Talk:Waddington1956 13

From Embryology


1. Overall growth

In everyday usage the word ‘growth’ is used to mean any type of increase in size. This is obviously one of the important phenomena in embryonic development and requires discussion. There have been two ways of approaching the problem; one is content to accept the everyday meaning of the word and to study the increases which take place in whole embryos or in their parts; the other has attempted to start from some more precisely defined process of growth and to set up general norms from which the facts as they appear in the development of particular animals can be deduced as special consequences. This second attempt has not as yet proved very successful but it will be easier to exhibit the complexity of the whole situation if we start by discussing it (General Reviews: Needham 1931, Medawar 1945).

If we wish to consider a precisely defined process of growth we shall have to find some way of limiting the concept so that it is confined to the increase in size of something which retains a certain similarity to itself. Size may increase merely by the imbibition of water or by the laying down of relatively inert material such as shell, bone, cartilage, etc., and such processes obviously differ in kind from the increase in amount of the living material itself. Various definitions have been offered with the purpose of excluding them from the concept of growth as that is required for a precise theory. Gray (1931) speaks of growth as “essentially concerned with the formation of new living material’. Medawar (1941) states that ‘what results from biological growth is itself typically capable of growing’. Weiss (1949) gives a more formal definition; growth is ‘the increase in that part of the molecular population of an organic system which is synthesised within that system’, and he further amplifies this, pointing out that it means ‘the multiplication of that part of the molecular population capable of further continued reproduction’. This puts its finger on the important point; if we are trying to formulate a precise concept of growth we must confine it to the increase in the amount of the system which is capable of growing. The main general problem which then requires study is this—at what rate does this increase take place and how does the rate change as time passes?

The simplest possible situation would be one in which the rate of multiplication per unit mass remained constant. We could formulate this


mathematically by the equation — a = k constant (where w is the weight 1

or mass of the system). This, of course, leads to the absolute size increasing

ever faster and faster, at an exponential rate. The equation is solved to give w = wre" or log w = log wo + kt

when 1 is the initial size and k is a constant.

It is impossible to find a naturally occurring biological system which behaves so simply, and it is difficult to make one experimentally, though it can be done. Ifa small population of yeast cells, or bacteria, is inoculated into a large mass of nutrient medium, allowed to grow for a time, and a new inoculum transferred to fresh medium after a fairly short period, the growth rate per unit mass may be kept constant indefinitely. The essential points are that neither lack of nutrient nor the presence of harmful excreta are allowed to inhibit the system. If frequent transfers are not made, one or other or both these are certain to occur, and the rate of growth will slacken, till the growing mass becomes stationary and eventually begins to decline when the death-rate of cells overtakes the rate of increase. Samples taken from such declining cultures usually take a little time to get going when transferred to fresh medium, so that in the ‘typical’ growth curve of a colony of cells (yeast, bacteria, tissue-cultures and the like) the logarithm of size when plotted against time, is not a straight line, but has the form shown in Fig. 13.1.



FIGURE 13.1 Typical growth curve ofa population of isolated cells (e.g. yeast cells, bacteria, etc.). If the population starts with a group of cells taken from a non-growing colony, there is first a ‘lag phase’ (1) then a phase of exponential growth (2) in which the growth rate per unit mass is constant, then a phase of retardation (3) when the medium is becoming exhausted, and finally a regression phase (4) when the medium can no longer support the population. GROWTH 281

The growth curve of a developing animal has a somewhat similar form; although there is no definite lag before growth commences, the curve relating mass to time is sigmoid or roughly S-shaped. It was Minot, at about the beginning of the century and following him Brody, who particularly pointed out that it would be more profitable to consider


the so-called ‘specific growth rate’ (i.e. growth rate per unit mass — Te w

which is the same as a - **) rather than the simple growth rate (dw/dt)

(Fig. 13.2). As we have just seen, it is only in exceptional circumstances that this can be expected to be constant. Many formulae have been advanced, on a variety of grounds, in an attempt to produce a theoretical scheme which fits the facts better.

Ww ogW

(a) d)

ew dlogW e at - (b) (e) t E t + ew d?hbgW “ot dt? t - (©) (f) FIGURE 13.2

Various ‘growth functions’. The three curves in the left side are concerned with the absolute growth. In a weight is plotted against time to give the curve of growth (a Gompertz equation is assumed); in b growth rate is plotted against time, and in c the change of rate (i.e. acceleration) of growth is shown against time. The curves on the right give similar graphs of the functions of the specific growth rate; that is, in e we plot ‘growth rate per

dW dlogW. ; unit mass’ or, = wee instead of simple growth rate aa and make

W edt dt de corresponding changes in the other curves d and f. Notice that the specific growth rate falls steadily from the beginning of life (curve e), and does so at

an ever-increasing rate (curve f). (From: Medawar 1945.) 282 PRINCIPLES OF EMBRYOLOGY

It is worth while just to glance at the main varieties of these. (1) The ‘monomolecular’ formula is derived from the idea that the growing substance is formed from a store of some substance a which is

gradually used up. This gives the relation

dw a= (a —w), whence w = a(t — be“),

when b is a constant depending on the initial amount of a.

