On Growth and Form

in a peripheral equatorial circle (Figs. 48, 49). This is precisely what actually takes place. Moreover, before the breaking up of the nucleus, long before the chromatin material has broken up into separate chromosomes, and at the very time when it is being fashioned into a “‘spireme,” this body already lies in a polar field, and must already have a tendency to set itself in the equatorial plane thereof. But the long, continuous spireme thread is unable, so long as the nucleus retains its spherical boundary wall, to adjust itself in a simple equatorial annulus; in striving to do so, it must tend to coil and “kink” itself, and in so doing (if all this be so), it must tend to assume the characteristic convolutions of the “‘spireme.”

After the spireme has broken up into separate chromosomes, these particles come into a position of temporary, and unstable, Fig. 52. Chromosomes, undergoing splitting and separation. (After Hatschek and Flemming, diagrammatised.) equilibrium near the periphery of the equatorial plane, and here they tend to place themselves in a symmetrical arrangement (Fig. 52). The particles are rounded, lnear, sometimes annular, similar in form and size to one another; and lying as they do in a fluid, and subject to a symmetrical system of forces, it is not surprising that they arrange themselves in a symmetrical manner, the precise arrangement depending on the form of the particles themselves. This symmetry may _ perhaps be due, as has already been suggested, to induced electrical charges. In discussing Brauer’s observations on the splitting of the chromatic filament, and the symmetrical arrangement of the separate granules, in Ascaris megalocephala, Lillie*

remarks: ‘‘This behaviour is strongly suggestive of the division of a colloidal particle under the influence of its surface electrical charge, and of the effects of mutual repulsion in keeping the products of division apart.” It is also probable.that surfacetensions between the particles and the surrounding protoplasm would bring about an identical result, and would sufficiently account for the obvious, and at first sight, very curious, symmetry. We know that if we float a couple of matches in water they tend to approach one another, till they lie close together, side by side; and, if we lay upon a smooth wet plate four matches, half broken across, a precisely similar attraction brings the four matches together in the fcrm of a symmetrical cross. Whether one of these, or some other, be the actual explanation of the phenomenon, it is at least plain that by some physical cause, some mutual and

Fig. 53. Annular chromosomes, formed in the spermatogenesis of the Mole-cricket. (From Wilson, after Vom Rath.) symmetrical attraction or repulsion of the particles, we must seek to account for the curious symmetry of these so-called “ tetrads.”’ The remarkable annular chromosomes, shewn in Fig. 53, can also be easily imitated by means of loops of thread upon a soapy film when the film within the annulus is broken or its tension reduced. So far as we have now gone, there is no great difficulty in pointing to simple and familiar phenomena of a field of force which are similar, or comparable, to the phenomena which we witness within the cell. But among these latter phenomena there are others for which it is not so easy to suggest, in accordance with known laws, a simple mode of physical causation. It is not at once obvious how, in any simple system of symmetrical forces,

the chromosomes, which had at first been apparently repelled from the poles towards the equatorial plane, should then be split asunder, and should presently be attracted in opposite directions, some to one pole and some to the other. Remembering that it is not our purpose to assert that some one particular mode of action is at work, but merely to shew that there do exist physical forces, or distributions of force, which are capable of producing the required result, I give the following suggestive hypothesis, which I owe to my colleague Professor W. Peddie.

As we have’ begun by supposing that the nuclear, or chromosomal matter differs in permeability from the medium, that is to say the cytoplasm, in which it les, let us now make the further assumption that its permeability is variable, and depends upon the strength of the field. In Fig. 54, we have a field of force (representing our cell), consisting of a homogeneous medium, and including two opposite poles: lines of force are indicated by full lines, and loci of constant magnitude of force are shewn by dotted lines.

