoiiai}Ie working hypothesis for fm'ther analysis.
Before discussing the nature of the force which may be exerted on the cytoplasm by means of the asters, it is of value to recollect that the evidence from microdissection (Chambers, 1917) and from the use of the centrifuge (Heilbrunn, 1921), indicates fairly clearlv that the region of the cytoplasm occupied by the astral rays is of a more rigid or viscous nature than the non-radiate regions. The initial increase in the viscosity of the egg which takes place soon after fertilisation is directly associated xvith the existence of the fullv formed sperm aster which pervades the whole egg. As soon as this aster fades away the c}i:oplasm again resumes the fluid state. Similarly, Chambers (1917) has shown that the asters during cleavage are areas of considerable rigidity w^hen compared vith the peripheral regions of the cell.
Theory of astral cleavage
If we are prepared to regard the asters as elastic spheres possessing a definite degree of elastic rigidity (see p. 158) and if we are prepared to admit that they grow in size at the expense of the fluid cytoplasm.
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it seems possible to formulate a tentative theory of astral cleavage.
Consider two solid and perfectly rigid spheres separated from each
other and each surrounded by a film of liquid material (fig. 90 ^). If
these two spheres are allowed to come into contact vhth each other
aiey will adhere together by their liquid films, and if the latter are
sufficiently voluminous there will be an accumulation of fluid at the
region of contact, since in this way the total free surface of liquid
is 'reduced to a minimum. Similarly if we start with two clean
contiguous spheres and add to their surface a liquid, the latter will
distribute itself as in fig. 90 B, and as the amount of liquid is increased,
so the external surface of the liquid wflll more and more approximate
to that of a sphere. The two contiguous spheres are, of course, held
together by the surface tension of the fluid phase and can only be
separated by applying a force sufficient to overcome this tension and
Fi2. 90. A, Two solid spheres with a surface layer of liquid; B, the same spheres in
contact. Note the aggregation of liquid at the equator of tiie system.
the viscous resistance set up by the fluid when in a state of flow. If instead of using two rigid spheres in the above experiment, we use two elastic spheres whose degree of elasticity is such that the tension exerted by the common liquid surface is sufflcient to distort the spheres in an obvious way, then the region of contact between the spheres will be marked by a flat interface and each sphere will be compressed along its polar axis. An extreme case of such a system is provided by soap bubbles where the liquid phase is extremely thin, so that the equatorial accumulation of fluid is very small. Another example is provided by drops of water immersed in a drop of oil of the same specific gravity (Gray, 1924). If a fairly large drop of olive oil be immersed in a mixture of alcohol and water of the same specific gravity, it is possible to inject into the oil two drops of the external medium. If these drops are gradually enlarged, the external surface of the oil remains spherical until the diameter of each of the
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CELL DIVISION
enclosed and equal sized water drops is nearly half the diameter of the oil. If, now, the volume of the water drops be increased, or if the volume of the oil be decreased, a marked change in the form of the system takes place. The whole s\ stem elongates along its polar axis, the enclosed water drops flatten equatorially and are separated by a film of oil : simultaneously the oil flows away from the poles and collects at the equator as sIioato in fig. 91.
Fig. 91 . Two water drops enclosed in a drop of olive oil. Note changes in the distribution of the oil and in the form of the water drops which occur when the relative volumes of water and oil are altered. The oil is black, the water white.
Starting from the assumption that the asters represent two
spherical elastic spheres which increase in volume at the expense of
the peripheral fluid c}i:oplasm, we can apply the above principles
to the cleavage of an egg. One would expect the egg to maintain its spherical outline imtil the combined diameters of the two
asters was equal to that of the spherical cytoplasm. At this point
three tilings must happen : (i) the asters will be pressed against each
other in the equatorial plane, (ii) the polar axis of the egg will
increase in length as soon as the elastic force exerted by the asters
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209
is sufficient to overcome the tendency of the cytoplasmic and hyaline surfaces to resist a change in form, (iii) as the polar axis increases with the grovdh of the asters, so the finid material ronnd the asters
- i.e. the peripheral cytoplasm and the fluid between the hyaline
nieinbrane and the cytoplasm) will begin to flow to the equator of the egg and this flow will continue until (a) the asters cease to grow, ih) the force required to keep the fluid material in motion is equal to that of the elastic forces exerted by the compressed asters. It will be recalled that a peripheral flow of cytoplasm from the poles of the cell to the equator has actually been observed during normal cleavage (Erlanger, 1897).
Fig. 92. Diagram to illustrate the conversion of fluid c>i:opiasm into two elastic
.spheres (marked by astral rays). During this process the fluid phases viii distribute
themselves largely in the equatorial furrow.
The theory of astral division here outlined stands or falls by
the possibility of regarding the asters as elastic spheres capable
of generating sufficient elastic energy to overcome the resistance
offered by the peripheral cytoplasm and by the hyaline layer. An
adequate proof of this fundamental point is not easy to obtain : it is,
however, a reasonable interpretation of the observations of Chambers
(1917) and of Heilbrunn (1921). It is also supported by the fact that
when the astral rays fade away after cleavage the two blastomeres
are more readily compressible than is the case when the asters are
still in situ (see also fig, 59).
There is one series of facts which are at once a support and a criticism of these conceptions. Most non-spherical cells divide at right angles to their longest axis. If the two asters are to be looked upon as two spherical masses free to move within the viscous c}i;oplasm, they will naturally orientate themselves along the long axis of the cell, as is the case in Nematode eggs (see fig. 93). On the other
GC
14
210 CELL DIVISION
hand, such an. orientation is absent during the incomplete cleavagt^ eggs and in the unec^ual cleavages characteristic of ovarian maturation divisions. In such cases, the asters do not appear to be free to move within the cytoplasm but are apparently ancliored in an eccentric position. It is just conceivable that in these cases the viscous resistance of the cytoplasm is greater than the elastic or plastic strength of the cytoplasmic surface, so that as the asters grow they distort the surface of the cell instead of moving bodily through the cv’toplasm and long before their combined diameters are equallro that of the whole egg.
333
Fi ’. 03. Rotation of the first mitotic spindle in the egg of Ascaris; the arrows e and s show the path of approach of the male and female pronuclei. Note final positica of spindle in Iona axis of the egg. (From Korsehelt and Heider.)
To some extent, the utility of any biological hypothesis depends
on its width of application, and an obvious objection to be urged
against any theory of cleav^age which ascribes a specific role to the
nfitotic asters is the fact that some cells exhibit no asters during
cleavage. As far as is knovvm, however, when astral rays are absent
from a dividing animal cell, the orderly formation of a geometrical
cleavage furrow is never clearly marked, although it is said to occur
in certain plant cells (Farr, 1918). It will be noted, however, that the
essential character of the aster is not the presence of astral rays, but the
possession of a definite degree of elastic rigidity. It is quite possible
that such a physical state might exist locally in the cell without a
visible radiate structure. The presence of two such regions would
account for the ellipsoidal form of dividing leucocytes. In other
CELL DIVISION
211
words, the cleavage mechanisms of an egg and of a fibroblast may
be essentially the same, except that, in the latter case, there is no
visible sign of the elastic regions at the poles of the cell.
Burrovs (1927) has recently ascribed the cleavage of fibroblasts to the ■ eentrospheres ’ (= asters) and although this conception harmonises ■nith the hqjothesis sketched above, it must be admitted that no very obvious ■woof exists to show that centrospheres are actually present in such cells
as risid structures.
When all has been said in its favour, any theory of cell division is at present open to the fundamental objection that we are unable, by direct experiment, to measure the magnitude, nature and distribution of the forces generated within the cell. All we can do is to rely on visual phenomena and interpret them as best we may. Unfortunately, visual phenomena are seldom identical in any two types of cell. An observer is likely to attribute greater importance to a particular phenomenon if this is more strikingly obvious than another in the particular material he is observing: in another type of cell the clarity of the two phenomena may be reversed and a different perspective is obtained. For this reason, it is not hard to reach a position more adapted to dialectic skill than scientific enquiry.
Alternative theories of astral cleavage
Just’s (1922) theory has already been mentioned. This author regards the hyaline layer as the effective mechanism of cleavage and claims that an equatorial accumulation of hyaloplasm occurs before the polar axis begins to elongate and before any equatorial furrowing begins. If this be true, then the theory outlined above must be revised. A very careful observation of the normal eggs of Eckin-us eseulentus leads to the belief that Just’s conclusions are not Mpplicable to this material; only in abnormal eggs, wliich fail to divide, is there any local aggregation of hyaloplasm W'hilst the egg is in the spherical condition. There can be no doubt whatever, that in Arbacia or Echinarachnius eggs the hyaline layer is much thimier than in E, eseulentus, and for this reason close observation is more difficult. Just’s point is, however, of fundamental importance and should be determined without delay : there is no reason why such a difference of opinion should exist, since the truth could be established by cinematography with reasonable ease. At the same time,
14-2
CELL DIVISION
the behaviour of eggs denuded of the hyaline layer seems to preclude
Just’s main conception of cleavage.
In marked contrast to Just’s theory is the hypothesis put forward bv Chambers (1919). This author, far from regarding the hyaline layer as the active cause of division, denies that it plays any part in determining the form of the dmding egg. Chambers claims that the hyaline layer can be removed (by microdissection) from the egg
5.40 5.45
F • 'tl Development of an Asterias esg after manipulation -n-ith a needle so as to
stippreK the Brst cleavage furrow. The egg ultimately juelds a normal larva. (Froa
Chambers.)
prior to division, and that, after such treatment, normal cleavage ensues. This view' overlooks the fact that the hyaline laj^er is ter\ rapidly regenerated in normal sea 'ivater, and that it unquestionably controls the form of the cell during the intercleavage periods. On the other hand, Chambers was the first author to suggest that the asters are to be regarded as rigid bodies which are the active agents of cleavage. ‘The segmentation process may be explained as consisting essentially in a growdh within the egg of two bodies of material through a gradual transformation of the cytoplasm. This transformation is associated with a change in the physical state of the
CELL DIVISION
213
protoplasm, two semisolid masses growing at the expense of the more
Jkid portions of the cytoplasm’ (Chambers, 1919, p. 52).
Py moans of specially prepared, needles Chambers was able to operate on the dividing eggs of ^7'hacia and A.stevias. In one experiment the ainphiaster was destroyed by mechanical agitation, and consequently no eleavage furrow formed until new asters had developed preparatory to the second cleavage into four cells. That practically the whole c\'topiasm
Fig. 95. By means of the needles shown at the top of the figure, an egg of Asterim was cut as shown in a when the asters were well developed. Note that the form of the cut surface is retained for some minutes. (From Chambers.)
of the egg possesses considerable rigidity when the asters are fully developed is shown by fig. 95. If a cut is made into an egg at tliis stage, the form of the egg is retained, and the edges of the cut are well defined: this is not the case if a cut is made before the asters are well developed. The results of these experiments lead to the conclusion that the changes in shape during cleavage are due to the formation of the two rigid asters, and it is this process which leads to the elongation of the egg axis prior to cleavage.
The three hypotheses now considered all attribute cleavage to the mechanical pressure exerted either by the hyaline layer, or by the
214
CELL DIVISION
gro’n’iiig asters, or both. lu this they differ from the tjpe of hypothesis put forward some years ago by Robertson (1909—13). McClendon (1912, 1913), and more recently by Spek (1918). These authors attribute cell cleavage to localised alterations in the ^ surface tension ^ c*f the cytoplasm- It has already been mentioned that during the de-\-elopment of a cleavage furrow there is a peripheral flow of liquid cytoplasm vlth its granules from the poles of the cell to the equatorial furrow. Whereas earlier observ'ers were inclined to regard these moving currents as the active cause of cleavage, Spek suggests that they are caused by localised changes in surface tension on the ceil surface and that it is these changes which are the direct cause of both cleavage and current formation. As Chambers (1924) points out, the currents seen in the slowly cleaving echinoderm eggs are much less obvious than those seen in the more rapidly dividing nematode eggs observed by Spek.
The theories of Robertson, McClendon, and Spek are all based upon analogies drawn from the behamour of oil drops floating or immersed in water. IMcClendon infers that cell cleavage is due to a reduction in the interfacial tension at the poles of the cell ; Robertson on the other hand infers that the reduction takes place at the equator. For the details of these arguments reference must be made to the original papers, but it is necessary to draw attention to the fact that the models put forward will only wmrk successfully under certain conditions. In practice, an oil drop can only be made to divide by alterations of interfacial tension when {a) the drop is of considerable size, (b) when the rate at which the differential surface tension develops is very rapid, and in order that this may be the case very powerful reagents must be used. If the drop of oil be veiy small, any difference set up in the interfacial tension at one point is rapidly transmitted over the whole surface, and onty a momentaiy disturbance in the form of the drop is observed. In the case of a larger drop, cleavage only occurs when the alkali employed for the local change in interfacial tension is sufficiently strong to act vith great rapidity: otherwise the whole surface comes into equilibrium before cleavage can occur. The living cell is extremely small in comparison to the oil drops used for such experiments, and the application of such reagents as were used by McClendon or by Robertson would immediately cause the death of the cell. Again, the process of normal cleavage is relatively slow; it may take at least half an hom-.
CELL DIVISION
215
The velocity at which a cleavage furrow cuts through the equator of
5 cell does not appear to have been recorded, although it is of some interest,
4 few observations on the eggs of Echinus indicate that the velocity at
which a furrow cuts through the cell is very slow; if the cell is 100/x in
diameter, cleavage may occupy about 30 minutes at 11-0^ C.— this is
equivalent to a velocity of about 1 cm. in two da^^^s. At lower temperatures the process is very much slower. It is interesting to note that the
velocity of cleavage is more or less independent of the size of the cell, so
that large cells take longer to divide than do smaller cells— a fact which
is in marked contrast to the mitotic division of the nucleus (see p. 146).
There is no reason to suppose that the energy required to cleave an echinoderm egg is of a different order to that required to cleave a Paramecium, and this (according to Mast and Root, 1916) is of the order of at least 383 dynes per square centimetre. When we compare this with the differences in interfacial tension which can be set up at an oil/water surface, it is difficult to accept the view that there is any real comparison to be drawn between the cleavage of a single-phase oil drop and that of a living cell.
Both Robertson and McClendon make one very important assumption. They assume that the surface of the living cell is of a liquid nature. Further, both authors leave their analogy at the point where the cleavage is just complete. One of the most striking features of the fully cleaved cell is that the two resulting blastomeres show no tendency to fuse with each other. Newly cleaved oil drops, however, fuse together readily as soon as they are again in contact : they can only be prevented from fusing if a third phase be present which forms a protecting layer on the surface of the oil sufficiently strong to oppose the operation of surface forces (see p. 250). There is no evidence that either McClendon’s or Robertson’s experiments would succeed under such conditions.
One significant fact is often overlooked. If, after a cleavage furrow' has begun to form, it be brought to a standstill by mechanical destruction of the aster — by cold, or by chemical means — the furrow itself is relatively stable, andis only slowly obliterated (see figs. 87, 88). All incomplete furrow's would be highly unstable if the cell surface were liquid or were under mechanical tension. Since the egg surface is solid, such forms are readily explicable. The hyaloplasmic membrane is extensible but is not perfectly elastic, so that when once it has been elongated by the growth of the asters, it tends to prevent the cell regaining its original spherical form when the asters are removed from the partially cleaved cell.
216
CELL DIVISION
The energetics of cleavage
Although the elastic properties of the cell surface can be demonstrated with ease, it is by no means a simple matter to obtain a quantitati\'e estinmte of tiie force which must be applied to effect a change in surface area equal to that produced by normal cleavage.
An attempt to obtain such data has been made by Vies (1926;. whose estimate of the surface energy of a spherical cell is based on the fact that when isi equilibrium with a distorting force the degree of departure from the spherical form is a function of the surface energy. When a spherical egg cell is resting on a horizontal plane and is in equilibrium with g^a^-ity, the surface energy (a) of the cell surface can be expressed by the empirical formula
where a is the Iiorizoiital diameter of the egg and b is the vertica! diariieter: is the density of the egg and the density of tlie
rnediinn. At pH 8*0 — which is the appropriate value for sea water— the surface forces have a value of approximately 20 dynes per square ceiitiriietrej or roughly that characteristic of an olive oil/water interface. Prior to and during the process of cleavage the eccentricity of the egg in equilibrium with gravity fluctuates considerably and immediateiv prior to the normal elongation of the mitotic axis there is a niarked increase in the power of the egg to resist deformation (see fig. 96 j.
It will be noted that the distorting force of gravity is opposed by more than the so-called surface tension of the egg surface. This surface is composed of an elastic solid, so that Vies’ observations are probably a measure of the elasticity of the surface rather than of the intensity of forces strictly^ comparable to surface tension. It is also rather doubtful how far it is legitimate to assume that the only force opposed to gravity is located at the egg surface for this would only be true if the interior of the cell is entirely fluid ; if it has, at any time, a finite degree of rigidity', the resistance offered to gravity would be temporarily' increased. Since the mitotic asters possess rigidity, the marked increase in the value of a immediately^ prior to cleavage may be due to changes inside the cell rather than at its surface. It would be interesting to consider how far Vies’ data would enable us to predict the amount of energy^ required to increase the surface area
CELL DIVISION 217
of an egg by 25 per cent., which is approximately that produced by equal cleavage.
Apart from this isolated observation all our data concerning the energy disturbances during cell division are based on indirect methods of attack. In 1904 Lyon attempted to measure the intensity of carbon dioxide production during the cleavage of the eggs of Arbacia. His results, admittedly based on a someAvhat indifferent technique, indicated that the actual process of cell division was accompanied by an increased production of COg. Inapparent contrast
Fig. 96. Surface tension, expressed in dynes per sq. cm., of an egg of Paracentrotiis prior to and during cleavage. (From Vies, 1926.)
to this observation, Lyon found that this period of increased carbon dioxide production did not coincide with that period of the division cycle during which the egg is most susceptible to lack of oxygen or to the presence of potassium cyanide. ‘When oxygen is most necessary and presumably is being used in largest amount, COo is produced in least amount.’ Lyon made it abundantly clear that he did not regard his experiments as of sufficient accuracy to warrant far-reaching conclusions, but he inferred tentatively that the energy for cell division is derived from a non-oxidative reaction. Some years later Warburg (1908) investigated the rate of oxygen con
21S
CELL DIVISION
sumption of echinodom. cirgs at varj-ing stages of segmentation, and shosL quite conclusively that as development proceeds so the demand for oxvgen inereases. There is some tendency to aceept aesc facts as an hidication that the process of cleavages mtmiately associated with increased respiration and. at first sight this point
of view is supported bv the more recent observations of t les lKs).
m author Ibscr.-cd the ehanges in the hydrogen-ion concentration
Fig. 9T.
Correlation betrveen evolution of CO, and cell ^vision (after Vies).
Each cleavage appears to initiate an outburst ot CUo,
of the sea tvater in immediate contact vith the dividing eggs
of Faracentrotus, and reported marked cyclical changes m respect
to each cleavage cycle. Vlfes’ data are embodied in fig. 97. The
respiratorv changes observed by Vies are obviously different to
those deskbed by Lyon, since in the former case the penod of
most intense COj production follows cleavage, whereas m the latter
case it marked the actual period of cleavage itself.
CELL DIVISION 219
In view of the theoretical significance of a change in respiratorv activity during cell cleavage, it may perhaps be permissible to point oiit one or two peculiarities in Vies curve. It would appear that just prior to the third cleavage there is an actual absorption of CO^, unless this point is due to experimental error. If this be so, however, many of the points employed to show that there is a periodic formation of CO. also lie ,rithin the experimental error. Again, after the third cleavao-e the ecro-s do not appear to have given off any CO^ for more than one hour Before attaching implicit faith to these facts one would like to know more precisely the conditions under which the experiment was earned out. In experiments dealing with small variations in the respiration of cells it is essential that the conditions should be accurately defined. For this reason, the results of Vies cannot strictly be compared to those described below. In Vies’ experiments the COg was allowed to accumulate and the ews were not agitated.
In order that an accurate estimation of the rate of carbon dioxide production or of oxygen absorption may be made at different stacres during the whole mitotic cycle, it is necessary that the conditions of the experiment should be such as will allow the eggs to develop normally and at the same rate, so that practically all the cells cleave at the same time. Again, in order that several determinations can be made during the comparatively short time occupied by the cleavage process, it is advisable to prolong this period by carrying out the whole experiment at a fairly low temperature. Aar attempt to fulfil these conditions was made by Gray (1925). The eo-gs of Echinus esculentus were used, their oxygen consumption beinv measured by means of a differential manometer. In these eggs the first cleavage furrow cuts through the egg in about 30 minutes (at 1 1 -0 = C. ) after its first appearance ; the time required for subsequent cleavages is shorter. The results of such experiments (see figs. 98, 99) indicate that there is no measurable change in the rate of oxygen consumption associated with the act of cell division. At the same time it is important to remember that a cell when deprived of oxygen will not dhide. This was first shown by Loeb (1895).
Mathews (1907) found that agents such as cold, quinine, and anaesthetics which are known to reduce oxidations also prevent cell dhision,
and cause a disappearance of the astral rays. Mathews concluded that
the whole process of cell division is intimately associated with the oxidative processes in the egg, and that the periodicity of the former is due to
a periodicity in the capacity of the cell to carry out oxidations involving
the use of atmospheric oxygen, this periodicity in oxidative power being
due to the periodic liberation from the nucleus of an oxidase whenever
0001
30 1 4 O 1 50 I OO ] 70 1 OO 1 00300 2 lO 220 230 2-t O 250 2(]
Tiino ill i«iiiiit<‘K
Halt' t»l* t»xyj't‘ii (iht iiiiii.)
CELL DIVISION
221
iie nuclear membrane breaks down. In opposition to this conclusion is
^lie fact established by Warburg that the level of oxygen consumption
of the eggs can be maintained almost unchanged when the periodic
diaiK^es of the nucleus are entirely inhibited.
Table XXVIII. Mm. pressure Og used per half hour by fertilised
eggs of Echinus
No. of
experiment
30 minutes immediately previous to division
30 minutes during division
30 minutes immediately after division
No. of di\ision
A
13-0
12-3
14*0
1st
A
14-8
150
13-7
2nd
i A
16-4
15-9
18-3
i 3rd
1 ®
14-1
13*6
13-0
! 1st
B
13-3
13-4
13-7
2nd :
C
6-5
61
7-1
j 1st ‘
D
21-0
190
21-0
i 1st
Totals 99*1
95-3
100-8
20 40 60 80 100 120 140 160 180 200
Time in minutes
Fig. 99, Graph showing the rate of oxygen absorption during the process of cleavage. Note the absence of any measurable change in oxygen consumption prior to or after cleavage. The upper graph shows the rate of oxygen consumption during successive ten minute intervals ; the lower graph shows the rate during successive hve minute intervals. (Gray.)
It seems necessary to distinguish between a general disturbance of the celFs activity which accompanies a lack of oxygen and those specific reactions within the ceU which require atmospheric oxygen.
222 CELL DIVISION
From the evidence available ve naay draw one of two conclusions. Either the process of cleavage does not involve redistributions of ener<TV which involve oxidative reactions; or, the oxidative changes wMch provide the energv for cleavage (being less than 2 per cent, of the total oxidations of the whole egg) cannot be detected by the methods so far emploved. The same unfortunate position is reached from a consideration of the heat production during cleavage. Meverhofs (1911) curve was not based on experiments having the particular objective now involved, but its close resemblance to the curve of oxvgen consumption suggests that the two processes are closelv associated with each other. There is, in other words, no positive e\-idence to indicate a disturbance in the rate of heat production during cleavage. The more recent work of Rogers and Cole (1925) is less easily interpreted, but it does not seem to elucidate the
nature of the cleavage process. ... j? ,
It is clear that a spherical egg 'with its plastic surface layer cannot be divided into two parts without the expenditure of energy; during this process there must be a thermal disturbance. It seems reasonable to nippose that this disturbance could be measured if the technique employed were sufficiently accurate. From the data at present available, we can only conclude that the energy which the ceil Expends during cleavage forms only a very small fraction of the total energy which the cell requires to maintain its normal life. From the point of view of energetics, cleavage, like grmvth, is a comparatively insignificant process in the life of the cell.
The effect of cell division oti the form of epithelial cells
Just as the form of the first cleavage furrow of a sea urchin’s egg is in part determined by the mechanism which afterwards binds one cell to another, so to a much greater extent would one expect the same factor to operate when a dividing tissue cell is completely surroimded by its neighbours. The changes in form of an epithelial cell undergoing division have not been observed in life, and v ould form an interesting object of study. In some cases it would appear as though a prismatic epithelial cell becomes spherical prior to division (Seeliger, 1893 ; Korschelt, 1888) and that its cleavage is not unlike that of an unsegmented spherical egg. Whilst this may sometimes be the case, it can hardly be true of all epithelial divisions. B\ subjecting the segmenting eggs of Echinus esculentus to gentle pressure, it is possible to observe the cleavage of cells which are in
CELL DIVISION 223
intimate contact with their neighbours, and in no case has a cell been seen to become spherical before cleavage. The first sign of approaching cleavage is an elongation of the polar axis whreh is accompanied by a bending of the e<^uatorial interfaces tow^ards the centre of the cleaving cell (fig. 100, 2). This distortion of the interfaces involves marked changes in the form of the adjacent cells w'hich accommodate themselves accordingly. The actual cleavage furrow cuts through the dmding cell in a plane at right angles to the long
Pig. 100. Camera luoida drawings of cleaving cell in E. esculentm blastula. Note that the neighbouring cells a and e have accommodated their form to that of the dividin g cell. The furrow / cuts vertically through the cell. *
Fig. 101. Diagram of division of a hexagonal epithelium cell. The equatorial interfaces flfli and bbi are distorted so that — after the vertical furrow f has cut through tiie dividing cell B — each daughter cell is a pentagon and the two adjacent cells *4~aiid C have each acquired a new interface, making a gross increase of six interfaces.
axis and at right angles to the plane of the epithelium, so that when cleavage is complete the two daughter cells have acquired between them four new interfaces and the adjacent cells have each acquired one extra interface (see figs. 100, 101).
The cells in the wall of a blastula, like those in a typical epithelium, have a variable number of interfaces, although the average uumber is no doubt six (see p. 257). Taking a six-sided cell as\ typical unit, Lewis (1926, 1928) has considered in some detail the
224 CELL DIVISION
theoreticaldtectofcelldivisto, Haregular hexagonal cell (flg W!i
divides vith the mitotic spindle orientated asong one ot the three major axes, the cleavage plane trill lie along one of the axes a b, ore. Ck--.v,oe trill result in the production of ttro vert- irregular pentagons. If t‘lK iell interfaces are plastic and tend to reduce the tansrerse section of each cell to a regular pentagon, the net resu t of ditision is the production of ttro pentagons and ttro heptagons (see hg. lot,. Each product of dirision ( a and a.) is a pentagon trhereas t™ neighboiirine cells (6 and 6, 1 acquire an additional surface. Sii^arlt , if m a sheet o't hexagonal eeils any one eell and its six neighboiirs ditode
- imnltaneouslv.theretrinresuIteightnetrhex«gonnleeUs,aiidsLxue,v
“.. ..h. .-,-.,1 ceils while two peripheral non-dividmg cells ’mil become it 1 iit ■ t •- ni . ar. d two octagonal ; the average number of sides possessed
bv ad the new or reoraanised cells being exactly six. The existence of p'entagonah heptagonal, or octagonal cells in a normal epithelium of hexagonal cells mav therefore be the direct result of cell db ision. Lewis accepts tliis' point of %-iew and has put forward possible h\-potheses which account for the existence of cells vith less than five or more than eight surfaces in transverse section. It may be mentioned, however, that an alternative interpretation of the various types of polygon was put forward by Wetzel (1926), who stresses the disturbing effect of unequal growth on the symmetry of a hexagonal system (see Chapter X).
There can be little doubt that in the wall of a blastula the irrefudaritv in the number of facets possessed by different cells is largely due to'initial irregularities of size, rather than to the effect of cel division or to variation in the growing powers of the ceU. The ideal system considered by Le-wis is none the less of interest and of con
CELL DIVISION
225
siderable importance when applied to plant tissues. In animal cells
the junction between two interfaces is not fixed, but can move in
response to altered stresses throughout the system, and consequently
the length of any given interface (as seen in section) may vary
eonsiderably when a neighbouring cell dmdes. Whether this is true
ill plant cells is doubtful, and if Lewis is correct in assuming that it
is not the case in Cucumis, interesting problems at once arise. By
actual measurement Lewis found that in section every ceil interface is approximately of the same length irrespective of the number
of sides possessed by the cell, and this implies that the act of cell
division involves a marked change in the area covered, not only by
the dmding cell, but also by its neighbours. According to Levis
(1928) the area covered by a cell is roughly (n — 2) a, where u is a
constant and n the number of sides in transverse section, so that the
area of the original hexagonal cell A is 4a, and that of each daughter
pentagon is 3a. The two daughter cells therefore together cover an
area 50 per cent, larger than the cell from which they were derived.
Similarly each of the cells b and see fig. 102, by acquiring a
seventh side increase from 4a to 5a — or together add an area
equal to 50 per cent, of a hexagonal cell. Thus the total and
immediate effect of cell division is materially to increase the area
covered by the whole series of cells affected. Levds associates the
increase in surface area postulated at cell division with the groviih
of the cells involved, but it is difficult to understand how this could
occur with such rapidity. Until the volume of the cells in the neighbourhood of dividing plant cells has been assessed, and until the
process of division has been seen in life, it seems doubtful how far
further speculation is advantageous.
If a hexagonal cell divides so as to give two daughter pentagons whose total area is equal to the original hexagonal cell, and if the two daughter pentagons are regular, then the length of one of the sides of the pentagon must be 0*869 times the length of the side of the original hexagonal cell. This could only occur if there were a corresponding reduction in the length of all the sides of the adjacent cells. Some such adjustment probably occurs in animal tissues, but in plants Lewis suggests that ail the non-dividing cells can retain their normal length of side by growth on the part of the pentagons and of two of the neighbouring cells as above described. By similar reasoning, a non-di\dding pentagon in contact with two dividing cells would increase its surface area by more than 60 per cent.
It is interesting to note that epithelial cells do not appear to
GC 25
CELL DIVISION
divide when thev attain a critical size, for the main factor associatea with the cleavage of Cucumis cells appears to be the number oi interfaces nresent. The hisher the number of interfaces the greater of cleavages observed Since the volume of the cell appears to increase with the number of interfaces, it follows that the larcrer the cell the more iikely it is to divide.
The factors zchich determine the direction of the planes of cleavage
From a biological standpoint the cleavage of a cell involves more fundamental changes than a quantitative division of the cell mas. Since the entire animal with its differentiated parts owes its ultimate sh-ine to the size, position, and form of its constituent cells, thefactors wWch detoniin; the direction of each cell cleavage are of very real simuiicance in an attempt to understand the mechanism which underlies the nrocesses of embryology. Is an animal s form determined bv those mechanical conditions which control the form, size •ird position of the constituent cells? Alternatively, do particular eeds cleave in a particular manner and orientate themselves m a particular position because of an inherent property of the living niaterial of which thev are formed? A discussion of the problem in\his form would lead far away from the scope of this work: all that concerns us here is the evidence which throws light on those forces which can influence, if not determine, the plane in which a given cell vdll divide. Roughly speaking, the evidence can he divided into two sections: an analysis of the relation of a cieava<^e plane to an organised or predetermined axis of the organism oirthe one hand, and to the external environment of the cell Dll the other.
One of the most obvious features of all cleavage planes is the fact that they are at right angles to the long axis of the existing mitotic spindle: it therefore follow'S that the direction of the resultant cleavage plane in respect to the whole cell is determined by those forces which are responsible for the orientation of the w'hole mitotic figure. If we consider an inter-kinetic nucleus lying towards the centre of a spherical cell, it is obvious that the long axis of the subsequent spindle is determined (so far as the nucleus is concerned) as soon as the centrosomes have orientated themselves at the poles of the nucleus. In the case of some eggs, the poles of the nucleus (as defined by the position of the centrosomes) bear a definite relationship to the cytoplasmic elements of the cell. This is clearly the case
CELL DIVISION
227
la the frog’s egg where the first cleavage plane passes through the
aainial and vegetable poles of the cell. We can. however, go back
a step further. In frogs’ eggs Roux (1885) and afterwards Morgan
and Boring (1903) showed that the first cleavage plane, in the
majority of cases at least, marks out the median line of the future
enibr\'o. A.t the same time the first cleavage furrow passes through
or near the point of entry of the spermatozoon into the egg, e.g. in
frogs’ eggs (Roux, 1887), in the sea urchin Toxopneustes (Wilson and
Mathews, 1895) and in Nereis (Just, 1912).
The series of events which relate the entry of the spermatozoon with the cleavage furrows were clearly described by Wilson and
Flii. 103. Diagrams from successive camera lucida drawings of the iivino enns of
Toxopneustes. E, Point of entry of sperm. M, Position of fusion between male and
female pronuclei. C, Axis of first mitotic spindle. F, First cleavage plane. fFroni
Wilson and Mathews.)
Mathews (1895). The fertilising spermatozoon may enter at anv point on the surface of the egg of Toxopneustes and its point of entry is marked by the so-called ‘entrance cone’ (see p. 424). After inclusion into the cell, the sperm nucleus is marked by a sperm aster and both structures move into the interior of the cell on a path closely approximating to, but not coinciding with, a radius of the egg (fig. 103). During the time occupied by the approach of the female pronucleus, the sperm nucleus may be slightly deflected from its original penetration path, but the angle of deflection is slight; after fusion, the zygote nucleus passes to the centre of the cell. Within certain limits, therefore, the sperm nucleus travels straight to the centre of the egg, so that the central point of the male astro
.JOS CELL DIVISION
sphere lies on or near a line joining the centre of the zygote nucleus to the point of entrv of the spermatozoon. The asters of the first cleavage are apparently formed by a polar migration of ’ archiplasur from the centre of the male aster as described elsewhere (see p. 162 , so that the axis of tlie first mitotic spindle is at right angles to tht path of entrv of the spermatozoon. Since the cleavage plane is at riaht amrles to this mitotic axis, it follows that the cleavage furrow must pass tlirough or near the point of entry of the spermatozoon. This close relationship between the point of entry of the spermatozoon and the direction of the first cleavage plane is found also in fr.Krs- e.^-s 'Roux, 1887) and in the polychaet Nereis (Just, 1912). Curiouslv enough, the rule is not absolute. In Just’s experiments (in wliicii the point of entry was deternuned by a trail of Indian ink
r: . ina rif^vine of the C'T'.' of Xereis showing cleavage plane passing through the mV rt .-,tentr%“of the sperniaTozcon. This point is marked by the trail of Indian ink left of the spermatozoon through the gelatinous egg membrane. (From Just. i
left in the cortical jellv of the egg by the fertilising spermatozoon
{see fis. 104)), out of a total of fifty-six eggs the first cleavage furrow
passed through the point of entry of the spermatozoon in forty-six
eases, whereas in ten cases this rule xvas not obeyed. How far these
exceptions to the rule are only apparent is uncertain ; it is possible
that in some cases the egg rotates within the cortical jelly before tk
cleavage furrow develops, so that the trail of the spermatozoon
through the jelly no longer indicates the point of entry into the egg.
This remarkable relationship between the first cleavage furrow and
the point of entry of the spermatozoon is of considerable theoretical
importance. As already mentioned, the first cleavage furrow is often
either coincident with, or closely approximates to, one of the mam
axes of symmetry of the resulting organism, so that if the spermatozoon can enter at any point on the egg’s surface, it follows that the
CELL DIVISION
229
axes of sTOimetry cannot be predetermined before the egg is fertilised, but are determined by the point of entry of the spermatozoon.
In this respect the recent work of Morgan and Tyler (1930) is highly
significant. These authors found that the degree of correlation
between the first cleavage plane and the point of entry of the spermatozoon varies in different types of egg: in Cumingia it is as high
as 78 per cent., in Chaetopterus it is only 41 per cent. Morgan and
Tvler’s results are summarised in Table XXIX.
In all these cases the first cleavage is unequal and passes to the right or to the left of the polar axis (as defined by the position of the polar bodies) of the egg. In Cumingia either the first or the second cleavage furrow may become the median plane of the body. These two facts must be taken into account in any attempt to define the factors which control the direction of the early cleavages (see p. 235).
Table XXIX
Species
Total number of eggs observed
Percentage of eggs with first cleavage through point of entry of sperm i
i
Percentage of eggs with first cleavage ^vithin 45® of point of entry of sperm
Percentage of eggs with first cleavage between 45' and 90® of point of entry of sperm
Cumingia
98
78 !
14
8
Chaetopterus
116
41 I
30
29
Nereis
64
51 i
27 I
22
In egg cells, which are not spherical or in which there is a marked
physical heterogeneity in different parts of the cell, the direction of
the first cleavage furrow is clearly not solely dependent on the point
of penetration of the spermatozoon. In nematode eggs (Erlanger,
1897) the polar axis of the zygote nucleus lies at first along one of
the shorter axes of the cell, but gradually rotates so as to lie in the
plane of the long axis ; eventually the first cleavage furrow is formed
at the equator of the cell (see fig. 93). A comparable phenomenon
can sometimes be seen during the second cleavage of echinoderm
eggs (Gray, 1927).
From this point onwards twm fairly well-defined lines of enquiry appear to be open. We may follow the relationship between particular cleavage planes in early ontogeny and the major axes of the subsequent organism; or we may- seek by experiment to alter the
230 CELL DIVISION
natural course of cieaA-age and. by changing the normal plane of cell division, gain some insight into the nature of those forces which are the controlling factors in natural development. Since one of the main purposes of this book consists in delving into the mechanical characters of cell activity, we shall first follow the latter line and then, retracing our steps, attempt to see how far its course diverges or ;>T ipH' w the path of experimental embrj ologji.
The ejfeci of mechanical pressure upon cleavage playm
Roughly speaking, the laws associated with the names of 0. Hertwig flSiiSj and of P.hiiger (1SS4) can be summed up in one sentence,
Fis. 105. E^g of Echinus microiuberciilotus segmenting under pressure; a, the third cleavase yields a flat plate of eight cells instead of two tiers of four each; b, 16-celled stage showing tangential fourth division; c, the lines show the mitotic axes of the fifth division^ in every case this is in the long axis of the cell; d, shows the resultant 02-celled stage; e, 64-cells: -h signifies a vertical division; a line indicates a horizontal division. (From Ziegler.)
‘ The cleavage plane is at right angles to the longest axis of the protoplasmic mass ’. The real significance of this fact is, however, more
clearly expressed in Pfluger’s dictum, ‘ The mitotic figure elongates
in the line of least resistance’; consequently the cleavage plane is at
CELL DIVISION
231
ri^iit angles to this line. Pfliiger s conclusion was based on a series
(I experiments in which the eggs of the frog were induced to cleave
under pressure; in such circumstances the cleavage plane was always
iii the direction of or in the same plane as the applied pressure.
Pfluger’s results w^ere confirmed and amplified by Roux, and were
extended to echinoderm eggs by Driesch (1898 a), Ziegler ( 1894 ), and
Vatsu ( 1910 ). Ziegler’s results are perhaps the most interesting, as
with the aid of an irrigated compressorium he w'as able to follow’ the
cleavages of a compressed egg through several divisions. His results
diowed clearly that, as long as the pressure was exerted by two flat
plates, each cleavage plane was at right angles to the plates, whilst
the mitotic figure lay in a plane parallel to the plates. It is worth
noting that the two plates of the compressorium were fixed during
the whole of Ziegler’s experiments, and consequently there was no
force exerted by the weight of the cover-slip. Ziegler was inclined
to regard each cell as a fluid drop and consequently it is a little
difficult to see w’hy the pressure wuthin the drop should vary from
one plane to another. There can be no doubt whatever that the
cleavage planes are at right angles to the plane of the externally
applied pressure, but it does not follow that the mechanical pressure
of the plates is in any way transmitted directly to the mitotic figure.
Since the cytoplasmic matrix of the cell is liquid, the pressure at all
points must be equal even if the surface of the cell is subj ected to lateral
compression. If, however, we are prepared to regard the two growing
asters as regions of elastic rigidity, then they will be subjected to
pressure as soon as they come into contact with the periphery of the
cell; until then they will not be subjected to compression. If one
axis of the cell is longer than another, then polar compression of the
asters can be delayed by a rotation of their axis into the longest axis
of the cell, just as occurs in the normal egg of the nematode. A similar orientation often occurs in normal echinoderm eggs (see fig. 106 ).