When time is plotted horizontally, this gives a curve which is convex upwards and which approaches the upper limit a. Rather few growing systems behave in this way.

(2) The ‘logistic’ formula can be deduced from a number of different assumptions. For instance, if the substance tw is formed from a precursor aas before, but if the rate of formation is also increased in proportion to the amount of w already present (i.e. if the reaction is ‘autocatalytic’), we

shall have


ar = kw(a — w).

Or, if we suppose that the rate of formation per unit mass decreases in proportion as is formed, we shall have

1 dw

vd (q— »)

where p and q are constant, which amounts to the same thing. The differential equation can be solved to give an expression of the form ee t+ be

This when plotted gives a sigmoid curve, which eventually approaches the limit a.

. 1 dw . ; (3) Another assumption 1s that — i decreases as time goes on, but ina w

different way, being proportional to log w. This is the ‘Gompertz’ equation:

pay = plogw— w dt 5 1 This gives a solution of the form w = ae ™

which is again a sigmoid curve which approaches the upper limit a. GROWTH . 283

. . tr dw. _ (4) Again, we can take it that — i decreases simply in inverse proporw

tion to the lapse of time

w dt

1 dw k t’

whence w = bt*.

This is the ‘parabolic’ or “double-log’ curve; it should give a straight line when log weight is plotted against log time, whereas the ‘exponential’ or

‘single log’ formula w = be*’, which holds when = = is a constant, gives a straight line when log w is plotted against time. The double-log formula fits better with the weights of such growing systems as embryos, at least in the early stages, but like the single-log expression, it has no upper limit as time increases and can therefore obviously only hold for part of the life-history of most animals, which reach a final adult size. (It is possible that certain animals, including fish, continue growing indefinitely.)

All the formulae have been applied by various authors to the actual data derived by weighing embryos during their growth. Such observed growth curves are generally roughly sigmoid in shape, but they may give evidence of a number of cycles of growth, so that applying any one type of formula one may have to invoke a set of different constants for each cycle. Even so, it has never been possible to show that any one of the above formulae fits the facts so exactly that it must represent the actual situation and the others can be excluded. There are many snags in fitting theoretical curves to the actual observations. In the first place, many growth curves have been derived by weighing a sample population at each of a series of ages, taking the average of each age group, and joining the points together to give the overall curve. It is difficult to do anything else if we are interested, for instance, in the foctal growth of a mammal. But there will, of course, be a certain variation in the stage of development reached by individuals of the same temporal age, and if there were any sudden spurts or slowings-down of growth these might be obscured by taking averages. For instance, there is usually a sudden spurt in the growth of a boy at the time of puberty. In some boys this occurs rather earlier, in some rather later. If one derives a growth curve by weighing groups of boys at various ages, the spurt becomes distributed among a number of different groups and its existence concealed.

Even when a growth curve can be obtained by weighing a single individual at various times during its life, the curve is bound to suffer from a 284 PRINCIPLES OF EMBRYOLOGY

certain lack of precision. There may have been unavoidable alterations in the environmental conditions, amounts of food, temperature, disease, etc., and each weighing will only be accurate within certain observational limits. Thus what we shall have as a basis for setting up the growth curve is not a set of absolutely precise points but rather a zone of greater or less width within which the curve must lie. It will always be possible to fit quite a number of different theoretical curves into such a zone, particularly if we allow ourselves to consider the possibility of a set of growth phases for each of which a new set of constants may be calculated. Thus it is extremely improbable, and in fact does not happen in practice, that a set of empirical observations can suffice to discriminate between the various theoretical possibilities.

Moreover, it is quite obvious that when dealing with the growth of an entity such as an embryo, we are not confronted with a “growth’ which corresponds to any precise definition. The embryo contains a highly heterogeneous collection of tissues, some of which are growing, probably at different rates, while other parts of the embryo, such as the blood plasma, are not growing in any normal sense at all.