Let us now consider a body whose permeability (uw) depends on the strength of the field F. At two field-strengths, such as F,, F,, let the permeability of the body be equal to that of the medium, and let the curved line in Fig. 55 represent generally its permeability at other field-strengths; and let the outer and inner dotted curves in Fig. 54 represent respectively the loci of the field-strengths F, and F,. The body if it be placed in the medium within either branch of the inner curve, or outside the outer curve, will tend to move into the neighbourhood of the adjacent pole. If it be placed in the region intermediate to the two dotted curves, it will tend to move towards regions of weaker field-strength.

The locus F, is therefore a locus of stable position, towards which the body tends to move; the locus F, is a locus of unstable position, from which it tends to move. If the body were placed across F,, it might be torn asunder into two portions, the split coinciding with the locus F,. Suppose a number of such bodies to be scattered throughout - the medium. Let at first the regions Ff, and F, be entirely outside the space where the bodies are situated: and, in making this supposition we may, if we please, suppose that the loci which we are calling F, and Ff, are meanwhile situated somewhat farther from the axis than in our figure, that (for instance) F, is situated where we have drawn F,,, and that F, is still further out. The bodies then tend towards the poles; but the tendency may be very small if, in Fig. 55, the curve and its intersecting straight line do not diverge very far from one another beyond F,; in other

words, if, when situated in this region, the permeability of the bodies is not very much in excess of that of the medium. Let the poles now tend to separate farther and farther from one another, the strength of each pole remaining unaltered; in other words, let the centrosome-foci recede from one another, as they actually do, drawing out the spindle-threads between them. The loci F,, F,,, will close in to nearer relative distances from the poles. In doing so, when the locus F, crosses one of the bodies, the body may be torn asunder; if the body be of elongated shape, and be crossed at more points than one, the forces at work will tend to exaggerate its foldings, and the tendency to rupture is greatest when F, is in some median position (Fig. 56).

When the locus F, has passed entirely over the body, the body tends to move towards regions of weaker force; but when, in turn, the locus Ff, has crossed it, then the body again moves towards regions of stronger force, that.is to say, towards the nearest pole. And, in thus moving towards the pole, it will do so, as appears actually to be the case in the dividing cell, along the course of the outer lines of force, the so-called ‘“‘mantle-fibres” of the histologist*.

Such considerations as these give general results, easily open to modification in detail by a change of any of the arbitrary postulates which have been made for the sake of simplicity. Doubtless there are many other assumptions which would more or less meet the case; for instance, that of Ida H. Hyde that, * We have not taken account in the above paragraphs of the obvious fact that the supposed symmetrical field of force is distorted by the presence in it of the more or less permeable bodies; nor is it necessary for us to do so, for to that distorted field the above argument continues to apply, word for word.

during the active phase of the chromatin molecule (during which it decomposes and sets free nucleic acid) it carries a charge opposite - to that which it bears during its resting, or alkaline phase; and that it would accordingly move towards different poles under the influence of a current, wandering with its negative charge in an alkaline fluid during its acid phase to the anode, and to the kathode during its alkaline phase. A whole field of speculation is opened up when we begin to consider the cell not merely as a polarised electrical field, but also as an electrolytic field, full of wandering ions. Indeed it is high time we reminded ourselves that we have perhaps been dealing too much with ordinary physical analogies : and that our whole field of force within the cell is of an order of magnitude where these grosser analogies may fail to serve us, and might even play us false, or lead us astray. But our sole object meanwhile, as I have said more than once, is to demonstrate, by such illustrations as these, that, whatever be the actual and as yet unknown modus operandi, there are physical conditions and distributions of force which could produce just such phenomena of movement as we see taking place within the living cell. This, and no more, is precisely what Descartes is said to have claimed for his description of the human body as a “mechanism *.”’

