A text-book of experimental cytology (1931) 9
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Gray J. A text-book of experimental cytology. (1931) Cambridge University Press, London.
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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 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. exceedingly 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
Fig. 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 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 division.
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 observations 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.
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 evidence 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, but 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 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
Fig. 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.
reason why 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
Fig. 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 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 above 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.
Fig. 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 can each of these spherical regions be correlated with the regions occupied by each of the two mitotic asters?
The role 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 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 concentration 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
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.
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.
The 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.
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 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 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 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.
Fig. 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 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, 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
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 protoplasm, two semisolid masses growing at the expense of the more Jkid portions of the cytoplasm’ (Chambers, 1919, p. 52).
By means 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 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-.
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.
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 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 consumption 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.
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.)
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.
From the evidence available ve naay draw one of two conclusions. Either the process of cleavage does not involve redistributions of energy 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 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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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 cvcle.’ Amer. Journ. Physiol, 61, 505,
Kvthabinek, L. (1901). ‘Ueber die bedingte Unabhangigkeit der Ent* wicklung des polar differenzierten Eies von Schwerkraft.’ Arch. Eniiv. Mech. 12, 597,
KOKSCHELT, E. (1888). ‘Zur Bildung des mittleren Keimblatts bei den Echinodermen.’ Zoolog, Jahrb. Anat. Hefte, 3, 653.
Lambert, R. A. and Hanes, F. N. (1913). ‘Beobachtungen an Gewebskulturen in vitro.’ Virchow's Archiv, 211, S9.
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.
.(1926). ‘The effect of cell division on the shape and size of hexagonal
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(1928). ‘The correlation between cell division and the shapes and size
of prismatic cells in the epidermis of Cucumis. Anat. Record, 38, oil.
Lillie, F. R. (1895). ‘The embryology of the Unionidae.’ Journ. Morph.
10 , 1 .
(1901). ‘The organisation of the egg of Unio, based on a study of its
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Lyon, E. P. (1902). ‘ Effects of potassium cyanide and of lack of oxygen upon the fertilized eggs and the embryos of the sea-urchin ( Arbacia punctiilatn).' Amer. Journ. Physiol. 7, 56.
(1904 «). ‘Rhythms of CO^ production during cleavage.’ Science, 19.
350.
(1904 b), ‘Rhythms of susceptibility and of carbon dioxide production
in cleavage.’ Amer. Journ. Physiol, 11, 52.
McClendon, J. F. (1912). ‘A note on the dynamics of cell division. A reply to Robertson.’ Arch. f. Entw. Mech. 34, 263.
(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.
Meyerhof, O. (1911). ‘Untersuchungen iiber die Warmetonung der vitalen Oxydationsvorgange im Seeigelei. I— III.’ Biockem. Zeit. So, 2 46.
Morgan, T. H. (1893). ‘Experimental studies on echinoderm eggs.' Anat. Anz. 9,141.
(1896). ‘The production of artificial astrospheres.’ Arch.f. Entw. Mech,
3, 339.
(1899). ‘The action of salt-solutions on the fertilised and unfertilised
eggs of Arbacia.^ Arch. f. Entw. Mech. 8, 448.
(1900). ‘Further studies on the action of salt-solutions and other agents
on the eggs of Arbacia.^ Arch. f. Entw. Mech. 10, 489.
(1910). ‘ The effects of altering the position of the cleavage planes in eggs
with precocious specification,’ Arch. f.. Entw. Meek. 29, 205.
246
CELL DIVISION
Morgan', T. H. and Boring, A. (1903). ‘The relation of the first plane of cleavage and the orescent to the meridian plane of the embrj'o of the frog.’ Arch.f^Ent-Ji-. Mech. 16, 6S0.
Morgan, T. H. and Tyler, A. (1930). ‘The point of entrance of the spermatozoon in relation to the orientation of the emhryo in eggs with spiral cleava 2 e.‘ Biol. Bull. 58, -59.
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(1913). -Further explanatorj' remarks concerning the chemical mechanics of cell-division.’ .-irch.f. Entw. Mech. 35, 692.
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4 - 9 . -j'j'S,
Rorx, W. (1SS5). 'Beitrage zur Ent%vickliingsmechamk. III. Ueber die Bestinimung der Hauptricbtungen des Froschembryo im Ei und iiber die erste Teilimg des Froscheies.’ Breslau drztl. Zeit.
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(1914). ‘Beitrage zur Physiologie der Zelle insbesondere iiber die
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CELL DIVISION
247
Wii-soNj E. B. (1892). ‘The cell lineage of Nereis. A contribution to the cytogeny of the annelid body.’ Journ. Morph. 6, 361.
(1901 a). ‘Experimental studies in c:yi:olog>^ I. A c>i:oiogical studv
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(1901 b). ‘Experimental studies in cytology. II. Some phenomena of
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(1898 fl)- ‘Experimentelle Untersuehungen liber die Zeliteiiung. I. Die
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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 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.
Fig. 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 minimal 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 which would be 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 way 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
Fig. 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.
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 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 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 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 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 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).
References
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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 ^
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