If this is sound doctrine, Pfluger’s law of cleavage acquires a real
meaning; without such an assumption the phenomena of cleavage
under pressure seem curiously irrational. A disturbance of the
subsequent cleavage planes is not a response to a change in intracellular pressure but to a change in the shape of the cell whereby
one axis becomes longer than either of the other two.
There can be little doubt that the application of an external pressure has proved by far the most efficient method of influencing the direction of a cleavage furrow. The facts clearly show that the
232 CELL DIVISION
direction of cleavage of a compressed cell is the result of a movement on the part of the astral axis: in other words, the whole mitotic apparatus moves bodilv tlirough the cell until it comes to lie in the lon<Test axis of the ceil. This movement could only occur if the pressure exerted on the asters (presumably by the cell surface) is greater than the viscous resistance of the cjdoplasm. If this resistance were relatively great, a ceil could divide in a plane paraUel to instead of at right angles to its longest axis, and this may possibly sometimes
Fin. 106. .Movement of two as\TiimetricaUy situated asters in an Echinus egg. In 1 the centres of the asters are at a, in 2, they lie at 6, in 3, they lie at c, c^; in 4’ the diameter of each aster is equal to the radius of the egg, so that the centres of the asters {d, d^} must lie on a diameter of the egg and produce symmetrical cleavage.
be the case in nature. Wilson (1892) and Conklin (1898) have given
examples of such anomalous cleavages. It may be remembered that
in echinoderm eggs, which are the favourite object of compression,
the spindle with the asters can be moved through the cell by centrifugal force, and that there is independent evidence to support the
view that the e\doplasmic \-iscosity is of a low order. It would be
interesting to know whether the cytoplasmic viscosity of the mesoblast cells described by Wilson and by Conklin is of a distinctly
higher order of magnitude.
CELL DIVISION
233
The so-called effect of gravity on the direction of cleavage planes
The directions of the early cleavages during the segmentation of an egg are not infrequently defined in terms of inclination to gravity. Thus, in frogs’ eggs or in sea urchin eggs the first two cleavages are often described as vertical, whereas the third cleavage plane is horizontal. This nomenclature is convenient, but misleading, since the force of gravity exerts no direct effect on the planes of cleavage either during their formation or afterwards. In the frog’s egg the accumulation of heavy yolk at one pole, with a consequent accumulation of cytoplasm at the other, impresses on the undivided egg a definite visible polarity, and a definite orientation in respect to gravity. The whole egg is only in equilibrium vdtli gra\dty when the flat disc of cytoplasm lies vertically over the yolk; two out of the three rectangular axes of the C5rtoplasm are equal in length and lie horizontally; the third axis is shorter than the others and is vertical. By dividing the cytoplasm into equal divisions at right angles to its longest axis, the first two cleavage planes are naturally meridional and vertical, whereas the third cleavage plane is more or less equatorial and horizontal. Both Hertwig (1898) and Pfliiger (1884) clearly recognised that gravity exerted no direct action on the orientation of the spindle itself, for, as shown by Kathariner (1901), the first two cleavages in eggs rotating on a clinostat retain their orientation in respect to the organised polarity of the egg and exhibit no orientation in respect to the centrifugal force.
Giglio-Tos (1926) and his associates have recently maintained that the first cleavage furrow of echinoderm eggs (species unnamed) is always inclined at an angle of 45° to the vertical and that this is due to the orientation of the cleavage spindle prior to division. These authors maintain that the two asters are free to move on each other and wdthin the cell and that, when the asters are fully formed and equal in size, their position of mechanical equilibrium is reached when the mitotic axis is inclined at an angle of 45° to the vertical.
The observations of the author (Gray, 1927) do not confirm any of the conclusions of Giglio-Tos, but indicate that the effect of gra’sdty on the fertilised eggs of Echinus esculentus and E, milians is of an entirely different nature.
A large number of observations wdth both Echinus esculentus and E, miliar is leave no doubt that the direction of the first three cleavages obeys quite strictly the Hertwig-Pfliiger law and that the
234
CELL DIVISION
axis joining the centres of the two asters (mitotic axis) can lie in any
plane relative to gravity. The asters having taken up their position
at the poles of the nucleus maintain the orientation thus acquired
until the egg begins to show signs of cleavage furrows. Further, an
e 2 *g can be rotated so as to bring the mitotic axis into any desired
position, and this position is stable. It is only when cleavage begins
Fig. lOT, Orientation of a cleaning egg of Echinus in which the astral axis was originally vertical.
that gravity exerts any affect on the orientation of the system. This
is most readily observed in an egg whose mitotic axis is vertical as
in fig, 107, As the egg elongates up^vards (fig. 107, 2) it soon becomes
unstable and falls on to one side (fig. 107, 3). This movement is
clearly due to gravity, and the egg orientates itself so as to bring its
centre of grainty to the lowest possible position. In this way the
mitotic axis becomes more or less horizontal (fig. 107, 3). Having
reached this position the egg continues to elongate, and its long axis
CELL DIVISION 235
may either continue to remain horizontal or it may tilt upwards as in fig- 10'^; Both types of movement are obviouslv induced by the accommodation of the egg to the confines of the fertilisation membrane; as the egg elongates, the two points of contact (fia. 107, X and y) move apart forming a longer and longer arc.
When the first cleavage is completed, the long axis of the egg may therefore lie in any position from the horizontal (fig. 107, 3) up to the maximum inclination of about 35° (fig. 107, 6). The first cleavage plane is eventually therefore either vertical or deviates from the vertical by an angle not exceeding 35°. It is clear that these phenomena are due to the fact that on the initiation of cleavage the ecroceases to be spherical and, were it not for the presence of the fer^ tilisation membrane, the egg w^ould only be in equilibrium with gravity when its long axis was horizontal, and the cleavage furrow vertical. As the egg must accommodate itself to the confines of the fertilisation membrane, the egg can be in equilibrium as long as the inclination of its long axis does not exceed a value which depends on the forces exerted at the points of contact with the membrane.
As far as the eggs of Echinus are concerned, therefore, the effect of gravity on the orientation of the early cleavage planes is only of an indirect nature, and is based on the fact that in the segnrentincr eggs the whole system tends to reach an equilibrium position with its centre of gravity in the lowest possible position.
Internal factors which determine the direction of cleavage planes
If Hertwig’s law were strictly obeyed by all spherical egg cells (with uniformly distributed yolk and equal cleavage), it follows that only one pattern of cell cleavage planes would be possible. The arrangement is that exemplified by Echinus eggs, and is known as the orthoradialtype of cleavage characteristic of Echinus, AmpMoxus, Synapta, Antedon, and Sycandra (Conklin, 1897). In all these eases the long axis of the third cleavage amphiaster is meridional and at right angles to that of the previous cleavage plane, so that the third cleavage cuts the egg equatorially leaving the twm daughter cells of each cleavage in the same meridian of the egg (see fig. 108 A). As pointed out by Conklin, orthoradial cleavage is uncommon and eA'en in cases where the early cleavage planes conform in this way to the Hertwig-Pfliiger law the later cleavages show a contrary arrangement. By far the most frequent type of cleavage pattern exhibited by spherical eggs during cleavage is the spiral pattern seen in
230
cell division
ri<y. 108. Orthoradial (^4 and B) and spiral cleavage (C-F). In orthoradial cleavage the third mitotic spindle is at right angles to the surface of the paper so that the two products of division lie vertically over each other (A). The fourth cleavage is at right-angles to the third (B). In spiral cleavage the third mitotic spindle is displaced as shown in C, so that each micromere lies between two macromeres. It (as in t and E) the displacement of the mitotic axis is to the right, the third displacement at the next division is to the left (as in F). (From Korschelt and Heider.)
CELL DIVISION
2sr
molluscs, platode worms and annelids. In these instances the axes
of the di^dding cells do not coincide with the plane of the long axis
of the original undivided cells, but are inclined at an angle to it. The
final result of this displacement of the cleavage axis leads to the
arrangement (in a four- celled and eight-celled stage respectively)
shown in fig. 108 C and E. It can be seen that the two products of
cleavage (in figs. 108 C-E, 109) do notlieinthesameradiusofthe egg,
but one of them is displaced so as to lie in the furrow between two adjacent cells of the other quartet. The term spiral cleavage was applied
by Wilson to this arrangement to signify the fact that the products of
(iinsion lie on a curved radius of the egg for if this curv’e were
produced, it would form a spiral about the egg axis. A typical
example of spiral cleavage is provided by the eggs of Crepidula
described by Conklin (1897). The first cleavage divides the egg
Fig. 109. Typical spiral cleavage of Crepidula. The development of the polar furrow ipj,) is seen in 2. Note the displacement of the micromeres in 3. (After Conklin. |
equally into two blast omeres. These cells are at first nearly spherical and touch each other only over a comparatively small area of their surface, although later on they become more closely pressed together and each cell becomes an almost complete hemisphere (fig. 109, 1 ). At the close of the first cleavage the nuclei and their asters lie directly opposite each other, but, as soon as the blastomeres begin to flatten against each other, the mitotic axes begin to rotate in the direction of the hands of a clock and this direction is often constant in all the eggs of the species. As the time for the second division approaches the two spindles are no longer absolutely parallel to each other, for (when the egg is viewed from one side) they are inclined at an angle to each other; consequently the second cleavage planes do not meet at the centre of the egg but a polar furrow is formed (fig. 109, 2 pf-). Polar furrows are essentially t}q>ical of spiral cleavage, although they can readily be induced in orthoradial cleavage by experimental means (Gray, 1924 and fig. 112). The axes
CELL DIVISION
of the amphiasters of the third cleavage of Crepidida are at first
rather variable in their orientation in respect to the axes of the cells,
although their inner ends are at a higher level than their outer ends
and the axes may be radial. As the process of cleavage becomes
more complete the spindles, whatever be their original orientation,
rapidly begin to show a rotation towards the right-hand side, and
after the divisioii wail between the dividing cells has appeared the
process of rotatioji is continued by the blastomeres themselves. In
this way each micromere conies to lie in the furrow between two
macromeres and to alternate with the macromeres in position (fia.
lOS D-F). It is to be noted that if in one cleavage the resultant
blastomeres are rotated to the right, then at the next division the
rotation is to the left; each successive division is, in other words,
alternately clockwise and anti-clockwise.
Tile account of spiral cleavage given above closely follows that of Conklin for Crepidula. In contrast to orthoradial division, spiral cleavage appears to exhibit three main features, (i) The displacement of the mitotic axes in respect to the radius of the egg and in respect to each other, (ii) the formation of polar furrows, (iii) the displacement of individual blastomeres in respect to the egg radius.
It has been known for many years that the final result of spiral cleavage leads dhectly to a geometrical arrangement of cells, which is mechanically stable in that each cell exhibits a minimum surface area to its neighbours and to the environment. Fig. 110 shows that polar furrows and a radial displacement of indiwdual units are as characteristic of soap bubbles as they are of dividino eggs.' We ha%'e, therefore, to consider how far the arrangement of the cells in Crepidula is due to purely mechanical principles, and how far they are the result of biological activity. There can be no question that the rotation of blastomeres (from the orthoradial to the spiral arrangement) reduces the free surface of the individual cells, or that the cells are held together by forces which tend to reduce such surfaces to a minimum (see p. 254); at the same time, from a mechanical point of ^^e■u' there is no reason why rotation should invariably be to the right or to the left, both are equally eftecfcive, and one would expect that a given group of egg cells wmuld tend to show both types of rotation with equal frequency. In gasteropod molluscs this does not appear to be the case for the direction of rotation of the cleavage axis appears to be a fixed and hereditary characteristic (for any particular cleavage). For this reason both
CELL DIVISION
239
Conklin (1897) and Wilson (1892) concluded that spiral cleavage
cannot be solely the result of purely mechanical causes which
operate at the moment of cleavage. Since the final result produces
a geometrical pattern conforming to the law of minimum surface,
Fig. 110. Comparison of the form of four contiguous soap bubbles, 1-3 (after Robert)
Mth tj^ical spiral cleavage of living eggs. 4 and 5, A dexiotropie division followed
by a leiotropic division. 6 and 7, A leiotropic division followed by a dexiotropie
division. (After Korschelt and Heider.)
Conklin (1897) concludes that ‘We must find the ultimate cause of this anti-clockwise (or clockwise) rotation, not in such external conditions which are, however, incidentally fulfilled but in those more complex internal conditions which direct the course of onto
24-0
CELL DIVISION
geny and M'hich in our ignorance ^ve call the coordinating force or
hereditary tendency’ (p. SO). .q u 4.1
This cmichision is. however, somewhat weakened the recent work of Morgan and Tyler (1930). In the mollusc tie
third ..1-- V- “ is always dexiotropic, so that by the classical rule of alternate' displacements the second cleavage should ahva>^ be leiotropic. In practice, however, the direction of rotation at the
ni The position of the cleavage planes of the egg of Cnmxngxa ^ith respect 0 u rJatn'ire; point of the spermatozoon. In la the first cleavage passes to the nght of the PC e i as in.arked bv the polar bodies which are uppermost), and the blaston em « ies to the risht of the point of entr>- of the sperm In 2 a the situation n rever:ed and AB liesho the left of the point of entry. The second cleavages iue ^lown in 16 and 26 respectively, and are leiotropic and dexiotropic respectively. (From Morgan and Tyler.)
second cleavage can be either clockwise or anti-clockvise according
to whether the first cleavage furrow passes to the right or to the left
of the polar axis of the cell.
Accordhig to Morgan and Tyler the direction of the spindle axes during the second dmsion show no sign of spiral orientation; a fact which differs from Conklin’s observations on Crepidula. Further in Cum ingia either the first or the second cleavage plane may become the median plane of the body and this can only be determned after the third cleavage has occurred. In Nereis, where the third clea\ ap is also dexiotropic, only one configuration of cells is found m the four-celled stage, tiz. that illustrated in fig. Ill, 1&.
CELL DIVISION
241
In attempting to analyse the nature of the forces which are
responsible for the form and position of individual cleavage plaiieSj
it is useful to distinguish between two different processes. Firstly*
the mechanical principles which control the form and position of
the cells after the process of cleavage is complete and secondly,
those factors which determine the orientation of the ceils during
cleavage. These two principles may or may not be the same (see
p. 254).
There can be no doubt that if a so-called ‘ spiral ’ pattern has not been the result of normal cleavage, it can readily be brought about by suitably applied external pressure. This is the case, for example, ill Echinus when the egg is exposed to superficial pressure after the first two cleavages are complete; it also occurs normally in a definite percentage of eggs belonging to species whose natural cleavage pattern is orthoradial, e.g. in Amphioxus, Spiral patterns of tliis type are clearty the result of movements executed by fully formed blastomeres and are probably strictly comparable to the movements of soap bubbles or other mechanical systems. When an Echinus egg is subjected to pressure before cleavage has occurred, however, it is significant to note that the spiral pattern v'liich results is not reached by way of an orthoradial stage, but is acquired by a gradual orientation of the dividing cells in a way strikingly similar to that observed during segmentation of a normally spiral type such as Nereis or Crepidula (see fig. 112). Since the spiral pattern can be produced by artificial pressure, and since the final result is obviously in conformity wdth the law of minimal reaction to external pressure, it seems reasonable to suspect that where it occurs normally it does so in response to an externally applied pressure which owes its origin to the mechanical environment of the blastomeres. At the same time this mechanical environment may be the result of definite ontogenic factors, and it is useful to bear in mind that mechanical conditions may be the result and not the cause of biological activit^n This point of view is very clearly expressed by Wilson (1892), Conklin (1897), and by F. R. Lillie (1895); two striking quotations from Lillie are perhaps admissible: Almost every detail of the cleavage of the ovum of Unio can be shewn to possess some differential significance. The first division is unequal. Why? Because the anlage of the immense shell-gland is found in one of the cells. The apical pole ceUs divide very slowh" and irregularly, lagging behind the other cells. Why? Because the
242 CELL DIVISION
formation, of apical organs is delayed to a late stage of development. The second generation of ectomeres is composed of very large cells. Why? Because thev form early and voluminous organs (larval maiit'le). The left member of this generation is larger than the right. WhV^ Because it contains the larval mesoblast. ... One can thus go over everv detail of the cleavage, and knowing the fate of the cells, can explain ail the irregularities and peculiarities exhibited’ (pp. 38,
cleavage planes seen in 4.
39). In tlie same paper, Lillie discusses the orientation of the
mitotic spindle and subsequent cleavage planes; he concludes that
no mechanical explanation will suffice. ‘ Let us look for a moment at
the cleavages of X (First somatoblast). The first position of the
spindle is on its left side; the second position on the right side; the
third in the middle Ime towards the apical pole; the fourth in the
middle line towards the vegetative pole. In none of these cases does
the spindle occupy more than a fraction of the diameter of the
blastomere in question. The nucleus has been wandering through
CELL DIVISION
243
the cytoplasm from one side to the other, from the front to the back,
stopping at various stations, and giving off a cell at each one.
Finally the nucleus stops in the centre of the cell and a perfectly
bilateral spindle (the fifth) is formed. Why does it stop there? Is
it because its environment has changed? If so, the change is such
as to eiude the closest scrutiny. In fact the cell is a builder which
lays one stone here, another there, each of w’^hich is placed with
reference to future development’ (p. 46).
The facts of orthoradial and of spiral cleavage lead to a curious situation. In orthoradial cleavage the division planes are in strict accordance with Pfliiger’s Law, but result in an arrangement of cells which fails to conform to the law^ of minimal surface area. In spiral cleavage, on the other hand, there is an apparent deviation from Pfliiger’s Law% but the final result gives a geometrically stable svstem. Were it not for the fact that the spiral displacements of mitotic axes is believed to begin before the cells begin to elongate, one would suspect that a mechanical solution to these anomalies would not be difficult to locate.
The phenomena of unequal cleavage require some consideration. All observers are agreed that unequal cleavage is associated with an asmnietrical arrangement of the mitotic figure. The most striking cases of unequal cleavage are provided by the formation of polar bodies. Conklin (1924) calculates that the polar bodies of Fulgar are less than one-millionth of the volume of the egg. In Crepidiiki the maturation spindle can first be observed towards the centre of the egg where, according to Conklin, the two asters appear to be of the same size. Gradually the whole mitotic system migrates to the periphery of the cell and as it does so it shortens in length, and the two asters are no longer equal in size. Conklin believes that the spindle moves passively under the influence of unknown forces, and that the inequality of division is not so much due to an inequality in the size of the asters, as to an inequality in the distribution of the protoplasm which is controlled by each aster. On the other hand, according to Lillie (1901), an inequality of asters can be detected in the eggs of Nereis long before the mitotic system migrates to the periphery. A further investigation of the intracellular movements of maturation spindles might throw considerable light on the forces which orientate the asters, but the facts described by Conklin suggest that the rate of growth of an aster is determined in part by the distribution of cytoplasm, rather than vice vei^sa.
244
CELL DIVISION
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Gray, J. (1924). ‘The mechanism of cell-dRdsion. I. The forces whicli control the form and cleavage of the eggs of Echinus esculentus: Pmc. Canih. Philos. Soc. Biol. Series, 1, 166.
■ (1925). "The mechanism of cell-diNision. II. Oxygen consumption
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(1927 a). ‘The mechanism of cell-divdsion. III. The relationship between
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Hertwig, O. (1898). ‘Ueber den Werth der ersten Furchungszellen fiir die Organbddung des Embryo.’ Arck.f. mikr. Anat. 42, 662.
Just, E. E. (1912). "The relation of the first cleavage plane to the entrance point of the sperm.’ Biol. Bull. 22, 289.
CELL DIVISION
245
jcsT, E. B. (1922). ‘Studies of cell di\’ision. I. The effect of dilute seawater on the fertilised eggs of Echinarachnius parma during the cleavage
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Lewis, F. T. (1923). ‘The typical shape of polyhedral cells in vegetable parenchyma and the restoration of that shape following cell division.' Proc. Amer, Acad. Sci. 58, 537.
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(1904 b), ‘Rhythms of susceptibility and of carbon dioxide production
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(1913). ‘The laws of surface tension and their applicability to living
cells and cell division.’ Arch.f, Entw. Meek. 37, 233.
Mast, S. O. and Root, F. M. (1916). ‘Observations on amoeba feeding on rotifers, nematodes, and ciliates and their bearing on the surface tension theory.’ Journ. Exp. Zool. 21, 33.
Mathews, A. P. (1907). ‘A contribution to the chemistry of celi-di\dsion, maturation, and fertilisation.’ Amer. Journ. Physiol. 18, 87.
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Morgan, T. H. (1893). ‘Experimental studies on echinoderm eggs.' Anat. Anz. 9,141.
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246
CELL DIVISION
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CELL DIVISION
247
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(1901 b). ‘Experimental studies in cytology. II. Some phenomena of
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CHAPTER TEN
The Shape of Cells
The shape and form of cells
In the majoritv of instances, the form of an isolated cell clearly depends upon the particular source from which the cell has been derived, and therefore, to some extent, cell form is a predetermined character which owes its origin to a highly specific type of cellgro^\1h or organisation. An isolated muscle fibre, a nerve cell, a red blood corpuscle, and all the Protozoa have their own characteristic foniis, which are retained after the death of the cells if suitable killing agents are employed. This diversity of form can readily be correlated with the existence of a solid membrane at the cell surface : a membrane of this type is clearly demonstrable in many cases (see p. 103), and we may'safely assume that a given cell maintains its characteristic form by virtue of the rigidity of its surface.
In certain specific cases the form of an isolated cell approximates t('j that of a sphere, and most analyses of cell form are based on a studv of the shapes which such cells assume when subjected to close contact with other similar cells. In anah’ses of this type there are two distinct problems. Firstly, why is the isolated cell spherical? and secondlv, why does it undergo a definite geometrical change in form when in contact with other cells? In just the same way we mi^ht consider why an isolated Paramecium maintains its characteristic form, and why it changes its form when compressed against its neighbours. Unfortunately the study of the beha\iour of spherical cells has been unduly influenced by the assumption that the form of the cells is necessarily due to the operation of forces peculiar to the interface betw^een two liquids (Robert, 1902; Thompson, 1917: Lewis, 1926-8). It would appear, how^ever, that this assumption is contrary to fact. If an isolated living cell is comparable to a homogeneous fluid drop, then when two such cells (immersed in water] come into contact with each other, they should unite together to form one single spherical cell. This is not the case. In order to approximate the ceil to a state comparable to a soap bubble, it is
THE SHAPE OF CELLS
249
necessary to assume that it is essentially a two-phase system cora’josed of a fluid or elastic core, whose surface is covered by a liquid
dim which is immiscible both with the core and with the surrounding
water. When two such drops come into contact, they would automatically unite by their fluid surfaces to form a stable system. This
is however not the case with living cells, since two isolated cells
show no tendency to form a single system. On the other hand, it can
be clearly demonstrated that, like other cells, isolated spherical
biastomeres possess solid elastic membranes at their surfaces. It is
more probable that the form of a spherical egg ow^es its characteristic
shape to the same forces as are responsible for the form of a typical
protozoon. If we attribute the form of a Paramecium to differential
growth along well defined and specific axes, Ave can equally well
account for the spherical form of an echinoderm egg to grow^th which
tends to be equal in all directions.
If growth occurs in a cell along specific and localised axes, the elastic cell surface wdll be stretched and will tend to oppose the elongation of these axes, so that presumably such directional growth must sooner or later be accompanied by intercalated growth of the cell membranes at the surface and in this way the elastic tension of the surface will be relieved; alternatively it is possible to suppose that localised growth begins within the solid surface membrane and the distribution of the cytoplasm conforms to the shape of the cell membrane. In either ease the final form of the cell depends upon factors which are highly specific, and concerning which we are in complete igiiorancca
The ^vhole study of cell form really involves the analysis of tw'o distinct sets of factors — firstly, those intrinsic factors which are intimately associated with specific cell organisation, and secondly, the effects which are superimposed on the natural form of a ceil by the mechanical presence of its immediate neighbours and by the external environment. In the followdng discussion ^ve shall regard all spherical cells as special cases of cell form ; this does not indicate that the isolated cell is in any real way comparable to a homogeneous liquid drop.
The form of contiguous spherical cells
For many years it has been known that the shapes of actively dividing or of newly formed cells of all tissues tend to conform to comparatively simple and generalised types, and it is difficult to resist the conclusion that this uniformity of cell form is the direct
230
THE SHAPE OF CELLS
result of mechanical principles. Since the form of the isolated cell is
readilv disturbed by the application of mechanical pressure, the
suggestion arises that the form of certain cells in situ is the result of
the mechanical restraint to which the cells are normally exposed. If
a spherical cell, enclosed -vvithin an elastic membrane, be subjected
to unilateral extraneous pressure, the form adopted by the cell will
depend on the degree of departure from the spherical state which will
enable the cel! to generate an elastic force equal to the extraneous
pressure; the form occupied by the cell will not depend on its
specific nature except in so far as this expression includes the
mechanical properties of the cell surface. It is therefore to be
expected that wherever spherical cells are compressed together, the
geometrical form of the rvhole system wdll be of the same type and
independent of the specific origin of the cells. The validity of this
conclusion is supported by the experiments made by Roux (1897)
This author showed that the form occupied by each cell of a se®nientiiig frog’s egg is accurately defined by the form occupied bv
the components of a suitable system of oil drops (in which each droj)
conformed in size and position to each particular blastomere), the
whole of which is subjected to centripetal pressure.
The remarkable accuracy of Roux’s models (fig. 113) adds considerable interest to the process by which they were obtained. The procedure involved the preparation of two fluid phases ; one of these consisted of olive oil, the other of a mixture of alcohol and water of the same specific gravity as the oil. When a drop of the oil was suspended in the aqueous phase the oil drop assumed a spherical form ; when two such drops came into contact they rapidly fused together to form a single spherical drop. In order to obtain a series of spherical drops which would remain as separate entities when in contact, Rou.x found it necessary to deposit on the surface of each drop a solid elastic membrane which was insoluble in oil and in water. This arrangement was reached by adding to the oil a little oleic acid and to the aqueous phase crystals of calcium acetate. When a drop of the oil came in contact with the surrounding solution, a film of calcium acetate was deposited on the surface of the drop and prevented its fusion with contiguous drops as there was no tendency for the surface membranes to coalesce. To obtain the models of living cells, Roux compressed a series of such oil drops within the rim of a conical wine glass, and by varying the size and number of the drops, and the relative size of the glass container, he showed that
251
THE SHAPE OF CELLS
most striking models could be obtained of segmenting eggs of different animal types (see fig. 113). If Houx’s oil drops are an^iiliiiig more than an analogy to living systems, three facts must be established : fi) each living cell must, when isolated from its neighbours, naturally
Fig. 113. Oil drops mutually compressed against each other. Note the similarity of
A,B and E to orthoradial cleavages of animal eggs. C, Z), and F are comparable to
unequal cleavages. (From Roux.)
Fig. 114. Three stages in the passage of a large drop of oil (a^) into the centre of a system of smaller drops. Comparable changes of position can be observ’ed when Echinus eggs segment under pressure. (From Roux.)
assume a spherical state, (ii) there must exist at the surface of the
cell a mechanism whereby two contiguous cells are prevented from
complete fusion when subjected to mechanical pressure, (iii) there
must exist within the living system a centripetal force compressing
all the blastomeres. For strict accuracy, the whole cell system should
232 THE SHAPE OF CELLS
be confined %dtMn a rigid spherical shell. So far, no attempt has Ijeen made to determine the truth of these assumptions for theparticular living material chiefly concerned in Roux’s models, since the blastomeres” of the frog are not readily isolated from each other. With other material, hovever, the evidence supporting the fundamental parallel lietiveen the inanimate and animate systems is perhaps convincing. Herbst (1900) shoived that when a segmenting eehinoderm egg is' exposed to artificial sea water which contains no calcium, the individual blastomeres readily separate from each other. From his figures and from subsequent observation (Grav it is clear that when isolated in this vav each cell is
spherical 'That the surface of the cell is normally covered with a stickv or adhesive substance which loses its adhesive character when in contact with the normal environment for any length of time has Jlreadv been shown (Chapter VI). This surface hyaline layer must be present and must enclose the cells in a common investing layer if the cells are to maintain their normal form. It is the removal of this layer which enables the cells to resume their natural spherical fonn. and it is, therefore, more than probable that it is this layer which exerts the centripetal pressure exerted bv the rim of Roux s wine glass. Anv environment which alters the mechanical properties of the hvaline laver of the cell alters the degree of mechanical pressure exerted on the individual blastomeres. This can be illustrated vith the eggs of Echinus esculentus (Gray, 1924). The hyaline membrane of these eggs rapidly loses water and contracts when exposed to acid sea water”eoiisequently when two celled stages of these eggs are treated with acid the pressure exerted by the hyaline layer is increased and the blastomeres are tightly compressed against each other (see fig. 84). By partially removing the hyaline layer from the egg, it can be shown that the compressing effect observed in acid Tea water is confined to the area from -which the hyaline layer has not been removed.
Similarly if the hyaline layer is lifted away from the egg surface by treatment ■\\-ith hypertonic sea water (Gray, 1924), the blastomeres become spherical (see fig. 83).
It is thus reasonably clear that the system of living echinodemi cells fulfils the fundamental requirements for Roux’s models. In other cases it is more likely that an indi-vidual blastomere when isolated would only become spherical if the isolation were effected immediately after cell division, and even then only over that region
253
THE SHAPE OF CELLS
diich is directly in contact with the new cleavage interface. Such cases, however, are susceptible to the same type of analysis as applies -0 echinoderm blastomeres.
The adequacy with W’hich Roux’s models reproduce the form of living cells can hardly be questioned, but we are still faced with the fundamental problem of defining the shape of compressed oil drops in such a way as will enable us to feel that the mechanical problem of cell form has been completely solved. Since each individual cell when isolated from its neighbours is assumed to be spherical, it follows that in situ its surface area must be greater than when the neighbouring cells are absent. The process of mutual deformation is opposed by the elastic force exerted by each deformed cell and will cease when tliis force equals that which is pressing the cells together.
Fig. 115. Two equal compressed oil drops are each dhided by an unequal dhision
shown by the dotted lines in A or as inB. The stable position reaeheri iv. case^
is shown in C. Note the ‘polar furrow’ in C and that the system has t-wo planes of
symmetry shown by the dotted lines. (From Roux.)
At the point of equilibrium the surface energy of each cell will be
the minimum which is possible under the circumstances, any other
condition will be unstable (see also fig. 115). The law of minimum cell
surfaces has been known for many years, but it is essential to remember
that in its strict and accurate form the law does not in any wa}" define
the nature of the forces operating at the cell surface — it simply depends
on the existence of free surface energy and this may be of any type.
As long as we are dealing with a cell which is completely surrounded
by other similar cells, the theoretical form can be deduced from
physical data with some degree of certainty, but -when we deal vrith
cells, part of whose periphery is not in contact with other cells, the
problem becomes much more difficult and much less suitable to
geometrical analysis.
254
THE SHAPE OF CELLS
The laiL- of minimal surfaces
The newlv-formed interface between contiguous cells has that form wherebv its surface area is reduced to a minimum. The truth otthk is clearly illustrated iu Thompson's „alysk of the
segmentation figures of ErythrolrkMa (fig. 116) To this author rve a masterlv discussion of the tvhole problem of cell form. Startin<^ with a flat unsegmented disc the first two cleavages dmde the disc into four quadrants with the interposition of the small polar furrow necessitated by the fact that four interfaces meeting in a point are physically unstable. The existence of the polar furro-ncharacteristic of the second cleavage is, as pointed out by Thoinpson (p. 309), the direct consequence of the law of minimal area, for it can
Fiff. 116- Segnientation stages of ErythrotHchia. (From Thompson.)
be slioTTii tiis-t ill dividing’ n closed space into a given number oi
chambers by partition walls, the least possible area of these partition walls,' taken together, can only be attained when they meet
together in groups of three at equal angles (see also W. Thomson,
issr).
For the third cleavage there are two possibilities whereby not more than three surfaces shall meet in a point : (i) the third cleavage planes may be periclinal as in fig. 1175, or (ii) it may be anticlinal as in fig. 117 C. Now in order that a quadrant may be divided by an antielind partition into two equal parts it is necessary that the circular arc cutting the side of the periphery of the quadrant should mclu(ie 55“= 22' of the quadrantal arc, and the length of the partition wall is 0-8751 where the radius of the original quadrant is 1-0000. In the
THE SHAPE OF CELLS 255
case of a periclinal partition the length of the partition wall (for equal cleavage) is ITll, so that the anticlinal cleavage is the more efficient type. In point of fact, it is this mode of cleavage which characterises the third division of discoidal systems in nature. Subsequent divisions of the two cells of each quadrant also conform to theory to a marked degree. The foursided cell X (figs. 116 and 117) divides periclinally as one might expect.
If we compare the theoretical arrangement of successive partitions in a discoidal cell as defined by Thompson (see fltr 118), with the arrangement actually Alternative cleavages of
found in nature (fig. 116), it is difficult " (F-m Thompson.)
to avoid the conclusion that the law of minimal surfaces is of profound importance in the determination of cell form.
Fig. 118. Theoretical arrangement of partition walls in a discoidal cell.
(From Thompson.)
The law of minimum surface as applied to parenchymatous cells
If it be assumed that a given cell when surrounded by other cells (all of the same size and all exerting the same influence on each other) occupies that form in which the law of ‘ minimal surfaces vith no intercellular spaces ’ is strictly obeyed, then the shape of each ceil can be predetermined from geometrical principles. Prior to 1887 it was generally believed that a given space could be completely dmded into equal subdivisions (the total surface of which covered a minimum area), when each subdivision had the form of a regular twelve-sided figure or orthic dodecahedron, each facet of which was a regular hexagon. In 1887, however, Kelvin demonstrated that a more stable and more efficient method of equal subdivision of space was presented by a fourteen-sided figure or tetrakaideca
050 THE SHAPE OF CELLS
heclron (fig. 119); of the fourteen surfaces, six are quadrilateral and
eight are hexagonal.
, . f this «(n!re have been described by Matzke (1927 ) and bv T nX S i If each cmadrilateral surface has a side of length a, the!i
Lems 192b-S ^ also a length a. If a section is cat
to'anv'^due of the solid tigure. a hexagonal figure results of whicir four deles are longer than the remaining two. The two short sides
p; . i,,. A aroup of fourteen orthlc tetrakaidecahedra : note the hexagonal and quadrilateral facets. The space enclosed by this group is itself an orthie tetrakas
decahedron. (From Matzke.)
have a leno-th a whUst the four longer ceUs have a length VSa = l-732ffl;
the perpendicular distance between two short sides is 2- 828a, whilst tk
nernerrdic’ilar distance between two long sides is 2-449a. The interna.
\nAe between two long sides is 109° 28' 16", while that between a long
mid a short side is 125° 15' 52". The total area of the whole hexagon is
4 '\'" 2 . a.
If the form of parenchymatous cells conforms to that of a series of orthie tetrakaidecahedra so arranged as to leave no interceUular spaces, then a section cut at right angles to any one ceU interface should jdeld a series of hexagonal figures all of a definite type. That living cells do, in fact, conform to such a system has been assumed on more than one occasion (see D’Arcy Thompson), but only recentb have definite data become available (Table XXX). Wetzel (1926)
THE SHAPE OF CELLS o.r
jias shown that the pigmented cells of the human retina n hen viewed as a horizontal section are polygonal in form and possess from four to nine interfaces. More than half of the cells ha^-e si.x interfaces •.Then seen in section. Lewis (1926) has demonstrated the same fact in sections of the pith of Sambucus canadensis.
Table XXX
So. of sides
4
5
6
7
8
' 9
Avera 2 ’e
Xo. of cells : retinal cells
2
106
242
98
1
5*093
Xo. of cells : pith cells
20
251
474
i
224
30
1
5*096
The cells of Sambucus have been examined in detail by Lewis, and
from serial sections the number of facets possessed by each cell has
been determined.
Table XXXI
Xo. of cell surfaces
6
7
8
9
10
11
12
13
14 : 15 16 IT IS 10 20
Xo. of cells
1
1
2
2
8
i 8
21 j
16 10 10 1 2 3 6 1
For the hundred cells examined (Table XXXI) the average number
of facets per cell wms 13-96. It would therefore seem probable that
the cell popidation tends, on the average, to conform to the tetrakaidecahedral form. Wax models of forty -two cells failed, however, to
reveal any individual cells with fourteen surfaces. In view of the
fact that all the cells are not of exactly the same size, and of the
distebing effect of cell divdsion, this departure from the theoretical
result is not altogether surprising. As Lewis points out, the expected
result of cell division would be a reduction of the mmiber of facets
from fourteen to eleven. Alternatively, Wetzel attributes the irregularity in the polygons seen in section to differential growth;
thus in fig. 120 a series of four hexagonal cells might resolve itself
into two pentagons and two heptagons if two of the cells increase in
size more rapidly than the other two, and thereby displace their
neighbours. It must be admitted, howmver, that there is no general
agreement concerning the origin of those cells which exhibit more
or less than six sides when viewed in transverse section. Cell division
(Lewis, 1926), cell growth (Wetzel, 1926), and cell absorption and
17
258
THE SHAPE OF CELLS
fusion (Grafer, 1919) may well cause irregularities but in no case
has the actual process been seen under the microscope.
As pointed out b\- Lewis, there is definite evidence against the view that the typical form of a parenchymatous cell is that of an ortkic tetrakaidecahedron. In a figure of this type any section cut transverse to any ceil surface yields an irregular hexagon (seep. 236; having four long sides and two short sides. The hexagons seen in actual sections of tissues are, however, variations not of thh irregular hexagon i>ut of a regular hexagon, all of whose sides are equal iii length. If this be the case, the cells cannot be packed together to form a system with no intercellular spaces.
Fill. 120. Diagram to illustrate the transition from hexagonal cross section to pentacronal and lieptagonai cross sections by differential growth. The two cells a and c liave displaced the two slower growing cells b and d. (After Wetzel.)
In any discussion of cell form it is essential to differentiate clearlv between the biological facts and the expectations w^hich are based on purely geometrical systems. In view of the natural variations in the size and properties of individual cells, and of the variations in external surroundings to which individual cells may be exposed, it is more remarkable to find such a close parallel between fact and geometrical theory than to find divergencies of a secondary nature.
Limitations of the law of yninimal surfaces
In assessing the value of the above facts, it is desirable to remember that a system of living cells differs in many ways from a physical system of soap bubbles, which displays to best advantage the operation of the minimal surface law.
If we are prepared to accept the facts in the form of Errera’s Law (as formulated by Thompson), viz. ‘A cellular membrane at the moment of its formation tends to assume the form w’-hich would be
THE SHAPE OP CELLS 259
assumed, under the same conditions, by a liquid film destitute of weight ’-we come very near to suggesting that these cellular membranes actually possess liquid properties. Both Errera and Hofajeister accepted this view. It is, however, contrary to manv well established facts. As already pointed out, the fundamentaflaw of minimal sm-faces does not depend upon the liquid nature of the interfaces, but on the fact that these are the seat of free ener<.v It seems therefore desirable to restate Errera’s Law in a form applicable to modern conceptions of the cell surface. ‘A cellular membrane at the moment of its formation tends to assume the form which would be assumed under the same conditions by an elastic membrane destitute of weight.’
There is also, however, a grave difficulty which has so far been overlooked in most theoretical
17-2
2(30
THE SHAPE OF CELLS
wav between the two centres, and the length (i.e. the diameter) of the partition wall, PO, is 1-732 times the radius
2 sill 00 “ r === 1 * ' ^2 t ,
or 0-866 times the diameter of each of the cells. This gives us the:, the form of an aggregate of two equal cells under uniform conditions.
pointed out elsewhere (Gray, 1924, see also p. 19o) this analysis of cell form can be seen to be inadequate by visual observation of anv suitable svstem of living cells. In their natural state the adiacent cells of a two-celled system are not portions of true spheres fia SOI The departure from the ideal form is probably due to the fact that the cell surface has a finite thickness.i Consider a group of eontivuous soap bubbles in which the films have a considerable tliic-knes’s In this case the surface energy of the system mil not be at its minimum when the free surface occupies the form of tivo
Fi.r !■>’ Two water di-ops enclosed \vithin a drop of olive oU. A, is unstable; B, ;s stahlervote the as%-nimetrical distribution of the oil phase and the compressed fori:: of the water drops in the stable condition. The oil phase is in black.
partial spheres, for the free surface will be still further reduced by
a flow of liquid from the poles of the system to the equator, whereby
the area in contact with the external medium is still further reduced
in area. The ne-iv equilibrium is shown in fig. 122 P, wherein it car
be seen that the two resultant drops are not partial spheres but bear
an unmistakable resemblance to the form of living cells (Gray, 1924).