The foregoing account is based on the provisional assumption that the phenomena of caryokinesis are analogous to, if not identical with those of a bipolar electrical field; and this comparison, in my opinion, offers without doubt the best available series of analogies. But we must on no account omit to.mention the fact that some of Leduc’s diffusion-experiments offer very remarkable analogies to the diagrammatic phenomena of caryokinesis, as shewn in the annexed figure+. Here we have two identical (not opposite) poles of osmotic concentration, formed by placing a drop of indian ink in salt water, and then on either side of this central _ drop, a hypertonic drop of salt solution more lightly coloured. On either side the pigment of the central drop has been drawn towards the focus nearest to it; but in the middle line, the pigment

is drawn in opposite directions by equal forces, and so tends to remain undisturbed, in the form of an “equatorial plate.” Nor should we omit to take account (however briefly and inadequately) of a novel and elegant hypothesis put forward by A.B. Lamb. This hypothesis makes use of a theorem of Bjerknes, _ to the effect that synchronously vibrating or pulsating bodies in a liquid field attract or repel one another according as their oscillations are identical or opposite in phase. Under such circumstances, true currents, or hydrodynamic lines of force, are” produced, identical in form with the lines of force of a magnetic field; and other particles floating, though not necessarily pulsating, in the liquid field, tend to be attracted or repelled by the pulsating

bodies according as they are lighter or heavier than the surrounding fluid. Moreover (and this is the most remarkable point of all), the lines of force set up by the oppositely pulsating bodies are the same as those which are produced by opposite magnetic poles: though in the former case repulsion, and in the latter case attraction, takes place between the two poles*. But to return to our general discussion. While it can scarcely be too often repeated that our enquiry is not directed towards the solution of physiological problems, save

only in so far as they are inseparable from the problems presented by the visible configurations of form and structure, and while we try, as far as possible, to evade the difficult question of what particular forces are at work when the mere visible forms produced are such as to leave this an open question, yet in this particular case we have been drawn into the use of electrical analogies, and we are bound to justify, if possible, our resort to this particular mode of physical action. There is animportant paper by R.S. Lillie, on the ‘‘ Electrical Convection of certain Free Cells and Nuclei*,” which, while I cannot quote it in direct support of the suggestions which I have made, yet gives just the evidence we need in order to shew that electrical forces act upon the constituents of the cell, and that their action discriminates between the two species of colloids represented by the cytoplasm and the nuclear chromatin. And the difference is such that, in the presence of an electrical current, the cell substance and the nuclei (including sperm-cells) tend to migrate, the former on the whole with the positive, the latter with the negative stream: a difference of electrical potential being thus indicated between the particle and the surrounding medium, just as in the case of minute suspended particles of various kinds in various feebly conducting media}. And the electrical difference is doubtless greatest, in the case of the cell constituents, just at the period of mitosis: when the chromatin is invariably in its most deeply staining, most strongly acid, and therefore, presumably, in its most electrically negative phase. In short,

+ In like manner Hardy has shewn that colloid particles migrate with the negative stream if the reaction of the surrounding fluid be alkaline, and vice versa. The whole subject is much wider than these brief allusions suggest, and is essentially part of Quincke’s theory of Electrical Diffusion or Endosmosis: according to which the particles and the fluid in which they float (or the fluid and the capillary walls through which it flows) each carry a charge, there being a discontinuity of potential at the surface of contact, and hence a field of force leading to powerful tangential or shearing stresses, communicating to the particles a velocity which varies with the density per unit area of the surface charge. See W. B. Hardy’s paper on Coagulation by Electricity, Journ. of Physiol. xx1v, p. 288-304, 1899, also Hardy and H. W. Harvey, Surface Electric Charges of Living Cells, Proc. R. S. LXxxtv (B), pp. 217-226, 1911, and papers quoted therein. Cf. also E. N. Harvey’s observations on the convection of unicellular organisms in an electric field (Studies on the Permeability of Cells, Journ. of Exper. Zool. x, pp. 508-556, 1911).

