On Growth and Form

(5) The rate of growth is directly affected by temperatude, and by other physical conditions. (6) It is markedly affected, in the way of acceleration or retardation, at certain physiological epochs of life, such as birth, puberty, or metamorphosis. (7) Under certain circumstances, growth may be negative, the organism growing smaller: and such negative growth is a common accompaniment of metamorphosis, and a frequent accompaniment of old age. (8) The phenomenon of regeneration is associated with a large temporary increase in the rate of growth (or “acceleration” of growth) of the injured surface; in other respects, regenerative growth is similar to ordinary growth in all its essential phenomena.

In this discussion of growth, we have left out of account a vast number of processes, or phenomena, by which, in the physiological mechanism of the body, growth is effected and controlled. We have dealt with growth in its relation to magnitude, and to that relativity of magnitudes which constitutes form; and so we _ have studied it as a phenomenon which stands at the beginning of a morphological, rather than at the end of a physiological enquiry. Under these restrictions, we have treated it as far as possible, or in such fashion as our present knowledge permits, on strictly physical lines.

In all its aspects, and not least in its relation to form, the growth of organisms has many analogies, some close and some perhaps more remote, among inanimate things. As the waves grow when the winds strive with the other forces which govern the movements of the surface of the sea, as the heap grows when we pour corn out of a sack, as the crystal grows when from the surrounding solution the proper molecules fall into their appropriate places: so in all these cases, very much as in the organism itself, is growth accompanied by change of form, and by a development of definite shapes and contours. And in these cases (as in all other mechanical phenomena), we are led to equate our various magnitudes with time, and so to recognise that growth is essentially a question of rate, or of velocity.

The differences of form, and changes of form, which are brought about by varying rates (or “laws’’) of growth, are essentially the same phenomenon whether they be, so to speak, episodes in the life-history of the individual, or manifest themselves as the normal and distinctive characteristics of what we call separate species of the race. From one form, or ratio of magnitude, to another there is but one straight and direct road of transformation, be the journey taken fast or slow; and if the transformation take place at all, it will in all likelihood proceed in the self-same way, whether it occur within the life-time of an individual or during the long ancestral history of a race. No small part of what is known as Wolfi’s or von Baer’s law, that the individual organism tends to pass through the phases characteristic of its ancestors, or that the life-history of the individual tends to recapitulate the ancestral history of its race, lies wrapped up in this simple account of the relation between rate of growth and form.

But enough of this discussion. Let us leave for a while the subject of the growth of the organism, and attempt to study the conformation, within and without, of the individual cell. In the early days of the cell-theory, more than seventy years ago, Goodsir was wont to speak of cells as “centres of growth” or “centres of nutrition,’ and to consider them as essentially “centres of force.” He looked forward to a time when the forces connected with the cell should be particularly investigated: when, that is to say, minute anatomy should be studied in its dynamical aspect. ““When this branch of enquiry,” he says “shall have been opened up, we shall expect to have a science of organic forces, having direct relation to anatomy, the science of organic forms*.” And likewise, long afterwards, Giard contemplated a science of morphodynamique,—but still looked upon it as forming so guarded and hidden a “territoire scientifique, que la plupart des naturalistes de nos jours ne le verront que comme Moise vit la terre promise, seulement de loin et sans pouvoir y entrery.”

To the external forms of cells, and to the forces which produce and modify these forms, we shall pay attention in a later chapter. But there are forms and configurations of matter within the cell, which also deserve to be studied with due regard to the forces, known or unknown, of whose resultant they are the visible expression. . In the long interval since Goodsir’s day, the visible structure, the conformation and configuration, of the cell, has been studied far more abundantly than the purely dynamic problems that are associated therewith. The overwhelming progress of microscopic observation has multiplied our knowledge of cellular and intracellular structure; and to the multitude of visible structures it

has been often easier to attribute virtues than to ascribe intelligible functions or modes of action. But here and there nevertheless, throughout the whole literature of the subject, we find recognition of the inevitable fact that dynamical problems lie behind the morphological problems of the cell. Biitschl pointed out forty years ago, with emphatic clearness, the failure of morphological methods, and the need for physical methods, if we were to penetrate deeper into the essential nature of the cell*. And such men as Loeb and Whitman, Driesch and Roux, and not a few besides, have pursued the same train of thought and similar methods of enquiry.