Weiss (1949a) has given a very clear and vivid picture of the type of complexity which is involved, even in the growth of a single organ, such as the eye. He writes: “The original eye vesicle consists of a certain initial allotment of cells from the embryonic brain wall. At first, all of these cells divide. The growth function at this stage is therefore a volume function. In the cup stage the retina becomes multilayered, with a sharp division into a germinal and a sterile zone. Only the cell layer in contact with the outer surface, corresponding to the ventricular (ependymal) layer of the brain, continues to proliferate, while the cells released into deeper layers differentiate the various retinal strata without further multiplication. The source of growth thus has become reduced to a two-dimensional one, causing a marked decline in the relative growth rate taken over the whole organ (e.g. from measurements of diameter). Later, the cells of the germinal layer themselves cease to proliferate and transform into sensory cells, a process which starts from the centre (macula) and spreads rapidly toward the periphery (ciliary zone) of the retina. Eventually, only the cells at the rim retain residual capacity to multiply. Further growth is then essentially by apposition from this rim; that is, the growth source has shrunk from planar to linear extension. Meanwhile some of the neuroblasts, though no longer multiplying, grow in size as they sprout nerve processes, which, grouped into plexiform layers, add to the thickness of the retina. During the later stages a gelatinous secretion, supposed to come from cells of both retina and lens, fills the interior with vitreous humour, thereby GROWTH 285

progressively distending the eyeball. In addition, blood vessels and other mesenchyme penetrate into the eye from the surroundings.

“This diversity and complexity of the component processes contributing to eye size makes the search for a single “growth-controlling” principle appear utterly unrealistic . . .”

Further, it must be remembered that the growth of an organism or organ may be due to a multiplication of cells, which remain about the same size, or to an enlargement of cells which do not increase in number. The final number of muscle or nerve cells in a vertebrate, for instance, is probably attained fairly early in embryonic life, the growth of the organs thereafter occurring mainly, if not entirely, by increase in cell size. It is not entirely clear whether the two types of growth depend on quite different underlying synthetic processes, but there is obviously some considerable difference between them, so that there is no reason to expect that they would follow identical growth laws.

Finally, it is possible for organs, or even entire organisms of relatively simple structure, to ‘de-grow’ or become smaller. Flatworms or coclenterates may respond in this way to deprivation of food supplies. In higher animals, the regression of a tadpole’s tail at the time of metamorphosis is a striking example. It is hardly to be expected that any very simple formula can fit all such cases. Attempts have been made to elaborate more complex ones. Perhaps the most valiant is that of Wetzel (1937) who set up an equation of extreme complexity containing over a dozen different constants, each of which was designed to deal with one or other of the factors which he supposed to be involved in the growth of a heterogeneous collection of tissues, such as an embryo. The formula was so complex, and therefore so flexible, that it could have been made to fit almost any set of data. Its justification would in fact have to be sought not in the accuracy with which it could be fitted to observations of growth, but in the experimental justification of the various parts of the formula which were concerned with the postulated underlying processes. We still know far too little about the unit processes which go to build up the overall growth rate of an embryo for such an experimental justification to be provided.

Most authors recently have been content to accept the situation that the growth of a complex organism cannot either be formulated adequately in terms of any simple, global hypothesis, such as those listed above, nor can it as yet be adequately analysed into a series of part processes; whence it follows that we have to use the various growth formulae merely as convenient means of summarising the empirical observations without attempting to attribute any profound meaning to them. For further 286 PRINCIPLES OF EMBRYOLOGY

progress in the study of growth as a precisely defined concept we shall have to look to investigations on the synthesis of definable and isolatable proteins, such as those of Spiegelman, Monod and others, on the rate of formation of adaptive enzymes (pp. 400, 409).

Meanwhile, empirical studies on the growth of the organism as a whole present many points of interest which, however, there will not be space to follow in any detail here.

One most interesting and technologically important aspect of the matter is in connection with the interaction between environmental and genetic factors in the determination of growth rate and absolute size. Very little indeed is known about the physiology of such process in animals, and they present a promising field for investigation. Some work of potentially fundamental importance is being made by the use of identical twin cattle. The members of such pairs of twins have exactly the same hereditary constitution. Bonnier, Hansson and Skjervold (1948) have shown that their growth rates, although considerably influenced by the genes, can be modified to quite an important extent by the level of feeding during the growing period, but that two identical twins, one reared with abundant nutrition and the other with much poorer supplies, will eventually tend to reach about the same final adult size although approaching this at different rates. Again, King (1954) finds that if a twin is kept for a period on a low-level dict and then changed to a high level, it soon makes up for any stunting it may have undergone, and proceeds to grow at the fast level characteristic of its abundant nutrition. After a certain period on the high diet, it will be heavier than its co-twin if the latter has been given the same diets in the reverse order, first high and then low.

The mechanisms controlling final size, i.e. the factors which cause an animal eventually to stop growing, are scarcely understood at all. Some species probably never cease growth; this is said to be the case for fish. Others stop at a certain size, although the tissues are still capable of growing, and will do so if a part of the body is amputated. Others again (e.g. mammals) grow till they reach a certain age, and, as we have just seen, tend to reach a characteristic limiting size in the growing period.

