Talk:Waddington1956 19

CHAPTER XIX THE DIFFERENTIATING SYSTEM

IT IS now time to try to formulate a general theory of differentiation based on the various factors which have been discussed above.

Perhaps the first problem which should be considered is the development of differences between the various regions of the embryo. In the scheme of intra-cellular reactions which was suggested earlier (see Fig. 16.1, p. 349), the nature of the cytoplasm affects the course of events at two different stages; on the one hand it provides the raw materials for gene activity and may thus differentially activate or inhibit different genes, and on the other it has the same relationship to the immediate gene products (and plasmagenes, if any). It is therefore easy to see how the constitution of the cytoplasm could set going a number of dissimilar processes of differentiation. In fact, it would be quite possible for this to occur through the interaction of the cytoplasm with the gene products, even if the activity of the genes themselves was exactly the same in all cells; but as we have seen there is actual evidence of nuclear differentiation in the various tissues, and there seems no reason to doubt that both the possible influences of the cytoplasm—on genes and on gene products— are effectively in operation.

The next point is the existence of distinct alternative pathways of chemical change, leading to the production of a finite number of definite tissues; and the peculiar mixture of permanence and lability revealed in the phenomena of determination and modulation. The explanation for the distinctness of the developmental paths can probably be found in the nature of the cytoplasmic influences on the genes and gene products. All the different genes are made out of similar building blocks, i.e. the aminoacids and peptides which go to form the protein, and the nucleotides which form the nucleic acids. The same situation holds for the gene products. Thus we must suppose that the various genes (and gene products) will compete with one another for the available raw materials. There may also be other types of competition; for instance a high concentration of one gene product A may inhibit the formation of another B, and so on. There will therefore be a situation of ‘competitive interaction’ in the formation of the gene products and another in their production of cytoplasmic substances,

406 THE DIFFERENTIATING SYSTEM 407

Now in a system consisting of a mixture of raw materials for which several synthetic processes are competing, situations can easily arise in which a slight change in initial conditions will have a great effect on the final state; in fact, such systems will often be such that there are only a limited number of final states to which they can attain, the choice between one end-state or another depending on the concentrations of substances present at the beginning (Waddington 1948), 1954). To take a simple example of what may happen, consider two substances P and Q, which are being formed out of the raw materials A, B, and C, for the supplies for which they compete. Suppose competition occurs because P is formed from A and B, while Q is formed from B and C. Again for the sake of simplicity, let the reaction constants be the same for the two syntheses, as shown in Fig. 19.1; and let A, B and C diffuse into the system at rates proportional to the difference in their concentration inside (A, B, C) and outside (a, b, c), while P and Q are removed at rate ky. Finally, let us suppose that the coupling of A and B to form P, and of B and C to form Q, are autocatalytic processes, i.e. are speeded up by the presence of already-formed P and Q. This is a simple form of a ‘feed-back’ mechanism. The equations for the rates of change of the various components

will be

& = ka — A) — k,PAB + kyP*

dB

& = kb —B) — PAB + baP* — k,QBC + bxQ? = = k(c — C) — hQBC + k,Q?

a = k,PAB — kyP* — bP

= = QBC — QQ? — kQ

At the steady state, we find a relation between P and Q of the form (kRoc + k3)P = (kkea + k*%s)Q + kke(a—c) . . . (2)

Now if ky is small compared with k (i.e. diffusion out of the system is slower than diffusion in), then we can neglect its higher powers, and we

find PeeOpso ...-..

DD 408 PRINCIPLES OF EMBRYOLOGY

Thus if initially in a certain region the supply of A is increased relative to that of C, we find that P will be increased relative to Q by something more than a proportionate amount, the excess being expressed by the last term on the right. And if the rate of removal of P, (that is k,), is greater than the rate at which P breaks down again into A and B, (that is kg), this excess can be considerable. We can also see from expression (2) that the exaggeration will be the more important the smaller the absolute values of P and Q; and these will also be reduced if kg is fairly large, so that P and Q are rapidly removed.