Whitman f, for instance, puts the case in a nutshell when, in speaking of the so-called “caryokinetic” phenomena of nuclear division, he reminds us that the leading idea in the term “caryokinesis” is motvon,—‘“motion viewed as an exponent of forces residing in, or acting upon, the nucleus. It regards the nucleus as a seat of energy, which displays itself in phenomena of motion t.” In short 1t would seem evident that, except in relation to a dynamical investigation, the mere study of cell structure has but little value of its own. That a given cell, an ovum for instance, contains this or that visible substance or structure, germinal vesicle or germinal spot, chromatin or achromatin, chromosomes or centrosomes, obviously gives no explanation of the activities of the cell. And in all such hypotheses as that of “pangenesis,”’ in all the theories which attribute specific properties to micellae,

* Entwickelungsvorgdnge der Hizelle, 1876; Investigations on Microscopic Foams and Protoplasm, p. 1, 1894. ~ While it has been very common to look upon the phenomena of mitosis assufficiently explained by the results towards which they seem to lead, we may find here and there a strong protest against this mode of interpretation. The following is a case in point: “Ona tenté d’établir dans la mitose dite primitive plusieurs catégories, plusieurs types de mitose. On a choisi le plus souvent comme base de ces systémes des concepts abstraits et téléologiques: répartition plus ou moins exacte de la chromatine entre les deux noyaux-fils suivant qu’il y a ou non des chromosomes (Dangeard), distribution particuliere et signification dualiste des substances nucléaires (substance kinétique et substance générative ou héréditaire, Hartmann et ses éléves), etc. Pour moi tous ces essais sont a rejeter catégoriquement a cause de leur caractére finaliste; de plus, ils sont construits sur des concepts non démontrés, et qui parfois représentent des généralisations absolument erronées.”’ A. Alexeieff, Archiv fiir Protistenkunde, x1x, p. 344, 1913.

idioplasts, ids, or other constituent particles of protoplasm or of the cell, we are apt to fall into the error of attributing to matter what is due to energy and is manifested in force: or, more strictly speaking, of attributing to material particles individually what is due to the energy of their collocation. The tendency is a very natural one, as knowledge of structure increases, to ascribe particular virtues to the material structures themselves, and the error is one into which the disciple is likely to fall, but of which we need not suspect the master-mind. The dynamical aspect of the case was in all probability kept well in view by those who, like Goodsir himself, first attacked the problem of the cell and originated our conceptions of its nature and functions.

But if we speak, as Weismann and others speak, of an “hereditary substance,’ a substance which is split off from the parent-body, and which hands on to the new generation the characteristics of the old, we can only justify our mode of speech by the assumption that that particular portion of matter is the essential vehicle of a particular charge or distribution of energy, in which is involved the capability of producing motion, or of doing “work.”

For, as Newton said, to tell us that a thing “is endowed with ~ an occult specific quality, by which it acts and produces manifest effects, is to tell us nothing; but to derive two or three general principles of motion* from phenomena would be a very great step in philosophy, though the causes of these principles were not yet discovered.’ The things which we see in the cell are less important than the actions which we recognise in the cell; and these latter we must especially scrutinize, in the hope of discovering how far they may be attributed to the simple and well-known physical forces, and how far they be relevant or irrelevant to the phenomena which we associate with, and deem essential to, the manifestation of life. It may be that in this way we shall in time draw nigh to the recognition of a specific and ultimate residuum.