There may, perhaps, be no general mechanism which operates in all these different situations; if there is, it is still obscure. Moment (1953) has suggested that the limit might be set by the gradual building up of differences in electrical potential. Since tissues consist of cells, which are semipermeable bags containing electrolytes among which active chemical changes are going on, it is to be expected that potential differences will exist; and they have in fact been detected (Review: Lund 1947). Moment GROWTH 287

supposes that the extremities of an animal tend to become electropositive and thus favourable to oxidations, and this, he argues, is inimical to growth. The evidence for the existence of such a situation (or for-its effectiveness if it does exist) is not very strong. Perhaps a more plausible mechanism is to be found in auto-inhibitory effects, of an immunological nature, such as those postulated by Rose and others (p. 193).

Another aspect of the overall growth rate is its dependence on endocrine secretions, particularly those of the pituitary. There is not space here to deal with this subject, which belongs to endocrinology rather than embry ology.

2. The relative growth of parts

It is obvious that the different parts of an embryo do not always grow at the same rate. Several different lines of attack on the problem have been followed.

Perhaps the simplest is that opened up by Huxley (summarised Huxley 1932, see also Medawar and Clark 1945, Symp. Soc. exp. Biol. 1948, Zuckerman 1950). He showed that if x is the magnitude of a whole organism and y that of some part of it, the relation between them can often be represented by the equation

y = bx*

or, what is the same thing, log y = log b + a log x.

As the second equation shows, the two magnitudes will give a straight line when their logs are plotted against one another (Fig. 13.34). There is no doubt that the formula does fit rather well to very many sets of data and is a very useful generalisation. The phenomena has passed under a variety of names, of which heterogony and allometry seem to be the most usual,

It is not at all casy to decide just what the formula means in biological terms. Taking it from the simplest point of view, we may say that b is a relatively unimportant constant, which specifies the size of the organ y when the whole organism x is unity. The other constant a is the one which relates to the rate of growth of the organ: if the growth rate of both x and y is proportional to their actual size we shall have

dx dy

— = Ax, + = Bx, dt * dt a

BIA) or y= bx*, when a =B/A,


But if we adopt a more realistic formulation of the growth rates of x dx

aa in the previous section, it can be shown that although the allometry

formula is often a good approximation, it will only be exactly true in exceptional cases.

There are other reasons why the formula cannot be accepted as a strictly accurate description of the situation. The most important is that if two

and y, making

(x, t), when f(x, t) is one of the functions discussed

“ c 0 2 e z 8 10 = ——— S 5 0-9} xeoOT 4 é 6 O-8r 2 prox. Carpus 2 dist. segments segments B Log wt. carpus A FIGURE 13.3

A, the log weight of the two distal segments (crosses) and the two proximal

segments (circles) plotted against the log weight of the middle segment

(the carpus) of the claw of the Fiddler crab Uca pugnax. The slope of these

lines defines the allometric growth constants B, the gradient in growth

constants along the claw in Uca (full line) and the spider crab Maia (dotted line). (After Huxley 1932.)

segments of an organ, y, and ys, are each related heterogonically to the whole organism, then the sum of the two segments cannot be so related, since if y, = b,x%! and y. = b,x then y, + yz cannot be of the form bx*, though the discrepancy is usually not very large.

One must conclude that the allometry formula, like the other growth equations discussed previously, can at best be taken as a useful empirical summary of a set of data, but that it is not a firmly based theoretical principle.

Even with this limitation, a number of conclusions can be drawn from it. In the first place, as long as a remains constant, the rates of growth of the two parts are preserving a constant relation to one another; and it is GROWTH 289

a remarkable fact that they so often do so. One simple physiological explanation of such a system would be the hypothesis that the organs are each competing, with constant efficiencies per unit mass, for a generally available supply of nutrients. An attempt to test this has been made by Twitty and Wagtendonk (1940), who transplanted eyes of various ages and sizes between different individuals of axolotl, which were fed at different levels. They found that the simple scheme of constant efficiencies of competition was certainly not the whole story, since, for instance, a young eye transplanted to an older host which was starved might continue to grow even when the host was declining in weight. They concluded that the assimilative capacity of an organ must change (usually if not always decreasing) during the course of development (cf. p. 298). A similar conclusion emerges when one studies the growth of fragments of an organ isolated in vitro: pieces of chick heart, explanted from embryos of increasing age, show an increasing lag period before they start growing and a decreasing rate of growth in the first few days, though these differences fairly soon disappear (Medawar 1940).

Several authors, beginning with Teissier in 1931 and Needham in 1932, have applied the allometry formula to the increase in various chemical entities during development (reviewed in Needham 1942). If wet weight is plotted on double-log paper against dry weight, or glycogen, fat, protein, ash, calcium, phosphorus, etc., plotted against each other or against wet or dry weight, a series of straight lines are obtained. This indicates that the entities are related in the manner of the allometry equation

log x = a log y + constant.

