Volume-shape relationships in variant foams A further study of the role of surface forces in three-dimensional cell shape determination

IT HAS been suggested for a long time by various investigators that surface forces play a part in threedimensional cell shape determination and, consequently, in plant and animal development. Recently the importance of such forces has been analyzed through a study of bubbles of uniform size in a specially constructed foam. While investigation of such an almost perfect foam serves to throw light on the general and theoretical aspects of this whole problem, no tissue has been studied in which the cells, like the bubbles, were all of equal volume. In order to achieve more direct comparisons between nonliving and cellular systems, an additional series of experiimients has been conducted in which the volumes of the bubbles in a foam were varied in specific and controlled ways. The data assembled should make possible, first, a further comparison between cells in tissues and bubbles in foam; secondly, and this is of greater importance, such data should permit a more complete analysis of the part which surface forces play in the establishment of the three-dimensional shapes of cells, and therefore, inevitably, in certain aspects of the development of plants and animals. LITERATURE REVIEW.-An extensive survey of the literature dealing with soap films and their bearing on the general subject of cell shapes has recently been made (Matzke, 1946). Since the present article is in a sense a continuation of that one, in which complete citations are given, only those aspects of the literature which deal specifically with the problem outlined in the preceding paragraph will be mentioned here. All the cells which have been studied and modeled have varied in size. Data are available for comparison with soap bubbles especially in the following tissues which have been investigated by various authors: 100 elder (Sambucus canadensis) pith cells (Lewis, 1923), 100 human fat cells (Lewis, 1925), 50 tadpole precartilage cells (Lewis, 1933), 100 Eupatorium purpureum pith cells (Marvin, 1939b), 100 A4ngiopteris evecta petiole parenchyma cells (Higinbotham, 1942), 100 Citrus grandis carpel vesicle cells (Dodd, 1944), 100 Eupatorium perfoliatumpith cells (Marvin, 1944), 150 Ailanthus glandulosa pith cells (Hulbary, 1944), 600 Anacharis densa .(Elodea) cortical cells (Hulbary, 19-14). The data on soap films gain added significance when they are compared and contrasted with the cellular statistics presented by these investigators, as shown below. A system in which the effect of surface forces in shape determination is not of major significance had been analyzed previously; lead shot of uniform size were compressed in a steel cylinder to eliminate interstices, and the pellets were then picked apart and the number of contacts re1 Received for publication June 12, 1945. corded by Marvin (1939a). Similar investigations on large and small shot, mixed in varying proportions and compressed to eliminate interstices, were made by Matzke (1939). The work on large and small soap bubbles mixed in varying proportions described below is a counterpart of this earlier study on the large and small shot. In the soap films, in contrast to the shot, surface forces are obviously of marked importance. Comparisons of two such systems, composed of units of varying sizes, with cells in tissues, the cells also not uniform in size, should throw further light on the part which surface forces play in three-dimensional cell shape determination. The general topic of cell shapes has been reviewed in recent years by Thompson (1942), Lewis (in Bremer-Weatherford, 1944), and Mlatzke (1940). MIATERIAL AND METHODS.-The technique used in the three sets of experiments described below was essentially similar to that described for bubbles of uniform size (Matzke, 1946), except that in the present work bubbles of two different sizes were made, one by one, and mixed in definite and known proportions. The soap solution, as previously, conisisted of the following parts: triethanolaminie oleate 7.5 g., glycerine 34 g., and distilled water 58.5 g. These materials were shaken together and then allowed to stand for several weeks. Each bubble was made separately by setting the plunger of a Yale tuberculin syringe, graduated to 1/100 cc., so that the syringe contained .05 cc. or .4 cc. of air (depending uponi whether a small or a large bubble was to be made), then touching the tip of the syringe in the soap solution, and pushing down the plunger. In that way it was possible to make bubbles of fairly precise and known volumes. After each bubble was "blown," the tip of the syringe was wiped on cheesecloth to remove excess soap solution. The bubbles were placed, one by one, into a cylindrical dish having an inside diameter of 6 cm. and an inside height of 6.5 cm., with a volume of 188 cc. The inside of the dish was moistened beforehand with the soap solution. A glass plate was used as a cover. The dish was never completely filled, so that the bubbles did not come in contact with the glass plate on top even when temperature increases resulted in expansion. The dish was rotated from time to time, to keep the solution distributed as uniformly as possible and to allow the bubbles to slip and adjust themselves; if the bubbles were to be kept for some time, the dish was rotated on its long axis on a clinostat. Although the bubbles would last for days, they were always studied as soon as possible, after a brief rotation, on the same day on which they were made. The general appearance of the dish with bubbles was similar to that shown in figures 1 and 2 of a