On Growth and Form

The spicules of the calcareous sponges are commonly triradiate, and the three radii are usually inclined to one another at equal, or nearly equal angles; in certain cases, two of the three rays are nearly in a straight line, and at right angles to the * See for instance the plates in Théel’s Monograph of the Challenger Holothuroidea; also Sollas’s Tetractinellida, p. 1xi. third*. They are seldom in a plane, but are usually inclined to one another in a solid, trihedral angle, not easy of precise measurement under the microscope. The three rays are very often supplemented by a fourth, which is set tetrahedrally, making, that is to say, coequal angles with the other three. The calcareous spicule consists mainly of carbonate of lime, in the form of calcite, with (according to von Ebner) some admixture of soda and* magnesia, of sulphates and of water. According to the same writer (but the fact, though it would seem easy to test, is still disputed) there is no organic matter in the spicule, either in the form of an axial filament or otherwise, and the appearance of stratification, often simulating the presence of an axial fibre, is due to “mixed crystallisation” of the various constituents. The spicule is a true crystal, and therefore its existence and its form are primardy due to the molecular forces of crystallisation ; moreover it is a single crystal and not a group of crystals, as is at once seen by its behaviour in polarised light. But its axes are not crystalline axes, and its form neither agrees with, nor in any way resembles, any one of the many polymorphic forms in which calcite is capable of crystallising. It is as though it were carved out of a solid crystal; it is, in fact, a crystal under restraint, a crystal growing, as it were, in an artificial mould; and this mould is constituted by the surrounding cells, or structural vesicles of the sponge. :

We have already studied in an elementary way, but amply for our present purpose, the manner in which three or more cells, or bubbles, tend to meet together under the influence of surfacetension, and also the outwardly similar phenomena which may be brought about by a uniform distribution of mechanical pressure. We have seen that when we confine ourselves to a plane assemblage of such bodies, we find them meeting one another in threes; that in a section or plane projection of such an assemblage we see the. partition-walls meeting one another at equal angles of 120°; that when the bodies are uniform in size, the partitions are straight lines, which combine to form regular hexagons; and that when

the bodies are unequal in size, the partitions are curved, and combine to form other and less regular polygons. It is plain, accordingly, that in any flattened or stratified assemblage of such cells, a solidified skeletal deposit which originates or accumulates either between the cells or within the thickness of their mutual partitions, will tend to take the form of triradiate bodies, whose - rays (in a typical case) will be set at equal angles of 120°(Fig. 214, F). And this latter condition of equality will be open to modification

Fig. 214. Spicules of Grantia and other calcareous sponges, (After Haeckel.) in various ways. It will be modified by any inequality in the specific tensions of adjacent cells; as a special case, it will be apt to be greatly modified at the surface of the system, where a spicule happens to be formed in a plane perpendicular to the cell-layer, so that one of its three rays lies between two adjacent cells and the other two are associated with the surface of contact between the cells and the surrounding medium; in such a case (as in the cases considered in connection with the forms of the cells themselves

on p. 314), we shall tend to obtain a spicule with two equal angles and one unequal (Fig. 214, A, C). In the last case, the two outer, or superficial rays, will tend to be markedly curved. Again, the equiangular condition will be departed from, and more or less curvature will be imparted to the rays, wherever the cells of the system cease to be uniform in size, and when the hexagonal symmetry of the system is lost accordingly. Lastly, although we speak of the rays as meeting at certain definite angles, this statement applies to their axes, rather than to the rays themselves. For, if the triradiate spicule be developed in the interspace between three juxtaposed cells, it is obvious that its sides will tend to be concave, for the interspace between our three contiguous equal circles is an equilateral, curvilinear triangle; and even if our spicule be deposited, not in the space between our three cells, but in the thickness of the intervening wall, thenewe may recollect (from p. 297) that the several partitions never actually meet at sharp angles, but the angle of contact is always bridged over by a small accumulation of material (varying in amount according to its fluidity) whose boundary takes the form of a circular arc, and which constitutes the “bourrelet” of Plateau.