It is important to notice that the form of the blastomeres of a seaurchin is precisely' the same as that of a small soap bubble, -where
the thickness of the films is significantly large in compa.rison
with the total area of the bubbles. The tendency for fluid to
accumulate at the junction of two liquid surfaces was clearly recognised by Willard Gibbs (1906, p. 290), and the area concerned
is sometimes known as Gibbs’ ring. Unfortunately the exact oral
1 See footnote, p. 297, Thompson, 1917.
261
THE SHAPE OF CELLS
of this area has not yet been shown to be susceptible to geometrical or mechanical definition. The departure from the simple theoretical form does not in any way invalidate the law of minimal surfaces, it jiiiiply indicates that factors other than those represented in fig, 121 control the form of the minimal surfaces in the region common to two or more surfaces. Thompson’s simplified system, whilst applicable to oil films which are negligibly thin compared to the volume of the space they enclose, becomes insufficient when applied to very small drops or to living cells; the ‘surface of continuity ’ becomes in such cases of major importance. There is therefore no true aiisfle of contact between cell surfaces, for at each angle there exists a prismatic accumulation of intercellular substance (see fig. 123 ). The net result of this disturbing factor was clearly recognised by Thompson in the following paragraph (p. 297 ) : ‘ We have seen that, at and near the point of contact between our several surfaces, there is a continued balance of forces, carried, so to speak, across the interval ; in other words there is a physical continuity between one surface and another. It follows necessarily from this that the surfaces merge one into another by a continuous curve.
Whatever be the form of our surfaces ^
Fig. 123. Section of the pareii and whatever the angle between them, chymaofmaize; note the prismatic
this small intervening surface. . .is large interstitial spaces and absence of , T T . true angles of intersection. (From
enough to be a common and conspicu- Thompson.)
ous feature of the microscopy of tissues
One is inclined to go further than this and admit that in many cases the simpler laws of minimal surfaces are masked with, sufficient effect as to render it difficult to define the geometry of cell form with any real accuracy. It will be realised without further comment that the existence of a series of interfaces meeting at a definite angle of 120" is only a theoretical conception.
As far as the evidence goes, it seems fairly clear, however, that the average form of some parenchymatous or epithelial cells approximates with surprising accuracy to the theoretical form of closely packed units which enclose a maximum volume by a minimum of surface. In other cases, however, this is far from being true. The
2Q2
THE SHAPE OF CELLS
branchial epithelium which covers the gills of Mytilus is composed
of cells whose outline is greatly wrinkled (fig. 124), and the neighbouring ciliated cells are often rectangular in
section. The underlying causes of these anomalies are unknown, but they indicate the
danger of applying the principle of minimum
cell surfaces over too wide a field.
Finally, it is perhaps permissible to doubt \l0^x far future observations of the precise form of prismatic epithelial cells wall conform to theoretical expectation, and how” far the living cells will be found to vary in form to such Fig. 124 . Outline of cells
a deoTce as to restrict geometrical analysis to branchial epitheliur;)
. ^ *' Mijiilus. (Diairram.
a I’cw selected tissues. matic.)
Biological conception of cell form
If the form of a cell is strictly controlled by extraneous mechanical f( ^rees, it follow's that the specific differences seen in the segmentation of different types of spherical eggs must be due to differences in the iiieehanical surroundings of each cell, rather than to more fundamental differences in the nature of the cells themselves. From this point of view”, the segmentation process, as seen in an Echinus egg, conforms closely to that of Arbacia, not because the tw^o species belong to the same group of animals, but because the mechanical surroundings of each blastomere are closely similar in each case. The segmentation of an Echinus egg, from the same point of wev, differs from that of Nereis because the mechanical surroundings of
O
the blastomeres are different. Similarly, the marked similarity of cleavage pattern seen in Polychaet annelids, gastropod molluscs, and polyelad turbellarias is not so much due to any phylogenetic affinity as to a similarity in the mechanical surroundings of each comparable blastomere. Such an ultra-mechanical conception of segmentation w”ouId ascribe the differences in form of all animals to the fact that there comes a time in the segmentation of the egg when a given blastomere divides at a different time or at a different rate in any two given cases. If the mechanical conception of cleavage be extended to include the thesis that the direction of cleavage is itself determined by the mechanical environment of the cell, then the only basis left for differential development lies in inequalities of size of comparable blastomeres or in inequalities of
•263
THE SHAPE OF CELLS
rates of division. In other words, we would be forced to conclude tiiat if the cleavage of a sea urchin’s egg could be controlled, so that tiie size and position of each early blastoniere were made to conform to that of a mollusc, the resultant organism would belong to a different phylum to that of the original egg ! Putting the mechanistic conception of cell form on one side, it must be admitted that a more comprehensive conception of the development of a living egg is that put forward by F. R. Lillie (1895). ‘. . .Each component cell of the organism appears to take up a position and behave in such a manner as clearly foreshadows the final r61e which it will be required to play.’ In so doing it must conform to mechanical principles — and if it disobeys Errera’s Law, it must do so by definite mechanical means: the cell wall may cease to be the seat of tension energy at the moment of formation, or the cell must prevent this tension from operating in the normal way by an appropriate expenditme of energy.
Grave errors may readily be the result of driving limited data to their logical conclusions. The fact that two equal and contiguous ioap bubbles conform to a simple geometrical pattern and that a series of small contiguous soap bubbles tend to approximate to orthic tetrakaidecahedra, does not enable us to define the form of the foam which collects at the surface of a Avashtub. So with liAuiiff cells, we can detect unmistakable signs of mechanical forces, but the more delicate forces which are fundamental for the determination of the form of tissues or of whole animals are the result of deep-seated and predetermined characters inherent in the cells, and are not the result solely of those simpler forces to which the cells, once they are formed, are undoubtedly subjected.
The shape of the mammalian red blood corpuscle
In 1919 Hartridge suggested that the characteristic discoidai form of mammalian erythroc 3 d:es is an adaptation to the physiological functions of the cell. In order that oxygen should reach the centre simultaneously from all points of the surface, the cell must be either a sphere or an infinitely thin disc. If the red blood cell were spherical, however, it would present a minimum surface per unit volume, and consequently the rate at which oxygen would enter would be reduced to a minimum. In a flat disc, however, oxygen would reach the centre more readily at the periphery than elsewhere. The peculiar form of the mammalian erythrocyte compensates for
264
THE SHAPE OF CELLS
this by its greater thickness at the periphery — so that oxygen ’nir
reach the centre of the cell simultaneously from all parts of it
surface. An interesting extension of this conception has been mad”
by Ponder (1923-6), who points out that if a gas starts from a lipfof equal velocity potential and passes along a line of flow toward^
one of two adjacent sinks, in doing so it will pass at right angles to
all the lines of equal velocity potential which it traverses. If th
strength of the two sinks be and and if the sinks are separated
by a distance a, then the lines of equal A-elocity potential can be
defined by the equation applicable to the equipotential curves
Cayley (1857):
, OT, _ k
>2 ~ a ’
where i 1 = C.
?-2
Ponder has shown that if suitable values for the velocity potential (d) are selected, the lines of equipotential round the two' sinks bear a marked resemblance to the form of an erythrocyte. Such a ficure* when rotated about its minor axis, yields a solid appro.ximating to the form of a red blood cell and the equipotential line forming'the curve becomes the equivelocity potential surface of the solid of revolution. Gas starting from any point on this surface and moving inwards (from any point on the surface) along lines of flow will reach the circular sink in the same time. Further, any line of equal velocity potential must also be a line of equal gas concentration. If a red blood cell containing no oxygen is exposed to a fluid containing the gas, the surface of the cell will be one of equal gas concentration, and therefore gas will pass across the surface towards the inner parts of the cell to form a series of surfaces of equal gas concentration and of equal velocity potential, and Avill converge on the circular sink simultaneously from all parts of the cell’s surface. Ponder points out that the red blood cell is not quite so rounded at its ends as is the solid of revolution of the curve ^ = 7-5, and that its concavity is not quite so deep ; further, the volume of a blood cell is about 110^®. whereas that of the theoretical solid of revolution is 196 p.®. Ponder concludes that, although the form of the cell cannot be rigidly defined by one of the equipotential curves of Cayley, yet the general resemblance between the two systems supports Hartridge’s original suggestion. The appro.ximation to the theoretical form indicates that
THE SHAPE OF CELLS
265
ijjg efficiency of the cell to absorb oxygen is very great compared to
other systems of the same volume and very much more efficient than
if the cell were spherical.
As long as a mammalian red blood corpuscle is suspended in oiasma, it retains its biconcave form more or less indefinitely; if, however, the cells are suspended in isotonic saline (0-85 per cent. XaCl) the form is altered in a curious way as soon as the cells lie rdthin a critical distance of two flat surfaces. If a suspension of corpuscles is enclosed in a thin film between a coverslip and a glass ilide, the cells very rapidly lose their typically biconcave shape and become perfect spheres (Ponder, 1929). The reason for tliis change is obscure, but the rate at which it occurs clearly depends on the distance between the two opposing glass surfaces ; if these are very close together the change may be complete within a fraction of a second. Neither the pressure of the coverslip or the use of quartz slides alters the phenomenon. The only factor — apart from the absence of plasma — which is necessary for the cells to acquire the spherical form, is that the surfaces should be such as will be wetted by the saline; if glass is covered with paraffin Avax, the normal biconcaA’e form is retained in saline. The AA'hole phenomenon is A'ery obscure, but Poirder is inclined to the belief that it is due to the molecular attraction fields which are knowm to exist A\ithin lOp of tAvo closely applied surfaces (Hardy and Nottage, 1926).
REFEEENCES
Cayley, G. (1857). ‘On the equipotential curve = C' Phil. Mag .
r
14, 142.
Ekkera, L. (1886). ‘Sur une condition fondamentale d'equilibre des cellules \ivantes.’ C.R. Acad. Sci. Paris, 103, 822.
Gibbs, J. Willard (1906). Scientific Papers. Vol. 1. (London. |
Grafer, L. (1914). ‘Eine neue Anschauung iiber physiologisclie Zellaussclialtung.’ Arch.f. Zellforsch. 12, 387.
(1919). ‘ Mechanische Betrachtungen und Versuche iiber Zeliform und
Zellgrosse.’ Arch.f. Entw. Mech. 45, 447.
Gray, J. (1924). ‘ The forces which control the form and cleavage of the eggs of Echinus esculentus.^ Proc. Camh. Philos. Soc. Biol. Series, 1, 164. Hardy, W. B. and Nottage, M. (1926). ‘Studies in adhesion. I.* Proc. Roy. Soc. A, 112, 62.
Hartridge, H. H. (1919). ‘Shape of red blood corpuscles.’ Journ. Physiol. 53, Ixxxi.
Herb ST, C, (1900). ‘tJber das Auseinandergehen von Furehungs- und Gewebezellen in kalkfreiem Medium.’ Arch.f. Entw. Mech. 9, 424.
266 THE SHAPE OF CELLS
Lewis, F. T. (1926). 'The typical shape of polyhedral cells in vegetable parenchyma and the restoration of that shape following cell-division * Proc. Amer, Acad, Sei. 58. oS7,
— (1926). ^The efft-ct of eeli-di vision on the shape and size of heva^Anro
cells.' Afifit, Rtvord. dd, ooL
— iT928|. *Tlie o^rrelatioii between cell-dhdsion and the shapes and size
of prismatic evils in the epidermis of Cucumis: AnaL Record, 38, Ui ^ Lillie. F. R. (I895|. 'The embryology of the Unionidae.’ Joum. 3/orn/.
iO. L ^
Matze^e. E. ih (192T|. 'An analysis of the orthic tetrakaidecahedron.^ Torrt'fi Boi. Club, 54. 341.
Fond EH, E. il925-Gp 'The shape of the mammalian er\i:hroc\te and hrespiratory function.* Journ. Gen. Physiol. 9, 197.
a 929). 'On the spherical form of the mammalian er\d:hroc%“te.’ Bri^
Journ, Eijj. BioL 0. 3-S7.
Robert, A. (1962). “Recherches sur le developpement des troques.' Arel de Zfjoi. eipt'r, ei gen. f'3), 10, 269.
Rorx, W. (1897). •UeberdieBedeutung^'geringer” VerschiedenheitendeT
relativen Crosse der Furchungszellen fiir den Charakter des Furchuno-... schemas.* Arcli.f. Enkc. Mech. 4, 1.
11031 psox, D'A. W. (1917). On Growth and Form. (Cambridge.) TH03IS0X, W. (1SS7). -On the dhdsion of space 3\ith minimum partition-^ area.* Phil. Mag. 5th Series, 24, o03.
Wetzel, G. (1920). ‘ Zur entwicklungsmechanischen Analyse des Einfaebe prismatischen Epithels.* Arch.f. Entie. Mech. 107, 177, ^
CHAPTER ELEVEN
The Growth of Cells
It is by no means easy to define the process of gro’srth. When we speak of the growth of cartilage wthin the bodv of an embrvo at least three concepts are involved. Firstly, there is an increase in the bulk of the whole tissue, which is largely due to the deposition of an intercellular secretion having no ob^-ious vital properties. Secondly, there is a marked increase in the number of cells present! Thirdly, each individual cell undergoes, during each intercleavage period, an increase in size. In order to avoid confusion, it is conrenient to restrict the term ‘cell growth’ to the last of these three phenomena, which is essentially concerned with the formation of new living material.
The growth of a cell must be clearly distinguished from cell division, and for this reason it is convenient to consider at the outset the growth of cells w^hich are not undergoing periodic cleavao-e. Cells this type are found in at least twm highly differentiated forms— viz. muscle fibres and nerve cells. In the newly-hatched eggs of nematodes the full number of nerve cells and muscle cells of tL adult are already present, and as the animal increases in size these cells grow sufficiently rapidly to keep pace wdth other tissues; no new myoblasts or neuroblasts are formed. It foUow^s that the size of indiddual cells of this type must be determined by the size of the whole animal or vic6 vcTSCi, Analogous facts apply to vertebrate animals. If the myotomes of a young fish embryo are examined, the muscle fibres are seen to originate as small myoblasts which fail to show any trace of striation until the two ends are fixed to the anterior and posterior walls of the myotome. At this stage striations appear and the ceU begins to grow. It continues to grow throughout the whole growdh cycle of the animal so that it often increases its bulk many thousands of times without undergoing any process of cell dhision. Unlike the myoblast of the nematodes, however, the growth of the fish’s muscle fibre does not keep pace with the growth in girth of the fish, for new fibres are continually being added to the myotomes from fresh undifferentiated myoblasts (see fig. 126 and Table' XXXII).
Pi., T>', CaPiera iucida drawings of transverse sections of somatic muscle fibres of
fhf tr;ut 1 FUh W3cm. long, cross-sectional body area 1-0 sq mm. Eelative
area of fibre 1-0. 2, Fish 1-63 cm. long, cross-sectional body area 1-90 sq,
m4 Re ative average area of fibre 2-18. Ratio of cross-sectional body area to
cross-section' of muscle fibre is 1-0 and 0-9 respectively. (From data
collected by D. Bhatia.)
Transverse-linear Dimension of Fish
Flo- 126. The graph illustrates that the rapid growth of the somatic muscle fibres
during the period of larval life is not maintained at a later stage. Dunng
life the relative rate of growth of the muscle fibre is less than that of the whole body
THE GROWTH OF CELLS 269
Similarly, most if not all the nerve cells of an adult animal are Diesent at an early stage in development. In both muscle and nerve hie differentiated cell appears to have lost all faculty for cleavage, i^tliough it retains its capacity to grow, and the cessation of cleavage precedes the process whereby these cells begin to exhibit their characteristic and differentiated form. Prior to differentiation, cell division is active.
Table XXXII. Relative area of cross-section of complete fish {Salmo fario) and of muscle fibre
Fish
Average muscle fibre
1-0
1-0
2‘0
2*1 ;
5-0
4*1 1
16*8
5*3
69*0
6*5 i
200*0
S*1 1
592*0
11*3 *
In marked contrast to muscle fibres and nerve cells are epithelial
cells. The average size of the epithelial cells in the liver, kidney, gut
or skin of an adult vertebrate is not markedly larger than that at a
much earlier stage in the life history (Illing, 1905). It is not easy to
estimate the volume of a tissue cell, but Berezowski’s (1910)
measurements of cross-sectional area shows clearly that the gut cells
of the white mouse rapidly reach their maximum size at an early
stage in the growth cycle of the body (see Table XXXIII).
Table XXXIII
- Age of mouse
10
days
1
month
2
months
3
months
4
months
5
months ;
Body volume
4
7
14
20
21
25
Average length of gut cells (jLi)
14*3
18*9
20*2
22
21*7 23-2
Average width of gut cells (/Li)
4*9
4*9
5*1
4*8
5*1
4*7
i Relative crosssectional area (10 i days taken as
- unity)
1*00
1*32
1*47
1-51
1*58
- 1-55
270 THE GROWTH OF CELLS
RrobEbly no bard and fast distinction sKould be dxawn.betwccr: epithelial cells on the one hand and muscle fibres and nerves on the other, for Plenk (1911 ) found quite a definite increase in the size ofthe epithelial cells of amphibians with increasing size of the whole animal..
Table XXXIY
Volume of cells (fx^)
Aire of salamander
Oesophageal
epithelium
Stomach
epithelium
Birth ;
1458
1242
2 months
3796
2788
12 months
6328
8268
As far as the efficiency of an organ is concerned, there is no very
obvious reason why a muscle should increase in size by increasing
the size of the existing fibres, whereas the liver should increase in
size by increasing the number of its constituent cells.
(From Plenk.)
The factors which control the growth of cells are very imperfectly understood. In the case of muscle cells there can be little doubt that mechanical forces play an important part. The size of a fibre varies
THE GROWTH OF CELLS
271
with its position in the body: it will grow in length wherever it is
stretched between two relatively fixed points— a fact well exeniolified by the hypertrophic growth of the pregnant mammalian
uterus.
The nucleo-cytoplasmic ratio during gro-^th
For many years it has been known that for any given type of epithelial cell, the volume of the cytoplasm tends to bear a fixed ratio to the volume of the nucleus. When, however, a cell is undergoing a series of successive divisions, this nucleo-cytoplasmic ratio [s not constant, but varies at different phases of the divisional cycles. For example, Koehler (1912), working with the eggs of StrongylocentTOtus lividus, found little or no e\ddence of increase in the total endoplasmic volume of the whole eggs between the moment of fertilisation and the formation of the gastrula, but the total volume of the nuclei increased about ten times during the same period. If we judge grovdh by increase in bulk, obviously the growth of the nucleus is of a different order of magnitude to the growth of the endoplasm.
Table XXXV. Cytoplasmic and nuclear growth in Strongylocenirotus eggs (16° C.). (After Koehler.)
No. of
cells
present
Volume of single nucleus
Volume of cytoplasm in a single cell
Total volume of nuclei
Total volume of c>i:oplasm
Ratio
-VC
2
1395
142625
2790
285250
0-0097S
4
742
75078
2968
300312
0-0098S
8
607
30324
4856
242592
0*02009
16
547
16659
8754
! 266544 i
1 0*03284
1 32
366
8230
11722
1 263370 1
0 04451
i 64
332
4197
21235
268576
0*07907
1 501
63
510
31563
255510
0*12255
607
46
386
27665
234644
011917
1 820
32
263
26294
215396
. 012168 ^
i 1163
19
242
22121
281790
007851
i
Up to about the ninth cleavage there is a very marked increase in
the total volume of the nuclei, whereas the volume of the c\doplasm
remains unchanged, and during this period the nucleo-cjdoplasmic
ratio increases to about ten times its original value. Except for
those obtained at low temperatures, Koehler’s results suggest that
this period of rapidly increasing NjC ratios is followed by a period
in which the ratio is fairly steady.
■272
THE GROWTH OF CELLS
Koehler's results are also of interest when applied to the earli?observations of Popoff (1908) (see also p. 132). Popoff determined tf "
relative volume of the cytoplasm to the nucleus at different stages i-the divisional cycles of Fronionia and other protozoa. Ten minuteafter a vegetative division the volume of the macro-nucleus was foun ;
to be approximately 1-3 per cent, of the volume of the cytoplasrr"
from this period onwards the volume of the cytoplasm was found
to increase more rapidly than that of the nucleus, so that after some
hours the -V C ratio had fallen to 1-0. Hertwig (1908) pointed out
that this process could not go on indefinitely and suggested that i^
would lead to a state of ‘ nucleoplasmic strain which in turn miofit
induce the nucleus to undergo a process of division during which it
would increase in volume and thereby re-establish the norma!
nucleo-ej-toplasmic ratio, -iceording to Popoff, the onset of c\i:oplasmic cleavage is preceded by a phase of very rapid increase in the
volume of the nucleus so that, when cleavage occurs, the nueleoc}i:op!asniic ratio has regained its normal value. It will be noted
that the kinetic cycle of cleavage resembles that in sea urchin
eggs in that it is associated with an increase in the volume of the
nucleus, whereas the interkinetic cycle is characterised bv cvtoplasmic growth, a process which is absent in sea urchin eggs, since
there is no clearly defined interkinetic period during the'earlv
cleavages of the egg cell (Gray, 1927).
Quite how much significance should be attached to observations of nuclear volume is uncertain. If nuclear volume were clearlv an index of the amount of an essential nuclear compound the situation would be less indefinite : unfortunately this is not demonstrably true Masing (1910) and Schackell (1911) failed to obtain any evidence of nuclein synthesis during the period in which the total volume of the nuclei of sea urchin eggs is known to increase by at least ten times. These results have recently been confirmed by Needham and Needham (1930), who concluded that all eggs, except those of terrestrial animals, contain, before fertilisation, all the nuclein constituents requisite for early development. We are forced to assume either that nuclear volume is not an adequate index of nuclear material, or that during development this material gradually passes from the cjiioplasm into the nuclei. In both cases it must be admitted that nucleocytoplasmic ratios have, at present, no definite chemical significance. For further discussion, reference may be made to Robertson (1923) and Faure-Fremiet (1925).
THE GROWTH OF CELLS
273
Metabolis^n of groxi:ing cells
The physiological state of a groAving cell is clearly different from that of a cell whicli is in equilibrium vdth its enA-ironment — at the
- ame time little or no precise information is aA-ailable concerning
4e metabolic actiA-’ities specific to groAA'ing cells. As groAA-th proceeds, two distinct phenomena can be recognised: (a) the synthesis of neAv ihing material, (h) a rise in the total metabolism inA-olA*ed by the nresenee of this neAv material. As far as can be judged, the SAntheses "of aroAA-th are peculiarly efficient in the sense that little or no dissipation of free energy is involved in the process, so that vhether a cell is groAAing or not the amount of energy set free per unit time per unit of liA-ing matter is the same. This conclusion AA'ill be considered in detail elseAvhere ; at the moment it is sufficient to stress the fact that it is by no means easy to define any one chemical or physical property Avhich is peculiar to groAA’ing cells — in spite of the fact that the outAA-ard and -visible signs of groAAdh are themselves obA'ious. A possible exception is provided by the AA'ork of Warburg (1927 i, Avho found that young embryonic cells or cancer cells are able to effect anaerobic glycolysis to a much greater extent than the ceils of older tissues Avhieh are either groAving more sloAvly or not at all. Warburg found that malignant tumour cells produce three to four times more lactic acid per unit of oxygen consumed than do benign tumours, AAdiile three to fiA'e day old chick embryo tissue in the absence of oxygen produces lactic acid at almost the same rate as malignant tissue, but in the presence of oxygen normal respiration takes place Avith the formation of very minute amounts of lactic acid. According to Warburg, both groAA-ing and non-groAsing tissues can be classified into four groups according to the nature of their metabolism, (i) Normal resting tissue, characterised by a high rate of respiration and by slight poAvers of anaerobic glycolysis, (n ) Embryonic tissue Avith a high rate of respiration and high anaerobic glycoh^sis, but Avith Ioav poAvers of aerobic glycolysis, (iii) Malignant tumour cells Avith Ioav respiration and high aerobic and anaerobm glycolysis, (iv) Benign tumour cells Avith less actWe glycolytic powers than those possessed by malignant tissues. Many of W arburg’s conclusions have been confirmed by Murphy and HaAAkins (1925), but these authors failed to find any sharp segregation of
other tissues into the four categories.
Quite clearly a cell -will not gro-w unless pro-vided -with the raAV
274
THE GROWTH OF CELLS
materials with which to build up its essential parts. Each type ef
cell is to some extent dependent on the presence of specific materia^
and these are doubtless of two types. Firstly, raw material for tii*provision of the free energy required for maintenance ; secondly, the
raw materials (nitrogenous and otherwise) for ceil S3mtliesis. The
iieki of enquiry opened these conceptions is almost unlimited
and only one or two salient features will here be considered.
Ill the first place tlie requisites for growth are at times of a verv simple character. Koser and Rettger (1919) have shown that maiiv bacteria are capable of active growth when the only available source of nitrogen is a single amino-acid or even ammonium phosphate: it more than probable that some types rely soleR on free aninioiiia. Similarly a number of ' tj^phoid ’ bacteria can reh' on such simple compounds as acetic acid, oxalic acid or glycerol as their source of carbon. The work of Peters (1921) suggests that not oiilv bacteria but also some protozoa are peculiarly modest in the niaterials required for growth. Between such types on the one hand and the iiiucli more specific requirements of mammalian cells on the other, there are doubtless intermediate types of great varietv.
In the econoni}’ of most animal cells which are undergoing growth, sugars often pla}" an essential rdle. Krontowski and Bronstein (1926) have shown that actively growing cultures of cells in litro absorb sugar from their emdronment, and Watchorn and Holmes' (1927) work indicates that the sugar is used for maintenance, and is responsible for the production of free energy ; in the absence of sugar, the cells fall back on proteins for these purposes with consequent elimination of ammonia and urea.
In addition to the t\'pe of material already mentioned, it is necessary to consider two others of a more intricate nature. Some bacteria fail to grow, or onh" grow" to a limited extent, in an otherwise adequate medium if vitamin B is absent (Hosoya and Kurova. 1923). Similarly, Allen (1914) found that the diatom Thalassiosim failed to grow in s}mthetic media unless a small trace of natural sea water was added; on the other hand, Jameson, Drummond and Coward (1922) obtained a good gro^vth of another genus, Atoc/u'c, in purely s\mthetic media. Determinations of the vitamin requirements of isolated cells are peculiarly difficult, since it is essential to eliminate the technical errors which can readily creep into the experiments. For example, it does not seem clear whether the “bios' postulated by Wildiers for the growth of yeast is to be regarded as
THE GROWTH OF CELLS
vitamin B, inositol (Eastcott, 1928), or the hydrogen ion (Darby,
1930 ). In addition to substances of the vitamin type, cell growth is
often dependent on substances peculiar to young or rapidlv growing
animals— the obvious example of this type being the embryo extract
essential for the growth of vertebrate tissues grown in vitro and the
more problematicar trephones ’ described elsewhere (see p. 294).
The efficiency of growth
The efficiency of growth can be expressed in terms of material or in terms of energy. On the former basis it is customary to express the dry weight of new tissue formed as a percentage of the dry weight of the material utilised in its formation. The value so obtained by various authors is found, for ordinary conditions of experiment, to be of the order of 60 per cent. From a practical point of view this figure is of some interest, but theoretically it is not of great significance. The true efficiency of growth is independent of the processes of maintenance peculiar to the tissue, for this only occurs when the new tissue has actually been formed. Over a short period of time the material efficiency is expressed as a ratio
Weight of new tissue formed
Weight of raw material used — Weight of raw material used for maintenance ’
In practice, the weight of raw material used for maintenance ha^ tu be calculated from the rate of respiration of the tissue, converting the Og consumed, or the COg eliminated, into terms of raw material. Data of this type have been collected from a number of sources and may be illustrated by Table XXXVI, which applies to the developing trout (Gray, 1926). It is clear that after allovdng for the 'wastage' of material involved by the maintenance of the living tissue after it is formed, there is no evidence which suggests that the conversion of raw material into new tissue is anything than a highly efficient process.
Returning to the figure of 60 per cent, as an estimate of the gross efficiency of growth, it will be noted that this figure must vary to some extent as time proceeds for an increasingly large percentage of available raw materials will be used up for maintenance leaffing, under most experimental conditions, a smaller amount available for grovdh. Further, the actual value of the efficiency coefficient will vary with any factor which affects differentially the processes of growth and of maintenance.
276
THE GROWTH OF CELLS
Table XXXVI
Day of
development
(after
fertilisation) '
Dry weight of embryo
- Dry weight
of yolk equivalent to Oo consumed
Dry weight of remaining yolk
Total yolk :
(mg.)
(mg.)
(mg.)
(mg.) ;
40
a-04
1-3S
33-21
37-63
50
3*78
1-SS
31-57
37-23 1
50
4*00
i 2-34
30-75 i
37-62 :
57
O'SS
3-11
i 27-68
37-67 1
00
8*48
j 3-S4 1
1 25-01 1
37-33
1.3-00
6-45
18-53 1
37-98
71
15*50
I T'77
17-63
40-90
7 5
is-os
i 9-56 '
14-76
42-40
- 7S
20-10
- 10-83
7-79
38-78 1
80
23-04
1 11-40
7-38
41-82
Observed average amount of yolk in an unfertilised egg 37-72 mg.
It is, perhaps, more satisfactory to assess the efficiency of cell
growth from the point of view of a redistribution of energy rather
than of materials, since in some cases a gram of organised tissue may
contain a higher energy content than a gram of raw materials.
A fairly extensive series of observations are available for the growth
of Aspergillus from the work of Terroine and Wtirmser (1922). The
mould was grown in a suitable synthetic medium containing glucose,
riie energy content of the initial and final media, together with that
of the mould formed, wms determined calorimetrically and expressed
in calories. Thus the gross efficiency^ is
Energy of organised tissue {T)
Energy of initial medium (dii) — Energy of final medium {M^} *
In one experiment the medium originally contained 6*0 calories; it yielded a mycelium containing 3-48 calories, wdth a final medium containing 0T25 calories; thus the gross efficiency is approximately 60 per cent. Were these figures expressed as grams dry weight of substance the result would be slightly different, since 1 gr. of my'eelium is equivalent to 4-8 calories, wffiereas a gram of glucose contains only 3*76 calories. To reach the true estimate of efficiency it is necessary to allow for the energy dissipated by respiration; knowing the heat produced by the formation of the observed amount of CO 2 from sugar, it was found that 1*97 calories were expended in this w^ay.
THE GROWTH OF CELLS
277
Table XXXYII
EfiprffV in original 6-00 cal.
Energy in final mycelium
3-4S eal.
niediuiii
Energy in final medium
0*12
6-00 cal.
Energy equivalent to CO. evolved Unaccounted balance
1-fiS
0-42 ..
0-00 ea!.
The figures show that only 7 per cent, of the total energy of the
original medium is unaccounted for and this (0*42 calories) is
probably within the region of experimental error. It now remains
to consider how far the energy accounted for by respiration can
uroperly be regarded as normal maintenance. From a purely material
basis it would seem as though the whole of the heat of respiration
can be attributed to this source (see Gray, 1926), but using an indirect method and basing their conclusions on observations of
energy, Terroine and Wurmser concluded that this is not the case,
and that only about one-half of the dissipated energy can be attributed to normal upkeep — and that the true efficiency of gro^^tli is
thereby reduced to about 72 per cent, when estimated in terms of
energy. It is possible that this dissipated energy is stored in the
organism as free energy, although the figure (28 per cent.) seems
somewhat high. It is worth noting that Terroine and Wiirmser’s
analysis only applies to the rather unusual conditions of grovlli,
where the rate of formation of new tissue is constant and independent
of the amount of tissue present.
The kinetics of cell growth
When a cell divides into two and each daughter cell acquires the size of the parent cell, we are usually prepared to admit that growth lias occurred. Similarly, when a cell increases in size, without any apparent accumulation of secretory products or of excess w^ater, the cell is again exhibiting a process of gro^vth. In actual practice, however, it is exceedingly difficult to put forward a definition of ceil growth which will enable us to express the process in a quantitative manner. The final unit of growth must ultimately be expressed in terms of ‘growing’ material just as the rate of a chemical reaction is expressed in terms of the molecules or ions of each substance involved. For the moment we shall assume that the cell is a natural unit of living matter, and consider how^ far this conception enables us to express the facts of growth in a reasonable and orderly manner.
278
THE GROWTH OF CELLS
Given an acti^-ely dividing bacterium, or tissue cell in vitro, it
seems certain that the cell will grow and reproduce itself at a constant speed as long as the conditions in which it lives are maintained
at a satisfactory and constant level. Observations of this type were
made by Barber (1908), who isolated single individuals of Bacillm
coli from a rapidly growing culture, and observed their rate of
reproduction at a constant temperature. Table XXXVIII shows that
the time which elapsed between one generation and another was
approximately constant at 20-0 minutes. Darby’s (1930) figures
sliow that tlie same fact is probably true for protozoa such as Paramecium, although in this case the facts are less complete and the
degree of variation between individual growth cycles is not yet
definable. Using cells grown in vitro, Carrel and Ebeling (1921 fc)
found that fibroblasts in a given culture reproduced themselves once
in every forty-eight hours. In this ease also, the data are as yet
Table XXXVIII
Generation time in minutes
lS -7
20-2
21-2
19 v 5
21-2
19*4
20-2
200
19-8
incomplete, for it is by no means easy to subject growth in vitro
to quantitative measurement. Ebeling (1921) has given evidence,
however, which indicates that the rate of increase of the surface area
of an active culture can be accepted as an index of growth which is
accurate to within 6 per cent., and using this method it seems clear
that, given a suitable medium, the rate of grow^th of fibroblasts in vitro
can be maintained at a high and constant level for very prolonged
periods. As long as the conditions of the environment are satisfactory, therefore, there is no inherent tendency for an isolated cel!
to show a decreasing ability to grow^ and divide (see, however, Calkins
(1926)). Under such circumstances the total number of cells present
at any particular multiple of the generation time can theoretically
be calculated by^ a process of compound interest as long as no cel!
dies or as long as a fixed percentage of the population dies per unit
time. If the rate of gro'svth and the frequency of division of eacli
individual derived from the single parent cell were identically the
same, it follow’s that the growi:h of the culture — as measured in
279
THE GROWTH OF CELLS
terms of individual cells— would fluctuate between two extremes.
At the moment at which all the cells di^^de the rate of reproduction will be determined by the number of cells (r) present:
immediately after division 2x cells are present, and there will be
no further increase until the next di\usion period is reached. It
is a simple matter to calculate the number of cells (r) present at
any given time, since x = where k is a constant equal to
M^^time’ ^ calculated to the preceding
period of cleavage. In practice, this state of affairs is never completely realised, although it is comparable to the cleavage cvcles of the early divisions of a sea urchin’s egg (Gray, 1927). Systems of this type do not reveal the rate at which changes are going on within the cell itself, they simply define a hypothetical population in which a definite series of changes are completed within the limits of one generation period, since the unit of growth is the individual cell and the unit of time is one generation period.
In nearly every natural case the conditions of groviih (even under optimal conditions) are more complicated. When one bacterium is isolated and its products segregated as a pure culture, the generation time of each cell is not identically the same as that of its neighbours, and consequently at any given moment some cells are dividing, whereas the others are at various intermediate stages of the reproductive cycle. The rate of increase of such a population will be determined by the percentage of cells actually dividing at any instant, and the actual grow^th of the population can be plotted as a smootli curve (dotted in fig. 128), instead of a series of points restricted to the end of each reproductive period (see fig. 128); the smooth curve is a parabola.
dw
dt
= kx, where k is equal to
log. 2
generation time’
or iv = Xq where Xq is the number of cells originally present.
Such an analysis only holds good when the average generation time of
individual cells is the same for all the cells present, although for any
given series of filially related cells the generation time may fluctuate
from one successive cycle to another. This so-called logarithmic law
of growi:h applies in practice to rapidly growing populations of
bacteria (Lane-Claypon, 1909) and to yeast (Slator, 1913; Richards,
1928 a and &). In cultures of fibroblasts Fischer (1925) states that the
280
THE GROWTH OF CELLS
average {growth rate fluctuates in periodic cycles, so that the law of compound interest 'U'ill only hold with even approximate accuracy over long periods of time (see p. 293).
The expression .r = e- is so frequently applied to the kinetics of growth that it is desirable to appreciate its full significance. It implies two things : (i) that ail the cells or a fixed percentage of them are alwaj's growing and dividing during the whole of their existence,
Fig. 12S. Graph showing the rate of increase of a cell population in which (a) di\isioii is s\Tie}ironous, and the number of cells is suddenly doubled at the end of each L^eneration period, (b) division is not synchronous, but a constant proportion of cells are dividing at any given instant.
and (ii) that although the generation times of all the cells present are not all identically the same, yet the variability in this respect remains unchanged; in other words, a cell which dmdes unduly rapidly must tend to give rise to cells which will di\dde slowly and vice versa. There must be no accumulated tendency to increase the percentage of rapidly dividing cells and to decrease the percentage of slowly dividing units (see p. 311).
THE GROWTH OF CELLS
281
It is necessary to remember that in all such systems the units
concerned are individual cells, and that the act of cell cleavage is a
discontinuous process for the purposes of assessing grovth. Hence,
although we get a smooth curve which relates cell number to time,
the fundamental change is not capable of analysis by such methods.
By growth we mean increase in the amount of living material: this
olniously goes on in the intercleavage period. If we restrict our data
to arbitrary units of whole individual cells all we can say is that,
taken as an average of the population, a given cell will produce an
amount of new substance equal in bulk to the original cell in a given
period of time. Until recently no single cell had been observed at
frequent intervals during a period of grovi:h, and our knowledge of
the actual rate of intracellular growth was based on indirect
analysis. In the case of yeast and bacteria it is possible to estimate
the total amount of material present by weighing the cells or by
observing their volume (Slator, 1918; Coombs and Stephenson,
1926). Similarly, the respiratory activity can be taken as a measure
of the living substance present (Slator, 1913). In both cases the
logarithmic law seems to hold with remarkable accuracy. The grovtli
of individual cells has, ho-wever, recently been followed by
Sclimalhausen and Bordzilowskaja (1930), who have measured the
rate of increase in size of bacteria and yeast cells. They find that the
rate of growth per unit length (SllSi.l/l) of Bacillus megatherium and
of certain other forms remains constant during intercleavage periods
of gro\\i:h, and consequently the course of growth obeys the logarithmic law (see Table XXXIX and fig. 129). This logarithmic increase
in size only occurs if the ratio of cell surface to cell volume remains
relatively constant during the process of grovi:h. In spherical cells,
this is clearly not the case, for as such cells increase in size so the area
of cell surface per unit of volume decreases, and at the same time the
growth rate declines. Schmalhausen concludes that the absolute
rate of growth of cells is controlled by two opposing factors, one
of which is directly proportional to the surface area, while the other
depends on the volume of the cell.
From the evidence available, it seems fairly safe to assume that a growing cell, of the types mentioned, will produce new material at a constant rate per unit of its own mass if the environment is strictly controlled at a satisfactory and constant level. At the same time this conclusion may not be of general application. Comparatively few types of cells have been investigated by quantitative
2S2
THE GROWTH OF CELLS
methods, and within the group of the Protozoa there is considerable
evidence to support the view that the growTli rate of a populatioB
may decline even in a satisfactory medium. In Urolepius and allied
forms the growth rate appears to be affected by the intrinsic* changes
effected by conjugation (see Calkins, 1926, pp. 465-508).
Table XXXIX. Bacillus megatherium, 28-29'^. Average
cross-section, l*54/x
Time in
0- minute
intervals
Length in
.wC'/j
0 0-44
1 ; 0-92
2 7'4-t
3 i T-90
4 S-52
5 0-I2
6 9-SG
T 10-48
8 11-10
0 11-90
10 12-SS
’eloeity
' gro\\i:h
!
Calculated | surface j
1
Specific rate of gro’wth (SZ/Sni/7)
Ratio of surface to
1 volume
()-4S
1
36-03 1
0-0120
2-00
0-52 !