* This is the old philosophic axiom writ large: Ignorato motu, ignoratur natura; which again is but an adaptation of Aristotle’s phrase, 7 dpx} Tis Kwijoews, as equivalent to the “Efficient Cause.” FitzGerald holds that ‘all explanation consists in a description of underlying motions”; Scientific Writings, 1902, p. 385. And lacking, as we still do lack, direct knowledge of the actual forces inherent in the cell, we may yet learn something of their distribution, if not also of their nature, from the outward and inward configuration of the cell, and from the changes taking place in this configuration; that is to say from the movements of matter, the kinetic phenomena, which the forces in action set up.

The fact that the germ-cell develops into a very complex structure, is no absolute proof that the cell itself is structurally avery complicated mechanism: nor yet, though this is somewhat less obvious, is it sufficient to prove that the forces at work, or latent, within it are especially numerous and complex. If we blow into a bowl of soapsuds and raise a great mass of many-hued and variously shaped bubbles, if we explode a rocket and watch the regular and beautiful configuration of its falling streamers, if we consider the wonders of a hmestone cavern which a filtering stream has filled with stalactites, we soon perceive that in all these cases we have begun with an initial system of very slight complexity, whose structure in no way foreshadowed the result, and whose comparatively simple intrinsic forces only play their part by complex interaction with the equally simple forces of the surrounding medium. In an earlier age, men sought for the visible embryo, even for the homunculus, within the reproductive cells; and to this day, we scrutinize these cells for visible structure, unable to free ourselves from that old doctrine of “ pre-formation*.”

Moreover, the microscope seemed to substantiate the idea {which we may trace back to Leibnizt and to Hobbest), that there is no limit to the mechanical complexity which we may postulate in an organism, and no limit, therefore, to the hypotheses which we may rest thereon. But no microscopical examination of a stick of sealing-wax, no study of the material of which it is composed, can enlighten * As when Nageli concluded that the organism is, in a certain sense, “ vorgebildet” ; Beitr. zur wiss. Botanik, u, 1860. Cf. E. B. Wilson, The Cell, etc., p. 302.

+ “La matiere arrangée par une sagesse divine doit étre essentiellement organisée partout...il y a machine dans les parties de la machine Naturelle a Vinfini.”” Sur le principe de la Vie, p. 431 (Erdmann). ‘This is the very converse of the doctrine of the Atomists, who could not conceive a condition “ubi dimidiae partis pars semper habebit Dimidiam partem, nec res praefiniet ulla.” i Cf. an interesting passage from the Hlements (1, p. 445, Molesworth’s edit.), quoted by Owen, Hunterian Lectures on the Invertebrates, 2nd ed. pp. 40, 41, 1855.

us as to its electrical manifestations or properties. Matter of itself has no power to do, to make, or to become: it is in energy that all these potentialities reside, energy invisibly associated with the material system, and in interaction with the energies of the surrounding universe. That “function presupposes structure” has been declared an accepted axiom of biology. Who it was that so formulated the aphorism I do not know; but as regards the structure of the cell it harks back to Briicke, with whose demand for a mechanism, or organisation, within the cell histologists have ever since been attempting to comply*. But unless we mean to include thereby invisible, and merely chemical or molecular, structure, we come at once on dangerous ground. For we have seen, in a former chapter, that some minute “organisms” are already known of such all but infinitesimal magnitudes that everything which the morphologist is accustomed to conceive as “structure” has become physically impossible; and moreover recent research tends generally to reduce, rather than to extend, our conceptions of the visible structure necessarily inherent in living protoplasm. The microscopic structure which, in the last resort or in the simplest cases, it seems to shew, is that of a more or less viscous colloid, or rather mixture of colloids, and nothing more. Now, as Clerk Maxwell puts it, in discussing this very problem, “one material system can differ from another only in the configuration and motion which it has at a given instant 7.” If we cannot assume differences in structure, we must assume differences in motion, that is to say, in energy. And if we cannot do this, then indeed we are thrown back upon modes of reasoning unauthorised in physical science, and shall find ourselves constrained to assume, or to “admit, that the properties of a germ are not those of a purely material system.”