The very interesting fact emerged that if we measure a number of different substances, x, y, z, etc., in two different animals A and B, we find

relations of the kind

log =a log 7 = 8 log 1 3

Ny Yo _ 2 log 3 a log B, B log B,’ in which A,, B,, etc. are different constants, but a, 8, remain the same, whatever the animals in which x and y are measured.

There is thus the same general relationship between a particular x and y (say fat and glycogen) throughout the animal kingdom or a great part of it. Needham spoke of this as a “chemical ground-plan of animal growth’. Waddington (1933¢) suggested that one might envisage the situation in terms of a general speeding up or slowing down of a basic chemical 290 PRINCIPLES OF EMBRYOLOGY

programme, We can express the growth rates of entity x in animals A and B as two time-functions:

im x, log A = filé), log B = fill).

Now we could choose another unit for measuring time, f, such that

f(t) =f,(t). This would amount to measuring the growth rate of a 1

in time-units which made it identical with that of B . The important point 1

is that this same transformation of the time-unit would automatically

convert the growth rate of 44 into that of 2°, and that of “# into that of 2 A; By A; B,

etc. Thus one change in time-scale would convert the whole chemical growth system of one animal into that of another (apart from the complication due to the constants A,, Ag, etc. which express the initial state of the system when growth starts). We have here an approach to a concept of ‘biological time’, by which is meant the notion that events in, say, a mouse or an elephant, are similar but are all uniformly speeded up in the former as compared with the latter. It is not yet clear to what sort of entities such a notion can be applied: for instance it seems most improbable that any such relation can hold for molecular enzymatic processes. Further discussions of it will be found in Brody (1937) and du Noiiy (1936) and some highly critical remarks in Medawar (1945).

3. Growth gradients and transformations of shape

In a complex organ, it is often found that the growth rate, relative to some standard part, varies in a graded manner from place to place. The simplest expression of this can be seen when there is a series of more or less comparable parts, for each of which an allometric growth constant (a) can be ascertained. Huxley (1932, Reeve and Huxley 1945) has described many examples, relating for instance to the joints within a crustacean limb, or the series of limbs attached to the different segments of the body. Fig. 13.3b shows how the a’s for the different segments fall into an orderly sequence, which can be taken as defining a growth gradient.

If one measures the growth constants for a series of distinct sub-units within an organ such as a limb, there are of course definite jumps in its value between adjacent segments, and what should, perhaps, be a continuous gradient, is described in terms of a discontinuous series of steps. Examination of other cases indicates that in fact the gradients within a single mass of tissue are usually, if not always, continuous in gradation. GROWTH 291

One method of illustrating this was introduced by D’Arcy Thompson (1916), although he used it to compare adult forms which are evolutionarily related rather than ontogenetic stages of a single individual. He took one adult form as a standard, drew it in outline as seen when projected on to a plane, and superposed on the drawing a rectangular network. He showed that if this network is treated as a grid of co-ordinates, and is then distorted in the appropriate manner, the drawing of the original shape will be distorted at the same time into a fairly good outline of some other type of animal (Fig. 13.4). Such distortions of a co-ordinate network will produce alterations which are continuously gradated over the whole area, and thus the growth gradients which are affected are probably also continuously graded, since they are likely to depend on the same fundamental mechanisms as produce the distortions which differentiate one form from the other. More recent workers have in fact shown that the same method can be used to compare different developmental stages of a single species.

areorane ° co


A transformation of a co-ordinate grid which converts the outline of Diodon (left) into that of its relative the sunfish Orthagoriscus. (After D’Arcy Thompson 1942.) 292 PRINCIPLES OF EMBRYOLOGY

D’Arcy Thompson’s suggestions opened up a large field for investigation, but unfortunately this has not been as systematically studied as might have been hoped. We can deal with the recent work under three heads: firstly, improvements in the method; secondly, the general physiology of growth gradients and shape transformations, and thirdly, attempts to discover the physiological mechanisms underlying them.