Lillie comes easily to the conclusion that “electrical theories of mitosis are entitled to more careful consideration than they have hitherto received.” Among other investigations, all leading towards the same general conclusion, namely that differences of electric potential play a great part in the phenomenon of cell division, I would mention a very noteworthy paper by Ida H. Hyde*, in which the writer shews (among other important observations) that not only — is there a measurable difference of potential between the animal and vegetative poles of a fertilised egg (Fundulus, toad, turtle, etc.), but that this difference is not constant, but fluctuates, or actually reverses its direction, periodically, at epochs coinciding with successive acts of segmentation or other important phases in the development of the eggt; just as other physical rhythms, for instance in the production of CO,, had already been shewn to do. Hence we shall be by no means surprised to find that the “materialised”’ lines of force, which in the earlier stages form the convergent curves of the spindle, are replaced in the later phases of caryokinesis by divergent curves, indicating that the two foci, which are marked out within the field by the divided and reconstituted nuclei, are now alike in their polarity (Figs. 58, 59).

It is certain, to my mind, that these observations of Miss Hyde's, and of Lillie’s, taken together with those of many writers on the behaviour of colloid particles generally in their relation to an electrical field, have a close bearing upon the physiological side of our problem, the full discussion of which hes outside our present field. The break-up of the nucleus, already referred to and ascribed to a diminution of its surface-tension, is accompanied by certain diffusion phenomena which are sometimes visible to the eye; and we are reminded of Lord Kelvin’s view that diffusion is implicitly

* On Differences in Electrical Potential in Developing Eggs, Amer. Journ. of Physiol. xt1, pp. 241-275, 1905. This paper contains an excellent summary of various physical theories of the segmentation of the cell. + Gray has recently demonstrated a temporary increase of electrical conductivity in sea-urchin eggs during the process of fertilisation (The Electrical Conductivity of fertilised and unfertilised Eggs, Journ. Mar. Biol. Assoc. x, pp. associated with surface-tension changes, of which the first step is a minute puckering of the surface-skin, a sort of interdigitation with the surrounding medium. For instance, Schewiakoff has observed in Huglypha* that, just before the break-up of the nucleus, a system of rays appears, concentred about it, but having nothing to do with the polar asters: and during the existence of this striation, the nucleus enlarges very considerably, evidently by imbibition of fluid from the surrounding protoplasm. In short, diffusion is at work, hand in hand with, and as it were in opposition to, the surface-tensions which define the nucleus.

Fig. 58. Final stage in the first Fig. 59. Diagram of field of force segmentation of the egg of Cerebrawith two similar poles. tulus. (From Prenant, after Coe.) + By diffusion, hand in hand with surface-tension, the alveoli of the nuclear meshwork are formed, enlarged, and finally ruptyred: diffusion sets up the movements which give rise to the appearance of rays, or striae, around the nucleus: and through increasing diffusion, and weakening surface-tension, the rounded outline of the nucleus finally disappears.

As we study these manifold phenomena, in the individual cases of particular plants and animals, we recognise a close identity of type, coupled with almost endless variation of specific detail; and in particular, the order of succession in which certain of the phenomena occur is variable and irregular. The precise order of the phenomena, the time of longitudinal and of transverse fission of the chromatin thread, of the break-up of the nuclear wall, and so forth, will depend upon various minor contingencies and “interferences.” And it is worthy of particular note that these variations, in the order of events and in other subordinate details, while doubtless attributable to specific physical conditions, would seem to be without any obvious classificatory value or other biological significance*.

As regards the actual mechanical division of the cell into two halves, we shall see presently that, in certain cases, such as that of a long cylindrical filament, surface-tension, and what is known as the principle of “minimal area,” go a long way to explain the mechanical process of division; and in all cells whatsoever, the process of division must somehow be explained as the result of a conflict between surface-tension and its opposing forces. But in such a case as our spherical cell, it is not very easy to see what physical cause is at work to disturb its equilibrium and its integrity.