* “Wir miissen deshalb den lebenden Zellen, abgesehen von der Molekularstructur der organischen Verbindungen welche sie enthalt, noch eine andere und in anderer Weise complicirte Structur zuschreiben, und diese es ist welche wir mit dem Namen Organisation bezeichnen,” Briicke, Die Elementarorganismen, Wiener Sitzungsber. xuiv, 1861, p. 386; quoted by Wilson, The Cell, etc. p. 289. Cf. also Hardy, Journ. of Physiol. xxtv, 1899, p. 159. t Precisely as in the Lucretian concursus, motus, ordo, positura, figurae, whereby bodies mutato ordine mutant naturam.

But we are by no means necessarily in this dilemma. For though we come perilously near to it when we contemplate the lowest orders of magnitude to which life has been attributed, yet in the case of the ordinary cell, or ordinary egg or germ which is going to develop into a complex organism, if we have no reason to assume or to believe that it comprises an intricate “mechanism,” we may be quite sure, both on direct and indirect evidence, that, hke the powder in our rocket, it is very heterogeneous in its structure. It is a mixture of substances of various kinds, more or less fluid, more or less mobile, influenced in various ways by chemical, electrical, osmotic, and other forces, and in their admixture separated by a multitude of surfaces, or boundaries, at which these, or certain of these forces are made manifest.

Indeed, such an arrangement as this is already enough to constitute a “mechanism”; for we must be very careful not to let our physical or physiological concept of mechanism be narrowed to an interpretation of the term derived from the delicate and complicated contrivances of human skill. From the physical point of view, we understand by a “mechanism” whatsoever checks or controls, and guides into determinate paths, the workings of energy; in other words, whatsoever leads in the degradation of energy to its manifestation in some determinate form of work, at a stage short of that ultimate degradation which lapses in uniformly diffused heat. This, as Warburg has well explained, is the general effect or function of the physiological machine, and in particular of that part of it which we call “cell-structure *.” The normal muscle-cell is something which turns energy, derived from oxidation, into work; it is a mechanism which arrests and utilises the chemical energy of oxidation in its downward course; but the same cell when injured or disintegrated, loses its “usefulness,” and sets free a greatly increased proportion of its energy in the form of heat.

But very great and wonderful things are done after this manner by means of a mechanism (whether natural or artificial) of extreme simplicity. A pool of water, by virtue of its suriace, * Otto Warburg, Beitrige zur Physiologie der Zelle, insbesondere iiber die Oxidationsgeschwindigkeit in Zellen; in Asher-Spiro’s Ergebnisse der Physiologie, XIV, pp. 253-337, 1914 (see p. 315). (Cf. Bayliss, General Physiology, 1915, p. 590). is an admirable mechanism for the making of waves; with a lump of ice in it, it becomes an efficient and self-contained mechanism for the making of currents. The great cosmic mechanisms are stupendous in their simplicity; and, in point of fact, every great or little aggregate of heterogeneous matter (not identical in phase”) involves, zpso facto, the essentials of a mechanism. Even a non-living colloid, from its intrinsic heterogeneity, is in this sense a mechanism, and one in which energy is manifested in the movement and ceaseless rearrangement of the constituent particles. For this reason Graham (if I remember nightly) speaks somewhere or other of the colloid state as “the dynamic state of matter”; or in the same philosopher’s phrase (of which Mr Hardy* has lately reminded us), it possesses “energiat.”

Let us turn then to consider, briefly and diagrammatically, the structure of the cell, a fertilised germ-cell or ovum for instance, not in any vain attempt to correlate this structure with the structure or properties of the resulting and yet distant organism ; but merely to see how far, by the study of its form and its changing internal configuration, we may throw light on certain forces which are for the time being at work within it. We may say at once that we can scarcely hope to learn more of these forces, in the first instance, than a few facts regarding their direction and magnitude; the nature and specific identity of the force or forces is a very different matter. This latter problem is likely to be very difficult of elucidation, for the reason, among others, that very different forces are often very much alike in their outward and visible manifestations. So it has come to pass that we have a multitude of discordant hypotheses as to the nature of the forces acting within the cell, and producing, in cell division, the “‘caryokinetic” figures of which we are about to speak. One student may, like Rhumbler, choose to account for them by an hypothesis of mechanical traction, acting on a reticular web of protoplasmi{; another, like Leduc, may shew us how in