Actually rather little has been done to make D’Arcy Thomson’s method of the distortion of a co-ordinate network into a means of exact analysis. Medawar (1944, 1945) has made some steps in this direction (see also Richards and Kavanaugh 1945). He considered the changing shape of the human body during its development from the early foetus to the adult. The body was first reduced to a two-dimensional shape by representing it as a series of outline drawings when seen from the front (Fig. 13.5). It becomes obvious then that in the early stages the legs grow faster than the parts nearer the head, and it appears probable that there is a single continuous growth gradient with its high point towards the feet, falling off as one goes higher up the body. Medawar pointed out that this could be represented by a transformation of co-ordinates and that this transformation could theoretically be specified in algebraic terms. To illustrate how this might be done he reduced the shape of the whole living body still more drastically and considered only certain points on the vertical midline; the foot, fork, navel, nipples, chin, etc. The original threedimensional shape was thus reduced to a line on which certain intervals are marked. Suppose now that P,, P:, Ps, etc. are the heights from foot to fork at successive points in time, and similarly Q,, Q:, Qs, etc. the heights from fork to navel at the same times, and so on for the other intervals. We can from the actual measurements work out empirical equations connecting the successive Ps and again, another set of equations connecting the successive Qs, and so on. Each equation will give the changes of one part of the network as time proceeds. We can also find algebraical relations between the equations relating to the Ps and those relating to the Qs, the Rs and Ss, etc. at any given point in time. With the aid of these two sets of equations, the whole series of transformations can be expressed algebraically. It is clear, however, that quite a lot of arithmetic is required to produce even a fairly clumsy algebraical description of a series of shapes, notwithstanding that these have been reduced to their very simplest form, the original three dimensions having been whittled away to one. Such labour is only justified if it enables one to see certain relations which would otherwise be missed. So far, such evidence of a real usefulness of the method has not been forthcoming.

There are contexts, however, in which it seems probable that Medawar’s GROWTH 293

methods would be useful if they were applied. The changing shape of animals as they mature is of practical importance in relation to the production of livestock. Hammond (1950) has been particularly concerned with the problem and has demonstrated a number of general points about the physiology of growth gradients. These he has been able to illustrate pictorially, but it has so far not been easy to reduce them to a precise and manageable form; Medawar’s methods might be very useful in this connection.


a Cc d € 0-42 0:75 275 675 12°75 25°75 Years FIGURE 13.5

Changes in the proportions of the human body during growth. The heights of certain landmarks (knees, fork, navel, mouth, etc.) were ascertained for each age, and related to one another by means of empirical equations. From these equations the heights were recalculated, to give the horizontal lines which are drawn on the figures. The goodness of fit of these lines indicates the degree to which the changes in proportions have occurred in a regularly graded manner, so as to lend themselves to summarising in relatively simple algebraic functions. (From Medawar 1945.)

Hanimond shows that the various species of wild animals from which our domestic livestock have been derived have each their characteristic pattern of changes in shape during development. These can be illustrated rather vividly if one takes as a standard an early developing part such as the head and shows a series of drawings or photographs of different stages of the animal, all of which have been adjusted to the same head size. We then sce that in the horse, for instance (Fig. 13.6), up to the time 294 PRINCIPLES OF EMBRYOLOGY

of birth there is a great decrease in the length of leg relative to the remainder of the body, whereas after birth the most important changes are a lengthening and deepening of the body. In wild sheep the changes are somewhat similar, though perhaps not so marked. In wild pigs there are no very marked changes in proportions from the foetus up to the adult. It is these basic developmental patterns which are altered either by the genes selected by the livestock breeder or by the conditions of feeding


Changes of proportion in the growing horse. The upper row of drawings show a primitive type of horse at various stages from the foetus to the adult, adjusted in size so as to have the same length of cranium. By the stage of the first drawing (late foetus) there has already been a great development of the legs; later there is a preponderant growth of the trunk. The two drawings below show on the left a thoroughbred, and on the right a draught-horse; the later phase of growth has been minimised in the former and enhanced in the latter. (After Hammond 19 50.)

and husbandry under which he keeps his animals. Among horses, for instances, the strains bred for speed have been produced by selecting genes which partially suppress the later changes, so that the adult horse retains the long legs and slim body of the normal juvenile phases. In the heavy draught horses, on the other hand, genes have been selected which increase these later changes so that one obtains an animal with a very large and heavy body and relatively shorter legs. In the mutton breeds of GROWTH 295

sheep it is again genes which encourage the later changes in body conformation which are required and in the improvement of pigs it is also the late-developing hindquarters rather than the early-developing head and forequarters that it is necessary to emphasise.

The changes in body proportions can be affected not ony by genes but also by the level of nutrition on which the animals are kept. For instance, if two comparable sets of pigs are kept, one on a high plane of nutrition and another on a low plane, until they both reach the same weight, it will not only be found that the high-plane pigs reach the specified weight more quickly, but that the two sets of animals differ in conformation at the end of the experiment. The low-plane animals retain a more juvenile shape. One can say that in spite of maturing more slowly they mature in a conformation which is characteristic of a younger animal than do the similar pigs reared on the high plane of nutrition. Hammond explains the situation in the following ways: The different regions of the body, such as the head and the forequarters, the hindquarters, etc., attain their greatest rate of relative growth in succession. The same is true of different tissues, such as bone, muscle, fat, etc. The fundamental sequence in which these various parts come to the fore is never altered, but changes in genes or changes in nutrition can either compress the sequence into a shorter length of time or spread it out over a longer interval. High nutrition brings the successive phases nearer together in time; so do the genes which determine the draught type of horses or the meat-producing type of sheep or cow. Low nutrition spreads the phases further apart and so do the genes for racehorses (Fig. 13.7).