In any sample of the triradiate spicules of Grantia, or in any series of careful drawings, such as those of Haeckel among others, we shall find that all these various configurations are precisely and completely illustrated. The tetrahedral, or rather tetractinellid, spicule needs no explanation in detail (Fig. 214, D, Z). For just as a triradiate spicule corresponds to the case of three cells in mutual contact, so does the four-rayed spicule to that of a solid aggregate of four cells: these latter tending to meet one another in a tetrahedral system, shewing four edges, at each of which four surfaces meet, the edges being inclined to one another at equal angles of about 109°. And even in the case of a single layer, or superficial layer, of cells, if the skeleton originate in connection with all the edges of mutual contact, we shall, in complete and typical cases, have a four-rayed spicule, of which one straight limb will correspond to the line of junction between the three cells, and the other three hmbs (which will then be curved limbs) will correspond to the edges where two cells meet one another on the surface of the system.

But if such a physical explanation of the forms of our spicules is to be accepted, we must seek at once for some physical agency by which we may explain the presence of the solid material just at the junctions or interfaces of the cells, and for the forces by which it is confined to, and moulded to the form of, these intercellular or interfacial contacts. It is to Dreyer that we chiefly owe the physical or mechanical theory of spicular conformation which I have just described,—a theory which ultimately rests on the form assumed, under surface-tension, by an aggregation of cells or vesicles. But this fundamental point being granted, we have still several possible alternatives by which to explain the details of the phenomenon.

Dreyer, if I understand him aright, was content to assume that the solid material, secreted or excreted by the organism, accumulated in the interstices between the cells, and was there subjected to mechanical pressure or constraint as the cells got more and more crowded together by their own growth and that of the system generally. As far as the general form of the spicules goes, such explanation is not inadequate, though under it we may have to renounce some of our assumptions as to what takes place at the outer surface of the system.

But‘in all (or most) cases where, but a few years ago, the concepts of secretion or excretion seemed precise enough, we are now-a-days inclined to turn to the phenomenon of adsorption as a further stage towards the elucidation of our facts. Here we have a case in point. In the tissues of our sponge, wherever two cells meet, there we have a definite surface of contact, and there accordingly we have a manifestation of surface-energy; and the concentration of surface-energy will tend to be a maximum at the lanes or edges whereby the three, or four, such surfaces are conjoined. Of the micro-chemistry of the sponge-cells our ignorance is great; but (without venturing on any hypothesis involving the chemical details of the process) we may safely assert that there is an inherent probability that certain substances will tend to be concentrated and ultimately deposited just in these lines of intercellular contact and conjunction. In other words, adsorptive concentration, under osmotic pressure, at and in the surfacefilm which constitutes the mutual boundary between contiguous

cells, emerges as an alternative (and, as it seems to me, a highly preferable alternative) to Dreyer’s conception of an accumulation under mechanical pressure in the vacant spaces left between one cell and another. But a purely chemical, or purely molecular adsorption, is not the only form of the hypothesis on which we may rely. For from the purely physical point of view, angles and edges of contact between adjacent cells will be loci in the field of distribution of surface-energy, and any material particles whatsoever will tend to undergo a diminution of freedom on entering one of those boundary regions. In a very simple case, let us imagine a couple of soap bubbles in contact with one another. Over the surface of each bubble there glide in every direction, as usual, a multitude of tiny bubbles and droplets; but as soon as these find their way into the groove or re-entrant angle between the two bubbles, there their freedom of movement is so far restrained, and out of that groove they have little or no tendency to emerge. A cognate phenomenon is to be witnessed in microscopic sections of steel or other metals. Here, amid the “crystalline” structure of the metal (where in cooling its imperfectly homogeneous material has developed a cellular structure, shewing (in section) hexagonal or polygonal contours), we can easily observe, as Professot Peddie has shewn me, that the little particles of graphite and other foreign bodies common in the matrix, have tended to aggregate themselves in the walls and at the angles of the polygonal cells—this being a direct result of the diminished freedom which the particles undergo on entering one of these boundary regions*.

It is by a combination of these two principles, chemical adsorption on the one hand, and physical quasi-adsorption or concentration of grosser particles on the other, that I conceive the substance of the sponge-spicule to be concentrated and aggregated at the cell boundaries; and the forms of the triradiate and tetractinellid spicules are in precise conformity with this hypothesis. A few general matters, and a few particular cases, remain to be considered.