38-44
0-0121
1 2-SS
0-52
40-96
0-0113
i 2-86
0-50
4:3-57 i
0*0113
1 2-S4
0-00
46-37
0-0113
1 2-82
O-OS
49-47 I
0-0120
j 2-Sl
0-6S
52-76 1
1 0-0112
i 2-79
0-GS
56*05
1 0-0105
2-78
O-SO
59-62
1 0-0115
0-92
63-78
j 0-0123
2-70
Fig. 129. Logaritliniic growth of single bacteria. The ordinates represent the logaritrmi of the length in microns. (From Schmalhausen and Bordzilowskaja.)
Inhibition of growth
If the number of cells in a given culture is allo%ved to increase, there comes a time when the compound interest law quite clearly breaks down. Sooner or later the growTli rate declines and eventually sinks to zero : after this there is a rapid decline in the number of bacteria present. The factors responsible for this breakdown of the
THE GROWTH OF CELLS
283
io«Taritluiiic law of population growth are not completely known.
Graham-Smith (1920) has shown that under certain conditions the
iniount of foodstuffs available plays an important role. In a pardeular culture medium, Graham-Smith found that Staphylococcus
^'lureiis reproduces itself until there are approximately ten million
orfyanisms present per 0*01 c.c. of medium, and that this figure is
independent of the number of bacteria originally inoculated into tlie
medium.
Table XL
So. of bacteria
in original
inoculum
^Maximum no. of bacteria obtained
No. of bacteria in original inoculum
Maxiiiiiim no. of bacteria oljtained
520
9,248,000
84,400
8,720,000
1392
10,606,000
1 4,300
' 8,544.000
1784
9,280,000
i 420
' 8,490.000
5660
9,872,000
1 59
7,584.000
There is therefore an upper limit to the density of bacteria which
can be obtained in any given culture. This limit is largely depeipent
on the concentration of nutrient substances in the medium (Table
XLI) — see also Penfold and Norris (1912).
Table XLI
Relative concentration of food
Maximum no. of bacteria obtained
100
25,840,000
75
20,300,000
50
15,760,000
25
9,416,000
10
4,273,000
Hand in hand wuth the decline in growth rate of such cultures there
is a decrease in the size of the individual cells, which itself is probabl^^
due to a diminution in the concentration of available food (Heiirici,
1923 6).
The far-reaching effect of food supply upon the gro\^i:h rate is seen when identical cultures of bacteria are grown at different temperatures (Table XLII). The higher the temperature the more intense are the metabolic processes of the cells, and consequent \ a higher concentration of food is required to maintain a maximum
284
THE GROWTH OF CELLS
population. In other words, with identical cultures, the food supply
begins to rim short sooner at a high temperature than at a loiv
temperature, and the maximum density attainable is corresponciiiigly lower.
7S0'ri^
720
66G
X
600 *-^
0'2 0*3 0-4 0*5 0*6 0-7 0-8 0-9 1*0
Percentage concentration of peptone
Fill. 130. Grir -7;'- vrn'.L" the influence of nutritive material on the rate of : i-acteria. (From Penfold and Norris.)
Table XLII
Inciibation
temperature (■ C.)
Maximum density of bacteria |
Time in days required to reach maximum density
17
18,272,000
8
27
15,164,000
j 5
37
10,448,000
- ^
Even when the food supply of a cell culture is very rich, the
growth rate ma}’ still decline, indicating that other factors are
operative in addition to lack of food. Richards has shown that if
yeast cultures are subcultured regularly every three hours, the
logarithmic law is maintained until a concentration of 70 x 10® cells
per c.c. has been reached: failure to subculture results in a decreased
growth rate, although abundant food is present (see fig. 131).
Richards has shown that the decreased grovdh rate is largely due to
2S5
THE GROWTH OF CELLS
rlie accumulatioii of alcohol "which begins to inhibit ^row’iiii at a concentration of about 1 mg. per c.c.
Fig. 131. Graph showing the effect of the removal of toxic products on the gro\\i:h rate of yeast cells. (FVoni Richards, 102S b.)
Lag phase of growth
When for any reason an adverse medium effects a niarkedly depressant action on the growth rate, there is abundant evidence that the effect upon the cells is of a profound nature and that the external environment affects the cell in such a way as to make it'recovery in an optimum medium a slow if not impossible process. When cells from an actively , grooving culture are transferred to a fresh medium — ^there is no check in the growth rate — the cells con tinue to grow according to the logarithmic law. If, however, the cells are removed from an ageing culture in which the grovffh rate has fallen to a low value either from want of food or for any other cause, there is an appreciable period of time during which either no growth occurs or during which the growth rate is lower than that characteristic of later periods of culture. This critical period of depressed growth rate is known as the lag phase. The specific underlying causes of the lag in growth rate are obscure (see Penfold, 1914; Buchanan, 1918; Salter, 1919). When the external environment begins to exert a depressant action on growth, a number of cells might be so affected as to be permanently incapable of further growth
286
THE GROWTH OF CELLS
even. %vh.en transferred to fresh medium and an apparent lag phase would be observed: on the other hand, the evidence for such a suggestion is not clearly established, for Wilson’s (1926) figure^ suggest that the percentage death rate does not change to a marked degree until the population of the culture is definitely on the down ^rade It seems probable that e^ en if onl\ ^ iable cells are considerec the lag phase woidd still persist. The existence of this period i. perhaps not surprising, since the affects of adverse conditions or: organisms is often not readily and quickly reversible on transference to better conditions.
The general course of the growth of bacterial cultures is well illustrated Ijv Buchanan’s diagram (see fig. 132); although the data
Fi^ ’’ to illiistriitti; the phases of growth of a culture of bacteria. 1 i:
the "initial stationarv phase during which there is no increase in numbers; a ^ bis the V -V- wiiicli the rate of groi^-th per unit organism is increasing ; 6 -> c is th.during’ wiiieli the growth rate is constant; c d is the phase oi nc'^tive acceleration durinu wiiich the growdih rate falls to zero; d -> e, the number of “bacteria present is constant at a maximum value; e ^ / is a period of accelenitei death: / is the logarithmic death phase. (From Buchanan, 1918.)
for other types of cell are much less extensive, there is no reason to doubt that the general course of growth is essentially similar to that exhibited by bacteria.
Frequent attempts have been made from time to time to e.xpress the whole course of unicellular growTh in quantitative terms. It n very much open to doubt, however, whether such a procedure is useful in the present state of our knowledge (see Gray, 1929).
One of the most striking conclusions to be derived from the study of growth in vitro is that, given suitable conditions, a population of
THE GROWTH OF CELLS og;
edis, whatever be their properties in situ, will continue to ^row iudefinitely at a steady rate. Fibroblasts, bacteria, veast and“pr. .bably many protozoa, continue to grow and multiph-‘at a rate whidi i, constant within definable limits as long as the external enviroiirneiit is maintained at a satisfactory and constant level Tti fS-,, ^
of tissue cells, life under such conditions is clearlv not limited to t^io rate or duration characteristic of corresponding' cells in sHu ibody; Carreland Ebeling’s(1922 a)culture of chicken fibroblasts knxalready persisted far beyond the normal life of an adult fowl and the amount of tissue to which the original culture has given rise G in excess of that which would have occurred had the original f ion“biasts been grown in their normal positions in the body. To tuae extent, this is, of course, an artificial comparison, for it'rnivh' w.-T be argued that a fibroblast, growing in an excess of highly nutrient medium, is provided with an environment very different from tiie highly concentrated cell population present in an organised bodv. It is, perhaps, fairer to compare a cell in situ with a cell growincr i-' a dense suspension of cells in vitro. Here again, howe\-er. we mu-t conclude that the behaviour of the two types is curiously sirid^ar Just as the grovdh rate of a yeast or bacterial suspensioi; teriddo' decline to zero as the culture becomes older and more conceiitratt -d with cells, so a culture of fibroblasts in vitro will exhibit "the same phenomenon if it is not subcultured or provided %vitii fi-fsh medium. Such comparisons to normal growth in situ must not be pushed too far. Almost any disturbance of the external environment Awll affect the groxvth rate in vitro and from a quantitative point of \dew it is as yet impossible to distinguish between a \-ariety c.f factors (lack of food, accumulation of metabolites, lack of adequate growth accelerators)— all of which cause departure from the logarithmic law of growth (see Gray, 1929). We cannot sav wingrowth in situ is limited, but the facts of growth in vitro ciearly demonstrate that the surrounding medium, and the presence or absence of other cells, must play an important role.
The parallel between cultures of unicellular organisms and metozoan cells grown in vitro is clearly very close. Not only are the two tj-pes capable of unlimited logarithmic growth, but when conditions are unfavourable their reactions are closely similar. When a subculture is made from an old culture of bacteria' we have seen that there is a marked lag phase before growth is resumed in the fresh medium. Similarly, it has been known for many years that em
288
THE GROWTH OF CELLS
bryonic cells in vitro rmgvate, grow, and divide nauch more: rapidly than cells from older or adult animals; the younger the animal
from which the original fragment is removed, the more quicld} does it show signs of growth in vitro (Cohn and Murray, 192o).
THE GROWTH OF CELLS
289
Just as in the case of bacteria, there is a latent period before gro'wdh
begins, and the length of this period is a direct function of the age
of the fragment. This may conceivably be due to the accumulation
of a growth-inhibiting factor as the organism grows older; until this
substance can diffuse away from the cells into the medium, growth
would obviously be slow. On the other hand, it may be due to the
lack of specific nutritive substances which are only generated in
appreciable quantities in the embryo (see p. 294).
Tissue culture
That tissue cells can grow after excision from the body w^as first demonstrated by Ross Harrison (1910). Small fragments of the central nervous system of a frog, immersed in a hanging drop of lymph, clearly exhibited the outward migration of nerve cells and the subsequent outgrowth of nerve fibres from the cells. This important discovery opened up entirely new methods for the investigation of cell growth and its allied problems, for it was soon showm that the phenomenon is by no means restricted to nerve fibres, but is exhibited by many other types of cells (see Lewis and Levis, 1924). The technique for successful tissue culture has been described in detail by Strangeways (1924 b). Roughly speaking, success depends upon the isolation of an aseptic fragment of tissue in a suitable nutritive medium. For good results, it is desirable that the growing cells should be provided with a solid surface to which they can attach themselves, and this is usually provided by implanting the fragment in a drop of coagulable plasma, although foreign solids, e.g. glass wool or spider’s webs (Harrison, 1914), immersed in a fluid medium will suffice (fig. 134). More recently, Carrel has replaced the ‘hanging drop ’ technique by the ‘ flask ’ method, wherein the clot of plasma is attached to the bottom of a small aseptic flask, capable of containing a relatively large amount of fluid medium •which can readily be changed from time to time: this obviates the necessity of the constant subculturing necessary in the case of hanging drop cultures.
The growth of the excised fragment is preceded by the outw^ard migration of the cells from their normal position. The migrating cells are mostly derived from the peripheral regions of the fragment and, as already mentioned, movement seems to be restricted to solid surfaces or to the interior of solid media; if a culture is growing in a liquid drop the cells will only migrate w^hen attached to the coverslip or to the liquid/air film, whereas in a liquid medium containing
G C . 19
290 THE GROWTH OF CELLS
solid surfaces of fibrin or cotton wool, the cells migrate into the interior of the drop along such surfaces (Harrison, 1914; Fischer,
1925).
It will be noticed that although the phenomenon of migration increases the surface area covered by the fragment, no growth is involved in the sense that there has been an increase in the total
Fis. 134. Ceil from the medullary cord of a frog grown in vitro. Note attachment of the cells to spider’s web. x 300. (Ross Harrison, 1914.)
mass of the living cells present. The mechanism of migration is obscure. Harrison (1911, 1914) regards it as an instance of ‘stereotropism’ to solid surfaces, whereas Burrows (1913) suggested that the movement away from the periphery of the implant is essential!} a chemiotropic movement away from a region of abnormal acidit}.
The cells which migrate outwards from the surface of the fragment often show a marked difference in form to that which charac
THE GROWTH OF CELLS
291
teris^s them when in situ in the tissue. The characteristic form of
ixiiorating cells is illustrated in fig. 135, and is not greatly different
Fig, 135. A. Culture of frog’s artery in plasma; 6.C., red blood corpuscle; e? 2 d., eii othelial cell; lx., leucocyte. B. Culture of frog’s cerebrum; nv.c., nerve cell; ngl.c.,
neuroglia cell. (After Drew.)
for different types of tissue. To some extent the shape of the cells in a culture depends on the nature of the medium in which gro'v^i:h
19-2
292 THE GROWTH OF CELLS
is taking place. Uhlenhuth (1915) found that epithelial cells awH grow as a membrane and retain their characteristic form if the gro^rth occurs on the surface of the clot, but if the cells penetrate into the clot itself the cells separate from each other and become spindleshaped. It is generally admitted that when growing in vitro all cells, irrespective of the tissue from which they are derived, tend to
Fig. 136. Stained culture of epithelial cells, two months old, x 1425. (From Fischer, Journ. Exp. Med.) Note that the cells have grown as an epithelium and have not dissociated.
acquire a common spindle-shaped form not unlike normal fibroblasts.
This fact has been interpreted in two ways. Champy (1913 d. and 6)
believed that all tissue cells when grown in vitro lose their peculiarly
differentiated form and all revert to a common embryonic condition;
more recently (1921) he has shown that glandular cells when grown
in vitro do not produce their normal secretory products. On the
other hand, Barta (1923) and others claim that no real loss of differ
293
THE GROWTH OF CELLS
entiation occurs, and that the prevalent spindle shape is the result of abnormal cell environments : certainly in very few cases is there reliable evidence to show that one cell type can change into another as a result of growth in vitro. On the contrary, there are several examples of ^organised’ growth in vitro, when the conditions of growth approximate more closely to the normal. Thus A. H. Drew (1923) found that the presence of fibroblasts in a culture of kidney epithelium resulted in the production of kidney tubules, whereas in the absence of fibroblasts unorganised spindle-shaped cells alone were formed.
The migration of cells in vitro is both interesting and important, but it is not so fundamentally significant as the fact that migration may be followed by true growth and reproduction.
Having migrated from the periphery of the implant, a limited number of the active cells soon begin to show^ signs of mitotic division. Considerable caution is required in defining the nature of these cells since most tissue fragments contain cells of more than one type : by a process of subculture, however, it is possible to be reasonably sure that only one type of cell is present. If w’e regard the active cells of a tissue fragment as a homogeneous population in respect to the period of time which elapses betw^een tw’o successive divisions, we would expect to find that at any given moment there would be approximately the same number of cells undergoing division as at any other moment (see p. 278). Fischer (1925), however, concluded that this is not a true picture of the facts. Using a nine months’ old culture of chicken fibroblasts it was found that there were definite periods during wdiich no mitoses were visible; between such periods there w'ere others in wliich mitoses were relatively frequent. Fischer interprets these observations as an indication that the mitotic activity of one cell can induce a similar activity in another, possibly by means of the protoplasmic bridges which he believes are present between neighbouring cells (see also p. 178). According to Fischer, a single isolated cell will not grow owing to the absence of essential secretions (‘desmones ’) which normally pass from cell to cell; it is claimed that it is the passage of such substances from one cell to another wdiich enables the presence of actively dividing fibroblasts to incite a similar activity in a culture which has hitherto exhibited a much lower rate of growth. The nature of these substances seems problematical, but they may be related to the Hrephones’ described by
294
THE GROWTH OF CELLS
Carrel (1922). Trephones are the essential principles contained in
le-ucoc5i:es or extracts of leucocytes which stimulate groi^th in
fibroblasts and other tissue cells (see also Carrel and Ebeling^
1923 e).
Media for growth
Only a limited amount of growth in vitro will occur if fragments of tissue are isolated in a medium of pure saline (Lewis and Lewis, 1924), and numerous attempts have been made to extend the amount and duration of growth by the addition of nutrient substances to the medium. The presence of plasma is beneficial in that it provides a mechanically suitable medium — it does not, in itself, sustain unlimited growth and may even be toxic if derived from an old animal (Carrel and Ebeling, 1 923 a). A very large number of other substances have been investigated but only one — namely, the extract of young embryos — has proved really satisfactory. Using the aqueous extract of crushed chick embryos Ebeling (1922) succeeded in maintaining the growth of chick fibroblasts more or less indefinitely — ^the same strain having been kept alive in subcultures for at least fifteen years. During this time nearly 2000 generations of cells have occurred, and as far as can be judged there is no diminution in the rate of grovth. Of the efficiency of embryo-extracts there can be no doubt and the rate of grovLh, as judged by the area of new cells formed per unit time per unit of growing tissue, is roughly proportional to the concentration of embryo extract present (Carrel, 1923 6) and inversely proportional to its age. The full significance of this result will be considered later; at the moment it is useful to enquire into the nature of the substance introduced by the extract. We have already seen that for the growth of cell populations there must exist a suitable supply of nitrogenous compounds capable of being built up into new cell structures, and there must also exist a supply of a substance capable of sustaining the respiration of the cells when formed. As far as can be judged by the work of Warburg and Kubowdtz (1927) and Watchorn and Holmes (1927), the latter supply can be provided by the presence of glucose. There remains the possibility that embryo extracts provide a supply of nitrogen in a form not available in ordinary plasma. Baker and Carrel (1926-8) attempted to decide this point by dialysing embryo extracts in such a way as to remove amino acids, and found that the residue had lost its power of sustaining unlimited growth; on the other hand, the
295
THE GROWTH OF CELLS
addition of free amino acids did not raise the efficiency of the residue to its original value as a stimulant of grovi;h. The same authors found that if embryonic tissues are digested by pepsin for a very short period, the resultant medium has very high growth-promoting properties. Prolonged digestion with pepsin or digestion with trjTsin result, and consequently Baker and Carrel
concluded that the efficiency of the embryo extract depends on the presence of substances akin to the proteoses — and not to the smaller amino acid groupings which result from prolonged digestion. Attempts
Fig. 137. Graph showing the effect of embryo extract and of fibrin digests on the rate of growth of cells in vitro.
to repeat these observations by Willmer (1928) appear to suggest that other factors may also be operative. But, as pointed out by Willmer, the evidence brought forward by Baker and Carrel supports the conclusion that amino acids can provide a source of energy to the cells and that proteoses may provide a source of nitrogen for the formation of new cells.
Amino acids and proteoses cannot, however, be the sole constituents of embryo extracts which influence grovi^h. Carrel, Fischer and others have found that the extract loses its efficiency if
296 THE GROWTH OF CELLS
heated above 56° C., which suggests that an enzyme is probably involved. According to Carrel, the active principle will not pass through a Chamberland filter and appears to be adsorbed to protein surfaces. On the other hand, Wright (1926) has obtained a highly active gro^^dh stimulant which can readily be dialysed through parchment membranes — indicating that such substances need not necessarily have a high molecular weight.
Whatever be the nature of the growth-promoting principle it is present in its most potent form in young embryos and is less obvious in extracts from older individuals. Carrel believes that embryonic extract contains two principles, one which stimulates growth and one which inhibits it. We have already seen that the plasma of young animals sustains a higher rate of growth than does that of older animals. If this difference were due solely to the partial loss of a grovdh accelerator, the efficienc}^ of older plasma should be increased by concentration. According to Carrel and Ebeling (1921 6, 1923 a) this is not the case, and we have to infer the existence of a depressant factor, which increases in potency as age increases.
So far the culture of cells in vitro has been largely restricted to tissues of the higher vertebrates; there are comparatively few observations on invertebrate tissues. Goldschmidt (1917) succeeded in growing the follicular cells of the testes of Lepidoptera, but in most cases invertebrate tissues appear to exhibit only organised growth in vitro (Plananians (Murraj^ 1927); Diptera (Frew, 1928)).
Cell dijferentiation and metaphasia
There comes a time, sooner or later, when the resultant cells of a segmenting egg can be divided into a series of differentiated categories. This process of cell differentiation is not, as yet, susceptible to physiological analysis, although some of the underlying factors are now known. During the early development of amphibian eggs, in particular, it is possible to state with certainty that the subsequent fate of undifferentiated cells depends upon their position in respect to localised centres, which are capable of organising a series of specific cell types in such a way as to produce a complete embryo. At present, these ‘ organisers ’ are purely biological concepts and it is impossible to foretell how far their action on undifferentiated cells will eventually be explicable in physico-chemical terms. We may, however, consider certain minor aspects of cell differentiation. In the first place it is desirable to know how far the process is irreversible
THE GROWTH OF CELLS
297
or to what extent a particular type of differentiated cell retains the
potentiality of conversion into another form. As already mentioned,
Ciiampy (1913a, 1914) believes that when a differentiated tissue cell
loses its characteristic place in the body and migrates into an artificial medium, it loses its specific properties and reverts to an undifferentiated embryonic type which, theoretically, should be able
to give rise to a variety of other differentiated types. The bulk of
opinion is, however, against this view (see Lewis and Lewis, 1924),
and most authors believe that although cells grown in vitro are very
similar in form, yet minor characteristics of a specific nature remain,
and that there is no real dedifferentiation to a common embryonic
type. On the other hand, Fischer (1925) claims that leucocytes can
become fibroblasts, and that fibroblasts can give rise to macrophages.
A number of instances are known where the cells of one tissue, when growing in the body, have given rise to another tissue. According to Adami (1908) such instances of metaplasia always obey the rule that epithelial tissues can only be converted into other types of epithelia, and mesoblastic tissues only to other types of mesoblast. It would seem that columnar ciliated epithelial cells can form a squamous epithelium, if subjected to chronic irritation, and the pavement epithelium of the bladder can be converted in a columnar epithelium. Similarly, true bone can be formed in the lungs, or in the walls of arteries (Harvey, 1907). In nearly every case, however, it is exceedingly difficult to make certain that the new tissue has actually arisen from cells which were an integral part of the old tissue, and have not developed from undifferentiated or quiescent cells present in the original tissue in comparatively small numbers. In this connection the work of H. V. Wilson (1907, 1911) is of peculiar interest. Wilson found that if the tissues of the sponge Microciona are cut up into small fragments and squeezed through bolting silk, the resultant pulp of cells is capable of reorganising itself into compact tissues or even into new sponge individuals. In the macerated pulp there are cells of three main types: (a) dermal cells, (b) collar cells, (c) amoebocytes. If a group of dermal cells cohere together without the inclusion of either collar cells or amoebocytes, the subsequent mass will form only dermal cells. Similarly, the collar cells can only give rise to collar cells. The amoebocytes, on the other hand, can give rise to either dermal cells or to collar cells. Difficulties arise in the identification of these
298 THE GROWTH OF CELLS
three types of cells in a regenerating mass, for there is a tendency for each type of cell to acquire a common rounded form devoid of any collar. Wilson was inclined to think, however, that dermal cells and collar cells may in some cases actually dedifferentiate to a common type which is totipotent in the sense that, like amoebocytes, they may subsequently give rise to more than one type of differentiated cell. According to Galtsoff (1925), however, the regenerated sponge is derived from two types of cell; the amoebocytes give
Fio- 138. Restitution mass of Pennaria (6 days old) showing developing hydranths from a group of artificially separated cells: op, perisarc of original mass; ai, pensarc of outgrowth adherent to glass. (After Wilson.)
rise to the mesenchyme and skeleton, whereas the pinacocytes gh e rise to the dermal membranes and flagellated chambers (see Table XLIII). For a recent discussion of the whole problem reference should be made to Wilson and Penney (1930). Similar difficulties arise in the case of the restitution bodies of hydoids (fig. 138) (Wflson, 1911).
It is also 'ivithin the invertebrate kingdom that some of the mos striking cases of metaphasia are found. According to Morgan (1904 ),
THE GROWTH OF CELLS
299
the muscles of the regenerated crab’s claw are derived from the
original ectoderm, a fact which vitiates Adami’s rule. Similarly,
Kroeber (1910) showed that the pharyngeal epithelium of AllolohophoTCL can be regenerated from the endoderm of the alimentary
canal, although in ontogeny it develops from the ectoderm; a complete survey of such 'totipotent’ or ' pleuripotent ’ systems (see
Przibram, 1926) would carry us too far from a consideration of the
cell. As already mentioned, the technical difficulties associated with
the investigation of cell differentiation are considerable and there
are comparatively few instances known where it is safe to conclude
Table XLIII. (From Galtsoff.)
that new growth has not been restricted to previously undifferentiated cells. One of these is provided by the work of G. H. Drew (1911). Drew implanted a small fragment of the ripe ovary of Pecten into the adductor muscle of another individual (see fig. 139); a layer of fibroblasts quickly formed round the fragment which itself was then invaded by phagocytes so that it eventually degenerated. After a lapse of about six days no trace of organised ovarian tissue remained, but its site was marked by a cyst which was surrounded by fibroblasts and contained blood corpuscles and other bodies. Three ^veeks later the innermost fibroblasts gradually changed their shape and formed a cell layer resembling columnar epithelium which later
800 THE GROWTH OF CELLS
became ciliated. Eventually the whole cyst became lined with weUdefined ciliated epithelium; it seems reasonable to suppose that the new epithelium was actually formed from fibroblasts. This case is of peculiar interest for it is hardly conceivable that undifferentiated ciliated cells were originally present in the muscle.
•3«2IS2S!>,
1 ^
....
^ «... — msLfbr.
- fbl.lyr.
deg. 0 V.
-- b.c.
3 WWIS
msl.fbr, msl. nuc.
fbLlyr.
cil. ep.
■ %
- 7 %
’-deg. ov.
-b.c.
msl.fbr.
— msl. nuc.
Fig. 139. Formation of ciliated epithelium {cil, ep.) from a layer of fibroblasts (fbl. lur.) lining a cyst formed round a piece of ovary {deg. ov.) implanted into the adductor muscle of Pecten. 1, Portion of cyst wall after 23 days. 2, Cyst wall after 26 days. 3, Cyst wall after 30 days, 4, Cyst wall after 98 days, b.c., blood corpuscles; msl. fbr., muscle fibres; msl. nuc., muscle nuclei. (After Drew, 1911.)
THE GROWTH OF CELLS
301
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ScHACKELL, L. F. (1911). ‘Phosphorus metabolism during early cleavage of the echinoderm egg.’ Science, 34, 573.
ScHMALHAUSEN, I. and Bordzilowskaja, N. (1930). ‘Das Wachstum niederer Organismen. I. Das individuelle Wachstum der Bakterien und Hefe.’ Zeit.f. wissen. Biol. Abt. D, 121, 726.
Slator, a. (1913). ‘The rate of fermentation by growing yeast cells.’ Biochem. Journ. 7, 197.
Stephenson, M. (1930). Bacterial Metabolism. (London.)
Strange ways, T. S. P. (1922). ‘Observations on the changes seen in living cells during growth and division.’ Proc. Boy. Soc. B, 94, 137.
(1924 a). Technique of Tissue Culture. (Cambridge.)
(1924 b). Growth in Tissue Cultures. (Cambridge.)
Terroine, E. and Wiirmser, R. (1922). ‘L’energie de croissance. I. Le developpement de V Aspergillus nigerl Bull. Soc. Chim. Biol. 4, 519.
Uhlenhuth, E. (1914). ‘Cultivation of the skin epithelium of the adult . frog Ba7ia pipiensl Journ. Exp. Med. 20, 614.
(1915). ‘The form of the epithelial cells in cultures of the frog skin and
its relation to the consistency of the medium.’ Journ. Exp. Med. 22, 76.
(1916). ‘Changes in pigment epithelial cells and iris pigment cells of
Bana pipiens induced by changes in environmental conditions.’ Journ. Exp. Med. 24, 689.
Warburg, 0. (1927). ‘tiber die Kdassifizierung tierischer Gewebe nach ihrem Stoffwechsel.’ Biochem. Zeit. 184, 484.
Warburg, O. and Kubowitz, F. (1927). ‘ Stoffwechsel wachsender Zellen.’ Biochem. Zeit. 189, 242.
Watchorn, E. and Holmes, B. E. (1927). ‘Studies in the metabolism of tissues growing in vitro. Biochem. Journ. 21, 1391.
Willmer, E. N. (1928). ‘Tissue culture from the standpoint of general physiology.’ Biol. Reviews, 3, 271.
Wilson, G. S. (1922). ‘The proportion of viable bacteria in yoimg cultures, with especial reference to the technique employed in counting.’ Journ. Bacter. 7, 405.
306
the growth of cells
r « /iq-76^ .The proportion of viable “Bacilli” in agar cultures
Wilson, G. S. 09j6)- P P reference to the change in size
.1 '£ *>“
Wintoi- H“w(So 7 )!”‘"£ome phenomena of coalescence and regeneration
and Asterias' Journ. Exp- ‘The regeneration of sponges
(Mi™~«o)to» d ai.iy»wiitr
' “ pSpS' i” O' '“"VO™ >““•
T, nf a vroivth stimulating substance in the yolk of
— siaS ;i.'
CHAPTER TWELVE
Cell Variability
However similar they appear to be at first sight, the units of a
biological population are never identically alike: to this rule the cell
is no exception. In size, form and activity the individual members
of a cell population exhibit differences from each other, and these
differences may often play an important part in the history of the
whole system.
The variability within a cell population may be of two types. Firstly, there may be a state of static variability wherein each cell maintains a particular characteristic at a constant level. For example, the eggs of a trout or of a sea urchin are not all of equal size, but any given egg remains of a constant size, since large eggs do not suddenly become small eggs or vice versa. Statistical variation of this type can be defined in quantitative terms if sufficient measurements are available. So far, however, very few observations have been made on individual cell structures and consequently the data of Heiberg (1907) are of some interest. This author measured the diameter of the nucleus in the pancreas and liver cells of young mice and from his data fig. 140 has been constructed. The form of the curve is comparable to that which displays static variation within other types of population and can be expressed algebraically by standard methods (Fisher, 1925). In all such cases wm can assign to each member of the population a particular value for the character concerned which will remain constant as time proceeds. Thus one nucleus has a diameter of 6 p. and another nucleus has a diameter of lOp; as far as we know, these values do not change. On the other hand, other characteristics of cell activity may not remain constant in this way; they may vary from time to time, so that a given cell may be highly active at one moment and relatively inactive at a later moment. Such variability is known as dynamic variability and may play a very important r61e in biological phenomena. There can be little doubt that neglect of this factor has led to considerable confusion in certain types of cytological experiments.
3Qg CELL VARIABILITY
It may be noted at once that neither static nor dynamic variability within a cell population will seriously invalidate the results of any experiments or observations which are made on systems iu which all the members of the population are actively concerned during the whole operation. For example, if we take a million sea urchin eggs en masse and measure their total volume or then rate of respiration, we can express the volume or respiration of a single egg bv dividing the total volume or activity by the number of eggs. V e get, in this way, an average value, which is accurate m so far as an Litlmietic mean is a reliable guide to the activity of the whole popu
lation. The larger the number of cells which are employed, the more
likely are we to reproduce, in successive experiments, the results
obtained by any single observation. So far, cells are similar to any
other biological population which exhibits static variability, and ve
need not worry whether a particular individual cell exhibits variable
activity during an experiment; by using large numbers, the chances
are in favour of one cell compensating for the changes m another.
Variability introduces a very real difficulty, however, when the conditions of an experiment are such that the imits involved are no the same during the whole series of observations. If, for examp 6,^6
CELL VARIABILITY 309
are observing the onset of fatigue in a bundle of muscle fibres, the gradual diminution in contractile response to a stimulus may be due to one of two causes : (i) the response of every fibre may be reduced, (ii) the response of some fibres may disappear altogether, leaving others in a state of relatively normal activity. The same type of problem arises when a muscle or sense organ composed of many cells is exposed to weak stimuli (Hecht and Wolf, 1928 ). Here the increase in quantitative response to stronger stimuli may either be due to an increased response of every cell or to an increase in the number of cells which actually respond. The variability of response within a population of single cells can be illustrated by the observations of Lund and Logan ( 1924 ) on the coalescence of the intracellular vacuoles of Noctiluca as a result of an electrical stimulus. From Table XLI V it will be seen that as the intensity of the applied stimulus
Table XLIV
Current intensity
in milliamperes
Percentage of cells which responded
20-04
100-0
17-42
100-0
14-42
95-2
10-00
88-2
7-12
87-9
4-90
50-0
4-20
5-7
decreases, so the percentage of cells which respond falls. In a multicellular tissue it would be difficult, if not impossible, to distinguish
between a statistical variation of this kind, and a more fundamental
change occurring simultaneously in all the cells present. To some
extent these difficulties can be overcome by making observations on
single cells, and thereby eliminating the static variability of the cell
population. Examples of this type are available from several
sources — ^irritability of individual muscle fibres (Jinnaka and
Azuma, 1922 ; Brown and Sichel, 1930 ), nervous impulses (Adrian
and Brock, 1928 ), exosmosis (Gray, 1921 ). In many cases, however,
it is technically impossible to restrict observations to single cells,
and even where this is possible the difficulty sometimes persists (see
below). The disturbing influence of static variability upon the
observed course of biological processes is so persistent that it is
worthwhile to consider one or two specific instances.
310
CELL VARIABILITY
There seems to be only one case in which it is possible to obtain a
biological population which is essentially homogeneous in respect to
a given character. This fortunate state of affairs is found in rapidly
growing cultures of micro-organisms. If we start with two bacteria
in a culture, one of which is capable of division once every twenty
minutes and the other only once every forty minutes, then after four
hours the total number of bacteria will be 4160, of which 4096 are
derived from the more active member of the two original organisms;
if we now subculture the population there will quickly come a time
when the whole population is restricted to descendants of the faster
growing bacterium, all others will have been eliminated. In practice
the effect of a statistical difference between the growth rates of
different types of bacteria or tissue cells is a useful means of obtaining pure cultures. As long as only one type of bacterium is
present the rate of growth of a rapidly growing culture follows, very
accurately, the simple equation
■where x is the number of bacteria present, and where Aj is a constant
loff 2
whose value is determined by the expression — ^ , where r is the
T
time bet-^veen each successive reproductive act (see p, 279). This example is of interest for, as pointed out elsewhere (see p. 279), there still exists wdthin the population of growing cells a state of dynamic variation. All the bacteria do not divide at exactly the same rate; some bacteria divide after a shorter period of time than others; it is, however, no longer possible to divide the population up into separate permanent categories, since a bacterium which divides rapidly tends to give rise to daughter cells which divide slowly and vice versa. In other words, there is no change in the total variability of the population as time goes on. Throughout the whole period of observation there is only one variable, namely, the number of cells present. We must remember however that, since the generation time r is an average figure which represents the mean about which the whole population fluctuates, the constant k must also represent an average vmlue.
When we are concerned with the reproduction of a mixed population of cells the situation is much more difficult. In this case each type of cell will exhibit dynamic variability about the mean of its own species and not about a mean which is common to all the cells
CELL VARIABILITY sjj
present. The total number of cells formed from each particular species will be where n is the number originally present, k is the constant of reproduction of the species, and t is the time. Since the population is heterogeneous, the number of cells originally present can be divided into categories each possessing a characteristic value
% "b ^2 “b % ...
After a time t each category will have produced a number of daughter
cells — so that the total number in the increased population (A't)
will be
]Vi = ... 72^
It is obvious that the value of Nt cannot be determined theoretically unless we know the relative values of 72^, ng, 723 . . . , or in other words we must know the numbers of the members of each of the original categories together with the value of k characteristic of each. If we were able to stop the course of reproduction at appropriate intervals we would find that a mixed population alters in two respects as time goes on; (i) there is an increase in the total number of cells present, (ii) there is an increase in the percentage of rapidly dividing cells present. The effect of this second change is to alter the average generation time for the whole population. We are therefore dealing with a system containing two variables — one of which represents the total number of dividing cells and the other a change in the average generation time. Quite clearly we must stabilise one of these variables before the effect of the other can be determined. Before attempting to do this it is convenient to consider similar populations in which the number of cells is decreasing instead of increasing. A good example of such a system is provided by the reaction between a population of bacteria and a toxic reagent or a disinfectant. Here again we are dealing simultaneously with two separate processes: (i) the reaction between each bacterium and the disinfectant, which leads to the death of the cells, (ii) a change in the variability of the whole population. Only the most sensitive cells are d}’ing during the early stages of the reaction and only the most resistant cells at the end. When we make a graph which correlates the number of surviving bacteria with time, both these changes are involved and both will influence the nature and form of the curve. As a rule the first variable is known as the fundamental reaction. Miss Chick (1908, 1910) and others found that the curve relating the number of bacteria killed with the time of exposure to a disinfectant
312
CELL VARIABILITY
could be expressed by the equation of a first order reaction and
concluded that the fundamental reaction was of a monomolecular
nature* The extreme improbability of this conclusion has been
pointed out by Brooks (1918). The fundamental condition for a
monomolecular reaction is that the same percentage of existing
molecules undergoes change at any time during the reaction; it is
purely a matter of chance whether a particular molecule undergoes
change early in the reaction or late. If all the cells of a population
were equally sensitive at all times to the action of the disinfectant,
they would all die at precisely the same time. Since the cells do not
die simultaneously, there must be individual differences between the
cells. Miss Chick (1910) assumed that cyclical changes proceed
at the surface of a bacterium whereby its molecules will only react
with the disinfectant when they happen to possess a critical energy
content, and that the distribution of energy among the individual
molecules is of the random type found in inanimate monomolecular
systems. Under such circumstances there is no progressive change
in variability of the whole system — ^because both early or late in the
reaction the same type of distribution curve will express the population of molecules : there is only one variable, viz. the total number
of reacting molecules or cells. In other words the variability of the
bacterial population is of a dynamic nature, in that a cell may be
sensitive at one moment, and resistant at another. An hypothesis
of this type is not very convincing, for we know from other biological
systems that a difference in sensitivity between two individual members of a population is often something which is fixed for the life of
the animals and, as far as we know, a particular characteristic of this
type is not distributed fortuitously to another member of the population. If we assume that a given individual possesses a definite
sensitivity (k) to a toxic reagent, and another individual possesses
a different and smaller sensitivity {kj), then the first individual will
die before the second, and in a large population the order in which
the cells will die will be definitely fixed, and will not be due to chance.
In such a system the distribution curve expressing the population
in terms of sensitivity will change continuously throughout the
process of disinfection for the most sensitive organisms will die
before the others. In other words we have again introduced a second
and complex variable into the equation which defines the rate of the
reaction. As explained above, we cannot proceed further unless one
of these two variables can be determined independently; unless we
CELL VARIABILITY
813
can define the variability of the population of bacteria, we cannot
define the nature of the fundamental reaction which occurs between
any given bacterium and the molecules of the disinfectant. As
pointed out by Brooks, the disinfection/time curves of Chick and
others, with their marked similarity to the exponential or monomolecular type, may be explained in either of two ways, (i) We may
assume a monomolecular reaction between the molecules of disinfectant and the molecules of the bacteria, if we are prepared to
admit a state of dynamic variability in the sensitivity of the latter,
(ii) We can assume that the fundamental reaction between the
bacterium and the disinfectant proceeds at a uniform rate and that
individual cells differ from each other in sensitivity in a particular
way. The most probable type of curve relating the number of bacteria with specific degrees of sensitivity is Pearson’s (1895) skew
curve of limited range,
where and are the numbers of degrees of resistance beyond the mode possessed by the most fragile and most resistant classes of bacteria. If we put k^^ = 0, then the distribution curve becomes
and if is large the curve relating the number of surviving bacteria
mth time will approximate to the exponential type. How far either of these explanations are adequate may be doubted, for in the second case the type of distribution curve is highly abnormal and postulates a maximum number of bacteria with a sensitivity at or very near the limit of variation. The immediate point of interest is, however, focussed on the fact that it is impossible to analyse any single series of data in the production of which more than one variable has played its part. The more we try to escape from these difficulties the more unsatisfactory the position seems to become^. This is, perhaps, illustrated by the process of decay in the activity of spermatozoa (Gray, 1928). The observed facts can either be harmonised with the conception of a first order reaction occurring within a heterogeneous population of a particular type or as a process of autointoxication
^ The difficulties have been considerably reduced by the recent work of
Ponder (1930).
314 CELL VARIABILITY
within a population whose variability in respect to both directions of this reaction gives the same type of curve. Unless we have independent evidence, we can only base our opinions on the intrinsic probability of one or other hypothesis, and not on the goodness of fit of a particular equation. If we attempt to base our conclusions on the voodness of fit of a particular equation we find that we are dealin^v with equations involving several arbitrary constants. There is the constant peculiar to the fundamental reaction, and there are the constants defining the variability curve— viz. the mean, and the departure from the mean on the two sides. By suitable values a reasonable fit can always be obtained, but the fundamental truth remains that it is on the intrinsic probability of these values that the validity of the whole hypothesis will rest.