It appears from other experiments of Hammond and his associates that even if the plane of nutrition restricts the outward expression of the sequence of phases the basic physiological changes determining them may be proceeding nevertheless. Thus two sets of pigs were brought to the same weight in the same length of time, but by different routes; one being kept first on the high plane and later on a low, the other first on a low and later on a high plane of nutrition. They nevertheless showed characteristic differences in conformation. There is obviously a great deal more work to be done on the physiology and the genetics of these relations. It is one of the most fascinating, and also most practically important, aspects of the whole subject of growth.

Our knowledge of the mechanisms which control growth patterns is very meagre. We have to recognise in the first place that the processes which finally issue in an adult shape may be very complex. Waddington (1950a) has discussed one particular case from this point of view, that of the wings of Drosophila and shown how the final shape depends not only


on successive phases of cell division and cell expansion but also on deformations of the whole structure resulting from the changes in pressure of the body fluid contained in it. No very simple physiological account of the general growth pattern can be expected in such complex cases.

Even when we are dealing with a simpler case, in which the dominant factor is growth in the ordinary sense of cell multiplication and cell enlargement, our present knowledge does not provide a basis from which the phenomena can be easily understood. The growth pattern seems to

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Diagrammatic curves illustrating the succession of anatomical systems which are predominant in growth rate in mammals (particularly farm livestock). Curve 1 relates to the cranium and shanks, bone and gut-fat, which have a high growth rate at an early stage; the neck, main body musculature and subcutaneous fat grow fastest at a rather later stage (curve 2), and the hind-quarters and intra-muscular fat still later (curve 3). The upper set of curves show the situation when che animal is kept on a high plane of nutrition; the phases follow one another rapidly. Under conditions of poor nutrition (lower curves) the succession is more long drawn out. (After Hammond 1950.)

characterise whole regions, which may be made up of a number of anatomically different elements, and it is surprising how ofter: these elements appear to work together in a harmonious way. Fig. 1 3.8 shows in profile the skulls of a number of different types of dogs. The differences are presumably genetically determined and it is clear therefore that genes affect the pattern as a whole and not only the individual units comprising it. Moreover it must be remembered that each skull is made up of a number of different bones; to mention only the most striking example, the lower GROWTH 207

jaws are usually modified in a way consistent with the shape of the upper part of the skull to which they are attached. This subordination of individual parts to the whole to which they belong is the general rule, but it is not quite universal. For instance, in the F, and later generations of certain crosses between different breeds of dogs, some cases of definite disharmony between upper and lower jaws and between other parts of the body may be found, but they are relatively rare. Co-ordination usually extends not only between parts of the same general nature, such as bones, but affects tissues of quite a different kind, such as skin, muscle, etc. It is, however, rather commoner to find instances in which the growth rates of markedly different tissues are not properly assimilated to one another. For instance, in dogs with greatly shortened faces, such as bulldogs, the skin is often too large for the bony structure and therefore has to hang in folds (Stockard 1941).

FIGURE 13.8 Skulls of various races of dogs, adjusted to the same size, to illustrate how the structure, although complex, is modified as a whole. (a) German sheep dog; (b) Borsoi; (c) German Dogge; (d) St. Bernard; (e) Zwergspitz; (f) Italian Windspiel; (g) Englischer Mops; () Japanese spaniel. (After Huber 1948.)

Very little is known about the ways in which such growth correlations arise. General endocrine control affecting all types of tissue certainly plays a part in many cases. It seems probable also that the growth rate of one organ or part of an animal usually has some influence on the growth rate of the neighbouring regions. For instance, Huxley (1932) compared the growth rate of the limbs in Crustacea in species in which one sex has a very large, fast-growing limb, which is absent in the other. He showed that the presence of a fast-growing limb tended to affect its neighbours, in 298 PRINCIPLES OF EMBRYOLOGY

general increasing the growth of the limbs immediately posterior to it and depressing the rate of the limbs immediately in front. The mechanism of the effect—whether the fast-growing limb operates by secreting some growth-promoting substance or by competing in some way for a limited supply of available raw materials—is quite unknown.

One of the most extended series of studies of the physiology of growth rate of individual organs is that by Harrison, Twitty and others on the eyes and other organs of the Mexican salamander Amblystoma (Reviews: Harrison 1933, Twitty 1934, Needham 1942, Reeve and Huxley 1945). The eye of one species, A. figrinum (the normal axolotl) is very much faster growing than that of the nearly related species A. punctatum. It was first shown that if the eye-cups are interchanged and transplanted from punctatum to tigrinum or vice versa, each type retains its own characteristic growth rate even in the new situation. The growth rates are therefore inherent in the eye-cups themselves.