It matters little or not at all, for the phenomenon in question, what is the histological nature or “ grade” of the vesicular structures on which it depends. In some cases (apart from sponges), they may be no more than the little alveoli of the intracellular protoplasmic network, and this would seem to be the case at least in one known case, that of the protozoan Entosolenia aspera, in which, within the vesicular protoplasm of the single cell, Mobius has described tiny spicules in the shape of little tetrahedra with concave sides. It 1s probably also the case in the small beginnings of the Echinoderm spicules, which are likewise intracellular, and are of similar shape. In the case of our sponges we have many varying conditions, which we need not attempt to examine in detail. In some cases there is evidence for believing that the spicule is formed at the boundaries of true cells or histological units. But in the case of the larger triradiate or tetractinellid spicules of the sponge-body, they far surpass in size the actual “cells”; we find them lying, regularly and symmetrically arranged, between the “pore-canals” or “ciliated chambers,” and it is in conformity with the shape and arrangement of these rounded or spheroidal structures that their shape is assumed.

Again, it is not necessarily at variance with our hypothesis to find that, in the adult sponge, the larger spicules may greatly outgrow the bounds not only of actual cells but also of the ciliated chambers, and may even appear to project freely from the surface of the sponge. For we have already seen that the spicule is capable of growing, without marked change of form, by further deposition, or crystallisation, of layer upon layer of calcareous molecules, even in an artificial solution; and we are entitled to believe that the same process may be carried on in the tissues of the sponge, without greatly altering the symmetry of the spicule, long after it has established its characteristic form of a system of slender trihedral or tetrahedral rays.

Neither is it of great importance to our hypothesis whether the rayed spicule necessarily arises as a single structure, or does so from separate minute centres of aggregation. Minchin has shewn that, in some cases at least, the latter is the case; the spicule begins, he tells us, as three tiny rods, separate from one another, each developed in the interspace between two sistercells, which are themselves the results of the division of one of a little trio of cells; and the little rods meet and fuse together while still very minute, when the whole spicule is only about 1, of a millimetre long. At this stage, it is interesting to learn that the spicule is non-crystalline; but the new accretions of calcareous matter are soon deposited in crystalline form.

This observation threw considerable difficulties in the way of former mechanical theories of the conformation of the spicule, and was quite at variance with Dreyer’s theory, according to which the spicule was bound to begin from a central nucleus coinciding with the meeting-place of the three contiguous cells, or rather the interspace between them. But the difficulty is removed when we import the concept of adsorption; for by this agency it is natural enough, or conceivable enough, that the process of deposition should go on at separate parts of a common system of surfaces; and if the cells tend to meet one another by their interfaces before these interfaces extend to the angies and so complete the polygonal | cell, it is again conceivable and natural that the spicule should first arise in the form of separate and detached limbs or rays.

aN ; whose spicules are composed of amor- 6h T phous silica or opal, all or most of the Hoa 6 } © above-described main types of spicule occur, and, as the name of the group implies, the four-rayed, tetrahedral spicules are especially represented. A somewhat frequent type of spicule is one in which one of the four rays is greatly developed, and the other three constitute small prongs diverging at equal angles from the main or axial ray. In all probability, as Dreyer suggests, we have here had to do with a group of four vesicles, of which three were large and co-equal, while a fourth and very much smaller one lay Fig. 215. . Spicules of tetractighoyve and between the other three.

a-e, anatriaenes; d-f, pro- , triaenes. wise one large and three much smaller rays, the latter are recurved, as in Fig. 215. This type, save for the constancy of the number of rays, and the limitation of the terminal ones to three, and save also for the more important difference that they occur only at one and not at both ends of the long axis, is similar to the type of spicule illustrated in Fig. 213, which we have explained as being probably developed within an oval cell, by whose walls its branches have been conformed to geodetic curves. But it is much more probable that we have here to do with a spicule developed in the midst of a group of three coequal and more or less elongated or cylindrical cells or vesicles, the long axial ray corresponding to their common

line of contact, and the three short rays having each lain in the surface furrow between two out of the three adjacent cells. Just as in the case of the little curved or S-shaped spicules, formed apparently within the bounds of a single cell, so also in the case of the larger tetractinellid and analogous types do we find among the Holothuroidea the same configurations reproduced as we have dealt with in the sponges. The holothurian spicules are a little less neatly formed, a little rougher, than the spongespicules; and certain forms occur among the former group which do not present themselves among the latter; but for the most part a community of type is obvious and striking (Fig. 216).