Since it is intrinsically improbable that all the cells of a population will be identically alike, it is equally probable that no biological change involving an increase or decrease in the number of active cells present will ever yield a reaction curve comparable to that of a chemical system. Unfortunately we may have to extend this statement to "include reactions involving smaller units than cells: if there are units inside the cell which vary among each other and whose properties in this respect are more or less constant during the life of the units, we would be no further forward even if we were able to carry out a series of observations on one single cell. An example of this type is provided by the rate of exosmosis of electrolytes from a single egg cell of the trout (Gray, 1921). As long as the protoplasmic surface of the egg is intact no measurable loss of electrohdes occurs ; when the protoplasm dies the loss of electrolytes obeys the simple diffusion laws— so that the rate of loss of electrolytes is determined by the diffusion gradient between the inside and the outside of the cell and by the area of protoplasm which has become permeable. All regions of the egg surface do not become permeable at the same time, however, so that once again there are two variables : (i) the rate at which the surface becomes permeable — which differs in different regions, (ii) the diffusion gradient between the interior of the cell and the external medium. If the means employed to make the protoplasm permeable acts very quickly over the whole surface of the egg the resultant osmosis/time curve becomes concave to the abscissa very soon after the start — ^but in all other cases the curve clearly reflects the effect of both factors involved (fig. 141 B). When the protoplasm is exposed to a strong toxic reagent, the form of the
CELL VARIABILITY 315
curve obtained is that due to the effect of the diffusion gradient, since the processes of diffusion are slower than those producing protoplasmic permeability; under these conditions all the protoplasmic units are destroyed at a very early stage, and the fundamental reaction is very rapid compared with that of diffusion. When the toxic agent is -weak a considerable time elapses before all the protoplasmic units have been destroyed, and during this period the form of the curve reflects both the variability of the protoplasm and the effect of a falling osmotic gradient bet%veen the inside of the egg and the external solution. Similarly, if the fundamental process of disinfection or death of bacteria w'ere extremely rapid, the so-called percentage death/time curve might be in realitv
Fig. 141 . Curve A shows the rate of exosmosis from a single egg of the trout when exposed to a solution which rapidly destroys the normal impermeability of the protoplasm. Curve B shows the rate of exosmosis from an egg whose impermeability is more slowly destroyed by a less toxic solution.
the mortality curve of the population without reflecting in any obvious way the nature of the fundamental reaction. This was suggested by Loeb and Northrop (1917) for Miss Chick’s data. In most cases, however, the observed curve is probably the result of two variables (as pointed out by Brooks), as is quite clearly the case with the data of exosmosis in solutions of weak toxicity.
At this point it is of interest to divert from living cells to inanimate systems. Within the molecular population of a gas the total kinetic energy is not equally distributed among its members. Some molecules will at any given moment be moving very rapidly — others will be moving much more slowly. These facts are expressed in Maxwell’s distribution curve. If we were able to mark a single molecule and
816
CELL VARIABILITY
observe, from time to time, its kinetic energy, we would find that
this energy is not fixed and immutable, but varies with time over a
range identical with that characteristic of the whole population when
measured at any given moment. Such systems, like Miss Chick’s
conception of bacterial surfaces, are of a dynamic type and play their
part in many types of physical change. So far as is known, however
a h
Fig. 142. Distribution curves of size of particles in colloidal suspensions, a and 6, gold sols ; c, mercury emulsion. (From Svedberg.) Curve a is comparable to fig. 140. Curve 6 is similar to that described by Ponder (1930) for the sensitivity of redblood corpuscles to haemolytic agents. Curve c is comparable to those of Chick and others for the death of bacteria in solutions of disinfectants.
the phenomena of sialic variability are only of chemical significance
within colloidal systems. Within any given suspension the sizes of
the individual particles are not the same, but are distributed on a
variability curve of one form or another (fig. 142). The relative
number of particles of any given size can be estimated in such systems
by a variety of methods (see Svedberg, 1928, pp. 167-188). In many
CELL VARIABILITY
817
cases the size of s particle does not greatly influence the velocity of
chemical reactions in which the particle takes part, but in a few
cases there is good evidence to support the view that such a state
of static variability within colloidal populations has a very real and
profound effects Svedberg (1928) and others have shown that when
a photographic film is exposed to light and subsequently developed,
the individual grains of silver halide are either completely reduced
to silver and dissolved away or they are not dissolved at all. If,
however, potassium bromide is added to the developer there are a
certain number of grains which, after development, are only partially dissolved. According to Svedberg the sensitivity to development depends on the presence of one or more ‘ centres ’ at which the
process of development can occur. These centres are points at which
the sensitivity of the grain surface reaches a critically high value;
the sensitivity being measured by the least amount of energy required to induce the formation of a reduction centre. Ilflien the
film is exposed to a stream of a-particles the intensity of incident
energy is high enough to produce a centre wherever an a-particle
falls on a grain, consequently the process of development follows an
exponential curve, p = taa n _ ^-u\
where P = the percentage of developable grains and k = the number
of a-particles falling on one projective area of the halide grain per
second. When, on the other hand, the film is exposed to ordinary
light the energy of one quantum of light is too small to give a
developable centre. It is necessary for a minimum number of quanta
to be absorbed within a definitely limited area of the grain surface —
and this number varies from one part of the grain to another — consequently the effect of development after varying exposures follows
a sigmoid curve which is partly an expression of the variability of
the grains of the population and partly of the number of grains
present (fig. 143). Systems of this type are admittedly uncommon
in physical systems, but it is by no means uncertain that they may
prove to be the rule rather than the exception within living systems.
Quite clearly the introduction of a state of static variability into
a chemical system profoundly modifies the application of the normal
laws of mass action : instead of the rate of a reaction being pro
^ In this connection it is interesting to note that statistical variations in cell size have recently been held to be responsible for the form of the mortality curve of bacterial populations (Hahn, 1929).
318
CELL VARIABILITY
portional to the mass or concentration of the reacting units, it
becomes proportional to the mass or concentration of those units
which happen to possess a critical degree of statical sensitivity.
We may now consider how far it is possible to escape from some of these difficulties by means of a suggestion made by Ponder (1926).i This author was concerned with a population of red blood-corpuscles wffiose surface possessed varying degrees of resistance to the action of haemolytic agents. The velocity of haemolysis is proportional to the number of molecules of free haemolytic agent (c) and to the number of cells present (%) at any given time :
Average number of rays striking a grain
Fig. 143. The effect of radiant energy on a photographic emulsion.
(From Svedberg.)
If it be assumed that the variation in sensitivity be expressible by a frequency curve of the ty^pe n = where n is the number of
cells broken down by an amount of haemolytic agent cc, then as haemolysis proceeds the number of cells haemolysed will be, as ivitli other such systems,
% = 1 doc.
Jo
Expressed as a graph this will result in a sigmoid curve ABC (fig. 144). If we substitute this value for % in equation (ix) we are left with an expression the integration of which is exceedingly unwieldy.
^ Ponder’s recent work (1930) renders this treatment obsolete except as a first approximation.
CELL VARIABILITY 319
Ponder cut tlie Gordian knot by suggesting that if this curve be replaced by the straight line the errors introduced are not
greater than others which necessarily creep into experimental procedure. When simplified in this way it is possible to incorporate
h C
Fig. 144. The curve A\Ci is the distribution curve of the red blood-corpuscles in respect to their degree of sensitivity {x) to haemolysis. ABC is the integrated curve.
Fig. 145 . Frequency polygon illustrating the variation in susceptibility of red bloodcorpuscles to C5rtolysis by saponin. The susceptibility is measured in terms of milligrams of saponin required to produce cytolysis. (Ponder, 1927.)
into the analysis of experimental results a term which will be a quantitative expression of the change in variability of the system, and which at the same time leads to a differential equation which can be integrated to express the progress of the experiment. This pro
320
CELL tARIABILITY
cedure is satisfactory as long as we have some external evidence
with which to check the arbitrary values assigned to the constants
in the initial variability curve.
If such evidence is wanting, Ponder’s approximation is liable to be dangerous. An example has recently been quoted elsewhere (Gray, 1929).
An ageing culture of bacteria exhibits a rapidly declining growth rate (see p, 285): if the bacteria are subcultured into a satisfactorv medium the full growth rate is eventually resumed, but is preceded by a period of low^er growth rate w^hich gradually rises to the full value. Ledingham and Penfold (1914) obtained the following figures.
Table XLV
Time in minutes
No. of bacteria present
0
217*5
45
287
60
345
SO
470
100
718
120
1362
150
2535
180
7610
To account for these figures we might make the following hypothesis. At
the beginning of the experiment let us imagine that aU the bacteria are
alive but unable to reproduce, but as time proceeds they gradually recover
from the effects of their past history. All the bacteria will not recover at
the same rate, some will recover after a short time and some after a
longer time; at the end of three hours the culture is known to be growing
at a steady rate. If we express the variability of the bacteria by Ponder’s
approximation, and if the number of actively reproducing bacteria be x,
and the number of inactive bacteria be then
+ + »
loge2
^vhere ^ is— — .
generation time m minutes
Giving k the arbitrary value of 0*0285, we get a series of figures which conform very closely to the observed figures. If, however, k = 0*0285, then the generation time for the active bacteria should be 24*3 minutes; experimentally, however, k is found to be 0*0385 (= a generation time of 18 minutes), and if we put k = 0*0385 in equation (x) we get figures very far removed from the experimental observations.
This example indicates the danger of assigning arbitrary values to constants in any biological equation.
CELL VARIABILITY
321
Another useful contribution to the theory of static variation
within cell populations was made by Yule (1910). If a population of
cells is exposed to adverse circumstances (leading to a decrease in
their number) for a given number of time units, 1, 2, 3, these
periods can be regarded as equivalent to a successive series of incidents each one of which may lead to an elimination of the life of
the cell. For any given cell any one of these exposures may be
‘effective’ or ‘non-effective’ in that it may damage the cell or leave
it uninjured. Let it be supposed that r effective exposures cause the
death of the cell, and let the chance of any one exposure being
effective on any one individual be p. Such a condition of cumulative
death processes is not an unreasonable conception. Under such circumstances the proportion of individual cells which will have received 1, 2, 3, ... effective exposures after the nth exposure will be
given by the terms of the binomial expansion
3”, n.3”-ip, 2 (xi).
If r exposures are fatal then the total number of survivors at the end of the nth exposure will be given by the sum of the first r terms of series (xi) and the total proportion surviving at the end of (?i —1) exposures will be given by the first r terms of the series (xii)
q^-\ — ^qn-^^jyz ...(xiij.
The proportion of the original population which die between the onset of the (n — l)th and nth exposure will be the difference between the first r terms of the two above series, and this will reduce to
P"’ fP% ip" 9%
which is the binomial expansion of p‘^ (1 — q^^. The significance of this result is seen by substituting different values for r. If r = 1, one single effective exposure results in death and the series becomes strictly logarithmic, as is apparently the case mth bacteria exposed
to disinfectants, «
p.pq.pq^,,,.
If however r is greater than 1, the number of deaths per exposure rises gradually to a maximum and then declines as is usually the case. Yule has extended this argument to cover those cases in which death is not necessarily a discontinuous process, but for the present purposes it is sufficient to point out that the wide range of curves
322
CELL VARIABILITY
shown in fig. 142 can be deduced from Yuk’s treatment. Unless, therefore, we have reason to suspect that one is more likely to be true than the other, it is cpuite impossible to foretell what will be the precise effeet of sktical variation on the process of an intracellular reaction, such as muscle fatigue, or decay in rate of respiration.
As alreadv pointed out problems of statical variation are not restricted to phenomena in which the number of units in a populaundergoing irreversible decay, but are also found in functional systems of a different type. Quite recently Hecht and Wolf (1928) have shown that the resolving power of the bee s eye at different intensities of light can only be interpreted on the assumption that the threshold stimuli for the various ommatidia are not the same but are distributed on a fairly symmetrical distribution
curve.
It will readily be admitted that all these attempts to reduce the problem of statical variation to manageable proportions are unsatisfactory. The dominant fact remains that if the members of a cell population carrying out any reaction are themselves liable to become ineffective, there is introduced a factor which cannot adequately be expressed in quantitative terms. There are always two variables: (i) the intensity of the reaction being measured, (ii) the number of units concerned in the reaction at different times; as long as these two variables are unknoAvn in quantity any observed result can only be the result of their combined effects. The only safe and reliable procedure is to design experiments in which static variability plays no part; failing that, some method must be found for measuring the degree of physiological variation by other means, and then applying this value to a particular series of obseivations. The whole subject is one of great difficulty, but at the same time is of very far-reaching importance. It is significant that problems of a similar nature arise in colloidal suspensions; it may well be that further study of such inanimate systems will be of the greatest value to cell physiology.
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Adrian, E. D. and Brock, D. W. (1928). ‘The discharge of impulses iii motor nerve fibres. I. Impulses in single fibres of the phremc nerve.
Journ. Physiol. 66, 81. . . « • i, a
Brooks, S. C. (1918). ‘iV theory of the mechanism of disinfection, haemolysis, and similar processes.’ Journ. Gen. Physiol. 1,61.
CELL VARIABILITY 82.^
Bbown, D. E. S. and Sichel, F. J. M. (1930). ‘The myogram of the isolated skeletal muscle cell.’ Science^ 72, 17,
Chick, H. (1908). ‘An investigation of the laws of disinfection.’ Joiirn, Hygiene, S, 92,
(1910). ‘ The process of disinfection by chemical agencies and hot water.’
Journ. Hygiene, 10, 2S7,
FisHEE, R. A. (1925). Statistical Methods for Research Workers. (Edinburgh.)
Gbay, J. (1921). ‘Exosmosis from animal cells.’ Journ, Physiol. 55, o22,
- (1928). ‘The senescence of spermatozoa.’ Brit, Journ. Exp, Biol. 5, 34d,
(1929). ‘The kinetics of growth.’ Brit, Journ. Exp. Biol. 218.
Hecht, S. and Wolf, E. (1928). ‘The visual acuity of the honey bee.’ Journ. Gen. Physiol, 12, 727,
Heiberg, K. A. (1907). ‘Uber eine erhohte Grosse der Zellen und deren Teile bei dem ausgewachsenen Organismus vergliehen mit dem noch nieht ausgewachsenen.’ Anat. Anz. 31, 306.
JiNNAKA, S. and Azuma, R. (1922). ‘Electric current as a stimulus with respect to its duration and strength.’ Proc. Roy. Soc. B, 94, 49.
Ledingham, j. C. G. and Penfold, W. J. (1914). ‘Mathematical analysis of the lag-phase in bacterial growth.’ Journ. Hygiene, 14, 242.
Loeb, j. and Northrop, J . H. (1917). ‘On the influence of food and temperature upon the duration of life.’ Journ. Biol. Chem. 32, 103.
Lund, E. J. and Lo g an, G. A. (1924). ‘The relation of the stability of protoplasmic films in Noctiluca to the duration and intensity of an applied electric potential.’ Journ, Gen. Physiol. 7, 461.
Pearson, K. (1895). ‘Skew variation in homogeneous material.’ Phil. Trans. Roy. Soc. A, 186, 393,
Ponder, E. (1926). ‘The equations applicable to simple haemohtic reactions.’ Proc. Roy. Soc. B, 100, 199.
— — • (1930) ‘ The Form of the Frequency Distribution of Red Cell Resistances to Saponin.’ Proc. Roy. Soc. B, 106, 543.
Rahn, O. (1929). ‘The size of bacteria as the cause of the logarithmic order of death.’ Journ. Gen. Physiol. 13, 179.
Richards, O. W. (1928 a). ‘Potentially unlimited multiplication of yeast with constant environment and the limiting of gro^vth by changing environment.’ Journ. Gen. Physiol. 11, 525.
(1928 6). ‘Changes in sizes of yeast cells during multiplication.' Bot.
Gazette, 86, 93.
Svedberg, T. (1928). Colloid Chemistry. 2nd ed. (New York.)
Yule, G. U. (1910). ‘ On the distribution of deaths with age when the causes of death act cumulatively, and similar frequency distributions.’ Journ. Stat. Soc. 73, 26.
CHAPTER THIRTEEN
The EquiUhmim hetiveen a Living Cell
and Water
It is common knowledge that four-fifths of the total weight of
living cells consists of water and that in higher vertebrate animals
any significant variation in water content may involve far-reaching
consequences. Amphibia, however, exhibit a much higher resistance to desiccation, although it is not clear how far the water
w'hich can be lost is restricted to the blood and the skin or how far
it can be drawn from the cells of the more fundamental tissues;
newts can recover from a loss of water equal to half their normal
body weight (Gray, 1928 ). It is, however, within the invertebrate
kingdom that organisms exhibit maximum toleration to desiccation; .
rotifers and nematodes are the outstanding examples (see Davenport, 1897 , Vol. 1 ). The behaviour of the rotifer Philodina roseata
suggests, however, that the actual loss of water from the living tissues
is more apparent than real. When the rotifer is dried in sand on a
glass slide it becomes spherical and secretes round itself a gelatinous
envelope, wuthin which it remains encysted until water is again
available. This capsule is relatively impermeable to water, so that
the amount of water vdthin the cells always remains relatively high
(Davis, 1873 ).
Only in a few cases has any attempt been made to correlate the water content of specific types of cell with functional activity. All types of protoplasmic contraction eventually fail if water is removed from the cells beyond a critical level, whilst nuclear and cell division are also sensitive to lack of water (see Chapters VIII and IX).
In the simplest forms of life, e.g. bacteria, the water content of the cells exhibits considerable variation in response to the medium in which the cells are immersed, but in higher animals the normal water content is the result of a more complicated equilibrium. According to Mayer and Schaeffer ( 1913 , 1914 ), the ability of a cell to hold water depends on the ratio of cholesterol to fatty acids inside the cell, but
equilibrium between a living cell & WATER 325
for an elaboration of this view the original papers must be consulted. For the present purposes, the equilibrium between a living cell and water is chiefly of importance in that it is closely associated with the equilibrium between the cell and the solutes present inside and outside the cell respectively. By observing the passage of water into or out of a cell in different types of environment it is possible to gain some insight into the factors which control this all-important aspect of the cell’s activity.
Permeability to water
If living tissues are exposed to a solution whose osmotic pressure is higher than that of their normal environment the cells lose water. If the tissues are replaced in their normal environment they reabsorb the water which had previously been lost. Such facts were first established by Pfeffer (1877) in plant cells in which plasmolysis involves the passage of water from the central vacuole through the protoplasm of the cell. Both qualitatively and quantitatively plant cells behave as though their protoplasmic elements were freely permeable to water, but highly impermeable to the substances in solution. If the cell were not only permeable to water but also to the substances in the outside environment, no water would pass from the cell, since it is the differential pressure of the dissolved substances outside the protoplasm which provides the energy required to move the water. It thus appears that under certain specific conditions the protoplasm of a vacuolated plant cell may be comparable to a membrane such as copper ferrocyanide : it is, in fact, a semipermeable membrane being permeable to water but not to the sugars and other dissolved substances which are capable of exerting an osmotic pressure. The validity of this conception is supported by the following facts. If a membrane of copper ferrocyanide is interposed between a solution of cane sugar and a system of water, the force (P) under which the water tends to pass into the cane sugar is directly proportional to the molecular concentration of the sugar (C) and to the absolute temperature (T),
P = kCT,
as long as the membrane is completely impermeable to the sugar. The osmotic pressure of all molecules is the same, so that all solutions containing one gram molecule of solvent exert the same osmotic pressure. Overton (1899) found that filaments of Spirogyra are just plasmolysed by a 6*0 per cent, solution of cane sugar and
326
THE EQUILIBRIUM BETWEEN
remain unplasmolvsed by all weaker solutions. The molecular weight of cane sugar is 342 so that a 6 per cent, solution is equivalent to 0-175M. As long as a living cell of Spirogyra is completely impermeable to the molecules of the solute, it will be plasmolysed when the effective concentration of any substance reaches the value of 0-175M. In the following table are found the results obtained by Overton, who expressed his figures in terms of grams per 100 c.c. and not as gram molecules per litre.
Table XLVI
Substance
Molecular
weight
Critical coi for plas
Observed
(%)
icentration
jmolysis
Calculated
(%)
i"
i Cane sugar
342
60
—
j Mannite
182
3-5
3-19
j Dextrose
180
3-3
3*15
Arabinose
150
2-7
2-68
Er\i:hrite
122
2-3
2-14
Asparagin
132
2-5
2*32
T -QO
Glycocoll
75
1-3
As pointed out by Hober (1922) the molecular weight of a substance can, in fact, be determined by measuring the concentration necessary for plasmolysis. Thus before the work of de Vries (1888) the moiecular weight of raffinose was uncertain: it might have one of three values 396, 594 or 1188. But the cells of Tradescantia are plasmolysed by a 3-42 per cent, solution of cane sugar and by 5-96 per cent, raffinose. Since the molecular weight of cane sugar is 342, that of raffinose must be approximately 596.
In Pfeffer’s equation P = IcCT, the molecular concentration C is clearly the reciprocal of the volume occupied by one miit mass of the solute, so that this volume ( V) is related to the osmotic pressure by the expression PV = kT, which is of the same form as that which applies to the pressure and volume of a gas. In 1877 van’t Hoff showed that these two systems are not only similar but are identical, so that k is replaceable by the gas constant P:
PF= nRT where n = number of gram molecules present in unit volume.
In the case of a plant cell the volume occupied by unit mass of the solute is obviously proportional to the volume of the vacuole, so that
327
A LIVING CELL AND WATER
it is possible to test the relationship PF = by measuring the volume of the vacuole when the cell is in equilibrium with plasmolysing solutions of different concentrations. This was done by Hofler (1917) who used cells of filamentous algae.
Table XLVII
Concentration of
Relative volume of
Isotonic
plasmolysing fluid
the vacuole
concentration
P
V
PV
0-30
0*585
0*175
0-35
0*494
0*173
0-45
0*38-2
0*172
0*60
0*287
0*172
1
It is seen that van’t Hoff’s law holds with remarkable accuracy, and
that if the cells are to retain their normal volume ( F= 1), the concentration of the external solution must be approximately 0-17531.
The osmotic pressure and plasmolysing efficiency of all molecules is the same, but these properties also apply to electrolytic ions. Hence, if a molecule undergoes electrolytic dissociation its plasmolysing efficiency is increased, since each molecule will give rise to two or more ions. If 100 molecules of an electrolyte are dissolved in water and some of these {a) are dissociated to form ions according to the equation (xiii),
== nX + (xiii),
then the total number of ions present will be a (n -f n^) and the number of undissociated molecules left will be 100 — a. Hence the total number of molecules and ions will be
a (n + %) + 100 — a.
Each gram molecule of substance will therefore be equivalent, as far
j ^ ^ (^^ -T- m) ^ 100 — a
as osmotic pressure is concerned, to — gram
molecules of a non-electrolyte. This fraction is usually known as van’t Hoff’s factor i, and it can be calculated by a variety of physical methods. If living cells are completely impermeable to a particular type of molecule and to one or more of the ions to which it gives rise, then it should be possible to establish the value of i by obser^diig the concentration of electrolyte required to produce plasmolysis. Observations of this type were made by Fitting (1917) who used the cells of Tradescantia,
328 THE EQUILIBRIUM BETWEEN
A consideration of Tables XL VI and XLVIII shows that the plasmolytic efficiency of both non-electrolytes and electrolytes is slightly below the figures which can be calculated theoretically, and this suggests that the surface of the living plant cell is not absolutely impermeable to the substances exerting the osmotic pressure. At the same time the discrepancy is small, and hardly influences the conclusion that to a remarkable degree the protoplasmic elements in a mature plant cell behave as though they possessed true semipermeable properties, in that they are permeable to water but not to molecules of sugars or neutral salts . It is, however, very important to note that the relevant data apply only to experiments of short duration. Probably the protoplasm of plant cells is always permitting the passage of dissolved molecules and ions, but the rate at which this can occur is
Table XLVIII
Salt
van 't Hoff’s factor as calculated from
Plasmolysis
Freezing point
Electrical
conductivity
KNO 3
1-64
1*78
1-83
KCl
1-68
1-84
1-86
K 0 SO 4
2-2
2-36
2-38
NaNOs
1-65
1*8
1-83
LiCr
1*73
1-85
1-81
MgSO,
101
1-1
1-33
MgCl.
2-39
2-64
2-45
CaCl
2-37
2-59
2-45
very much less than the rate at which water can pass in or out of the
cell — so that it is only in experiments involving considerable periods
of time that any discrepancy will be observed which is due to a
penetration of the dissolved molecules or ions — assuming always
that the protoplasm does not undergo in any experiment a process of
irreversible injury. Injury or death rapidly entails a high degree of
permeability to sugars and salts (Stiles, 1924).
In being permeable to water the plant cell is not unique; similar properties are displayed by most animal cells. In the latter case, however, there are three important differences from plant cells, (i) There is no large central vacuole, so that changes in volume which result from the passage of w^ater into or out of the cell represent changes in the volume of the protoplast itself, (ii) Most animal cells become instable if the qualitative composition of the surrounding
829
A LIVING CELL AND WATER
medium differs materially from the normal environment of the cells. These two facts must be borne in mind during any discussion of the osmotic equilibria of animal cells, (iii) Most plant cells are surrounded by a tough cellulose membrane, so that if the cell be immersed in a hypotonic solution water will cease to enter the cell when the osmotic effect of the cell contents is balanced by the hydrostatic pressure of the cellulose wall. In animal cells the hyaline membranes of the cell are often very delicate structures possessing a considerable degree of plasticity, so that their elastic resistance to osmotic forces is probably not very great.
As will soon be evident, the equilibria between animal cells and their aqueous environments are more complex and less well defined than is the case of plants. One of the earliest types of animal cells to be investigated was the red blood-corpuscle of vertebrates. Hamburger (1902) carried out an extensive series of experiments and found that when the osmotic pressure of the medium exceeded a critical value the cells not only changed in appearance but also allowed the haemoglobin to diffuse out of the cell. In this condition, of course, the cell is no longer normal, so that although Hamburger's observations were of interest they were not of great value as a measure of the properties of normal cells. That red blood-corpuscles lose water when exposed to hypertonic solutions is illustrated by Hedin’s (1897) experiments in which the volume of the corpuscles was measured in a haemocrit after exposure to a constant centrifugal force for a fixed period of time.
Table XLIX
Concentration of KNO 3
in gram molecules
per litre
Volume in c.c. of red blood-corpuscles per i 00 c.c. of (Suspension
0-08
48:6 i
0*10
46-3
0-12
43-2
0-14
41-2
0*16
39-9 i
0-18
39-4 1
0-24
88 -T ;
0-30
37-2 I
A consideration of these figures (Table XLIX) shows at once that
the amount of water lost by exposure to hypertonic solutions is very
much less than that' calculated by the expression PV= kT, Either
330 THE EQUILIBRIUM BETWEEN
the cells axe permeable to potassium nitrate or the water content of the cells is only controlled by osmotic factors to a comparatively small degree. A similar conclusion is reached from a study of the osmotic properties of cells in intact tissues (Siebeck, 1912). Excised kidneys of the frog were weighed before and after exposure to Ringer solutions of varying strength and care was taken that in each case a true equilibrium was attained before the observations were recorded. If it be assumed that in each 100 gr. of excised kidney the dry contents together with the water held by forces other than osmotic is a grams, and if x is the observed weight when in equilibrium with any given solution, then ^ is the amount of water held in the cell by osmotic forces
{x ~ a) = k, so that p {x — a) = p^ {x^^ — a).
Table L
Concentration of
Ringer solution
P
Relative weight of excised kidney
X
Dry weight + non-osmotic fraction
a
2-0
79
58
1-0
100
—
! 0*75
111
68
i 0*5
127
73
0*25
174
75
From Table L it is evident that after allowing for the dry weight
of the kidney (= approximately 15 gr.) there must be at least 40 gr.
of water in every 100 gr. of normal tissue which is not held in the
cell by simple osmotic forces. This conclusion was originally reached
by Overton (1902). Calculations of this type obviously assume that
no appreciable mechanical pressure is exerted on the protoplasm
by the cell membranes. For example, if a cell is surrounded by a
tough and rigid envelope and the cell is then placed in a hypotonic
medium, no water can enter the cell since the volume of the latter
cannot increase : the osmotic pressure between the outside solution
and the protoplasm will be balanced by the mechanical pressure of
the envelope. Similarly, if such a cell is placed in a hypertonic solution, loss of water wall be inhibited unless the envelope is elastic and
can accommodate itself to the reduced volume without any significant changes in energy, or unless the protoplasm can separate itself
from the envelope as is the case of plant cells.
881
A LIVING CELL AND WATER
When animal cells are immersed in solutions of different osmotic pressure there is general agreement that the resultant changes in volume differ perceptibly from those which would be expected from a system bounded by a true semipermeable membrane, \\dthin which all the water was osmotically active. This is clearly the case with kidney cells and with sea urchin eggs (Liicke and McCutcheon, 1927). It does not follow, however, that Overton’s explanation is correct. As shown by Hamburger, animal cells readily lose their normal osmotic properties in abnormal environments, and any such change will obviously affect the power of the cell to imbibe or lose water. The recent observations of A. V. Hill (1930) indicate that this factor is, in fact, responsible for the apparent failure to account for the amount of water in muscle cells on the assumption that it is all ‘osmotically active ’. Instead of observing the changes in %veight of a single muscle in a hypertonic or hypotonic medium. Hill compared the changes in weight of two similar muscles in hy-pertonic and hypotonic solutions respectively; in this way it is possible to compensate, to some extent, for irreversible changes in permeability to solutes, since they will be more or less the same in both lots of tissue. Since the method is of general application it may be considered in some detail. Two gastrocnemii muscles of the frog are taken, having initial weights of xmity and which are in equilibrium w'ith Ringer solution of concentration R. Let a be the solid plus ‘bound’ water fraction, and x be the osmotically active fraction, then (1 — a — .r) is the osmotically inactive water fraction. One muscle is then brought into equilibrium with hypertonic Ringer solution (1 + r) R, and the other with a hypotonic solution (1 — r) R. If the permeability of the muscle cells change in any way x will become x (1 -r 3) where S may be positive or negative. If (1 — « — a:) changes it may become (1 — a — ») (1 -H S'). If A is the final weight of the muscle in the hypotonic solution and B is that of the musele in hypertonic solution, then
^ = a -K1 - a-£c)(l -1- S') +
B = a + {1 — n — ®) (1 -h S') -| — j •
A-B =
a; (1 -f- S) 2r
1 — {A — B)
and the final osmotically active fraction ^ (l-f 8) == ^ •
332
THE EQUILIBRIUM BETWEEN
When analysed in this way, the amount of water in a muscle cell which is not osmotically active is found to be extremely small, and it looks as though Overton’s results were due to irreversible changes caused in the muscle during the experiments or to the failure to reach a true position of equilibrium. It is of interest to note that Hill’s data are derived from experiments in which the cells remained alive during the whole series of observations.
We have already seen that a plant cell- comes into equilibrium with its surrounding medium when the osmotic force exerted by the cell sap against the external solution is balanced by the hydrostatic pressure of the cellulose wall. In animal cells there is no cellulose wall, and it seems doubtful whether the surface hyaline membranes could exert an elastic force capable of opposing a significant difference in osmotic pressure between the inside and the outside of the cell. It is therefore surprising to find that the cells of animals living in a fresh water environment do not burst or swell continuously. Either the effective difference between the osmotic pressure inside and outside is very slight, or the cell must have some means of excreting water from its interior. Many years ago Hartog (1889) suggested that the contractile vacuoles of Protozoa represented such a mechanism, and Day (1927) has recently reported an increase in the rate of excretion of water by Amoeba on transfer to pure distilled water. It is known that salts affect the frequency of contraction of these vacuoles and Gruber (1889) and others reported the absence of vacuoles in marine types. The more recent observations of Adolph (1926) make it doubtful, however, whether the total amount of water excreted by an Amoeba is strictly a function of the osmotic force exerted between the external medium and the interior of the cell, since the rate of excretion of water appears to be independent of body surface or volume. The absolute rate of excretion by the vacuole of Amoeba appears to be one cubic millimetre of water per square millimetre of body surface every 11-42 minutes, and from 4 to 30 hours are required for the excretion of a volume of water equal to that of the volume of the body.
Before considering the water equilibrium of the cell in greater detail it is useful to remember that the water content of a cell might conceivably be affected by circumstances other than the number of molecules or ions in the external medium. We have seen that the water content will change if there is a difference between the osmotic pressure inside and outside the cell which is not compensated by
338
A LIVING CELL AND WATER
mechanical or other forces. As long as the internal osmotic pressure is niaintained by non-electrolytic molecules or by the ions of strong electrolytes, the interior of the cell may legitimately be compared to a sugar solution enclosed within a membrane of copper ferrocvanide. If, however, the osmotic pressure inside the living cell is maintained wholly or to a significant degree by the ions of a weak electrolyte it will be sensitive to any treatment which alters the degree of ionisation of such systems. The importance of this point can be appreciated from the following facts. Powdered gelatin when washed in water absorbs a certain amount of water; if we wash this damp gelatin with sodium chloride which is faintly alkaline no marked change will occur, but if we now rinse the powder with distilled water the particles rapidly absorb a large amount of water which will be liberated again by the addition of sodium chloride to the medium. The nature of these phenomena are now fairly well defined. The amount of water which is taken up by the gelatin is determined by the degree to which the gelatin is ionised in the form of sodium ions and gelatinate ions ; when sodium chloride is added the number of free gelatinate ions is decreased and consequently the amount of water held by the particles is reduced. Proctor and Wilson (1916) have shown that the addition of neutral salts to a gelatin system reduces the amount of water which is absorbed in a way which is qualitatively and quantitatively in harmony with a system conforming to a Donnan equilibrium (see p. 899). Fundamentally the processes of swelling of gelatin and the uptake of water by a system surrounded by a copper ferrocyanide membrane are the same; the only difference is that in the former case the gelatin is impermeable to gelatinate ions and permeable to all the others, whereas in the latter case the impermeability is extended to much smaller molecules and ions.
It is clear, therefore, that when we maintain that the surface of a living cell is comparable to a copper ferrocyanide membrane we must base our views on stronger evidence than the plasmolysing action of neutral salts. On the other hand it is equally unsatisfactory to maintain, for similar reasons, that the cell is essentially equivalent to a particle of gelatin (Lapicque, 1924). There are a few significant facts which enable us to differentiate between these two possibilities. As shown by Proctor and Wilson the water content of a fragment of gelatin depends on two factors: {a) the amount of ionised gelatin present, {h) the nature of the salts in the surrounding medium. If
834 THE EQUILIBRIUM BETWEEN
a fragment of swollen sodium gelatinate is exposed to a weakly acid solution the fragment rapidly loses water owing to a reduction in the amount of ionised gelatin. If, however, a living cell is exposed to an acid medium, and care is taken to ensure that the acid penetrates into the cell, no detectible change in water content can usually be observed as long as the cell is alive. This fact alone indicates quite clearly that the water content of normal cells is not controlled by the same factors as control the swelling of gelatin: there must be some mechanism other than the presence of intracellular proteins
pH
Fig. 146. Curves showing the relation between the volume of an Amoeba and the hydrogen-ion concentration of the medium. The ordinates represent the percentage loss or gain in volume. (From Chalkley.)
which limits the entrance and exit of water. The inability of
acid to alter the water content of normal cells has been observed
by Beutner (1912, 1913), Liicke and McCuteheon (1926, 1927) and
others. Again, non-electrolytes influence the swelling of gelatin to
a negligible extent, and yet they readily plasmolyse living cells. It
should be mentioned, perhaps, that Chalkley (1929) has recently
reported changes in the water content of living Amoebae in response
to changes in the hydrogen ion concentration of their surrounding
media (fig. 146).
A LIVING CELL AND WATER
335
Post-mortem swelling
Tlie osmotic properties of the cell surface undergo profound and rapid alteration when the cell dies. When death occurs the factors controlling the water content of the cell change and become precisely similar to those of a gelatin system. This fact is often overlooked and merits perhaps a few illustrative examples.
Beutner (1912, 1913) showed that as long as a muscle retains its power of responding to stimuli its water content varied solely with the osmotic pressure of the surrounding medium, although the latter might be abnormally acid. After irritability is lost and the individual fibres begin to die, the water content of the cells increases owing to the acidity of the medium and, as with gelatin, the amount of increase depends on the concentration of neutral salts present. It is a simple matter to state that a cell begins to exhibit imbibitional swelling as soon as it begins to undergo the irreversible processes leading to death: it is more difficult to decide just when these changes begin. In a tissue, or in a population of cells, they do not begin in all the cells at the same time (see Chapter XII), so that we cannot say definitely whether imbibitional swelling is restricted to dead and dying units or whether it is equally distributed throughout all the cells. These difficulties can, however, be overcome to a large extent by using single cells. For this purpose the unfertilised eggs of the trout Salmo fario provide very useful material. As long as the cells are alive they are yellow and translucent ; wffien they are dead they are white and opaque. Structurally, each egg consists of a thin protoplasmic film enclosing a clear solution of globulin dissolved in neutral salts ; the whole system is enclosed within a tough translucent egg-shell or membrane. The salts which are present in the yolk are largely sodium and calcium chlorides and are pi'esent in a concentration equivalent to a depression of the freezing point ~ 0-45° C. As long as the cell is healthy no appreciable quantity of electrolytes diffuses out into the surrounding water, and this state is maintained for many days or even weeks; the moment the cell becomes unhealthy the exit of electrolytes can be detected by a rise in the electrical conductivity of the surrounding medium (Gray, 1921). This test is of extreme delicacy and can be demonstrated with considerable ease. As soon as sufficient electrolytes 'have left the cell, the globulin in the yolk is precipitated and it is for this reason that the cells become opaque; at no time, however, does the egg
336 THE EQUILIBRIUM BETWEEN
membrane (the shell) become permeable to colloids. It can readily be shown that the water content of the dead egg follows the same laws as an equal quantity of globulin enclosed within a parchment membrane, and behaves as a system which strictly obeys the Donnan equilibrium. As long as the cell is alive, however, the water
Imbibitional Osmotic Imbibiiional
swelling
swelling
sw^ling
H-aHvB-K
dead
CI.EAR
E, D,
Cl B C
D
E
B .OPAQUE,']; ■ ;■ cUe'a R • [
- i
- i i
- : 'w//m//vA
Imbibition^ swelling
Fig. 147. Diagram illustrating the effect of hydrogen and hydroxyl ions on the uptake of water by (A) living and (B) dead cells. Starting with a living egg of Salmofario the amount of water remains unaffected by the hydrogen ions in the medium until the protoplasmic membrane is destroyed, whereupon the intracellular electrolytes diffuse outwards and the cell becomes opaque ; as the acid or alkali diffuses inwards in sufficient concentration to dissolve the globulin the egg becomes transparent and swells : finally when the acid or alkali is present in excess the egg again loses water and becomes opaque (salt action of the excess alkali or acid).
content can only be changed by altering the number of osmoticallyactive ions outside the egg — and during this process the water content is independent of the hydrogen ion concentration of the medium.
The change from osmotic to imbibitional swelling, which attends the onset of surface injury, is of very general application. It can be seen in the curves given by Miss Jordan Lloyd (1916) describing the
837
A LIVING CELL AND WATER
effect of acids and bases on the water content of frogs’ muscles, although this author does not refer to the fact, and concluded, on the other hand, that ‘the osmotic phenomena of muscle can be fully explained without assuming the presence of a semipermeable membrane round the muscle fibres
If a muscle is exposed to dilute alkalies it first swells, then loses water, and finally swells again; corresponding to these changes are visible changes in appearance. During the first phase the muscle is milky white, in the second it is opaque, in the third it is glassy and transparent. During the two later phases there can be no reasonable doubt that the muscle is dead; during the first phase it is probably alive. From the evidence already presented the whole curve could be explained as follows. During the initial phase the external fluid
Fig. 148. Graph showing changes in weight of a frog’s muscle when immersed in dilute solutions of sodium hydroxide. Note the initial ’osmotic’ rise followed by the fall due to exosmosis of salts from the cells. Finally an ‘imbibitional’ rise occurs. (Fig. from Jordan Lloyd.)
is hypotonic and therefore the cell absorbs water osmotically ; after
a time, however, the alkali destroys the surface thereby causing a loss
of semipermeability ; a loss of water then occurs owing to the diffusion
outwards of the neutral salts normally present in the cell; finally the
alkali diffuses inwards and ionises the proteins which promptly
absorb water. Essentially the same phenomena are observed with
acids.