1

i

1

! a +, A

\ ky 3

=

k ke b —~> 8B |

I } ky {

! ———— Oc

i k k

k 2 3 ai

! 1

1 1

! |

FIGURE 19.1

A system of competing chemical reactions, by which substances A, B and C become converted into P or Q. See text. (From Waddington 19544.)

Without going into further details, we can see that if two autocatalytic processes compete for raw materials, we may under some conditions find that an initial change in the supply of the materials produces an exaggerated effect on the steady-state concentrations of the synthesised products, and thus on the rates at which these products can be made available outside the system.

If we suppose that A, B, and C are the raw materials out of which two genes manufacture their immediate products P and Q, we have now developed a picture by means of which we can see how a change in the concentrations of these raw materials leads to exaggerated differences in the rate at which P and Q are passed out of the nucleus into the cytoplasm.

It is, however, by no means the only model which might be appropriate. As Delbriick (1949) has suggested, there might be direct interactions between the two synthetic processes. These are perhaps most simply formulated by supposing that P is destroyed at some rate proportional to the concentration of Q (and vice versa). The equations for dP/dt and dQ/dt will then contain terms in PQ. If we regard the system as closed, THE DIFFERENTIATING SYSTEM 409

rather than open as was the system discussed above, and if the supplies of raw materials are taken as constant, the equations which result are of the same type as those which arise in the study of the growth of two populations of animals which compete with one another for a limited food supply. Lotka (1934) had discussed the relatively simple situation of two populations (or substances) for which the equations take the form

dP

T= MP — kyP* — kygPQ d

oe m,Q — k,Q? — ky PQ.

He shows that according as m,k, is greater or less than gk gs and my,Rop greater or less than m,k,, so the final state of the system is either ares P or wholly Q, or a certain fixed ratio between them, or finally the system is one which will finish up either entirely P or entirely Q according to the initial concentrations of these substances.

Kostitzin (1937) has also discussed shortly the more general case in which there are many competing and interacting substances (or populations), so that we have a large series of simultaneous differential equations, each containing terms of the second order, such as P? or PQ, etc. He shows that such a system may be expected to exhibit a number of alternative steady states, some at least of which are likely to be stable, and that the particular one which the system actually attains will in many cases depend on the initial conditions.

Competitive interactions are not only almost necessary consequences of the nature of the situation, but there is definite and direct evidence for their existence. Perhaps the most striking is that produced by Spiegelman (1948, 1950) from the study of adaptive enzyme formation in yeasts. If a yeast is grown in the presence of two substrates, for neither of which it originally possesses the appropriate enzyme, it will gradually manufacture the suitable adaptive enzymes, which are of course protein in nature. If the supplies of nitrogen are restricted, these two proteins enter into obvious competition with one another for it, one or both of the enzymes being formed more slowly when the yeast is adapting to two substrates simultaneously than when there is only one new substrate (Fig. 19.2). Spiegelman also shows that the systems producing the adaptive enzymes are self-reinforcing or ‘autocatalytic’; and the way in which a muscle cell, for instance, fills with myosin, suggests that the same is true of the formation of many cytoplasmic proteins. We have thus all the components 410 PRINCIPLES OF EMBRYOLOGY

required for a system which will tend towards a limited number of alternative end states.

It is not so easy to give an actual example of a system in which the alternative end states depend on specific inhibitions, of the kind postulated by Delbriick. However, Horowitz (1951) has mentioned a case, which, although it is still somewhat hypothetical, may serve as an example of the kind of situation which it would be most desirable to analyse. When the mould Neurospora is grown in sulphur-deficient media it develops

Simultaneous adaptation

maltose and galactose 280

ee ° 240 ° 200 / x 160 zi Qo, a A 120 80 N 40 A ZA ~e¢ oD 120 240 360 480 Minutes FIGURE 19.2