A curious and, physically speaking, strictly analogous formation to the tetrahedral spicules of the sponges is found in the spores of a certain little group of parasitic protozoa, the Actinomyxidia. These spores are formed from clusters of six cells, of which three come to constitute the capsule of the spore; and this capsule, always triradiate in its symmetry, is in some species drawn out into long rays, of which one constitutes a straight central axis, while the others, coming off from it at equal angles, are recurved in wide circular arcs. The account given of the development of this structure by its discoverers* is somewhat obscure to me, but I think that, on physical grounds, there can be no doubt whatever that the quadriradiate capsule has been somehow modelled upon a group of three surrounding cells, its axis lying between the three, and its three radial arcs occupying the furrows between adjacent pairs.

Fig. 217. Spicules of hexactinellid sponges. (After F. E. Schultze.) The typically six-rayed siliceous spicules of the hexactinellid sponges, while they are perhaps the most regular and beautifully formed spicules to be found within the entire group, have been found very difficult to explain, and Dreyer has confessed his complete inability to account for their conformation. But, though it is doubtless only throwing the difficulty a little further back, we may so far account for them by considering that the cells or vesicles by which they are conformed are not arranged in

what is known as “closest packing,” but in linear series; so that in their arrangement, and by their mutual compression, we tend to get a pattern, not of hexagons, but of squares: or, looking to the solid, not of dodecahedra but of cubes or parallelopipeda. This indeed appears to be the case, not with the individual cells (in the histological sense), but with the larger units or vesicles which make up the body of the hexactinellid. And this being so, the spicules formed between the linear, or cubical series of vesicles, will have the same tendency towards a “hexactinellid” shape, corresponding to the angles and adjacent edges of a system of cubes, as in our former case they had to a triradiate or a tetractinellid form, when developed in connection with the angles and edges of a system of hexagons, or a system of dodecahedra.

Histologically, the case is illustrated by a well-known phenomenon in embryology. In the segmenting ovum, there is a tendency for the cells to be budded off in linear series; and so _ they often remain, in rows side by side, at least for a considerable time and during the course of several consecutive cell divisions. Such an arrangement constitutes what the embryologists call the “radial type” of segmentation*. But in what is described as the “spiral type” of segmentation, it is stated that, as soon as the first horizontal furrow has divided the cells into an upper and a lower layer, those of “the upper layer are shifted in respect to the lower layer, by means of a rotation about the vertical axist.” It is, of course, evident that the whole process is merely that which is familiar to physicists as “close packing.” It is a very simple case of what Lord Kelvin used to call “a problem in tactics.” It is a mere question of the rigidity of the system, of the freedom of movement on the part of its constituent cells, whether or at what stage this tendency to slip into the closest propinquity, or position of minimum potential, will be found to manifest itself.

* See, for instance, the figures of the segmenting egg of Synapta (after Selenka), in Korschelt and Heider’s Vergleichende Entwicklungsgeschichte (Allgem. Th., 3*¢ Lief.), p. 19, 1909. On the spiral type of segmentation as a secondary derivative, due to mechanical causes, of the “radial” type of segmentation, see E. B. Wilson, not at all easy to determine) in relation to the tissues and chambers of the sponge, it is at least clear that, whether they be separate or be fused together (as often happens) in a composite skeleton, they effect a symmetrical partitioning of space according to the cubical system, in contrast to that closer packing which is represented and effected by the tetrahedral system*.

This question of the origin and causation of the forms of sponge-spicules, with which we have now briefly dealt, is all the more important and all the more interesting because it has been discussed time and again, from points of view which are characteristic of very different schools of thought in biology. Haeckel found in the form of the sponge-spicule a typical illustration of his theory of “bio-crystallisation’; he considered that these “biocrystals”’ represented “something midway—ein Muittelding— between an inorganic crystal and an organic secretion”; that there was a “compromise between the crystallising efforts of the calcium carbonate and the formative activity of the fused cells of the syncytium”; and that the semi-crystalline secretions of calcium carbonate “were utilised by natural selection as ‘spicules’ for building up a skeleton, and afterwards, by the interaction of adaptation and heredity, became modified in form and differentiated in a vast variety of ways in the struggle for existence f.” What Haeckel precisely signified by these words is not clear to me.

F. E. Schultze, perceiving that identical forms of spicule were developed whether the material were crystalline or non-crystalline, abandoned all theories based upon crystallisation; he simply saw in the form and arrangement of the spicules something which was “best fitted” for its purpose, that is to say for the support and strengthening of the porous walls of the sponge, and found clear evidence of “utility” in the specific structure of these skeletal elements.