The kinetics of osmotic equilibria
The rate at which water passes into living animal cells from hypotonic solutions has been investigated by R. S. Lillie (1916) and more recently by McCutcheon and Liicke (1926). The materials used were the eggs of sea urchins and the amount of water entering the cell in a given time was estimated by measuring the volume of the
338 THE EQUILIBRIUM BETWEEN
spherical eggs. As defined by Lillie the rate of entry of water may depend on three main factors, (i) The driving force of osmosis, which will be equal to the difference between the osmotic pressure of the external solution on the one hand, and the osmotic pressure inside the egg together with the elasticity or cohesive strength of the cell surface on the other, (ii) The frictional resistance to the passage of water through the egg surface, (iii) The area of the cell surface. In practice, the volume of an unfertilised egg which is swelling in hypotonic sea water can be determined by an empirical equation, identical with that of a reaction of the first order
(xiv),
t ^ ea'~ ^ t
where V is the volume of the egg in osmotic equilibrium with the hypotonic solution, F, is its volume at time t, and the initial volume of the egg. A: is a constant. ,
Lillie’s data and those of McCutcheon and Liicke harmonise remarkably well with equation (xiv). It is, however, by no means clear that they can be equally well harmonised with first principles (Nortlirop, 1927 c). Lillie made two assumptions: (i) that the elastic and cohesive forces of the cell membrane are negligible, (ii) that the change in surface area during swelling can be ignored. In such circumstances the rate of swelling will be proportional to the difference between the osmotic pressure of the cell contents and that of the surrounding medium ^j/
— = A)
where Pj is the osmotic pressure inside the egg and P^ the osmotic
pressure of the medium. If the egg is a perfect osmotic system
P,F* = P™F,, = h.
when Vt is the volume at time t, F,, is the volume when in equilibrium with the surrounding medium. Hence
dV^
dt
(h- h.\ =
VF* fJ
K
F., - F
F„Fr
_ Fa
~ K Jo
F
F — F
r a nr 'I
dV,
K=^{Vo-V,-V^ log,
where Fo is the original volume of the egg.
A LIVING CELL AND WATER
389
Table LI. Changes in volume of unfertilised eggs of
Arbacia. (From Lillie.)
Units of volume = =
21-3; r^ = 40-4
f M - T'o = 19-1
t
1
Time in
c*
1
o
Jl
h — ^ ^ eQ~ ^0 '
^ ^ eq"- t 1
minutes in
40 % sea water
- t
^ BQ ^ t
1
22-9
1-1
41 ■
2
24-0
1-2
40 1
3
26*1
1-4
49 i
4
27-9
1*6
51
5
29-2
1-7
46
6
30-7
1-9
47
7
31-3
2-1
46
8
320
2*3
45
9
32-7
2-5
44 1
10
336
2-8
45 i
11
34-6
3-3
46
12
351
3-8
48 !
13
35-S
4-2
48
14
36-3
4*7
40
Av.lfT
Fig. 149. Graph showing the rate of swelling of unfertilised sea urchin eggs in 60 per cent, sea water at 24-8°. On the left side volumes are plotted against times. On tiie
hght side log ^ is plotted against time. (From MeCutcheon and Liiche.)
840 THE EQUILIBRIUM BETWEEN
Conversion of K into absolute units gives
(-i).
where C is the c.c. of water which will pass through one square centimetre of the egg surface 1 cm, thick in 1 hour under a pressure of 1 mm. Hg, S = surface area of the egg, Pq the osmotic constant of the outside solution, and h the thickness of the membrane (Northrop, 1927 c).
Using equation (xvi) Northrop has calculated the value of Clhioi: Lillie’s data — see Table LII.
Table LII. (From Northrop.)
F, = 4-0x 10-’c.c.; F„ =
S = 1-7 X 10-5 sq. cm. =
2-1 X 10-7 e.c.;
4*6 X 10-® mm. Hg
Fertilised egg
Artificially parthenogenetic eggs
1 V X 10’
i c.c.
i hours
Km
Cjh X 10®
t hours
Km
C/h X 105 !
1 2*5
0-0080 i
12-9
3-52
0-0095
10-9
2-98
2-7
0-0130 !
12-7
3-62
0-0160
10-3
2-97
! 2*9 !
0-0200 '
11-9
3-57
0-0240
10-3
2-97
3-1
0-0290
11-2
3-52
0-0350
9-3
2-91
j 3-5
0-0550
1
10-5
3-66
0-0700
8-4
i 2-92
1
It will be noted that the values of Cjh are more uniform than is the
value of the first order reaction constant {Km) as calculated from
Lillie’s formula.
If we assume that the rate of entry of water is proportional to the surface area of the cell and inversely proportional to the thickness of the surface membrane, and that at all times the volume of the membrane itself remains constant, then
dV
dt
25C^F"
or
a
25Pot
1T5 log
+ vj yi +
(Fi- VJ)^
+ VBtan
2Fi+ V,,
VJ V3
- — const.
A LIVING CELL AND WATER 341
Northrop has calculated the value of the constant from Liicke and McCutcheon’s data; at 11° C. it has a value of 1-45 and at 20 - 5 '’ C. it is 2-60. If the sea urchin’s egg is a perfect osmotic system as postulated by these analyses, the absolute value of the permeability constant should be independent of the osmotic pressures used for changing the volume of the egg. Unfortunately this is not altogether the case. Liicke and McCutcheon’s constant varies verv
Vol.
100
3200
3100
3000
2900
2800
2700
2600
2500
2400
Fig, 150. Figure illustrating exosmosis of water from unfertilised eggs of Arbacia. The eggs were exposed to 60 per cent, sea water prior to placing them in normal sea water at 15° C. The curve shows the rate of loss of water on replacement in normal
a
sea water. The straight line shows the logarithm of — plotted against time, where
a — X
a is the initial volume and x the amount of water which has left the eggs at time t. (Prom McCutcheon and Liicke.)
greatly with different concentrations of hypotonic sea water and
even Northrop ’s more accurate formula breaks down when the
concentration of sea water falls below 60 per cent.
The value of Northrop ’s analysis does not lie in the ability of his equations to fit the observed data, but in the fact that it is an exact parallel to that applicable to the diffusion of water through an inanimate collodion sac (Northrop, 1927 a and b) and into particles of ionised gelatin (Northrop and Kunitz, 1927). We can therefore
842 THE EQUILIBRIUM BETWEEN
compare with, some degree of accuracy the relative permeability of living and non-living membranes: the value Cjh gives a basis of comparison. Northrop’s figures show that the membrane on the surface of a sea urchin’s egg is less than 1/lOOOth times as permeable as a collodion membrane of the same thickness. The apparent high degree of permeability is due of course to the extreme thinness of the egg membrane and the high ratio between surface and volume of the egg.
Although the kinetics of swelling of an echinoderm egg and a particle of gelatin follow the same law, there is an essential difference in the way in which the driving force of osmosis is generated in the two cases. In the egg it is due to ions or molecules whose concentrations are not altered by factors influencing the degree of ionisation of proteins; in gelatin on the other hand the osmotic pressure is largely due to protein systems. The facts show that once an osmotic gradient is set up between the interior of an egg or of a particle of gelatin, the equilibrium volume is reached by a flow of water which obeys the same laws in the two eases.
It may well be that different types of cell may generate their osmotic pressures in different ways. Liicke and McCutcheon’s (1926) data indicate quite clearly that the volume of echinoderm eggs does not fluctuate ■with changes in the of the medium or of the cell interior. Red blood corpuscles, however, behave differently and in this case it looks as though ionised proteins are responsible for a measurable amount of internal osmotic pressure within the cell (see p. 362).
Before leaving the problem of the osmotic equilibria of animal cells two points should be noticed, (i) In all available analyses the cohesive properties and elasticity of the cell surface have been ignored, (ii) The kinetics of swelling exhibit a very high temperature coefficient (p, = 16,000, McCutcheon and Liicke, 1926). (iii) The equilibria reached in solutions of different osmotic pressures show considerable deviations from the gas laws, although the rate at Avhich the equilibria are reached are explicable without serious deviation from these laws. These three facts arouse the suspicion that there may be other factors involved in addition to those incorporated into Northrop’s analysis and which under certain circumstances might seriously invalidate the equations of swelling.
A LIVING CELL AND WATER
843
Secretion of water
If the surface of a cell may be regarded as a simple semipermeable membrane then, on interposing a layer of cells between two solutions of the same solute in different concentrations, water should invariably pass from the dilute solution into the concentrated solution, and the rate of transference should be determined by the factors considered by Northrop. It seems clear, however, that there are outstanding deviations to this rule. Reid (1890) showed that the ability of water to pass through the skin of a frog does not simply depend upon the difference in the osmotic pressures of the solutions with which the skin is in contact. When a frog’s skin was bathed in normal Ringer solution on both sides, and 5 per cent, glucose was added to the solution in contact with the morphologically inner surface of the skin, 1-83 cubic mm. of solution passed through each square millimetre of the skin in 24 hours: when, however, the same concentration of glucose was in contact with the outer surface of the skin only 0*83 cubic mm. of fluid passed to the inner side. There thus appears to be a difference in the rate at which water will pass under an osmotic force from one side of the skin to the other. This difference is largely a specific property of the healthy living skin, for it is sensitive to the presence of anaesthetics and to those irreversible changes which accompany the death of the cells. Reid concluded that the living skin is able to absorb water from its outer surface and to secrete it on its inner surface, much as a gland cell will secrete fluid at one pole. If therefore an osmotic gradient is established between the two surfaces, the rate of water passing through the skin will depend upon whether the direction of osmotic flow is with or against the flow of water produced by the processes of active secretion. The polarisation of the frog’s skin in respect to water transference has been confirmed by Maxwell (1913) and by Adolph (1925 a). Under normal conditions a frog’s skin appears to be in osmotic equilibrium when lymph or Ringer is in contact with the inner side and with tap water on the outer side. Adolph found, however, that little or no disturbance in the distribution of water occurred if the tap water on the outside was replaced by Ringer, and concluded that as long as Ringer solution was on the inside of the skin the outer solution could be varied considerably without increasing or decreasing the rate at w^hich water passed through. When, however, tap water is placed in contact with the inner surface.
344 THE EQUILIBRIUM BETWEEN
water will pass out to all solutions except tap water. Adolph concluded that under normal conditions, i.e. with lymph on the inside and water on the outside, the natural tendency for the water to pass inwards was opposed by forces in the skin which worked in the opposite direction, i.e. a force which tends to pump water toward the outer surface. Some of Adolph’s results are difficult to harmonise with those of Reid and of Maxwell, for both these authors observed an active pumping of water from the outside inwards. Putting these discrepancies on one side, it seems doubtful whether the passage of water across a frog’s skin can be accounted for by normal osmotic gradients. The question arises, what is the nature of the forces producing anomalous osmosis? Reid attributed these forces to the active metabolism of the living cells. Adolph goes further and suggests that the forces are electrostatic in nature, since the skin is electrically polarised (Hashida, 1922) and the direction of flow of water tends to be in the direction of the negative side of the skin. On this view the anomalous behaviour of the frog’s skin is attributed to those forces which appear to be concerned with anomalous osmosis through inanimate charged membranes, where the flow of water is always towards the negative side ; this indicates that the water is itself positively charged.
It is important to bear in mind two points, (i) Within physico-chemical systems anomalous osmosis has only been observed in dilute solutions and where the membrane has been exposed to polyvalent ions ; in more concentrated solutions anomalous osmosis becomes negligible, (ii) The theory of anomalous osmosis is by no means clearly defined. If water is to pass continuously from a stronger solution to a weaker, the membrane must be doing work; precisely how a collodion membrane coated mth protein does this work is not too clear (see Freundlich, 1926); the fact remains that anomalous osmosis occurs. We are apparently dealing with two distinct sources of potential: there is the p.d. between the two sides of the membrane, and the p.d. between the surface of the pores in the membrane and the fluid flowing through the pores. If the positively charged water moves in the direction of the negative side of the membrane, the membrane potential will fall unless a current of electricity is flowing from one side of the membrane to the other. Until the whole situation is considerably clearer it seems a little risky to assume that the behaviour of the frog’s skin justifies a very close parallel. Since living frogs’ skins behave differently to dead skins, it seems certain that the energy expended by the living skin is not derived from the same source as that which produces anomalous diffusion through a collodion protein membrane (Adolph). In this respect it becomes of importance to know just how far a system Ringer/skin/Ringer is capable of transporting water continuously from one side to the other.
345
A LIVING CELL AND WATER
111 all cases of anomalous diffusion there must be a difference in the concentration of ions on the two sides of the charged membrane. According to Adolph no water passes through a living frog’s skin
unless there is a difference in ionic concentration on the two sides
but this disagrees with Reid’s data where, with Ringer on both sides, water passed to a sugar solution more easily in one direction than another: it is difficult to see why a non-electrolyte should affect the membrane potential or why there should be a membrane potential in the system Ringer/skin/Ringer, if the potential is solely dependent on a difference in concentration of ions on the two sides (see however p. 395). The only conclusion available seems to be that, by active metabolism, the skin performs work in driving water through the skin — and that it can do this more readily in one direction than in another. It would seem that the subject would prove to be a fruitful line of research — ^for if the skin is expending energy for the maintenance of an anomalous distribution of water, the permeability of the skin might change in the absence of Oo, and transport of water might continue irrespective of a difference in concentration of ions on the two sides of the membrane. Anomalous diffusion is not restricted to the frog’s skin, it occurs to a marked degree in the gut and the kidney^. It would be beyond the scope of this book to consider these tissues in any detail : a useful summary of the facts of intestinal absorption is provided by Goldschmidt (1921). It seems clear that both the gut wall and the kidney can effect a transference of water from a hypertonic solution to one which is more dilute, and as in the case of the frog’s skin there are two possibilities : (i) the transfer is effected by an active metabolic process of secretion in which the requisite energy is derived from the chemical energy within the cells, or (ii) the energy is derived from (a) an electrostatic source which itself depends on a difference of ions on the two sides of the membrane or (6) a difference in hydrostatic pressure.
It should be noted that although these latter considerations modify to some extent the applicability of the conclusions reached by Liicke and McCutcheon and by Northrop they do not invalidate them. Other things being equal, the rate at which a cell will come into osmotic equilibrium with a surrounding medium will depend on the net value of the differences in osmotic pressure on the two sides. As long as the vital or electrostatic forces remain constant, the curves which illustrate the rate at which equilibrium is reached
^ For a recent account of the roles played by the skin and by the kidneys in maintaining the water content of Amphibia, see Adolph (1930).
346 THE EQUILIBRIUM BETWEEN
will always be of the same type; it is only the final equilibrium value which will be affected, and this may account for the discrepancy found between the observed equilibria with those calculated for solutions of varying concentrations.
RET'ERENCES
Adolph, E. F. (1925 a). *Tlie passage of water through the skin of the frooin the relation between diffusion and permeability.’ Amer. Journ. Physio! 73, SS. ’ ^
(1925 b), ‘ Electrostatic forces in the diffusion of water through collodion
membranes between solutions of mixed electrol 5 rtes.’ Journ. Biol Chem 64, S39.
(1926). 'The metabolism of water in Amoeba as measured in the contractile vacuole.’ Journ. Exp. Zool. 44, 355.
(1930). ‘Living Water.’ Quart. Rev. of Biol. 5, 51.
Beutnek, R. (1912). ‘Unterscheidung kolloidaler und osmotischer Schwellung beim Miiskel.’ Biochem. Zeit. 39, 280.
(1913). ‘Einige weitere Versuche betreffend osmotische und kolloidale
Quellung des Muskels.’ Biochem. Zeit. 48, 217.
Chalkley, H. W. (1929). ‘ Changes in water content of in relation
to changes in its protoplasmic structure.’ Physiol. Zool. 2, 535, Davenport, C. B. (1897). Experimental Morphology. (New York.)
Davis, H. (1873). ‘A new Callidinai with the result of experiments on the desiccation of rotifers.’ Monthly Micr. Journ. 9, 201.
Day, H. C. (1927). ‘The formation of contractile vacuoles in Amoeba proteus: Journ. Morph, and Physiol. 44, 363.
Faure-Fremiet, E. (1923). ‘Proprietes osmotiques de I’oeuf de Sabellaria alveolatal C.R. Soc. Biol. 88, 1028.
Fitting, H. (1917). ‘Untersuchungen liber isotonische Koeffizienten und ihre Nutzen fiir Permeabilitatsbestimmungen.’ Jahrb. f. iviss Bot 57 563. ' ’
Freund LI CH, H. (1926). Colloid and Capillary Chemistry. (Eng. transl.) (London.)
Goldschmidt, S. (1921). ‘On the mechanism of absorption from the intestine.’ Physiol. Rev. 1, 421.
Gray, J. (1921). ‘Exosmosis of electrolytes from animal cells,’ Journ. Physiol. 55, 322.
(1928). ‘ The role of water in the evolution of the terrestrial vertebrates.’
Brit. Journ. Exp. Biol. 6, 26.
Gruber, A. (1889). ‘Biologische Studien an Protozoen.’ Biol. Zentralb. 9, U. Ha 31 BURGER, H. J. (1902). Osmotischer Druck wnd lonenlehre in den medieimschen Wissenschaffen. (Wiesbaden.)
Hartog, M. (1889). ‘Preliminary note on the functions and homologies of
the contractile vacuole in plants and animals.’ Ann. Ma^. Nat. Hist. (6),
3, 64. s V /
Hashida,K.( 1922). ‘ Untersuchungen tiber das elektromotorischeVerhalten der Froschhaut. (i-iii.)’ Journ. Biochem. 1, 21.
Hedin, S. G. (1897). 'tJber die Permeabilitat der Blutkorperehen.’ Pfliigefs Archiv, 68, 229.
A LIVING CELL AND WATER 34,7
HiLL; A. V . (1980). ‘ The state of water in muscle and blood and the osmotic behaviour of muscle.’ Proc. Roy. Soc. B, 106, 477.
HoBBK, R. (1922). Physikalische Chemie der Zelle und derGewebe. (Leipzig.)
HoFLEK, K. (1917). ‘Die plasmolytisch-volumetrisohe Methode und iine Anwendbarkeit zur Messung des osmotischen Wertes lebender Pflanzenzelle.’ Ber. deut, hot. Ges. 35, 706.
(1918^35). ‘Permeabilitatsbestimmung nach der plasmometrischen
Methode.’ Ber. deut. hot. Ges. 36, 414.
— - (1918 b). ‘Uber die Permeabilitat der Stengelzellen von Tradescantia elongata fiir Kalisaltpeter.’ Ber. deut. hot. Ges. 36, 426.
(1919). ‘tiber den zeitlichen Verlauf der Plasmadurchlassigkeit in
Salzlosung.’ Ber. deut. hot. Ges. 37, 304.
KoPPE, H. (1895). ‘Ueber den Quellungsgrad der rothen Blutscheiben durch aequimoleculare Salzlosung und iiber den osmotischen Druck des Blutplasmas.’ Arch. Anat. u. Physiol. Physiol. Abt. 154.
Lapicque, L. (1924). ‘La cellule est-elle enveloppee d’une membrane semipermeable?’ Ann. de Physiol, et de Physioehim. Mol. 1, 85.
Lillie, R. S. (1916). ‘Increase of permeability to water following normal and artificial activation in sea-urchin eggs.’ Amer. Journ. Physiol. 40, 249.
Lloyd, D. J ordan (1916). ‘The relation of excised muscle to acids, salts, and bases.’ Proc. Roy. Soc. B, 89, 277.
Lucre, B. and McCutcheon, M. (1926). ‘The effect of hydrogen ion concentration on swelling of cells.’ Journ. Gen. Physiol. 9, 709.
(1927). ‘The effect of salt concentration of the medium on the rate of
osmosis of water through the membrane of living cells.’ Journ. Gen. Physiol. 10, 665.
McCutcheon, M. and Lucke, B. (1926). ‘The kinetics of osmotic swelling in living ceUs.’ Journ. Gen. Physiol. 9, 697.
— — ^(1927). ‘The kinetics of exosmosis of water from living cells.’ Journ. Gen. Physiol. 10 , 659.
Maxwell, S. S. (1913). ‘ On the absorption of water by the skin of the frog.’ Amer. Journ. Physiol. 32, 286.
Mayer, A. and Schaeffer, G.(1913). ‘ Coefficient lipocjdique et imbibition des cellules vivantes par I’eau.’ Comptes Rendus, 156, 1253.
(1914 a). ‘Recherches sur les constantes cellulaires. Teneur des cellules
en eau. memoire, discussion theorique. L’eau constante ceilulaire.’ Journ. Physiol, et Path. gen. 16, 1.
(1914 h). ‘Recherches sur les constantes ceUulaires. Teneur des cellules
en eau. II. Rapport entre la teneur des cellules en lipoides et leur teneur en eau.’ Journ. Physiol, et Path. gen. 16, 23.
Northrop, J. H. (1927 a). ‘The kinetics of osmosis.’ Journ. Gen. Physiol. 10 , 883.
(1927 h). ‘The swelling of iso-electric gelatin in water. I. Equihbrixmi
conditions.’ Journ. Gen. Physiol. 10, 893.
- — -(1927 c). ‘Kinetics of the swelling of cells and tissues.’ Journ. Gen. Physiol. 11 , 43.
Northrop, J. H. and Kunitz, M. (1927). ‘The sweUing of iso-electric gelatin in water.’ Journ. Gen. Physiol. 10, 905.
Overton, E. (1895). ‘tJber die osmotischen Eigenschaften der lebenden Pflanzen und Tierzellen.’ Vjschr. naturf. Ges. Zurich, 40, 159.
848 equilibrium BETWEEN A LIVING CELL &WATEII
OvuRTON E (1899). ‘Uber die allgemeinen osmotischea Eigenschaften der Zelle, toe vermuthlicben Ursa,clien und ihre Bedeutung fiir die Physiolo^e.’ Vjschr. naturf. Ges. Zurich, 44, SS. u . v, ,
(1900). “studien iiber die Aufnahme der Amlinfarben durch die lebende
Zelle.’ Jahrb.f. wiss. Bot. Si, 669. i, • , . .
(1902). ‘Betoage zur allgemeinen Muskel- und Nervenphysiologie.’
PfluMefs Arckiv, 92, 115, a* ^ 77 7 m
Pfeffer, W. (1877). Osmotische Vntersuclmngen. Studien zur Zellrnechamk,
ProS^^'h. R. and Wilson, J. A. (1916). ‘The acid-gelatin equiUbrium.'
Journ. Cheni. Soc. 109, 307, . j j j u ?
Reid W. (1890). ‘Osmosis experiments vvith living and dead membranes.
- ^1901) ^‘Transport of" duid by certain epithelia.’ Journ. Physiol. 26, 436.
SiEBECK, R. (1912). ‘Uber die osmotische Eigenschaften der Nieren.’
Pfluger^s ArchiVi 148, 443.
Stiees W (1924). Permeability. (London.) . , * , .
WoFF n877b ‘Die Rolle des osmotischen Druckes m der Analogic
z^chen L^ungenundGasen.’ ZeU. f. phy^h. Cneni.i 4S1. ^
DE Vries (1888). ‘Osmotische Versuche nut lebenden Membranen.
.^(*^889) ^^sototiische Koefflzienten einiger Salze.’ Zeit. f. physik. Chm.
3, 130.
Zeit, /.
CHAPTER fourteen
The Permeability of the Cell Surface
Th e rate at Avhieh particular substances pass between the interior of a living cell and its external environment is usually known as the permeability of the cell to those substances. Since an adequate knowledge of cell permeability is perhaps one of the most fundamental needs of cell physiology, it is desirable to eliminate, as far as possible, all ambiguity from the terms employed. The ‘permeability of a cell in respect to a given substance’ is, in itself, a meaningless e.xpression; it acquires a meaning when the experimental conditions are rigidly defined. Thus, it is illegitimate to speak of the permeability of a sea urchin’s egg to water; it is only legitimate to speak of the amount of wmter which passes into a sea urchin’s egg over each square millimetre of surface in unit time from a knoAvn eiwironment whose osmotic pressure has a known value. The term ‘ permeability ’ involves, therefore, at least four attributes: (i) mass, (ii) area, (iii) time, (iv) concentration and specific nature of the eiwironment.
There can be little doubt that it is the specific nature of the cell surface which enables a living cell to maintain within itself the equilibrium which is essential for life, and it is useful to remember thatweare here concerned with a mechanism which is as fundamental and as delicate as that of respiration or any other more obAiously Altai phenomenon. When we survey all the facts, AAm are driA'en to the conclusion that the power possessed by the surface of the cell to allow the passage of some substances and to prevent the passage of others is unique to the living state and is not shared by any inanimate surface or membrane. The cell surface is, in fact, an integral part of the living cell; it may or may not be located within the tangible surface membranes which were considered in a preAuous chapter (see p. 102).
The data which have been accumulated Avithin recent years are too extensive to submit to reasonably short analysis, but certain outstanding facts are available, and they must be enumerated before any attempt can be made to frame a reasonable hypothesis concerning the structure of cell surfaces.
350 PERMEABILITY OF THE CELL SURFACE
Permeability to non-electrolytic solutes
As long as disturbing factors are absent it is reasonable to look upon a membrane, living or otherwise, as a sieve through whose Zxes a substance can pass as long as the diameter of its molecule is not larger than that of the largest pore. This theory in fact applies to various types of inanimate membranes, since Blitz (1910) Avas able to show that a particular type of collodion membrane would readilv permit the passage of all dyes whose molecules did not contain more than about forty-five atoms, whereas dyes with larger molecules only penetrated with much greater difficulty. Presumably only a limited number of pores were large enough to permit the passage of the larger molecules. Similar results have been obtained by Collander (1924), using copper ferrocyanide membranes as Avell as those of collodion.
Table LIII. Permeability of collodion membranes to crystalloids.
(After Collander.)
Substance
Molecular
diameter
Relative
permeability
Ammonia
Formic acid
Lactic acid
Malic acid
Methyl-etliyl-molonic acid
Citric acid
Cane sugar
5*78
8-57
19-19
25-27
32-98
36-04
70-35
100
86-4
30-3
18-2
11-7
6-0
1-6
Clearly anything which tends to clog the pores in a membrane or
which tends to enlarge them by effecting a shrinkage of the membrane Avill affect the permeability in respect to molecules or ions of
a critical size. Thus Brown (1915, 1917) was able to alter the permeability of collodion membranes by treatment with a dehydrating
agent such as alcohol, and more recently v. Risse (1926 b) and
Anselmino (1927) have shown that the pores of a gelatin membrane
are altered in diameter by the variation in the degree of swelling of
the gelatin which attends a departure from the isoelectric pomt.
It may be doubted how far pore size is the sole factor whick controls the permeability of the cell surface to non-electrolytes and, in any case, it is obvious that the sieve theory in its original form has to be substantiaUy modified; the living cell often exhibits a
PERMEABILITY OF THE CELL SURFACE 351
relative impermeability to very small ions and yet is able to allow larger molecules to pass through fairly readily. Tinker (1916) estimated that the average pore diameter of a copper ferrocyanide membrane is 15-20 /x/x, whereas the average diameter of the sugar molecules to which it is impermeable is very much less (100 times less). Either the molecules must be hydrated or the pores must be clogged in some way. The significance of these facts will be considered later, but at the moment we may consider the cell surface simply as a sieve-like structure, through the pores of which water can pass with greater freedom than can the molecules of most nonelectrolytes.
Since living cells alter their water content in response to alterations in the osmotic pressure of their surrounding media (see Chapter XIII), it follows that the cells must be relatively impermeable to those substances in the media which are exerting the osmotic pressure. It must be remembered, however, that most plasmol\i:ic experiments are of short duration, and the water gained or lost by a cell is measured as soon as the volume or weight of the cell no longer exhibits any change in a given solution. Such experiments do not prove that the cells are completely impermeable to salts or sugar, they only indicate that when the composition of the medium is changed the equilibrium in respect to water is established with much greater rapidity than is that of other substances. It is probable that salts and sugars can pass in and out of living cells with a speed which is of real biological significance, but which is negligibly slow when compared to the speed of movement of water. Complete impermeability to a given solute is probably a rare phenomenon, whereas low permeability is extremely common. If we wish to follow the diffusion of a slowly permeable substance into the cell, we must, therefore, either expose the cell to a relatively high concentration of the solute, or to a lower concentration for a long period of time. Unfortunately experiments of both types are liable to be misinterpreted, for in both cases there is grave danger of injury to the cell and, as we have already seen, this leads to a disorganisation of osmotic relationships.
If the cell surface is to be regarded as an imperfect osmotic membrane, and the cell is immersed in a hypertonic or hypotonic solution of a given solute, the loss or uptake of water will be less than if the surface were completely impermeable. The difference between the theoretical and the observed volume of the cell when the maximum
S52 PERMEABILITY OF THE CELL SURFACE
change in volume has occurred will depend on two factors : (i) the relative value of the coefficient of permeability of the solute in the cells (or in the medium) to that of water, (ii) the rate at which the equilibrium volumes are reached. If we plasmolyse a cell rapidly, the minimum volume observed will be very close to that recorded by a perfect osmotic system ; if, on the other hand, plasmolysis occurs slowly, the difference bet^veen observed and theoretical volume will be greater. If an experiment could be carried on long enough, then equilibrium would be reached wdien the volume of the cell had returned to the normal value which it possessed at the beginning of the whole experiment. Phenomena of this type are well known in the case of plant cells, although in many cases the secondary uptake of water from hypertonic solutions is due to an irreversible injury of the cells concerned. As far as is known, the rate of penetration of a solute into animal cells has, so far, not been estimated by the rate at which plasmolysis is reversed, but the method was applied by Lepeschkin (1908) to plant cells (see Stiles, 1924, p. 178). The water content of Spirogyra ceils was reduced by plasmolysis with a solution of sucrose, a substance which penetrates with extreme slowness. The cells w^ere then transferred to an isotonic solution of glycerol whose permeability it was desired to measure. As the glycerol entered, the volume of the cell vacuole increased, and this volume was measured after J hour and 2| hours respectively. The difference between these tw^o volumes gave the volume of glycerol solution which had entered, and since the concentration was known, it is possible to calculate the number of gram molecules entering per hour; by using suitable units of concentration and of cell surface, Lepeschkin estimated that 67-183 X 10“^ gram molecules of glycerol penetrated through each square centimetre of cell surface per hour. More recently both Fitting (1915) and Hofler (1918 a, b, 1919) have estimated the rate of penetration of solutes into plant cells by measuring the rate of de-plasmolysis. As already pointed out, it is essential in such experiments to guard against the danger of irreversible injury to the cells concerned.
In animal cells the permeability of a given solute has seldom been stated in any precise manner. As a rule a substance is regarded as ‘permeable’ if, witMn a reasonable time, its presence can be detected inside a cell which has been exposed to a solution containing the solute : if the solute cannot be detected in this way, it is often regarded as ‘relatively impermeable’. It must be remembered,
858
PERMEABILITY OF THE CELL SURFACE
however, that if the amount of solute passing into a cell by diffusion is proportional to the difference in concentration inside the cell and in the medium, then the rate of penetration will be affected by any process which tends to immobilise the solute within the cell!^ This factor probably plays some part in the case of some acid dyes (Ruhland, 1908-1914). A dye which is readily adsorbed to intracellular surfaces will accumulate in a cell more rapidly than one which is not so absorbed, although the coefficient of permeability of the two may be the same.
The permeability of living cells to non-electrolytic substances w^as extensively investigated by Overton (1895-1900), and his results have been admirably summarised by Jacobs (1924). The ability of an organic molecule to enter a cell appears to depend on whether it is polarised or non-polarised. A non-polar molecule has a structure wherein the electrons are shared by the atoms concerned in such a way as to eliminate intramolecular regions of dissimilar electrical charge. Polar molecules on the other hand possess a distribution of electrons such as will cause marked electrical dissimilarity in different regions of the molecule. The non-polar molecules tend to be more soluble in organic solvents, they do not ionise and are relatively inert: polar molecules tend to dissolve more readily in water, they ionise, and are chemically active. Roughly speaking, non-polar molecules enter living cells very readily: thus the hydrocarbons, acetylene, benzene, xylene, naphthalene were found to penetrate the cell by Overton. If, however, more than one polar group (e.g. OH; COOH; NHg) is present in a hydrocarbon molecule, the rate of penetration into the cell is very greatly reduced. Thus ethyl alcohol contains no polar group and enters the cell very readily, ethylene glycol will cause temporary plasmolysis, glycerol effects de-plasmolysis very much more slowly, whilst the tetrahydric alcohol, erythritol, is even less able to penetrate the cell (Jacobs, p. 115). Jacobs points out that almost all Overton’s results conform to the rule that the ability of any given organic compound to enter a living cell is increased by reducing the number of polar groups 'within the molecule, and is decreased by increasing the number of these groups.
From a physiological point of view the most important organic solutes are the sugars and the amino acids. Both these substances, as we might expect from their chemical constitution, appear to enter with very great difficulty, and yet it is quite certain that they normally enter in sufficient quantities to provide for the maintenance of
354 PERMEABILITY OF THE CELL SURFACE
life. How far the failure to detect their entry under experimental conditions is due to the extreme slowness at which they enter, or how far the normal process of penetration is essentially inhibited by the experimental procedures hitherto adopted remains obscure.
As in the case of water, so we must consider the possibility of an active secretory mechanism capable of maintaining a difference in the distribution of a solute on the two sides of the cell surface. Apparently little evidence is available in respect to non-electrolytes, although it is probable that the walls of the gut and the cells of the kidney are capable of transporting non-electrolytes by forces other than those concerned in normal diffusion gradients. There is also the related problem of an ' irreciprocal’ permeability to such substances recently investigated by Wertheimer (1923—4).
Permeability to electrolytes
The relative impermeability of cells to such non-electrolytes as sugar might possibly be explained by the assumption that the cell surface is a porous structure and that most of the pores are not sufficiently large to allow the passage of comparatively large molecules. In the case of electrolytes, however, this simple hypothesis does not cover the facts, since it will be shown that very often a molecule can pass in or out of a cell, whereas its constituent ions are unable to do so. Osterhout (1925) has recently shown that molecules of sulphuretted hydrogen can pass into plant cells with much greater rapidity than either the hydrogen ions or sulphide ions. This important fact was established by exposing Valonia cells to sea water containing a constant total amount of H 2 S at different pH. At about pH 5 practically the wffiole of the HgS was undissociated; at pH 10 it was all ionised as H* and HS'. It was found that the total amount of HgS present in the sap was strictly proportional to the amount of ionised HgS present in the external sea water (see fig. 151).
Similarly, w’-hen the total amount of undissociated HgS in the sea ivater remained constant, the total sulphide in the sap was independent of pH changes in the external solution.
Essentially similar results Were obtained by Osterhout and Dorcas (1925) using COg (fig. 152) , and it seems quite clear that little or no COg enters or leaves living ceils of Valonia except in the form of undissociated carbonic acid (see also Jacques and Osterhout, 1930). It seems probable that all feebly ionised acids may behave in this manner and that the ability of undissociated molecules of electrolytes to pene
PERMEABILITY OF THE CELL SURFACE 835
trate living cells may be fairly widely spread. Miss Irwin (1926 c) has shown that the rate of penetration of cresyl blue into the vacuole of Niiella is proportional to the concentration of undissociated molecules of the dye in the external solution (see also p. 378). There is, however, an important difference between the process of penetration by cresyl blue and by CO 2 . In the latter case the temperature coefficient suggests that diffusion is the essential factor concerned (Osterhout and Dorcas, 1925), whereas in the case of the dye the
HgS
Fig. 151. Curve showing the relation between the total amount of intracellular HoS and the pH of an external medium containing sulphides. (From Osterhout, 1925.) The figure shows that the total sulphide in the sap of Valonia corresponds with the undissociated H^S in the external solution. The concentration of total sulphide (H 2 S 4- HS' 4- S") in the sap (0) is expressed as a percentage of the total sulphide in the outside solution. The values for the concentration of undissociated H^S in the sea water as calculated from the dissociation constant (H) and as determined from the vapour tension (A) and from the rate of evaporation (x ) at various pH values of the external solution are expressed as a percentage of the corresponding values in the range pH 1—3, where all the H^S is regarded as undissociated.
temperature coefficient is surprisingly high, Qio == -^^*9 (Irwin, 1925 a), and suggests that the dye undergoes chemical combination as soon as it enters the cell.
Just as the molecules of a weak acid appear to penetrate readily into a cell, so they will leave a cell with equal facility, and the facts which apply to acids apply equally well to alkalies. It is for this reason that incompletely ionised acids such as carbonic acid, and weakly ionised bases such as ammonia, have a more rapid and profound effect upon intracellular processes than an equal concen
356 PERMEABILITY OF THE CELL SURFACE
tration of strong acid or base; similarly a cell will rapidly recover from the effects of a weak acid or alkali, and take a longer time for recovery from the effects of the more completely ionised acids or alkalies (Gray, 1922). That weak acids and weak alkalies penetrate readily into living cells was demonstrated by Newton Harvey (1911) by staining cells with neutral red and exposing them to solutions containing the substance to be investigated. For example, the eggs
T 7 V 1 rranh showing that the total CO^ in the cell sap of Vahnia corresponds the^^^^^^ H.CO^ (including CO,) in the sea water outside.
Th^ total CO' in the sap (@) is expressed as a percentage of that m the sea -vrater Imside The pe^ calculated from
thf^ssociaX constant is sho.vn by the symbol 0. The partial pressure of free CO, to toe sea water as determined by McClendon is shown by the s^bol /h Md is ’n ttiA units shown to the ri<tht of the figure. The concentration of HgCO, S w^Wr" eSrS^ed S aTe«e of that found at pH 3 ( where H CO, is regarded as 4dissooiated),is shown by the symbol x . (From Osterhout and Dorcas, 192o.)
of sea urchins when stained by the dye remain red even if there is
sufficient hydroxyl ions in the surrounding sea water to cause rapid
disintegration of the egg surface. If, however, the alkalmty ot
normal sea water is only very slightly varied by the addition of
ammonia, the eggs very rapidly turn yellow. On replacing the ceUs
in normal sea water they rapidly regain their red colour (see also
p. 85). This type of experiment illustrates two important facts,
(i) Ammonia in some form or other is capable of entering into living
PERMEABILITY OF THE CELL SURFACE 857
cells, and when inside it dissociates to form free hydroxyl ions, (ii) That ammonia is capable of leaving the cell as readily as it enters' Similar facts can be demonstrated with acids. Strong acids only penetrate cells with difficulty, and having entered they only diffuse away with equal difficulty. Weak acids such as carbon dioxide or butyric acid enter cells with much greater freedom, and at the same time they can readily diffuse away. These facts suggest that alkalies and acids do not pass in and out of the living cell in the ionised condition but in the form of undissociated molecules.
Permeability to ions
Since nearly all living cells adjust their water content in response to changes in the osmotic pressure of an external medium containing variable concentrations of fully ionised electrolytes (see p. 328), it follows that the cells must be relatively impermeable to either cations or anions, or to both. That ions cannot pass freely into or out of a cell is directly associated with the fact that all living ceils are very poor conductors of electricity {Fundulm eggs. Brown (1905);
Table LTV. Illustrating the relatively low conductivity of living blood corpuscles. (From Bugarszky and Tangl.)
Species
Relative conductivity of plasma and corpuscles
Plasma (10^ A)
Corpuscles (10^ A)
Horse
105
1-63
Dog
113
1-70
Cat
125
2-20
Table LV. Change in electrical resistance of Laminaria tissue on
exposure to isotonic NaCl solutions. (From Osterhout, 1914.)
Time
(mins.)
Resistance
(ohms)
0
980 cells alive
20
745
JS
40
590
5?
60
495
9J
100
395
9J
150
345
JJ
200
3201
cells dead
300
320/
(resistance of sea water 320 ohms)
358 PERMEABILITY OF THE CELL SURFACE
red blood-corpuscles, Stewart (1899); sea urchin eggs, McClendon (1910); Laminaria tissue, Osterhout (1922)). If both anions and cations were able to pass freely through a cell when exposed to an electric field, the conductivity would not differ greatly from that of the surrounding medium: as long as the cell is alive, however, the conductivity is low (Bugarszky and Tangl, 1897) and only rises to that of the surrounding medium when the cell dies (Osterhout, 1914; Shearer, 1919).