Simultaneous adaptation of yeast to maltose and galactose. The curve B

shows the activity in fermenting galactose, when that is the only sugar

present; D is the corresponding curve for maltose. When both sugars are

present, the splitting of galactose is not much affected (A) but the growth in

maltose-splitting activity is competitively inhibited (C). (After Speigelman 1948.)

the enzyme tyrosinase, and tends to become blackened with melanin pigment if any suitable substrate is available. It seems probable that in fact this enzyme is also produced in normal media containing sulphur, but that in them some sulphur-containing compound which inhibits tyrosinase activity is also formed. Horowitz asks what would happen if one of the products of tyrosinase activity could combine with the inhibitor and destroy it, or in some other way prevent its appearance. Then, he suggests, if a mould were grown for some time in a sulphur-deficient medium, it would acquire a high content of tyrosinase, and on transference to a normal medium this enzyme would continue to be active unless or until the production of inhibitor could overtake its inactivation by the tyrosinase-system. We might then have a very simple example of a system THE DIFFERENTIATING SYSTEM 4I1

with two alternative types of differentiation (with and without active tyrosinase and formation of melanin pigment), the choice between which would be dependent on the previous history of the strain (whether it had spent a period in a sulphur-deficient medium).

_There appears therefore to be no difficulty in accounting in one or other of these ways for the existence of distinct alternative paths of differentiation. Within a given path, there are two types of phenomenon for which we have to provide an explanation. The first is the existence of a range of variation of the kind which is exhibited in ‘field’ processes. For instance, if some cells in the limb region enter on the path of development leading to cartilage and bone formation, they may have the character of the femur or, on the other hand, of some other part of the limb skeleton. A somewhat similar phenomenon is that of ‘modulation’. In this case a given tissue assumes a range of histological forms in dependence on the nature of its environment, but throughout all such changes retains its essential character unimpaired. Presumably in both cases the variations are basically quantitative in nature, and indicate that the concentrations of the reacting gene-products and cytoplasmic substances can take a certain range of values while still remaining within one and the same alternative path of development.

In contrast to such flexibility of behaviour is the essential permanence which is alluded to by speaking of tissues as ‘determined’. When tissues are modulated by some external influence, they nevertheless retain their original character and can re-express it when suitable conditions arise. Can the hypothesis which attributes determination to competitive interaction provide a satisfactory explanation of this? The question has been little studied, either theoretically or practically. There is no doubt that one can invent systems of competitive interaction which would, if they actually existed, make differentiation very difficult to reverse. The mere co-existence of numerous interacting substances would almost suffice. Evolutionary changes hardly ever in practice get reversed, just because they depend on such numerous gene changes that it is extremely improbable that all the reversals will happen simultaneously. In the same way, a highly complex system of competitive interactions would scarcely ever be brought to retrace its steps. But that is a very generalised argument; and the occurrence of modulation, and of peculiar combinations of lability and fixity of character (such as the lability of avian epidermis which allows it to be induced to form a feather, combined with its fixity of tract-specificity, p. 259), make one wish for some rather more detailed understanding. This could probably come partly from a mathematical investigation of the theory of stability of competitively interacting systems. 412 PRINCIPLES OF EMBRYOLOGY

Much could probably be learnt, also, from specially designed experiments on simple examples of them.

Until such time as further theoretical or experimental studies have been made of the properties of such systems, one is left with a certain freedom of choice as to what hypothesis seems adequate to explain the facts of determination and modulation. It may well be that there is no need to assume anything more than competitive interaction between autocatalytic processes leading from genes to gene products, and from the latter to the final cytoplasmic constituents.

