In ordinary chemical reactions we have to deal (1) with a specific velocity proper to the particular reaction, (2) with variations due to temperature and other physical conditions, (3) according to van’t Hoff’s “Law of Mass,” with variations due to the actual quantities present of the reacting substances, and (4) in certain cases, with variations due to the presence of “catalysing agents.” In the simpler reactions, the law of mass involves a steady, gradual slowing-down of the process, according to a logarithmic ratio, as the reaction proceeds and as the initial amount of substance diminishes; a phenomenon, however, which need not necessarily {131} occur in the organism, part of whose energies are devoted to the continual bringing-up of fresh supplies.
Catalytic action occurs when some substance, often in very minute quantity, is present, and by its presence produces or accelerates an action, by opening “a way round,” without the catalytic agent itself being diminished or used up[167]. Here the velocity curve, though quickened, is not necessarily altered in form, for gradually the law of mass exerts its effect and the rate of the reaction gradually diminishes. But in certain cases we have the very remarkable phenomenon that a body acting as a catalyser is necessarily formed as a product, or bye-product, of the main reaction, and in such a case as this the reaction-velocity will tend to be steadily accelerated. Instead of dwindling away, the reaction will continue with an ever-increasing velocity: always subject to the reservation that limiting conditions will in time make themselves felt, such as a failure of some necessary ingredient, or a development of some substance which shall antagonise or finally destroy the original reaction. Such an action as this we have learned, from Ostwald, to describe as “autocatalysis.” Now we know that certain products of protoplasmic metabolism, such as the enzymes, are very powerful catalysers, and we are entitled to speak of an autocatalytic action on the part of protoplasm itself. This catalytic activity of protoplasm is a very important phenomenon. As Blackman says, in the address already quoted, the botanists (or the zoologists) “call it growth, attribute it to a specific power of protoplasm for assimilation, and leave it alone as a fundamental phenomenon; but they are much concerned as to the distribution of new growth in innumerable specifically distinct forms.” While the chemist, on the other hand, recognises it as a familiar phenomenon, and refers it to the same category as his other known examples of autocatalysis. {132}
This very important, and perhaps even fundamental phenomenon of growth would seem to have been first recognised by Professor Chodat of Geneva, as we are told by his pupil Monnier[168]. “On peut bien, ainsi que M. Chodat l’a proposé, considérer l’accroissement comme une réaction chimique complexe, dans laquelle le catalysateur est la cellule vivante, et les corps en présence sont l’eau, les sels, et l’acide carbonique.”
Very soon afterwards a similar suggestion was made by Loeb[169], in connection with the synthesis of nuclein or nuclear protoplasm; for he remarked that, as in an autocatalysed chemical reaction, the velocity of the synthesis increases during the initial stage of cell-division in proportion to the amount of nuclear matter already synthesised. In other words, one of the products of the reaction, i.e. one of the constituents of the nucleus, accelerates the production of nuclear from cytoplasmic material.
The phenomenon of autocatalysis is by no means confined to living or protoplasmic chemistry, but at the same time it is characteristically, and apparently constantly, associated therewith. And it would seem that to it we may ascribe a considerable part of the difference between the growth of the organism and the simpler growth of the crystal[170]: the fact, for instance, that the cell can grow in a very low concentration of its nutritive solution, while the crystal grows only in a supersaturated one; and the fundamental fact that the nutritive solution need only contain the more or less raw materials of the complex constituents of the cell, while the crystal grows only in a solution of its own actual substance[171].
As F. F. Blackman has pointed out, the multiplication of an organism, for instance the prodigiously rapid increase of a bacterium, {133} which tends to double its numbers every few minutes, till (were it not for limiting factors) its numbers would be all but incalculable in a day[172], is a simple but most striking illustration of the potentialities of protoplasmic catalysis; and (apart from the large share taken by mere “turgescence” or imbibition of water) the same is true of the growth, or cell-multiplication, of a multicellular organism in its first stage of rapid acceleration.
It is not necessary for us to pursue this subject much further, for it is sufficiently clear that the normal “curve of growth” of an organism, in all its general features, very closely resembles the velocity-curve of chemical autocatalysis. We see in it the first and most typical phase of greater and greater acceleration; this is followed by a phase in which limiting conditions (whose details are practically unknown) lead to a falling off of the former acceleration; and in most cases we come at length to a third phase, in which retardation of growth is succeeded by actual diminution of mass. Here we may recognise the influence of processes, or of products, which have become actually deleterious; their deleterious influence is staved off for a while, as the organism draws on its accumulated reserves, but they lead ere long to the stoppage of all activity, and to the physical phenomenon of death. But when we have once admitted that the limiting conditions of growth, which cause a phase of retardation to follow a phase of acceleration, are very imperfectly known, it is plain that, ipso facto, we must admit that a resemblance rather than an identity between this phenomenon and that of chemical autocatalysis is all that we can safely assert meanwhile. Indeed, as Enriques has shewn, points of contrast between the two phenomena are not lacking; for instance, as the chemical reaction draws to a close, it is by the gradual attainment of chemical equilibrium: but when organic growth draws to a close, it is by reason of a very different kind of equilibrium, due in the main to the gradual differentiation of the organism into parts, among whose peculiar {134} and specialised functions that of cell-multiplication tends to fall into abeyance[173].
It would seem to follow, as a natural consequence, from what has been said, that we could without much difficulty reduce our curves of growth to logarithmic formulae[174] akin to those which the physical chemist finds applicable to his autocatalytic reactions. This has been diligently attempted by various writers[175]; but the results, while not destructive of the hypothesis itself, are only partially successful. The difficulty arises mainly from the fact that, in the life-history of an organism, we have usually to deal (as indeed we have seen) with several recurrent periods of relative acceleration and retardation. It is easy to find a formula which shall satisfy the conditions during any one of these periodic phases, but it is very difficult to frame a comprehensive formula which shall apply to the entire period of growth, or to the whole duration of life.
But if it be meanwhile impossible to formulate or to solve in precise mathematical terms the equation to the growth of an organism, we have yet gone a very long way towards the solution of such problems when we have found a “qualitative expression,” as Poincaré puts it; that is to say, when we have gained a fair approximate knowledge of the general curve which represents the unknown function.