The effect of death on the electrical conductivity of bacteria was inv'estigated by Shearer (1919), who found that when B. coli are exposed to isotonic NaCl solution the conductivity of a dense suspension rose from a comparatively low figure to that characteristic of the surrounding medium (see fig. 153). An exposure to such solutions of NaCl is fatal to
Ohms
resistance
Fig. 153 . Graph showing the change in the resistance of bacteria in a solution of pure sodium chloride. (From Shearer.)
the cells after two hours. These results confirm those of Osterhout, but
according to Green and Larson (1922) and to Zoond (192T) the conductmty of dead bacteria is no higher than that of the living cells, and
the observed changes in the conductivity of a suspension are due to the
exosmosis.. of salts from the cells.
PERMEABILITY OF THE CELL SURFACE
359
Impermeability of the Cell Surface of Ions
That the barrier to the passage of ions is confined to the periphery of the cell is proved by the work of Hober (1910-13) and later workers who have shown that the resistance to an electric current is limited to the surface layers of the cell only, and that ions can move with comparative freedom within the main body of the cell. The methods employed for these observations are complicated, but in view of the theoretical significance of the results it is desirable to give some indication of the principles involved, Hober’s (1910) first method was based on the principle that if an electrical conductor is interposed between the plates of a condenser, the capacity of the condenser is increased and a current is allowed to flow tliroiigh the circuit. By suspending red blood-corpuscles in isotonic sugar solution and placing the suspension between the plates of a condenser, Hober found that the conductivity of the cells was equivalent to a 0-1 or O-OlM solution of potassium chloride, a much higher value than that obtained when the conductivity was measured by the Kohlrausch bridge : further this high value was unaffected by laking the cells. By another method, based on the ability of the cells to damp the oscillations of a high frequency current, Hober (1912) estimated the internal conductivity of the cells as approximately equal to that of the external serum. Hober (1913) also found that the resistance of red blood-cells to the passage of a ciurent (impedance) decreased with a rise in the frequency of the alternating current which was employed and that at very high frequencies it fell to the low value characteristic of haemotysed cells when measured with low frequencies. Such changes in impedance might be expected to occur if the cell circuits were comparable to that shown in fig. 154, where C is a condenser, r is a resistance equivalent to the resistance of the cell surface, and i2 is a resistance comparable to that of the cell interior. To the direct current the impedance of the whole circuit is r + R, but to currents of infinite frequency the impedance is jB. Thus using a variety of methods for the determination of R, Hober found that the internal conductivity of red blood-corpuscles was equivalent to that of a 0*4 per cent, solution of NaCl, whereas the conductivity of the whole cell was only equivalent to 0-02 per cent. NaCl. More recently Fricke and
360 PERMEABILITY OF THE CELL SURFACE
Morse (1925) and McClendon (1926, 1927) have found that the
resistance and the capacity of cell sus- I
pensions are independent of the frequency of the current used as long as that frequency is low ; above a critical frequency (co) they both decrease — a result which confirms Hober's original observations.
Fricke and Morse have shown that the resistance (Bco) to a current of a> frequency and the capacity satisfy the following equations :
1 1 . JL/
Bi Vl
Fig. 155.
R^' R,\l+ C^^oi^R
1 +
where is the static capacity of the corpuscle, and where is the
resistance of the external medium and Ri is the resistance of the
interior of the cells; these equations can be derived from first
principles if the living cell forms a circuit equivalent to fig. 155.
Table LVI. Capacity and resistance of ox blood for varying
frequencies. (From Fricke and Morse, 1925.)
i
1
Cycles per second
Capacity /x/xf
i
Resistance
1 Obs.
Calc.
Obs.
Calc.
87-000
146
146
191
191
833,000
130
135
181
183
1-17 X 10®
118
126 '
174 *
178
1-52
106
115
168
172
2-04
90
98
159
163
3-04 1
68
71
148
151
3-82 1
60
55
144
144
4-52
39
43
138
140
0-00 ^
—
—
(124)
126
The resistance to currents of infinite frequency can be calculated
by extrapolation, and the value of R^ so obtained gives the resistance
which would have obtained at low frequencies if the membranes of
the cells were absent :
I
1 1
PERMEABILITY OF THE CELL SURFACE 861
From this the internal resistance can be calculated from an equation (see Fricke and Morse) which relates the resistance of the external fluid to that of the whole corpuscle for any given suspension. In this way Fricke and Morse concluded that the specific resistance of the inside of red blood-corpuscles was 3-5 times that of the specific resistance of serum. Cole (1928) by similar means found that the internal resistance of Arbacia eggs was 3-6 times that of normal sea water.
From observations of the capacity (Cq) it is possible to determine the approximate thickness of the membrane which is opposing the migration of ions through the cell. Assuming a dielectric constant of 3 (= that of olive oil), Fricke (1925) estimates this thickness as 3-3 X 10-’ cm., which is comparable to 20-30 carbon atoms and is therefore equivalent to a monomolecular layer of a serum protein molecule. Using somewhat analogous methods, McClendon (1926) estimated the thickness of the surface membrane at 2-3 carbon atoms only.
675 ohms
Fig. 156.
McClendon’s (1926) conception of the red blood-corpuscle is illustrated in fig. 156.
The two surfaces of the cell membrane represent two plates of a condenser of 1500 micro-microfarads capacity: these are short circuited by a parallel resistance of 675 ohms, indicating that the cell membrane represents a leaking condenser. The cell interior represents a resistance of 400 olmis in parallel with the condenser. The resistance of the two very thin surface membranes is thus three times as great as that of the whole cell interior. We may therefore conclude that the barrier to the diffusion of ions is restricted to the surface layers of the red blood-cell and of sea urchin eggs, a conclusion which is in harmony with the conception of a peripheral semi-permeable membrane already reached from other data. The observations of electrical impedance do not, however, give us any information con
362 PERMEABILITY OF THE CELL SURFACE
cerning the nature of the ions to which the cell surface is impermeable ; the impermeability may be in respect to cations or anions or both.
PermeahilUy to Anions or Cations
These facts must be considered with reference to others. If red blood-corpuscles are suspended in a solution of sodium chloride and CO 2 is blown through the suspension, the external medium becomes alkaline and at the same time the chlorine content of the cells increases. If instead of being suspended in sodium chloride, the cells are immersed in isotonic sugar solution, no alteration occurs in the alkalinity of the solution Avhen CO 2 is blown through. Hober (1922) interpreted these results as follows. Carbon dioxide passes into the cells in the form of undissociated molecules of carbonic acid, but thereupon ionises to form bicarbonate ions and hydrogen ions. The former are assumed to be capable of rapid diffusion from the cell, but for every bicarbonate ion leaving the cell a chlorine ion must enter. This explanation is based on the assumption that the cell is impermeable to cations. The equilibria reached by blood corpuscles suspended in media of varying composition have recently been discussed in detail by van Slyke (1926), who has gathered together much evidence in support of the view that not only are the cells impermeable to metallic cations, but also that the composition and concentration of the intracellular anions (chiefly HCO 3 ' and CT) are determined by the concentration of the intracellular cations (chiefly potassium) and by the concentration of ionised protein (chiefly haemoglobin). The whole system conforms, in fact, to the requirements of a modified Domian equilibrium and the distribution of electrolytes and water thereby also receives a quantitative explanation. The amount of wmter in the cells is determined by the number of intracellular ions and these are partly those of haemoglobin; it follows that, unlike other cell systems, any alteration in the pH of the external medium should induce an alteration in the volume of the cells. This is shown to be the case by the following observations of Warburg (1922) (Table LVII).
The behaidour of red blood-corpuscles strongly suggests that their surface layers are impermeable to cations, but permeable to anions of the type of chlorine or bicarbonate. At the same time the evidence is far from complete. Hdber’s observations on the redistribution of hydrogen ions can receive an equally convincing ex
PERMEABILITY OF THE CELL SURFACE 36S
planation without postulating a permeability to anions. If blood cells are exposed to an electric field they will pass to the positive pole which would be the case if they were normally surrounded by a layer of cations. In solutions of sodium chloride these cations wUl be sodium, but in the presence of hydrogen ions (from the CO, in the medium) there may well be an interchange of Na' and H', w'hieh will increase the alkalinity of the external medium. That other types of cell (e.g. trout eggs) actually exhibit such surface reactions with hydrogen ions there can be no doubt (Gray, 1920), but it may be
Table LVII
pn
Volume of blood cells in percentage of their volume at pH. 6*5
Obs.
Calc.
6*50
1000
100
6-80
95-2
96
700
92-7
93
7-20
90-7
91
7*40
89-1
88
7*60
87-8
85
7-80
86-3
81 i
Table LVIII
Tissue
%
water
(W)
%C1
(c)
pH
(calc.)
pH (obs.)
P.D.
(calc.)
P.D.
(obs.)
1 .
a
Red blood-corpuscles
63-6
0-178
7-17
7-23
14-2
—
0-59 i
Brain (white matter)
70*0
0-155
7-06
20-7
17-28
0-45 :
Brain (grey matter)
81*5
0-115
6-87
32-7
—
0-30 i
Smooth muscle
80-0
0-112
6-87
6-40-7-04 1
32-9
0-29 :
Liver
84*0
0-096
6-78
38-3
—
0-24 i
Striped muscle
76*0
0-061
6-62
6-02-6-91 :
47-8
40-80
0-168,
that different types of cell behave in a different manner. Hober’s
h5rpothesis has been criticised by Rohonyi and Lorant (1916), since
these authors report that the anionic exchange between the corpuscles and external medium is not dependent on the integrity of
the cell membrane.
It is interesting, however, to note that if van Slyke’s analysis can be applied to mammalian cells in general a reasonable explanation is forthcoming for the potential differences which exist between the interior and exterior of different types of living cells (Haldane, 1925).
864 PERMEABILITY OF THE CELL SURFACE
Haldane’s calculations are based on four main assumptions : (i) the cell surface is permeable to water, (ii) it is impermeable to all cations, (iii) it is permeable to Cl' and HCO3' and that these are the only inorganic anions present in significant quantities, (iv) it is impermeable to colloids.
If a be the molar concentration of salt outside the cell, and y be the molar concentration of anions inside the cell, then the potential
JRT a
difference across the ceil surface (E) is ^ log^ - volts, so that at 38° C.
E = 0-0617 logio - volts. But y can be calculated from the percentage
of water in the cell {w) and from the percentage of chlorine content (c) • Cl' -i- HCO ' ^ ’
if the ratio of - — — -{= 1-23) holds for all tissues and if for isotonic
saline a is equal to 0-170, then log^o - = log^o w - log^g c - 2-32.
y
But the cK inside the cell is to that outside as a is to y, therefore pH of the tissue == pH of the medium - log^o + log^o c -4- 2-32, and the injury potential = 61-7 [logjo^xi — log^^ c - 2-32] millivolts.
It is, however, very difficult to believe that all cells are completely impermeable to cations, for under these circumstances such ions could only exert an effect on the cells by operating on their surface. As mentioned elsewhere, most cells respond actively and rapidly to any serious change in their cationic environment. For example, the heart is markedly affected by the ions of hydrogen, potassium, and calcium and if these ions cannot enter the cell they must operate solely at the surface of the tissue. If a heart is perfused with an acid Ringer solution it tends to stop beating in the relaxed condition, and if the excess of hydrogen ions are removed the beat is resumed. If the acid acts solely on the surface of the cells, one would expect to find that the efficiency of any particular solution would depend solely on the pH of the perfusion fluid and would not be increased if for any reason the acid were able to penetrate into the cells. This, however, is not the case. Philippson (1913) showed that the physiological action of an acid which can be shown to penetrate rapidly into the cells is higher than that of an acid which penetrates more slowly, although the pH of both perfusion fluids is the same. Similar facts apply to other tissues, e.g. ciliated cells (Gray, 1922); further, the respiration of cells is much more powerfully reduced by the penetration of acids into the cells than by the application of acids to their surface (Gray, 1924).
Again, if the physiological action of hydrogen ions is solely due to the changes they induce at the surfaces of cells, then these changes should be readily reversible by the addition of hydroxyl ions to the
PERMEABILITY OF THE CELL SURFACE 365
external medium. It is, however, found that the effects of h3^drogen ions are much more readily reversible by the addition of hydroxyl ions to the cell interior than by their addition to the external medium. A concrete case is provided by ciliated cells. If such cells are stained with neutral red it can be shown that they resemble many others in that ammonia is capable of producing rapid changes in the alkalinity of the cell interior, w^hereas this cannot be effected diudng life by adding sodium hydroxide to the external medium. Yet, if ciliated cells are rendered inactive by the presence of hydrogen ions in the external fluid, the cells are much more readily activated by ammonia than by sodium hydroxide (Gray, 1922). Similarly, although the length of time that the cilia of Mytilus wdll beat in acidified sea water depends to some extent on the pH, it depends to a larger extent on the carbon dioxide tension of the external medium (Haywood, 1925).
These and other facts seem to suggest that the impermeability of the cell surface to cations as exemplified by mammalian red bloodcorpuscles cannot readily be extended to other types of tissue.
Permeability to specific ions
So far we have not attempted to consider in any detail the specific relationship between any given ion and its power of penetrating the plasma membrane. To embark on this problem would be a formidable undertaking. In dealing with non-electrolytes many of the facts seem to harmonise with the view that there is a definite relationship between the size of a molecule and the ease with which it can penetrate certain types of membrane: the smaller the molecule the higher is the percentage of pores through which the former can pass. If we attempt to estimate the average pore size of living cells by noting the size of a non-electrolydic molecule which will pass in fairly freely, we must conclude that all the pores are probably of much wider diameter than that of the average electrolytic ion. In order to retain the sieve theory it is necessary to postulate a mechanical or forcible blocking of these pores. Various possibilities appear to exist. The pores may be partially blocked by an adsorbed film of water, or the walls of the pores may offer an electrostatic opposition to ions of opposite sign, or the size of the pores may be affected by adsorption of water by the membrane. These problems belong at the moment to the realm of physical chemistry (see also p. 397). In the present discussion it is desirable to emphasise a fact
866 PERMEABILITY OF THE CELL SURFACE
which is often overlooked in drawing conclusions from physical analogies. In the cell we- are dealing with a mechanism which can establish a definite equilibrium between the interior of the cell and its external medium. When a blood corpuscle is immersed in normal serum, or when VoloTtza is in sea water, we must assume that there is strict chemical equilibrium between the amount of potassium inside the cells and the amount in the external sea water. By postulating a membrane which is only very slightly permeable to potassium, we cannot reach a state of equilibrium comparable to that of the normal cell, where the concentration of potassium is much higher than that of the external medium. A physical membrane may alter the rate at which equilibrium is effected after a change occurs in the solutions on its two sides, but it cannot except in so far as it is absolutely impermeable to some active ion
waiter the final equilibrium position. It is therefore necessary to
^a,r in mind two concepts: (i) the mechanism responsible for the Kiblish^ent of an equilibrium condition between the concentramlA of a specific ion inside the cell and in its normal external medium, rMthe mechanism which comes into play when any disturbance this equilibrium takes place. Once again we have to consider flw far the normal concentration of an ion inside a cell is mainjBhed by the active processes going on in the cell— which processes Ky be comparable to those which are obviously operative in the Ktebrate kidney — or how far the concentration in the cell is deterBdned by a relatively simple concentration equilibrium on the two ■des of the cell membrane.
I It is convenient to start from an equilibrium concerning which Biere is seldom any doubt — ^viz. the equilibrium which exists between Ke concentration of a given ion inside the cell with its concentration E the normal environment in which the cell lives. In nearly every Ese the observed ratios indicate that free diffusion of potassium Kns does not occur between the cell and its medium; at the same Erne the equilibrium position is seldom the same for any two given Epes of cell — even where the environment is identical. A wellEnown example (see Table LIX) is provided by red blood-corpuscles lAbderhalden, 1898). An even more startling example is that given l»y Cooper and Blinks (1928) for Valonia and Halieystis (fig. 157). E'er any given ion, therefore, there may be marked differences in the Equilibrium concentration in different although allied types of cell. p± first sight, the heaping up of an ion inside a cell might be due in
permeability of the cell surface 367
part to its immobilisation within the cell (see p. 373), but this cannot be true for metallic ions such as sodium or potassium, for the conductivity of the cell interior is such that most of the electrolj-tes must be freely ionised.
Pig. 157 . Chart showing the molar concentration, expressed as per cent, of halide, of the chief elements in the saps of Valonia ventricosa, F. macrophysa, and Halicystis compared with sea water. (From Cooper and Blinks.)
If the sieve theory is to cover facts of this type, it must be capable of applying an effective block to one type of cation and not to another. In this connection the recent work of Michaelis and his collaborators (1926) is of interest, since it shows that membranes of a specific type may exert a marked effect on the relative rates of diffusion of different ions, e.g. potassium and sodimn. Michaelis’
368 PERMEABILITY OF THE CELL SURFACE
membranes do not account, however, for a state of equilibrium “oCarable to that shovm hr Tables LIX and LX. It will be noted that the cell selects not only one cation in preference to another but also one anion in preference to other anions; for example many marine cells have a very high content of phosphate ions although the concentration in sea water is extremely low. The only conclusion which can be drawn at present is that the cell membrane must be saturated with each ion independently or that the permeability of the membrane in the two directions must be different.
Table LIX
!
. Horse !
Pig
Dog
Cat
Parts per 1000
Serum
Cor- i puscles
Serum
Cor puscles
Serum
Cor- 1 puscles
Serum
i
Cor puscles
Sodium
4-396
—
1 4-251
—
4-278
2-839
1 4-439
2-705
Potassium
0-259
4-130
0-270
4-957
0-245
0-273
0-262
0-258
Table LX
Molar concentration of sap as percentage of halide
Sea water (Bermuda)
Ilalicystis
Valonia
macropkysa
Cl and Br
K
Na
Ca
Mg
S64
100-00
2-15
85-87
2-05
9-74
6-26
100-00
2-58
92-80
1- 36
2- 49
(Trace?)
100-00
86-24
15-08
0-288
(Trace?)
(Trace?)
It will also be noted that each type of ion must be considered as a
separate entity and it is not permissible to speak of permeability to
‘cations’ or to ‘anions’, we must consider each metal or radicle
separately. It must be admitted that a consideration of the normal
salt content of cells does not suggest any obvious mechanism whereby the equilibrium concentrations of intra- and extra-cellular
electrolytes is established. That the equilibrium is probably of a
dynamic nature is shown by the fact that growing cells maintam
their normal electroljde concentration, so that the cell must be able
to absorb electrolytes if the equilibrium is upset by active growth.
Many attempts have been made to set up within the cell a new equilibrium in response to a change in the external environment.
PERMEABILITY OF THE CELL SURFACE 369
Cells are placed in an environment differing quantitatively or qualitatively from the normal, and changes in the electrolyte concentration of the cell interior or of the environment are measured. As already pointed out, experiments of this type lead to definite results ^vhen incompletely ionised electrolytes are employed and suggest that ions seldom enter the cell. There are, however, a number of observations which suggest that an ion in the external medium can in some cases be exchanged for another within the cell bearing the same charge. Hamburger (1909) reported an exchange of calcium and other ions across the membrane of the red-blood corpuscle, although in this case it is not certain that the exchange was not limited to the surface of the cell. On the other hand Osterhout (1909) demonstrated the penetration of Ca“ into the cells of the root-hairs of Dianthus, and M. M. Brooks (1922) has shown that Sr’* can penetrate into the sap of Nitella, Concerning anions, similar phenomena have been observed (Hdber, van Slyke). In nearly all experiments of this type there is always some doubt as to how far the phenomena observed are typical of the normal plasma membranes. This doubt is least obvious when dealing with the penetration of hydrogen or hydroxyl ions, since the concentration of these ions can be measured with great accuracy within the limits capable of supporting life. We have already seen that the undissociated molecules of acids enter cells with greater readiness than their derivative ions : at the same time the hydrogen ion must penetrate to some extent. For example, if only undissociated carbonic acid penetrated from acid sea water, the effect on a cell ought to be independent of the and solely dependent on CO 2 tension, which is not the case (Haywood, 1925) . All the evidence suggests that when exposed to a strong acid, hydrogen ions are slowly set free inside the cell, and are slowly removed on returning the cells to their normal environment (Gray, 1922) and that corresponding phenomena are applicable to bases. Unfortunately most of the observations on the penetration of acids and bases into living cells (Harvey, 1911; Crozier, 1916 < 2 -c) have been performed with solutions of the same molecular strength and not with solutions of the same hydrogen ion concentration. It is possible that the penetration of molecules and of ions is controlled by two separate mechanisms. In the case of molecules we may be dealing with a true equilibrium between the concentration on the two sides of the plasma membrane, whereas the movement of ions may be restricted to a process of exchange,
870 PERMEABILITY OF THE CELL SURFACE
whereby an ion of a given type can only enter if another bearing the same charge leaves the cell. That this does not always occur is shovii by the observations of Cooper, Dorcas and Osterhout (1928), who failed to note any rapid exchange of anions or cations by Valonia, althoucrh when the cells are growing the uptake of salts is measurable. Und^r favourable circumstances Valonia absorbs only 3 x lO-® oram molecules per hour per square centimetre, and this movement was against a concentration gradient of 40 : 1.
There is so much evidence to show that the cell surface is not equally freely permeable to both anions and cations, that one tends to overlook the fact that nevertheless a growing cell must be in a position to abigorb both types. How far the recent work of Mond (1927) throws light on this difficulty remains to be seen. Mond has shown that if red blood-corpuscles are on the acid side of their isoelectric point their chlorine content goes up and their potassium content goes down, whilst on the alkaline side the relative concentrations are reversed. This is interpreted by Mond to mean that the permeability of the membrane changes the isoelectric point: this may be true, but there is just the possibility that the observed changes are due directly to the amphoteric nature of the cell envelope. It would be of interest to see whether there is any evidence of a fluctuating change in the pH of the cell interior during cell growth — but the experimental technique would not be easy.
W e may conclude that, so far as is known, the living cell exerts a selective influence on the substances which it absorbs of a much more intricate nature than is at present capable of resolution into physico-chemical terms. It should not be forgotten that although the osmotic activity of the interior of a cell may, under certain circumstances, be related to that of the external environment, yet the nature of the active molecules responsible may be qualitatively different on the two sides of the cell surface.
Since fat-soluble substances appear to enter living cells more readily than substances which are not thus soluble (Overton, 1895-1900; Meyer, 1899), it is possible that metallic ions enter the cell in the form of fat-soluble compounds. Little if any direct evidence is available, but there is definite evidence that metallic radicles move in this form from one part of the body to another. For example the crab, Carcinus moenas, calcifies its integument, after moulting, by the liberation of calcium salts stored in the liver (Paul and Sharpe, 1916). The calcium is stored in the
PERMEABILITY OF THE CELL SURFACE 3T1
liver cells as calcium phosphate, but is set free into the blood as calcium formate and calcium butyrate; in this form it reaches the superficial ectoderm and is there converted into calcium carbonate. It is possible that a similar transformation from water-soluble to the fat-soluble condition occurs during the absorption of metallic compounds by the intestine of vertebrates.
Permeability to dyes
As pointed out by Jacobs (1924), dyes form a unique class of substances for the study of cell permeability. Their penetration can be readily observed and their physical and chemical properties are varied: dyes may be acidic or basic, colloidal or crystalloid, and soluble or insoluble in non-aqueous media.
Table LXI
Dye
Basic or acidic
Solubility in cholesterol
Permeability of Ihing cells
Methylene green
Basic
0
+ + -r :
Thionin
5J
0
-t- -f ^
Malacite green
,,
0
-r -r -r
Bismarck brown
93
0
+ -f -r
Victoria blue
99
+ + +
j 0 i
Basle blue
99
1 ^ i
Diazin green
99
+ ^
Victoria blue
99
-r -f -h
4 - 1
Cyanosin
Acidic
+ -f -1 0 ;
Bengal rose
jj
+ +
! 0(4-) :
Oxamin maroon
’’ !
+ -f
0
The first attempt to analyse the nature of the plasma membrane
by measuring its permeability to dyes was made by Overton (1900).
Using a number of anilin dyes of various types, he found that all
those which entered living cells were absorbed by fat soluble substances, and were also absorbed by lecithin and cholesterol. This
result confirmed Overton in his conception of the plasma membrane
as a fatty membrane or as one composed of substances allied to fats.
From this point of view all substances soluble in fats should enter
living cells, all substances not soluble in fats should be unable to
enter. That this generalised statement is untrue became apparent
when more dyes were investigated. Ruhland (1908-13) showed that
there are a number of dyes (e.g. methylene green and thionin) which
enter cells readily but which will not dissolve in cholesterol: similarly there are a number of ‘fat-soluble ’ dyes (cyanosin, Bengal rose)
which will not enter the living cell (see Table LXI).
372 PERMEABILITY OF THE CELL SURFACE
Similar exceptions to Overtoil’s rule were found by Hober (1909) and by Garnius (1912). Ruhland finally rejected Overton’s b}^otbesis and suggested that the essential factor which controls the rate of penetration of dyes is their coefficient of diffusion through a gelatinous matrix, which in turn depends upon the size of the molecules. Hober’s (1922) conclusions are somewhat different. He points
out that the ability of dyes to enter a plant cell is often less than its abilit}^ to enter an animal cell, and that this is particularly obvious when the fat-soluble dye is in the colloidal state: it is therefore possible that the failure to enter the plant cell may be due to the inability of a molecular aggregate to penetrate the cellulose wall If this conclusion is justified, one grave objection to Overton’s hypothesis disappears, but it is still necessary to account for the fact that methylene green and thionin (both insoluble in lipoids) will enter both animal and plant cells. Hertz (1922) showed that the entrance of these dyes into Opalina is unaffected by the presence of anaesthetics, whereas the entrance of fat-soluble dyes was inhibited. Hober, therefore, suggests that lipoid-soluble and nonlipoid-soluble dyes enter by a different route or by a different mechanism. Similarly Nierenstein (1920) found that an adequate correlation betw’een the ability of basic and acid djms to enter Paramecium and their partition coefficients between a fat-soluble substance and water only exists wffien the fat solvent (e.g. olive oil) contains both a base and an acid (e.g. diamylamine and oleic acid). So far as these facts can be summarised, they seem to suggest that most cell surfaces are permeable to those dyes which can either (i) dissolve in fats, or (ii) react with some constituent of the membrane, provided that in all cases the molecular aggregates of the dyes' are not beyond a certain maximum size (Hober and Kempner, 1908; Hober and Chassin, 1908).
It will be obvious that the ability of a cell to absorb a dye is not a measure of the ability of the dye to penetrate the plasma membrane. Unless a dye is accumulated by the cell it is by no means easy to determine whether it has entered the cell from a dilute solution or not; further, if a dye is accumulated in a non-diffusible state within the cell the effective concentration gradient across the plasma membrane will be maintained for a long time, whereas if the dye is not being so accumulated the gradient will fall rapidly as the dye enters. As a general rule, basic dyes are accumulated by cells, and in the case of plant cells Ruhland attributed this to a reaction with tannic
PERMEABILITY OF THE CELL SURFACE 373
acid. The recent work of Miss Irwin (1922-8) has done much to clear up the situation in respect to one particular dye — ^viz. cresyl blue. In the first place, the dye clearly accumulates in the sap of vegetable cells— such as of VcUonia or Nitella. Miss Irmn (1925 b) has shown that cresyl blue in the form of the free base diffuses readily in and out (1926 b) of the sap of Nitella, and can therefore readily pass through the plasma membrane. When the dye is present as a salt, however, the rate of diffusion is extremely slow. Since the sap (pH 5-5) is normally more acid than sea water (pH 8-0), free base from
Fig, 158. Curve showing the percentage of undissociated molecules of brilliant cresyl blue at different pH values. The ordinates represent the percentage and the abscissae the pH values. Symbol O represents the data from rates of penetration of the dye into Nitella. Symbol x represents the data from the distribution of the dye between chloroform and water. The curve as drawn represents the calculation made from the equation
a = "^rr/ j where k = fFrom Irwin, 1926.)
^ UH
1 +
the sea water passes into the cells and on reaching the vacuole is ionised and therefore removed from the sphere of outward diffusion. The amount of dye within the vacuole depends therefore on the concentration of free base in the surrounding sea water and on the pH of the sap (see fig. 158). The rate of penetration of the dye depends, however, on factors which affect the protoplasm of the cell — e.g. sodium ions (1926 d, 1927 a, h). The close parallel between the factors involved during the absorption of cresyl blue and those involved during the absorption of H 2 S or COg is obvious.
874 PERMEABILITY OF THE CELL SURFACE
If dyes are only capable of penetrating in the form of the free base, it follows that dyes which can only exist as salts (over the range of pH compatible with life) should not enter living cells A strongly basic dye of this type is methylene blue. From a spectroscopic analysis of the dye found in the sap of uninjured cells of Valonia Miss Irwin (1926 d) concludes that methylene blue does not accumulate as such, but only in the form of a less basic derivative trimethyl-thionin. This conclusion has, however, been criticised by M. M. Brooks (1927), who claims that methylene blue penetrates Valonia and Nitella as such.
•In a recent paper. Miss Irwin (1928 b) has suggested a mechanism which might account for the observed distribution of a dye between an external medium of sea water and the sap of a vegetable cell The apparatus consists of a horizontal glass tube with three vertical arms. To the left arm is added a solution of the dye in sea water To the central arm is added chloroform (representing the nonaqueous layer of the living cell) until it fills the horizontal portions and the lower part of each upright tube. Upon the chloroform in the right arm is poured the sap, artificial or natural, from the living vacuole of Valonia. Each phase is kept stirred at a constant rate. Using cresyl blue, azure blue, basic fuchsin, toluidine blue and similar dyes, the dye collects in the ‘vacuole’ phase just as in the normal cell. Similarly dyes which do not collect in the vacuole of the normal cell are not absorbed by the ‘sap’ phase of the model. It is interesting to note that some dyes which are readily soluble in chloroform, e.g. crystal violet, do not penetrate into the ‘sap’ phase. Miss Irwin concludes that the accumulation of a dye in the ‘sap’ phase depends on the two partition coefficients,
^ ^ concentration of dye in the non-aqueous phase concentration of dye in the external solution ' ’
_ concentration of dye i n the non-aqueous phase concentration of dye in the aqueous sap
high the dye rapidly accumulates in the non-aqueous phase (chloroform or protoplasm) and if is low the dye will rapidly diffuse from the non-aqueous layer into the sap phase. By replacing the protoplasmic layer of Valonia by chloroform, an equilibrium in respect ■^o dyes essentially similar to that of the normal cell can be obtained (Irwin, 1928 b). It would appear, however, that during the process of penetration into the interior of the cell, the dye must take
PERMEABILITY OF THE CELL SURFACE 375
part in a chemical change, otherwise it is difficult to account for the high temperature coefficient characteristic of the process (Irwin, 1925 a).
In other cases the absorption of dyes appears to be influenced by factors other than those controlling the degree of dissociation of the molecules. M. M. Brooks (1926) found that the rate of absorption of di-brom-phenol was markedly affected by light. Mond (1924) has recently reported a case of so-called 'irreciprocaU permeability of the gut wall to cyanin; how far this may prove to be explicable by Miss Irwin’s hypothesis remains obscure.
In drawing comparisons between these results and those obtained with animal cells, it is advisable to remember that a large aqueous vacuole is not present in animal cells, and that the accumulation of a dye by a vegetable cell is no indication that it will also accumulate in an animal cell, although it is of interest to note that various authors claim that intra-vitam dyes accumulate in ‘vacuoles ’ of the animal cell. It is, however, probable that the surface layer of the animal cell is a separate phase from the cell interior, and since the latter is miscible with water, the whole system is not so radically different to that of plant cells as might appear to be the case at first sight.
Methods of determining the permeability to solutes
In addition to the methods already described, the permeability of a cell to solutes can be determined by a variety of methods. These have been summarised by Stiles (1924) and by Jacobs (1924), If a cell is exposed to the solute in question, its passage into the cell can be determined by an analysis of the cell contents or of the surrounding medium. Thus Janse (1887) exposed Spirogyra cells to a solution of KNOg, and detected the passage of nitrates into the sap by expressing the latter into a solution of diphenylamine and observing the blue colour reaction. A similar method has been more recently employed by Osterhout (1922 Z?), who used the cells of Nitella and obtained characteristic crystals on expressing the sap into a solution of nitron in 10 per cent, acetic acid. Using the same material Irvin (1923) detected the passage of chlorine ions into the cells by testing the sap with silver nitrate. Miss Irwin made the significant observation that the rate of accumulation of chlorine in the sap wms not increased by increasing the concentration of chlorides in the external medium. Instead of employing chemical tests for intracellular com
876 PERMEABILITY OF THE CELL SURFACE
position, it is possible to make use of characteristic emission spectra:
in this way M. M. Brooks (1922) observed the penetration of lithium,
caesium and strontium into the cells of Valonia. As a rule, direct
chemical or physical analysis of cell contents is only satisfactory in the
case of large vegetable cells, although comparable methods can be
and have been employed in the case of small animal cells, e.g. red
blood-corpuscles (Kozawa, 1914).
The analysis of the external medium as opposed to that of the cell contents has been used as an estimate of permeability from time to time. Demoussy (1900) determined the rate at which potassium and calcium disappeared from a medium in contact with the tissues of wheat and maize. The uptake of hydrogen ions by plant tissues was estimated electrometrically by Stiles and Jorgensen (1915 a), and by animal cells by Gray (1920), who used both colorimetric and electrometric methods. The great objection to these methods lies in the fact that we have no direct knowledge that the substances in question actually penetrate as such into the interior of the cell — ^they may be adsorbed to the surface.
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Meyer, H. H. (1899). ‘ Zur Theorie der Alkoholnarkose. Welche Eigenschaft der Anaesthetica bedingt ihre narkotische Wirkung?’ Arch, exper. Path, u. Pharm.. 42, 109.
Michaelis, L., Ellsworth, R. McL. and Weech, A. A. (1926). ‘Studies on the permeability of membranes. II. Determination of ionic transfer numbers in membranes from concentration chains.’ Journ. Gen. Physiol. 10, 671.
Michaelis, L. and Perlzweig, W. A. (1926). ‘Studies on the permeability of membranes. I. Introduction and the diffusion of ions across the dried collodion membrane.’ Journ. Gen. Physiol. 10, 575.
Michaelis, L. and Weech, A. A. (1927). ‘Studies on the permeability of membranes. IV. Variations of transfer numbers with the dried coUodion membrane produced by the electric current.’ J ourn. Gen. Physiol .11,147.
Michaelis, L., Weech, A. A. and Yamatori, A. (1926). ‘Studies on the permeability of membranes. III. Electric transfer experiments with the dried collodion membrane.’ Journ. Gen. Physiol. 10, 685,
380 PERMEABILITY OF THE CELL SURFACE
Mond, R. (1924). ‘Untersuchungen an isoHerten Diinndarm des Frosches. Ein Beitrag zur Frage der gerichteten Permeabilitat und der einseitio-en Resistenz tierischer Membranen.’ P finger’s ArcMv^ 206, 172, ^
(1927). ‘Umkehr der Anionenpermeabilitat der roten Blutkorperehen
in eine elektive Durchlassigkeit fiir Kationen.’ Pfiiigefs Archiv^ 217, 618.
Nieren STEIN, E. (1920). ‘Ueber das Wesen der Vitalfarbung.’ Pflilgefs Archiv, 179, 233.
OsTEHHOUT, W. J. V. (1909). ‘On the penetration of inorganic salts into living protoplasm.’ Zeit. f. physik. Chem. 70, 408.
(1914). ‘Chemical dynamics of living protoplasm.’ Science, 39, S44.
- (1922 «). Injury, Recovery, and Death. (Philadelphia.)
(1922 5). ‘Direct and indirect determinations of permeability.’ Jourri.
Gen, Physiol. 4, 275.
(1925). ‘Is living protoplasm permeable to ions?’ Journ. Gen. Physiol.
8, 131.
OsTERHOUT, W. J. V. and Dorcas, M. J. (1925). ‘The penetration of COo into living protoplasm.’ Journ. Gen. Physiol. 9, 255.
Overton, E. (1895). ‘Uber die osmotischen Eigenschaften der lebenden Pflanzen und Tierzelle.’ Vjschr. naturf. Ges. Zurich, 40, 159.
(1899). ‘Uber die allgemeinen osmotischen Eigenschaften der Zelle,
ihre vermuthlichen Ursachen und ihre Bedeutung fiir die Physiologic.’ Vjschr. naturf. Ges. Zurich, 44, 88.
(1900). ‘Studien iiber die Aufnahme der Anilinfarben durch die lebende
Zelle.’ Jahrh.f. wiss. Bot. 34, 669.
Paul, J. H. and Sharpe, J. S. (1916). ‘Studies in calcium metabolism. I. The deposition of lime salts in the integument of decapod Crustacea.’ Journ. Physiol. 50, 183.
Philippson, M. (1913). ‘L’action physiologique des acides et leur solubilite dans les lipoides.’ Resumes Cong. Internat. Physiol
Groningen, 136.
V. Ris SE, O. (1926 a). ‘ tJber die Durchlassigkeit von Kollodium und Eiweissmembranen fiir einige Ampholyte. I. Der Einfluss der H' und OH' lonenkonzentration.’ PfliigeVs Archiv, 212, 375.
(19265). ‘fiber die D urchlassigkeit von Kollodium und Eiweissmembranen
fiir einige Amphohd:e. II. Quellungseinfliisse.’ PfiilgeVs Archiv, 213, 686.
Rohonyi, H. and Lorant, A. (1916). ‘Zur Kenntnis der Wirkung von COo und Oo auf die Elektrolytpermeabilitat der roten Blutkorperehen.’ Koiloidchem. Beihefte, 8, 377.
Ruhland, W. (1908). ‘Beitrage zur Kenntnis der Permeabihtat der Plasmahaut.’ Jahrb.f. wiss. Bot. 46, 1.
(1912 a). ‘Studien iiber die Aufnahme von Kolloiden durch die pflanz liche Plasmahaut.’ Jahrh.f. wiss. Bot. 51, 376.
(1912 5). ‘Die Plasmahaut als Ultrafilter bei der Kolloidaufnahme.’
Ber. deut. bot. Ges. 30, 139.
(1913). ‘Zur Kritik der Lipoid und der Ultrafiltertheorie der Plasma*
haut.’ Biochem. Zeit. ,54, 59.
(1914). ‘Weitere Beitrage zur Kolloidchemie und physikalischen
Chemie der Zelle.’ Jahrb.f. zoiss. Bot. 54, 391.
Shearer, C. (1919). ‘Studies on the action of electrolytes on bacteria. I. The action of monovalent and divalent salts on the conductivity of bacterial emulsions.’ Journ. Hygiene, 18, 337.
permeability of the cell surface 381
van Slyke, D. D. (1926). Factors affecting the Distribution of Electrolytes, Water, and Gases in the Animal Body. (Philadelphia.)
Ste WABTj G. N . (1899). ‘ The behaviour of the haemoglobin and electrol;^i;es of the coloured corpuscles when blood is laked.’ Journ. Physiol, 34, 211.
(1901). ‘A contribution to our knowledge of the action of saponin on
the blood corpuscles and pus corpuscles.’ Journ. Exp. Med. 6, 257.
-(1909). ‘The mechanism of haemolysis with special reference to the
relation of electrolytes to cells.’ Journ. Pharm. Exp. Therap. 1, 19. ^Stiles, W. (1924). Permeability. (London.)
Stiles, W. and Jorgensen, I. (1915 a). ‘Studies in permeability. I. The exosmosis of electrolytes as a criterion of antagonistic ion action.’ Ann. of Bot. 29, 349.
^ — (1915 b). ‘ Studies in permeability. II. The effect of temperature on the permeabihty of plant cells to the hydrogen ion.’ Ann. of Bot. 29, 611. Tinker, F. (1916). ‘The microscopic structure of semipermeable membranes and the part played by surface forces in osmosis.’ Proc. Roy. Soc. A, 92, 357.
(1917). ‘The relative properties of the copper ferrocyanide membrane.’
Proc. Roy. Soc. A, 93, 268.
Warburg, E. J. (1922). ‘ Studies on carbonic acid compoimds and hydrogen ion activities in blood and salt solutions.’ Biochem. Journ. 16, 153. Wertheimer, E. (1923 a). ‘Uber irreziproke Permeabilitat. I.’ Pflugefs Archiv, 199, 383.
(1923 b). ‘liber irreziproke Permeabilitat. II.’ Pflugefs Archiv, 200,
82.
(1923 c). ‘ Die irreziproke Permeabilitat von lonen und Farbstoffen. III.’