+ As a matter of fact both phrases occur, side by side, in Graham’s classical paper on “Liquid Diffusion applied to Analysis,” Phil. Trans. cui, p. 184, 1861; Chem. and Phys. Researches (ed. Angus Smith), 1876, p. 554. { L. Rhumbler, Mechanische Erklarung der Aehnlichkeit zwischen Magne-~ many of their most striking features they may be admirably simulated by the diffusion of salts in a colloid medium; others again, like Gallardo* and Hartog, and Rhumbler (in his earlier papers) t, insist on their resemblance to the phenomena of electricity and magnetism {; while Hartog believes that the force in question is only analogous to these, and has a specific identity of its own§. All these conflicting views are of secondary importance, so long as we seek only to account for certain configurations which reveal the direction, rather than the nature, of a force. One and the same system of lines of force may appear in a field of magnetic or of electrical energy, of the osmotic energy of diffusion, of the gravitational energy of a flowing stream. In short, we may expect to learn something of the pure or abstract dynamics, long before we can deal with the special physics of the cell. For indeed (as Maillard has suggested), just as uniform expansion about a single centre, to whatsoever physical cause it may be due will lead to the configuration of a sphere, so will any two centres or foci of potential (of whatsoever kind) lead to the configurations with which Faraday made us familiar under the name of “lines of force||”’; and this is as much as to say that the phenomenon,

tischen Kraftliniensystemen und Zelltheilungsfiguren, Arch. f. Entw. Mech. xv, p- 482, 1903. * Gallardo, A., Essai d’interprétation des figures caryocinétiques, Anales del Museo de Buenos-Aires (2), 11, 1896; La division de la cellule, phénomene bipolaire de caractére électro-colloidal, Arch. f. Entw. Mech. xxvii, 1909, etc. || The configurations, as obtained by the usual experimental methods, were of course known long before Faraday’s day, and constituted the “convergent and divergent magnetic curves” of eighteenth century mathematicians. As Leslie said, in 1821, they were ‘“‘regarded with wonder by a certain class of dreaming philosophers, who did not hesitate to consider them as the actual traces of an invisible fluid, perpetually circulating between the poles of the magnet.” Faraday’s great advance was to interpret them as indications of stress in a mediwm,—of

though physical in the concrete, is in the abstract purely mathematical, and in its very essence is neither more nor less than a property of three-dimensional space. But as a matter of fact,-in this instance, that is to say in trying to explain the leading phenomena of the caryokinetic division of the cell, we shall soon perceive that any explanation which is based, like Rhumbler’s, on mere mechanical traction, is obviously inadequate, and we shall find ourselves limited to the hypothesis of some polarised and polarising force, such as we deal — with, for instance, in the phenomena of magnetism or electricity.

Let us speak first of the cell itself, as it appears in a state of rest, and let us proceed afterwards to study the more active phenomena which accompany its division. Our typical cell is a spherical body; that is to say, the uniform surface-tension at its boundary is balanced by the outward resistance of uniform forces within. But at times the surfacetension may be a fluctuating quantity, as when it produces the rhythmical contractions or ““Ransom’s waves” on the surface of a trout’s egg; or again, while the egg is in contact with other bodies, the surface-tension may be locally unequal and variable, giving rise to an amoeboid figure, as in the egg of Hydra*.