The fact that, when actual division of the cell takes place, it does so at right angles to the polar axis and precisely in the direction of the equatorial plane, would lead us to suspect that the new surface formed in the equatorial plane sets up an annular tension, directed inwards, where it meets the outer surface layer of the cell itself. But at this point, the problem becomes more complicated. Before we could hope to comprehend it, we should have not only to enquire into the potential distribution at the surface of the cell in relation to that which we have seen to exist in its interior, but we should probably also have to take account of the differences of potential which the material arrangements along the lines of force must themselves tend to produce. Only

* Thus, for example, Farmer and Digby (On Dimensions of Chromosomes considered in relation to Phylogeny, Phil. Trans. (B), ccv, pp. 1-23, 1914) have been at pains to shew, in confutation of Meek (ibid. com, pp. 1-74, 1912), that the width of the chromosomes cannot be correlated with the order of phylogeny. thus could we approach a comprehension of the balance of forces which cohesion, friction, capillarity and electrical distribution combine to set up. |

The manner in which we regard the phenomenon would seem to turn, in great measure, upon whether or no we are justified in assuming that, in the liquid surface-film of a minute spherical cell, local, and symmetrically localised, differences of surface-tension are likely to occur. If not, then changes in the conformation of the cell such as lead immediately to its division must be ascribed not to local changes in its surface-tension, but rather to direct changes in internal pressure, or to mechanical forces due to an induced surface-distribution of electrical potential.

It has seemed otherwise to many writers, and we have a number of theories of cell division which are all based directly on inequalities or asymmetry of surface-tension. For instance, Biitschhi suggested, some forty years ago”, that cell division is brought about by an increase of surface-tension in the equatorial region of the cell. This explanation, however, can scarcely hold; for it would seem that such an increase of surface-tension in the equatorial plane would lead to the cell becoming flattened out into a disc, with a sharply curved equatorial edge, and to a streaming of material towards the equator. In 1895, Loeb shewed that the streaming went on from the equator towards the divided nuclei, and he supposed that the violence of these streaming movements brought about actual division of the cell: a hypothesis which was adopted by many other physiologists+. This streaming movement would suggest, as Robertson has pointed out, a diminution of surface-tengion in the region of the equator. Now Quincke has shewn that the formation of soaps at the surface of an oil-droplet results in a diminution of the surface-tension of the latter; and that if the saponification be local, that part of the surface tends to spread. By laying a thread moistened with a dilute solution of caustic alkali, or even merely smeared with soap, across a drop of oil, Robertson has further shewn that the drop at once divides into two: the edges of the drop, that is to say the ends of the

diameter’ across which the thread les, recede from the thread, so forming a notch at each end of the diameter, while violent streaming motions are set up at the surface, away from the thread in the direction of the two opposite poles. Robertson* suggests, accordingly, that the division of the cell is actually brought about by a lowering of the equatorial surface-tension, and that this in turn is due to a chemical action, such as a liberation of cholin, or of soaps of cholin, through the splitting of lecithin in nuclear synthesis.

But purely chemical changes are not of necessity the fundamental cause of alteration in the surface-tension of the egg, for the action of electrolytes on surface-tension 1s now well known and easily demonstrated. So, according to other views than those with which we have been dealing, electrical charges are sufficient in themselves to account for alterations of surfacetension; while these in turn account for that protoplasmic streaming which, as so many investigators agree, initiates the segmentation of the eggf. A great part of our difficulty arises from the fact that in such a case as this the various phenomena are so entangled and apparently concurrent that it is hard to say which initiates another, and to which this or that secondary phenomenon may be considered due. Of recent years the phenomenon of adsorption has been adduced (as we have already briefly said) in order to account for many of the events and appearances which are associated with the asymmetry, and lead towards the division, of the cell. But our short discussion of this phenomenon may be reserved for another chapter.

However, we are not directly concerned here with the phenomena of segmentation or cell division in themselves, except only in so far as visible changes of form are capable of easy and obvious correlation with the play of force. The very fact of “development” indicates that, while it lasts, the equilibrium of the egg is never completet. And we may simply conclude the t Cf. Plateau’s remarks (Statique des liquides, 1, p. 154) on the tendency towards: equilibrium, rather than actual equilibrium, in many of his systems of soap-films.