Pflugefs Archiv, 200, 354.
(192^3 d). ‘Der Salzeffekt an der lebenden Membran. IV.’ Pflugefs
Archiv, 201, 488.
(1923 e). ‘ Weitere Studien fiber die Permeabilitat lebender Membranen.
V. tiber die Krafte die die Wasserbewegung durch eine lebende Membran bedingen.’ Pflugefs Archiv, 201, 591.
(1924). ‘Weitere Studien liber die Permeabilitat lebender Membranen.
VI. tiber die Permeabilitat von Sauren u. Basen, Einfluss der Temperatur auf die Permeabilitat.’ Pflugefs Archiv, 203, 542.
ZoOND, A. (1927). ‘ The' interpretation of changes in electrical resistances accompanying the death of bacterial cells.’ Journ. Bact. 14, 279.
CHAPTEE FIFTEEN
The Nature of the Cell Surface
The barrier which prevents the free diffusion of solutes between
the interior of a living cell and its surrounding medium is clearly
located at or near the surface of the cell. Although we have no real
knowledge of its essential nature, it is customary to speak of this
barrier as though it were a definite morphological structure to which
the term plasma membrane can appropriately be applied. Material
conceptions of the plasma membrane have been put forward on
many occasions and frequent attempts have been made to manufacture membranes possessing properties comparable to those of the
surface of living cells. As already mentioned (p. 371 ), Overton and
others concluded that lipoid substances must be present in the plasma
membrane, since substances soluble in such media usually enter the
cell more rapidly than any others. This suggestion was supported by
the observation of Stewart ( 1909 ), who observed that when red
blood-corpuscles are killed by 12 per cent, formaldehyde they still
retain their impermeability to strong electrolytes : if, however, these
cells are exposed to ether, this impermeability is at once destroyed.
Similarly a substance such as saponin, which is a strong emulsifying
agent for fats, is a powerful cytolytic agent. Additional interest was
attached to the lipoid theory of the cell surface by the work of
Clowes ( 1916 ). It had previously been shown by Osterhout ( 1911 )
that the semipermeable properties of Laminaria cells are lost if the
cells are exposed to any solution not containing divalent metallic
ions, and that the loss of semipermeability is partially reversible on
the addition of calcium. Clowes ( 1916 ) showed that the properties
of an emulsion of olive oil and water are markedly altered by the
presence or absence of calcium ions. Thus an emulsion of olive oil
and water in alkaline NaCl yields an emulsion of oil drops in a continuous phase of water: on the addition of calcium, however, the
phases are reversed, and the system is converted into water drops
dispersed in a continuous phase of oil. If the cell surface is normaOy
characterised by a continuous oil phase, we can understand how it
THE NATURE OF THE CELL SURFACE 883
becomes instable in the absence of calcium. According to Gortner and Grendel (1925) the mammalian red blood-corpuscle is bounded by a bimolecular layer of fatty substances, but Mudd and Mudd (1925) have criticised this conclusion and incline to the view that proteins as well as lipoids must be present at the surface of these cells. The arguments for and against the fatty nature of the plasma membrane have been recently summarised by Gellhorn (1929) and by Steward (1929) ; the latter author rightly criticises the possibility of determining the nature of the cell surface by direct analyses of substances diffusing from the cell into cytolytic media as were attempted by Hansteen-Cranner (1922).
The most obvious difficulty, encountered by the conception of the plasma membrane as a continuous lipoid film, is the necessity of endowing it with an adequate permeability to water. How far this difficulty is as great as it appears to be at first sight is not clear. If the plasma membrane is extremely thin (see p. 361) — and is of the nature of a monomolecular layer — ^it might be permeable to water, whereas a thicker layer might not be permeable. That water can pass through a thin film of olive oil is suggested by the older observations of Quincke (1894, 1902) and Butschli (1894), who found that water was absorbed by olive oil which contained potassium oleate. A permeability to water on the part of a fatty film can of course be obtained if it be assumed, with Czapek (1910), that the film is not continuous but is in the form of a discontinuous emulsion in a water permeable phase. Unless, however, this latter phase be impermeable to electrolytes we are no better off than before and, as Nathansohn (1904 a and h) points out, lecithin in the dispersed state does not accelerate the passage of lipoid-soluble substances.
Within recent years the chief interest in the lipoid theory of the plasma membrane has centred on its application to the theory of bioelectric currents. If the protoplasmic surface is immiscible with Avater, it is possible to draw — as Beutner did — a fairly close parallel between electromotive forces at inanimate phase boundaries and those characteristic of living cells (see p. 393).
The possibility of a protein composition for the plasma membrane was first considered by Pfeffer (1900), and the suggestion was later supported by Robertson (1908) and by Lepeschkin (1910-11). It can hardly be doubted that the conclusions reached by these authors were hardly justified by the evidence available (see Blackman, 1912), but certain outstanding phenomena must be considered. Firstly, as
S84 THE NATURE OF THE CELL SURFACE
pointed out by Robertson, proteins readily form precipitation membranes (see p. 77): the trouble lies, however, in the fact that such membranes are usually readily permeable to strong electrolytes and in this respect exhibit few of the selective properties of the living cell surface. It is doubtless true, as pointed out by Lepeschkin, that semipermeability is suddenly lost when the proteins of the cell are coagulated by heat, but this does not prove that the plasma membrane is related to the proteins except in so far as it may lie in a protein matrix. It may be remembered that the instability of the plasma membrane in the absence of calcium ions (as analysed by Osterhout) can be explained by the dissolution of a protein matrix just as readily as by the dispersion of a lipoid emulsion (see p. 107). That the plasma membrane is not of a simple protein type is shown by the fact that it can and does possess definite osmotic properties. If proteins play any part in the mechanism of the plasma membrane, they must act as a matrix in the pores of which is deposited a film capable of supporting an osmotic pressure ; such a film might consist of calcium phosphate and be comparable to the films examined by Meigs (1915) and Lapicque (1907). Such membranes are, it is true, impermeable to many salts, but in other respects they are unsatisfactory. More recent work raises the possibility that if the pores of a protein membrane are small enough they could be blocked by a film of adsorbed molecules of the solute or even by a water film (see p, 351).
It must be admitted that all attempts to manufacture artificial membranes with the requisite properties have so far failed, but if Fricke’s estimate of the thickness of the plasma membrane (see p. 861) is of the right order of magnitude, all attempts to reproduce it artificially have been of a rough and ready nature. For a discussion of the various theories concerning the composition of the plasma membrane reference may be made to Hober (1922), Stiles (1924), and Gellhorn (1929). It is, however, worth noting that most, if not all the attempts to reproduce the properties of the cell surface, have tended to overlook the fundamental fact that the living cell is bounded by a surface or a membrane which is capable of generating energy or of transforming energy which is supplied to it in an appropriate form (see p. 21). To suggest that lipoids or proteins are responsible for the observed properties of this surface is equivalent to saying that these bodies are responsible for the properties of protoplasm as a whole. The fundamental problem in both cases is
885
THE NATURE OF THE CELL SURFACE
the same, viz. to discover the precise orientation of the constituent parts of the surface, and so discover how the latter can function as a dynamic unit. We may look upon the cell surface from two points of view. Firstly, we may regard it as endowed with life in the sense that it can derive a store of energy from oxidative and other changes, and use this energy for specific purposes. Alternatively, we may regard the surface membrane as a relatively inactive structure only capable of distributing energy when the latter is supplied to it in a particular form ; in this case we may hope to find a parallel to the plasma membrane within the realm of inanimate systems.
The cell surface as a living unit
It has been mentioned on more than one occasion that the resistance offered by the cell surface to the diffusion of molecules and ions is greatly decreased when the cell dies. Since this change is irreversible it is difficult to say how far the increased rate of diffusion is the direct result of a decline in the vital activities of the cell, or how far both these phenomena are affected independently by the factor responsible for death; the fact remains, however, that the normal properties of the cell surface are invariably lost after death. If we restrict our attention to unicellular systems any correlation between the ‘semipermeability’ of the surface and the metabolic activities of the whole cell is at present of a hypothetical nature, but if we are prepared to consider other types of living membranes a number of relevant facts are available.
If a solution of a crystalloid be separated from distilled water by means of a semipermeable membrane, water will diffuse into the solution, and if the solution be confined within an osmometer the process can be made to perform work by lifting a piston or in other ways. The energy for this work is originally present in the solution. If a membrane is interposed between two solutions of equal osmotic pressure, there is no transference of water from one side to the other and no work can be done by the system, since the potential is the same on both sides. In other words, whenever a solution becomes less concentrated it has the capacity of doing work, whenever it becomes concentrated work must be done on the solution. The performance of work implies that two sources of energy are available, one of which is at a higher potential than the other. When a living cell executes a change in the relative concentration of its internal fluids and that of its external environment, where does the requisite
G C
35
386 THE NATURE OF THE CELL SURFACE
energy come from? In inanimate systems no energy source is available if the potential on the two sides of a membrane is identically the same— so that if we interpose a membrane, of any description, between two identical solutions no differential transference of water or solutes can occur and no work can be done. Conversely if a membrane is interposed between two identical solutions and a transference of water or solute spontaneously occurs, the membrane itself must be supplying the requisite energy. We have therefore the possibility of determining whether or not the cell membrane is an active ‘ living ’ structure, in the sense that it is the seat of a supply of potential energy which can be so orientated as to do osmotic work. The evidence in respect to the transference of water has already been presented (see p. 343), and although the data are far from completed certainly looks as though, in some instances, the cell surface is able to effect a transfer of water against or in the absence of any osmotic gradient. When we consider the transfer of dissolved substances the data also incomplete, give the same conclusion. For example, both Cohnheim (1898, 1899) and Reid (1901) found that dissolved solutes can pass through the gut wall to solutions of identically the same or even stronger concentrations. The same phenomenon occurs in the kidney where substances are not excreted from the blood in accordance with the osmotic gradients, but according to whether the threshold value in the blood is exceeded or not. As far as one can see, the cells selectively absorb substances in such a way as to maintain their internal environment at a constant composition. The respiratory activity of the kidney is clearly associated with its ■ excretory activity (Barcroft and Straub, 1910), which looks as though the requisite energy for excretion were derived from chemical changes of an oxidative nature. Both in the gut and in the kidney the problem is complicated by the presence of hydrostatic forces at the surface of the blood vessels and it is conceivable that this energy might be utilised in some way , although it would not be available at normal cell surfaces. For this reason the experiments of Cohnheim are of peculiar interest. Cohnheim (1901) excised the gut of Holothuria and, filling it with sea water, suspended the preparation in a bath of sea wmter; he reported that after twenty-fomhours the fluid within the gut was absorbed by the cells and excreted to the outside medium. Obviously such a transference could not be effected by an inert membrane but must involve active work on the part of the cells. According to Cohnheim, anaesthetics caused a
387
THE NATURE OF THE CELL SURFACE
cessation in the secretion of sea water. An attempt by the author some years ago to confirm Cohnheim’s results led to a different interpretation of the facts. It is true that the gut of Holothuria nigra filled with sea water and immersed in sea water loses weight after some hours, but in all the cases observed no change in weight occurred as long as the gut was healthy and maintained its normal muscular tone. Loss of water appeared to run parallel to a loss of muscular tone and the latter rapidly leads to disintegration of the gut wall; it will be remembered that sea water is not normally in contact with the external wall of the gut and that Cohnheim’s experiments were therefore performed on tissue in an abnormal environment; the published work of Oomen (1926) confirms this view. It would be interesting to repeat these experiments using coelomic fluid instead of sea water.
Rather more adequate evidence of a vital activity on the part of cells which are engaged in the establishment of osmotic and electrolytic equilibria is provided by the work of Heidenhain (1891) and Reid (1902), both of whom observed the transference of water and solutes across a gut membrane having identical media on both sides. Further investigation of these facts is much to be desired, for if substantiated they cannot fail to clarify our conceptions of the mechanism whereby a cell comes into equilibrium wuth its external environment. As noted above, the great difficulty associated with such experiments is the fact that when a living membrane is exposed to the same solution on both sides, the conditions are highly abnormal, and the time factor becomes of very^ considerable importance; as will be shown later, it is not difficult to find inanimate membranes which will for a short time effect a transfer of water or ions from isopotential solutions. The essential point is •whether this occurs to a significant degree for a prolonged period. It will be remembered that both Maxwell (1913) and Adolph (1925) failed to obtain any transfer of water through a frog’s skin wffien both surfaces were bathed in Ringer.
It is, however, possible to attack the problem from another angle. We know that the cell surface separates a relatively concentrated solution from one which is more dilute without any apparent means of opposing the osmotic force. If it does this in the way in which have suggested^ viz. by setting free a store of chenoncal energy and converting it into such a form as will provide a force equal and opposite to the osmotic force, then it is likely that this store of
388 THE NATURE OF THE CELL SURFACE
energy will ultimately be associated with oxidative reactions. The greater the osmotic force the greater must be the opposing force and the greater the output of energy and the more intense the oxidative processes. We would therefore expect to find (i) that if the oxidative processes are upset salts should begin to leak out of the cell, (ii) that if the osmotic gradient on the two sides of the cell is increased or diminished the respiratory activity of the cell should exhibit corresponding changes. Data of this type are not at present available, blit if respiration and cell permeability are closely associated with each other it is surprising to think that it has not been recorded hitherto. The possible relationship between metabolic activity and cell permeability has recently been discussed by Straub (1929). The nearest approach to pertinent data is, however, provided by Lund (1926-8) and by Mond (1924-7). It is known that the E.M.F. across a frog’s skin depends on the nature of the ions with which the two surfaces are in contact — and is, to some extent, a measure of the ions which can or cannot diffuse from one side to the other. Lund has shown that the e.m.f. of the skin is markedly affected by changes in the oxygen tension of the medium (fig. 159), or by the presence of cyanides. Lund suggests that the bioelectric current is essentially a measure of differences in the intensity of metabolic activity at the two points examined (see fig. 160).
It will be noted that Lund’s experiments do not bear directly on the problem concerning the extent to which a cell can perform work to maintain an anomalous distribution of electrolytes between its interior and its external environment: on the other hand they indicate that the source of a p.d. across the cell membrane may be traced to the liberation of metabolites of an electrolytic nature. The only direct proof, that the maintenance of the normal distribution of electrolytes between a cell and its medium involves the performance of osmotic work, would be to show that any appropriate alteration in the electrolytic content of the external medium is reflected by a corresponding alteration in the metabolic activity of the cell.
Alternatively, some indication of the vital activities of the plasma membrane is available from the observation of Osterhout, Damon and Jacques (1927) on the p.d. across the protoplasmic film of Valonia cells (see p. 23). If a cell can exhibit for a prolonged period a constant and measurable p.d. across its membrane when the same solution is on both sides— then, as long as the cell obeys the second
RD.MtLUVOLTS
0 ^ COMaNTRATiOM
Fig. 159 . Diagram showing the reversible effect of different concentrations of oxygen on the magnitude of the electric polarity of two different frogs’ skins. Skin A has a greater inherent electric polarity than skin B. Shaded areas indicate concentration and duration of exposure to oxygen. Arrows indicate oxygen concentration at air saturation. (From Lund.)
390
THE NATURE OF THE CELL SURFACE
law of thermodynamics, the membrane must be generating energy
— and in so doing may be regarded as a living unit.
We may approach the problem from still another point of view. If an inanimate membrane is interposed between two solutions of unequal concentration then, whatever be the nature of the membrane, its final effect will be independent of the orientation of the former. Thus if a membrane has side A in contact with solution of concentration and side -B in contact with a similar solution of concentration C 2 , the final position of equilibrium in respect to the distribution of ions will be the same as when side A is in contact with solution Cg, and side B in contact with solution C^. If the membrane is fairly thick, or if ions only adjust themselves to new positions very slowly, the transition period before equilibrium is established may be different in the two cases, but the final equilibrium condition will
Fig. 160 . Diagram of a root tip illustrating electrical polarity due to differences in intensity of respiratory activity. C, root cap; D, region of active cell division; B, region of lower oxidative intensity, (From Lund.)
be the same — in other words there cannot exist a condition of irreciprocal permeability in which substances can move through the membrane more easily in one direction than in the other. It is claimed by various authors that irreciprocal permeability is a specific characteristic of living membranes. This has recently been upheld by Wertheimer (1923-5) using frog’s skin: he found that sugar, ions, and gases pass more readily in one direction than in another, although the path of easiest penetration varies for different types of substance. It is, however, very important to differentiate between true irreciprocal permeability and the apparent irreciprocity which is produced when the diffusing substance is removed from the sphere of action on one side of the membrane, as in the cases of carbon dioxide and cresyl blue investigated by Osterhout and by Miss Irwin respectively (see p. 373). Mond (1924) found that
391
the nature of the cell surface
the dye cyanosin accumulates rapidly iu the gut and does not readily pass out again — but how far this may possibly be due to a change in the degree of its ionisation is not quite clear.
It may be argued that evidence derived from the absorptive properties of the gut or surface skin may not be applicable to cells in general; whilst this is true^ it does not invalidate the general argument that the normal plasma membrane may be a generator of energy or be capable of exerting its effects by the absorption of energy which is stored in other parts of the cell. In this respect it is interesting to note that plant cells appear to vary in their ability to absorb electrolytes in accordance with the energy of incident light. M. M. Brooks (1926). Trondle (1910) reported similar data.
The absorption of salts by somatic cells seems clearly defined in the case of growing cells, for in such cases the percentage of ash does not fall with an increase in the size of the cells; it is possible that in such cases the mechanism of absorption is not closely related to the mechanism which is responsible for the equilibrium conditions during intergrowth periods.
It may be frankly admitted that the conception of the cell surface as an electrical accumulator, which is kept charged by metabolic activity, is not too clearly defined: there are, however, sufficient facts to merit serious attention, particularly in view of its theoretical importance and of the facts to be considered later.
Physical conceptions of the cell membrane
From a physical point of view we may ignore, to some extent, the chemical nature of the membrane and simply consider ho'w far any known physical system exhibits properties comparable to the surface of the cell. We may first consider the maintenance of electrolytic equilibrium between the inside of the cell and the normal external environment. We have seen that the concentration of potassium inside a Valonia cell or inside certain red blood-corpuscles is very much higher than that in the external solution. If such systems are in strict thermodynamical equilibrium, then the cell surface must be impermeable to potassium ions or the potassium must be in the unionised condition inside the cells. The latter possibility can be eliminated — since the high conductivity of the interior of the cell makes it very improbable that there is any significant amount of potassium in the unionised condition within the cell. The only alternative is that the cell must be absolutely
392 THE NATURE OF THE CELL SURFACE
impermeable to potassium ions. If the cell surface were very slightly permeable to both potassium and to chlorine, exosmosis must occur although it might occur very slowly. If the cell were slightly permeable to potassium ions and not to chlorine, then, the ratio of potassium to sodium in the cell would sooner or later become the same as that in the external medium. The essential feature in all such systems is that the final position of equilibrium is independent of the rate at which ions diffuse through the membrane. We have seen (in the discussion of the equilibrium distribution of COg or fives between Valonia and its external medium), that the cell must possess a mechanism whereby the substances which diffuse inwards are prevented from diffusing outwards, or in other words, that the cell acts as a trap from which there is no escape. In the case of weak acids and dyes, the substances on entering the cell are converted into a form in which they are unable to diffuse across the membrane in an outward direction: in such cases the substances enter in the undissociated state and are prevented from out^vard diffusion by electrolytic dissociation; but this explanation is not available for metallic salts. It is important to bear in mind that the cell surface appears to establish a specific equilibrium in respect to individual types of ions and maintains these specific equilibria as long as the cell is alive. When a cell increases in size the different ions enter the cell in just the right proportions, although these proportions differ for different types of cell, e.g. sodium and potassium in Valonia BXidi H alley stis. Phenomena of this kind are so far unknown in inanimate systems, but find their parallel in the activities of the kidney. Only two alternatives seem possible — either (1) the nongrowing cell is absolutely impermeable to cations, but wdien growth is taking place selective absorption occurs, or (2) the cell is normally permeable and continuous selective absorption is taking place. In either case we require an explanation of selective absorption. It will be remembered that in the case of the red blood-corpuscle, the theory of van Slyke (1926) postulates a complete impermeability to potassium.
Instead of considering the equilibrium condition between the concentration of ions inside the cell and in the external medium, we may consider the evidence to be derived from bioelectric phenomena, since the orientation and magnitude of the observed potentials must ultimately depend on a heterogeneous distribution of cations or anions. This point of view is fraught with considerable difficulty and
THE NATURE OF THE CELL SURFACE
danger to the biologist and more properly belongs, at the moment,
to the realm of the physical chemist; it is, however, desirable to see
the type of evidence at our disposal. It will be recalled that two
distinct conceptions of the cell surface are associated with the names
of Overton and of Pfeffer respectively.
Overton’s results led him to the conclusion that the cell surface is essentially immiscible with water, and is of a fatty nature. It has already been mentioned (p. 2'2) that, under certain well-defined conditions, an electric current can be made to flow between two unlike aqueous solutions when these are separated by an oil phase of suitable composition. Further, the differences in potential between the two sides of such an oil phase are comparable in magnitude to those observed in living cells. Phase-boundary potentials of this type have already been considered in reference to protoplasmic structure (see p. 24), but for a study of cell permeability a more detailed analysis is desirable, even at the expense of some repetition of the facts.
For a full account of the electrical properties of inanimate membranes
and surfaces the monograph of Michaelis (1926) should be consulted; the
following description of a typical phase-boundary system is derived from
this source.
If we start with two liquids immiscible with each other but each capable of containing a common ion, the junction of the two solutions will be the seat of a phase boundary potential. If we connect the two solutions by a metallic wire as an external circuit, no current will flow because the
two solutions are in strict chemical equilibrium. The potential difference
will simply depend on the ratio of the solubility of the individual type of
ion in the two phases : since this ratio is fixed, no current can flow when
the two solutions form a circuit. On
the other hand the bounding surface
can act as an electrode reversible for
the common ion. If therefore we
arrange a suitable chain (see fig. 161),
composed of two aqueous phases
separated by a non- aqueous phase, a current will flow through the system
when part of a suitable circuit because the potential at A is not the same as at B, and there is no equilibrium in respect to this ion within the oil phase itself. Each phase boundary {A and B) will in fact act as a reversible electrode in respect to any ion which is common to all the liquid
phases present. The maximum e.m.f. will be RTln -h w^here K
depends on the nature of the ion. The direction of the current will depend upon the nature of the ion common to all phases. Thus, in the following
394
THE NATURE OF THE CELL SURFACE
system, used by Beutner (see fig. 161 ), both the aqueous phases and the
oil phase are capable of containing sodium ions Cj> Cg:
Water + NaCl Oil + salicylic acid Water + NaCl
Cx 0,
As soon as the sodium chloride solutions come into contact with the oil, a trace of NaCl passes from the water into the oil and a trace of salicylic acid into the aqueous phases. In the oil phase double decomposition can take place,
NaCl + salicylic acid := Na salicylate + HCl;
whereas in the aqueous phase this does not occur owing to the very low ionisation of salicylic acid. Hence, in the oil phase there are salicylate ions, Na' and H* ; but the distribution of these ions in the oil is not uniform, for each side of the oil phase is in equilibrium with a different concentration of sodium ions in the adjacent aqueous phase. Under such conditions the concentration of sodium ions at the interface between the oil and the more concentrated NaCl is greater than at the other interface and the former interface is consequently electropositive. Alternatively, systems having chlorine instead of sodium as a common ion, yield e.m.f.’s in which the more concentrated aqueous phase is electronegative to the more dilute phase.
Aqueous
phase (1)
Oil
Aqueous phase (2)
Na- (Cl)
Cl' (Cl)
Aniline ions i
cr(c/) cr(Co')
Na- (C,)
Cl' (Cl)
If a phase boundary is to exhibit an e.m.p., it is essential that the
non-aqueous phase should have an affinity for anions greater or less
than that for cations: otherwise the phase boundary potential is
zero. The application of these principles to the elucidation of bioelectric phenomena was first made by Beutner ( 1913 , 1920 ), see
p. 22. If the cell surface is the seat of a phase boundary potential,
then, on interposing a cell or tissue between two solutions of an
electrolyte in unequal concentrations, a galvanic current should fiow
between the two solutions when the circuit is completed:
Solution 1 I Cell | Solution 2
Using the uninjured surface of an apple, Beutner obtained welldefined E.M.E.’s whose magnitude approached the maximal value characteristic of the oil/water systems previously investigated; in each case the dilute soltition was electro-positive (see Table LXII).
THE NATURE OF THE CELL SURFACE 395
Further experiments indicated, however, that the living system is more complicated than the simplest types of phase-boundary systems. When an apple was subjected to superficial injury and both the injured and uninjured surfaces were in contact with Jf/50 KCl, an e.m.f. of approximately 40 millivolts was observed — this being the normal current of injury. When, however, the amount of tissue between the aqueous phases was decreased the e.m.f. fell rapidly to 10 millivolts. This result can only be explained by assuming that there is a difference between the outer and inner layers of the apple tissue and that when this heterogeneity is reduced, by removing the peripheral layers, so the e.m.f. of the system declines; it will be remembered that in a phase-boundary system the sine qua non for an e.m.f. is a heterogeneous distribution
Table LXII
E.M.F.
M/IO NaCI and iU/10 NaCl
0
M/10 „ „ M/50
0-029-0*024 volts
M/50 „ „ M/250
0-042-0-036 „
M/250 „ „ M/1250 „
0-041-0-038 „
of ions throughout the non-aqueous medium. As pointed out by
Michaelis (1926) the apple system represents a chain comparable to
1.
2* !
3.
1 4.
Nitrobenzene
Nitrobenzene
Salt solution
Salt solution
poor in
rich in
picric acid
picric acid
Within recent years the biological application of phase-boundary potentials has been developed by Osterhout, some of whose results have already been considered. As mentioned in Chapter III, Osterhout has demonstrated the presence of a persistent e.m.f. in the system,
Valonia sap | Protoplasm ] Valonia sap,
and has pointed out that if we assume the e.m.f. to be that of a phase-boundary system, then protoplasm must represent a heterogeneous system in respect to an ion common to the sap and the protoplasm. It is clear, however, that any system of this nature cannot be in strict equilibrium if a current is flowing spontaneously through an external circuit; in some manner the membrane must
896
THE NATURE OF THE CELL SURFACE
be capable of doing work. If the observed e.m.f. is maintained for
long periods in a steady state there must be a supply of free energy
available within the membrane — and in this respect we must look
upon the membrane as an accumulator — or in other words as a
living system. On the other hand, if the e.m.f. is of a transitory
nature, it is quite possible that the observed potential differences
are of a purely physical nature and only exist during the period of
adjustment to a new equilibrium condition where the e.m.e. of the
system is zero ; until the concentrations of ions at the two interfaces
have become equal to each other there will be an e.m.f. It must be
remembered, however, that the cell surface is extremely thin and that
the total amount of potential energy stored in the form of heterogeneously distributed ions is probably very small.
Beutner’s conclusions have not been uncriticised, and to some extent they lost part of their significance when Michaelis and Fujita (1925 a) showed that it is improbable that the living tissues of the apple are responsible for the observed e.m.f.’s. The conception of phase-boundary potentials is, however, valuable not only as an indication of the true state of the protoplasmic/aqueous solution interface, but because it is essentially concerned with a system in which one type of ion (anion or cation) is unable to pass through the membrane. For example, in the system
Aqueous solution Oil -h acid Aqueous solution
C, C,
there will be no leakage of ions through the oil phase as long as no electric circuit is established, and as we have seen this state of absolute impermeability is characteristic of the living cell.
Beutner’s conception of protoplasm as a water immiscible phase was, however, criticised by Rohonyi ( 1914 , 1922 ), who pointed out that the essential feature of the oil/water chains does not lie in the immiscibility of the two adjacent phases, but in the fact that only one type of ion — cation or anion — ^is able to react or be absorbed by the membrane. Membranes possessing this characteristic are not restricted to oils ; they may consist of precipitation membranes of the copper ferrocyanide type investigated many years ago by Pfeffer.
Such systems were also examined by Beutner (Michaelis, 1926 , p. 215 ). If a gelatin cup be filled with a solution of potassium ferrocyanide and immersed in a solution of copper sulphate, a current will flow through an external circuit between the sulphate and the
397
the nature of the cell surface
ferrocyanide. The copper solution is positive and the e.m.f. is approximately 100 millivolts. If KCl be added to the copper sulphate solution the e.m.f. is changed, whereas it is independent of the concentration of the copper sulphate. The magnitude of the change effected by different concentrations of KCl in the system is such as to indicate that the membrane is behaving as though it were able to absorb potassium ions but not chlorine ions, just, as is the case with an oil phase containing an organic acid. Whether we look on the cell surface as a water immiscible fluid or as a precipitation membrane is therefore immaterial, as long as they both show the same differential attraction for cations as opposed to anions. The real difficulty arises in that copper ferrocyanide membranes are permeable to many types of substances to which the cell is not.
Within recent years much attention has been paid by physicochemists to the properties of protein membranes at various degrees of departure from their isoelectric point. Many such membi’anes undoubtedly exhibit a, differential permeability to cations and anions — and the degree of this difference varies with the pH of the membrane. In this respect the work of Mond and Hoffmann (1928 a and h) and others may be consulted. It must be remembered, however, that all known protein membranes have a much higher capacity for conducting electricity than do copper ferrocyanide membi'anes, oil films, or the surfaces of living cells. In other words although protein membranes may show a marked difference in respect to their permeability to anions or cations, yet unless the pores in the membrane are extremely small both these types of ion diffuse through the membrane to a very significant extent, and this process of diffusion goes on whether the system is part of an electric circuit or not. In the case of living cells and copper ferrocyanide membranes on the other hand, the leakage of salts to distilled water is very small, although the observed E.M.F. ’s may be the same for all these systems. This point is of real significance when we remember that the membrane must not only be the seat of an e.m.f., but must also account for the permanent maintenance of different concentrations of molecules and ions on its two sides.
Until recent years the intensity and persistence of the bioelectric current of injury seemed to eliminate the possibility of attributing these phenomena to the diffusion potentials investigated by Osti^vald and others. Michaelis (1926) has, however, revived the conception
398 THE NATURE OF THE CELL SURFACE
of diffusion potentials in a modified form. If we interpose between two solutions of KCI {N/10 and N/lOO) a perfectly inert membrane, the initial e.m.f. ought to be 0*4 millivolts, this low value being due to the small difference between the migration velocity of potassium ions (64*67) and chlorine ions (65*44). Michaelis found, however, that if a dried collodion membrane is interposed between two such solutions much higher e.m.f.’s are observed. To account for this fact it is assumed that the migration velocity of ions within membranes having very small pores is markedly different to their velocity in water, and that the velocities of different ions are affected by the membrane to a different extent. Thus in an extreme case the velocity of migration of the anion may become zero and the e.m.f. between two solutions of concentrations 10:1 will become approximately 57 millivolts; the system will resemble a diphasic system where the non-aqueous phase reacts only with cations. The essential character of Michaelis’ theory lies in the possibility of having an infinite variety of conditions between a normal diffusion potential on the one hand (when the relative velocity of migration of different ions is the same as in water) and a maximum value (when the velocity of the anions or cations is reduced to zero) on the other. In the case of phase-boundary potentials (for all dilute solutions) the anions play no part — and the only factor which need be considered is the distribution of the cations within the non-aqueous phase. How far the two theories are strictly alternative to one another or mutually exclusive remains to be seen. It would, however, be interesting to know something of the properties of an aqueous-oil-aqueous system in which the oil contains both a base and an acid radicle which are insoluble in water — ^for it will be remembered that Nierenstein found that such a system acts reversibly to both acid and basic dyes.
If we look upon the current of injury as equivalent to a phaseboundary current or as due to a specialised type of diffusion potential, we undoubtedly gain some insight into one aspect of biological activity, but we are still a long way from understanding the fundamental nature of the cell surface. The facts must be considered as a whole, and it is perhaps useful to summarise from a biological point of view the main requirements of any theory of cell permeability which is based on the electrical properties of the surface membranes. Firstly, the membrane has an exceedingly high resistance to electric currents which are not of a high frequency of alternation. Secondly, it separates two fluids which differ from each
399
THE NATURE OF THE CELL SURFACE
other in two respects— one is more concentrated in electrolytes than the other, and the relative concentrations of any given ion in the system may be substantially different on the two" sides of the membrane. Thirdly, the membrane is the seat of a potential, the magnitude of which can only be accounted for on the assumption that the velocity of specific cations through the membrane is relatively very great in comparison with the velocity of their associated anions.
At present no known inanimate system has these properties : at the same time there is no sharp division of theory involved by the alternative suggestion of the plasma membrane as a ‘living’ unit. Fundamentally the biological structure with its specific properties will no doubt conform to a physico-chemical mechanism — even if it involves a negation of the second law of thermodynamics — the only point of issue at the moment is the source of the energy which is responsible for the maintenance of osmotic equilibria in the cell and of the mechanism whereby this energy is orientated and used in the manner requisite for life. In other words the plasma membrane is part of a dynamic system whose machinery is of a type not yet demonstrable outside the living cell.
The rdle of the Donnan equilibrium in cell physiology
The anomalous distribution of ions which is usually associated Avith the name of Donnan has played a considerable part in modern theories of cell permeability.
If on one side (1) of a membrane there be a salt NaR which is wholly or partially ionised, and on the other side (2) there be another salt (NaCl) with a common ion, then if the membrane is impermeable to the unionised salt NaR and to the ion R', but permeable to the molecules and derivative ions of sodium chloride, the system will come into equilibrium when the product of the concentrations of diffusible ions on the two sides of the membrane is the same, i.e. w'hen [Na]i[Cl]i = [Na] 2 [Cl ]2 = fc [NaCl], because the concentration of undissociated sodium chloride must be the same on the two sides. Since, however, [Na], = [ClJj,
[NaMCl], = [Cl]|, and since [Na]i = [R] + [Cl]i,
([R] + [CID [Cy = [Cl]|,
in other words, the concentration of chlorine ions and therefor^jrf sodium ions on side (1) must be less than on side (2).
400 THE NATURE OF THE CELL SURFACE
Assuming complete dissociation of NaR and NaCI, and equal volumes of solution on the two sides of the membrane, and if is the initial concentration of NaR and the initial concentration of NaCl, the equilibrium distribution can be defined by the following diagram in which os is the amount of Na* or Ch which has moved across the membrane :
I li
Na*
R'
cr
Na
cr
Cl
X
X
C 2 - 03
(Cl 4- cc) as = (C 2 - aj)\
Co - Cl 4- C 2
^ c, •
Taking arbitrary values of and Ci we get the following series of equilibria.
Table LXIII
Initial concentration of NaR
Initial concentration of NaCl
Ratio of ^
X
— distribution of NaCl between II and I
0-01
10
101
0-1
10
1*1
10
10
2-0
10
01
11-0
1-0
0-01
99-0
If the concentration of the ions R' is high compared to that of the
diffusible ions on the other side of the membrane, the membrane
will appear to be impermeable to NaCl.
It will be noted that there is a difference in chlorine concentration between the two sides of the membrane and consequently if chlorine electrodes are in contact with the two solutions they will be at a different potential. No current, however, can be produced by such a system, since it is in a state of true equilibrium, and consequently Donnan equilibria cannot be responsible for the electromotive properties of living cells. It is, nevertheless, important to decide how far such systems can account for the anomalous distribution of electrolytes between the cell and its external medium. Except in the case of secretory cells, the colloidal substances within a cell are not free to diffuse into the surrounding medium even if the cell be dead (see
401
the nature of the cell surface
p. 385). As long as there are within the cells proteins or other electrolytes of high molecular weight there will always be a Donnan efiect if the cell is immersed in an aqueous medium. At the same time this effect can only affect the final equilibrium in such a way as to keep the concentration of freely diffusible ions inside the cell at a lower level than their concentration in the external medium; the cells of most fresh-water organisms exhibit precisely the opposite phenomenon, for the concentration of freely diffusible electrolytes inside the cell is greater than that in the external environment.*^ In order that a Donnan equilibrium should be sufficiently powerful to account for the distribution of electrol>i:es within such cells, it is essential to postulate that the cell surface shall also be impermeable to other ions (e.g. potassium) in addition to those characteristic of protein and other substances of high molecular weight. An example of this type has already been mentioned in connection with the osmotic properties of the red blood-corpuscles (van Slyke, 1926). It will be noted, however, that although such postulates have their uses, we are still faced with the problem of how the potassium got into the cell in the first instance.
Functional significance of loenneahiUUf
From time to time a number of cases have been quoted which suggest that marked changes in permeability occur during the life of a cell and that these changes are associated with specific changes in normal activity. Examples of this type will be found in the text-books of Bayliss (1924) and R. S. Lillie (1923). How far some of the evidence is free from criticism is doubtful. It may be admitted that bioelectric phenomena are, in themselves, definite evidence to show that a redistribution of ions has occurred at the cell surface, but it is still uncertain how far the mechanism responsible for this redistribution is also involved in the maintenance of the equilibrium between the electrolytes in the interior of the cell and those in the external medium. R. S. Lillie (1909), Bernstein (1912), and others have urged the possibility that the essential act of cell stimulation iiivoh’^es a localised and transitory increase in permeability to ions. A direct test of this hypothesis was attempted by McClendon (1912, 1929), who observed an increase in the electrical conductivity of a tetanised muscle which was accompanied by an exosmosis of electrolytes from the fibres. The relationship which exists between a contracting muscle and diffusible ions has also been investigated by Mitchell and
402 THE NATURE OF THE CELL SURFACE
Wilson (1921), who found that when frog’s muscles are stimulated to contract under conditions which do not involve irreversible stages of faticjue, the cells lose no more potassium than is attributable to a potassium-free medium; on the other hand, it is only during contraction that a muscle will absorb rubidium or caesium. The interpretation of these facts is not easy, but they indicate that the act of contraction alters in some way the diffusibility of electrolytic ions. Parallel to McClendon’s results with excited muscle fibres are the observations of Blackman and Paine (1918) on the exosmosis from the pulvinus of Mimosoi during stimulation.
In accordance %vith a generalised conception of cell stimulation R S LUlie suggested that the act of fertilisation, like the act of stimulating a nerve, involved a temporary increase in the permeability of the cell surface to ions. In 1910 McClendon showed that a dense suspension of the eggs of sea urchins conducts electricity more readily after fertilisation and this fact was confirmed by Gray (1916). In view of the results obtained by the use of more modern methods, these conclusions must be accepted with some caution. Cole (1928), using very high frequency currents, was unable to detect any measurable increase in the internal conductivity of Arbacia eggs after fertilisation, although the effect of fertilisation seemed to stabilise the resistance at a level about three times that of normal sea water. Other attempts to associate fertilisation with a change in surface permeability were made by Bachman and Runnstrom (1912), who used the eggs of amphibia. Attempts by the author to detect such changes in fish eggs failed (Gray, 1920).
One of the clearest cases of altered permeability during the normal life of the cell is that described by R. S. Lillie (1916) for the diffusion of water into sea urchin eggs before and after fertilisation. Water passes into the eggs of Arbacia from hypotonic sea water considerably more rapidly after fertilisation than before; since the act of fertilisation profoundly alters the physical properties of the cortex of the egg an altered permeability is perhaps not surprising.
For the relationship between the inferred changes in permeability which accompany stimulation, reference may be made to Keith Lucas (1910), Hill (1910), and R. S. Lillie (1923).
It is by no means easy to co-ordinate the facts which bear on the structure and properties of the cell surface, and it is equally difficu t to reach a definite standpoint from which to review our present knowledge. The problems involved are, however, of fundamenta
408
THE NATUHE OF THE CELL SURFACE
importance. Until we know the factors which control the interchange of substances between a cell and its environment, we cannot hope to form an adequate conception of the way in which an organism will respond to a change in its external environment, and until the true nature of the bioelectric current is established, our knowledge of protoplasmic transmission must remain obscure. It is perhaps unfortunate that so much attention has been focussed on the cells of the higher vertebrates, for valuable data might ^vell be derived from a study of the cells of those animals whose internal fluids are known to change in response to changes in environment ; in most invertebrates the osmotic pressure of the internal fluids, unlike those of higher vertebrates, changes in sympathy with changes in the external medium. Similarly, the osmotic pressure inside the cells of moulds often bears a definite relationship to that of their medium, and if the cells of a salmon are permeable to \vater, it is curious to find that the animal can plunge from fresh water to sea water and vice versa without any obvious change in the volume of its cells or in the freezing point of its blood.
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