Within the ovum is a nucleus or germinal vesicle, also spherical, and consisting as a rule of portions of “chromatin,” aggregated together within a more fluid drop. The fact has often been commented upon that, in cells generally, there is no correlation of form (though there apparently is of s¢ze) between the nucleus and the “‘cytoplasm,” or main body of the cell. So Whitmany remarks that “except during the process of division the nucleus seldom departs from its typical spherical form. It divides and sub-divides, ever returning to the same round or oval form.... How different with the cell. It preserves the spherical form as rarely as the nucleus departs from it. Variation in form marks the beginning and the end of every important chapter in its

tension or attraction along the lines, and of repulsion transverse to the lines, of the diagram. history.” On simple dynamical grounds, the contrast is easily explained. So long as the fluid substance of the nucleus is qualitatively different from, and incapable of mixing with, the fluid or semi-fluid protoplasm which surrounds it, we shall expect it to be, as it almost always is, of spherical form. For, on the one hand, it is bounded by a liquid film, whose surface-tension 1s uniform; and on the other, it is immersed in a medium which transmits on all sides a uniform fluid pressure *. For a similar reason the contractile vacuole of a Protozoon is spherical in form: it is just a “drop” of fluid, bounded by a uniform surfacetension and through whose boundary-film diffusion is taking place. But here, owing to the small difference between the fluid constituting, and that surrounding, the drop, the surface-tension equilibrium is unstable; it is apt to vanish, and the rounded outline of the drop, like a burst bubble, disappears in a moment fT. The case of the spherical nucleus is closely akin to the spherical form of the yolk within the bird’s egg t. But if the substance of the cell acquire a greater solidity, as for instance in a muscle

* “Souvent il n’y a qu'une séparation physique entre le cytoplasme et le suc nucléaire, comme entre deux liquides immiscibles, etc.;”? Alexeieff, Sur la mitose dite “primitive,” Arch. f. Protistenk. xx1x, p. 357, 1913. + The appearance of “‘vacuolation” is a result of endosmosis or the diffusion of a less dense fluid into the denser plasma of the cell. Caeteris paribus, it is less apparent in marine organisms than in those of freshwater, and in many or most marine Ciliates and even Rhizopods a contractile vacuole has not been observed (Biitschli, in Bronn’s Protozoa, p. 1414); it is also absent, and probably for the same reason, in parasitic Protozoa, such as the Gregarines and the Entamoebae. Rossbach shewed that the contractile vacuole of ordinary freshwater Ciliates was very greatly diminished in a 5 per cent. solution of NaCl, and all but disappeared in a 1 per cent. solution of sugar (A7b. z. z. Inst. Wiirzburg, 1872, cf. Massart, Arch. de Biol. Lx, p- 515, 1889). Actinophrys sol, when gradually acclimatised to sea-water, loses its vacuoles, and vice versa (Gruber, Biol. Centralbl. tx, p. 22, 1889); and the same is true of Amoeba (Zuelzer, Arch. f. Entw. Mech. 1910, p. 632). The gradual enlargement of the contractile vacuole is precisely analogous to the change of size of a bubble until the gases on either side of the film are equally diffused, as described long ago by Draper (Phil. Mag. (n.s.), x1, p. 559, 1837). Rhumbler has shewn that contractile or pulsating vacuoles may be well imitated in chloroform-drops, suspended in water in which various substances are dissolved (Arch. f. Entw. Mech. vu, 1898, p. 103). The pressure within the contractile vacuole. always greater than without, diminishes with its size, being inversely proportional to its radius; and when it lies near the surface of the cell, as in a Heliozoon, it bursts as soon as it reaches a thinness which its viscosity or molecular cohesion no longer permits it to maintain.

cell, or by reason of mucous accumulations in an epithelium cell, then the laws of fluid pressure no longer apply, the external pressure on the nucleus tends to become unsymmetrical, and its shape is modified accordingly. “‘Amoeboid’”? movements may be set up in the nucleus by anything which disturbs the symmetry of its own surface-tension. And the cases, as in many Rhizopods, where “‘nuclear material” is scattered in small portions throughout the cell instead of being aggregated in a single nucleus, are probably capable of very simple explanation by supposing that the “phase difference” (as the chemists say) between the nuclear and the protoplasmic substance is comparatively shght, and the surfacetension which tends to keep them separate is correspondingly small *.