* Chall. Rep. Hexactinellida, pls. xvi, liii, Ixxvi, 1xxxviii. + “Hierbei nahm der kohlensaure Kalk eine halb-krystallinische Beschaffenheit an, und gestaltete sich unter Aufnahme von Krystallwasser und in Verbindung mit einer geringen Quantitat von organischer Substanz zu jenen individuellen, festen K6rpern, welche durch die natiirliche Ziichtung als Spicula zur Skeletbildung beniitzt, und spiterhin durch die Wechselwirkung von Anpassung und Vererbung im Kampfe ums Dasein auf das Vielfaltigste umgebildet und differenziert wurden.” Die Kalkschwdémme, 1, p. 377, 1872; cf. also pp. 482, 483.

Sollas and Dreyer, as we have seen, introduced in various ways the conception of physical causation,—as indeed Haeckel himself had done in regard to one particular, when he supposed the position of the spicules to be due to the constant passage of the water-currents. Though even here, by the way, if I understand Haeckel aright, he was thinking not merely of a direct or immediate physical causation, but of one manifesting itself through the agency of natural selection*. Sollas laid stress upon the “ path of least resistance” as determining the direction of growth; while Dreyer dealt in greater detail with the various tensions and pressures to which the growing spicule was exposed, amid the alveolar or vesicular structure which was represented alike by the chambers of the sponge, by the reticulum of constituent cells, or by the minute structure of the intracellular protoplasm. But neither of these writers, so far as I can discover, was inclined to doubt for a moment the received canon of biology, which sees in such structures as these the characteristics of true organic species, and the indications of an hereditary affinity by which blood-relationship and the succession of evolutionary descent throughout geologic time can be ultimately deduced.

Lastly, Minchin, in a well-known papert, took sides with Schultze, and gave reasons for dissenting from such mechanical theories as those of Sollas and of Dreyer. For example, after pointing out that all protoplasm contains a number of “ granules” or microsomes, contained in the alveolar framework and lodged at the nodes of the reticulum, he argued that these also ought to acquire a form such as the'spicules possess, if it were the case that these latter owed their form to their very similar or identical position. “If vesicular tension cannot in any other instance cause the granules at the nodes to assume a tetraxon form, why should it do so for the sclerites?”” In all probability the answer to this question is not far to seek. If the force which the “mechanical” hypothesis has in view were simply that of mechanical pressure,

* Op. cit. p. 483. ‘* Die geordnete, oft so sehr regelmiassige und zierliche Zusammensetzung des Skeletsystems ist zum gréssten Theile unmittelbares Product der Wasserstr6mung; die characteristische Lagerung der Spicula ist von der constanten Richtung des Wasserstroms hervorgebracht; zum kleinsten Theile ist sie die Folge von Anpassungen an untergeordnete aiussere Existenzbedingungen.” + Materials for a Monograph of the Ascones, Q. J. M. S. xi. pp. 469-587, 1898.

as between solid bodies, then indeed we should expect that any substances whatsoever, lying between the impinging spheres, would tend (unless they were infinitely hard) to assume the quadriradiate or “tetraxon” form; but this conclusion does not follow at all, in so far as it is to surface-energy that we ascribe the phenomenon. Here the specific nature of the substances involved makes all the difference. We cannot argue from one substance to another; adsorptive attraction shews its effect on one and not on another; and we have not the least reason to be surprised if — we find that the little granules of protoplasmic material, which as they lie bathed in the more fluid protoplasm have (presumably, and as their shape indicates) a strong surface-tension of their own, behave towards the adjacent vesicles in a very ‘different fashion to the incipient aggregations of calcareous or siliceous matter ina colloid medium. ‘‘The ontogeny of the spicules,” says Professor Minchin, “ points clearly to their regular form being a phylogenetic adaptation, which has become fixed and handed on by heredity, appearing in the ontogeny as a prophetic adaptation.” And again, “The forms of the spicules are the result of adaptation to the requirements of the sponge as a whole, produced by the action of natural selection wpon variation im every direction.” It would scarcely be possible to illustrate more briefly and more cogently than by these few words (or the similar words of Haeckel quoted on p. 454), the fundamental difference between the Darwinian conception of the causation and determination of Form, and that which is characteristic of the physical sciences.