Some authors, however, feel that a further factor tending towards persistence of character is required, and suggest that this can be found by invoking the presence of plasmagenes. This possibility was discussed in the last chapter, where the conclusion was reached that gene-initiated plasmagenes would seem the most likely kind to play a large role in development, but that although there is no doubt that the cytoplasm contains complex bodies of a roughly gene-like order, one requires more evidence of their independence of nuclear control before accepting them as plasmagenes. This additional evidence can, as far as one can see at present, be sought only in a further study of the properties of the microsomes to which Brachet has attached so much importance in the synthesis of proteins. Arc they indeed the main site of protein production, as he suggests? And if so, have they in addition the property of multiplying and retaining their own specific character in some degree of independence of the genes? If so, one might allow that they were plasmagenes of one or other of the types indicated in Fig. 18.2. Really conclusive evidence on these points will, probably, only become available when the technical difficulties of transplanting microsomes from one cell to the other are overcome, and their degree of autonomy over against the nucleus can thus be investigated. In the meantime, the best evidence we have as to the developmental functions of microsomes comes from the phenomena of evocation.

In evocation we are undoubtedly confronted with a situation in which an environmental influence, impinging in the first place on the cytoplasm of the competent cell, causes it to adopt one or other of the alternative paths of development open to it. The fact that the reacting tissue retains its own specific characteristics—T. alpestris ectoderm forming typical alpestris neural tissue even if evocated by T. cristatus mesoderm—shows that the developmental paths are under genetic control and that the evocation involves the differential activation of a particular set of genes. The problem of the mechanism of evocation therefore becomes that of the nature of the influences which can activate or inhibit genes; that is to THE DIFFERENTIATING SYSTEM 413

say, which can produce crucial changes in the systems of competitive interactions. We know that the initial evocating stimulus may be comparatively slight, even a mere change in pH. We do not yet know on exactly what part of the cell system this obtains its effect. Weiss (1947, 19494) has pointed out that an evocating stimulus might act at the cell surface, by causing the accumulation there of a particular molecular species, with a consequent depletion of the deeper parts of the cell and an alteration in the ‘molecular ecology’, or systems of competitive interaction (Fig. 19.3). There is, however, little convincing evidence that evocating actions take place primarily at the cell surface (cf. p. 213).

FIGURE 19.3

Diagram showing how two different substances (upper and lower rows)

acting on the surface of a cell might attract to the surface different specific

internal constituents, and thus cause progressive cellular differentiation. A conceivable mechanism for evocation. (From Weiss 19506.)

Indeed the most critical evidence as to the location of evocator action speaks in the opposite sense. Waddington and Goodhart (1949) investigated the position taken up within the cell by the sterol-like hydrocarbons which are extremely active evocators. It was found that they are not absorbed on the surface or on the nucleus, but on lipo-protein granules (lipochondria) in the cytoplasm, which then break down to give microsomes. 414 PRINCIPLES OF EMBRYOLOGY

This is the only case in which the location of an evocating substance within the cell has been verified; and the trail appears to lead to cytoplasmic particles and eventually to the microsomes. Brachet (1944, 1947, 1952) has advanced a number of lines of argument suggesting that these particles are intimately involved in evocation (p. 212). It may be that all or most of the many substances capable of evocating neural tissue act in the first place on these granules. We saw, however (p. 222), that the microsomes are only one element, though an important one, in the complex flux of cellular metabolism, and that one cannot consider the mechanism of evocation without taking account of gene action, protein synthesis, respiration, etc. The biochemical processes symbolised by the two cycles of reactions in Fig. 16.1, from the cytoplasm to the genes, and from the cytoplasm to the gene products, must actually involve all the basic metabolism of the cell. It is fruitless to envisage evocation as a special reaction, carried out by some particular part of the cell which can be, in theory, isolated from the general body of the living system. We must be prepared, therefore, to“find that several different types of influence, impinging on the double cycle of cellular metabolism, may result in the same effect of swinging these cycles into one or other of the alternative modes open to them. Similarly, when we think of particular groups of genes being activated in different tissues, the cytoplasmic conditions responsible for this probably cannot be reduced to the mere concentration of certain inactive raw materials which lie quietly there for the genes to utilise. The ‘substrates’, for which we have envisaged the genes competing, will themselves in many cases be involved in active chemical processes of respiration, energy transfer, etc. The genes and gene products must be thought of as focal points in a continuously active and dynamic system.