When organs are grafted into other animals of the same species but different age, the growth rate of a transplant younger than the host is speeded up, and that of an older one slowed down, until the grafted structures have reached asize appropriate to the body in which they lie. One hypothesis to account for this would be that the young organs have a greater assimilative efficiency than older ones, and are therefore able to obtain more than their normal share of nutrients from the blood stream when they have only older organs to compete with. But that can hardly be the whole story. Even when the competitive demand for nutrients was increased as much as possible (by starvation, to such a point that the host body lost weight, together with amputation of the tail which caused this to regenerate) the young transplanted eyes were still able to grow. Twitty came to the conclusion that at least two factors must be involved; not only a decreasing assimilative efficiency of an organ as it ages, but also an increase with age of the richness of the nutritive supplies in the blood (Twitty and Wagtendonk 1940). These ideas and observations are obviously closely related to those of Hammond mentioned above.

In other experiments by Twitty, the two main elements of the eye— the eye-cup and the lens—were combined in different ways. Here there was definite evidence of the influence of the growth rate of one element on that of the other. For instance, if a large eye-cup of Amblystoma tigrinum is combined with the small lens of A. pusctatum or is allowed to induce a lens in punctatum skin, we find that in the compound eye, the eye-cup of tigrinum grows more slowly than usual while the lens of punctatum grows more rapidly, so that the two finally come to bear a GROWTH 299

harmonious relation to one another. The same kind of thing is true in the opposite combination of a small punctatum eye-cup with a large tigrinum lens; the growth-rate of the eye-cup is increased and that of the lens decreased until the two fit. Again the mechanism of the effect is quite obscure. Weiss (1949a) has suggested that it may be a matter of tension exerted on the growing edge of the retina. In a combination where the lens is too small, it will permit some of the vitreous humour to flow out of the eye-cup and thus the tension will be reduced and the growth rate lowered. On the other hand, an over-large lens will exert a radial pressure against the edges of the retina and this might lead to an increased growth rate (Figs. 13.9, 13.10).


Reciprocal effects of lens and eye-cup. Figures a and b show the eyes of a fairly young tadpole of Triturus taeniatus in which the lens of the left eye (a) has been induced out of axolotl ectoderm grafted into the region; the lens is much too large in relation to the eye-cup. Figures c and d show a later stage from a similar experiment (at a lower magnification); the lens derived from axolotl tissue (in c) is still larger than the corresponding taeniatus lens, but it has caused its associated eye-cup to grow faster than normal, so that the relative sizes are nearly adjusted to one another. (After Rotmann 1939) 300 PRINCIPLES OF EMBRYOLOGY

Many other combinations between tissues from different species of Amphibia have been made experimentally. They often exert influences on one another’s growth but these differences are not always mutual. Rotmann (1933) for instance, found that if on the body of a newt of the species Triton taeniatus a limb was provided with a core of mesoderm of the

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Size index bp Oo

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0 0 20 30 40 50 60 70 80 90 100 110 120 130 140 Days after operation

FIGURE 13.10

Relative growth of eye-cup and lens in inter-specific grafts in Amblystoma. Curve A, growth of tigriium lens when associated with tigrinum eye-cup; curve B, growth of tigrinum lens when associated with punctatum eye-cup. The size of the lens is expressed as the ratio tigrinum lens to punctatum lens of same age. Note that the tigrinum lens in its own eye-cup reaches about 1-60 times the punctatum size, but when combined with a punctatum eye-cup only about 1-30 times. Curve C shows the growth of a punctatum eye-cup provided with a tigrinum lens, the ‘size index’ being its ratio to a normal punctatum eye-cup. Note that it becomes larger than usual, to about the extent required to fit the associated tigrinum lens. (After data of Harrison.)

species T. cristatus, but enclosed in skin belonging to the host’s species, the form of the limb up to the time of metamorphosis was entirely dictated by the species that contributed the mesoderm, which imposed its own growth rate on the ectoderm without being in any way influenced by it (Fig. 13.11). Interesting also in this respect are the experiments of Baltzer (see 1952a) who, however, was concerned not only with the growth rate in organs compounded out of combinations of tissues from two different species, but even more with the original induction of the organs and the laying down of their basic structure. On the whole he GROWTH 301

found that mesoderm was more likely than ectoderm to react to in fluences from its surroundings and become assimilated into a compound organ.

FIGURE 13.11

The two forelegs of a newt, T. taeniatus, in one of which (the lower in the

figure) the mesoderm of the limb-bud had been replaced with tissue from T.

cristatus. The operated leg has developed the long, rapidly growing toes typical of cristatus. (From Rotmann 1933.)

SUGGESTED READING _ Medawar 1945, Reeve and Huxley 1945, Weiss 19494, Zuckerman 1950.