POLYGONAL ASPECTS OF CELL FACES. III. CELL SIZE, CELL DIVISION, AND CELL FACE DISTRIBUTIONS

WHEELER, GEORGE E. (Brooklyni Coll., Brooklyn, New York.) Polygonal aspects of cell faces. III. Cell size, cell division, and cell face distributions. Amer. Jour. Bot. 50(8): 747-754. Illus. 1963.-The effects of cell size differences on cell face (polygon type) distributions, and the relationship of cell division to these effects were investigated, using published and original data. Only "relative" size was considered, i.e., the size of a body compared with the sizes of ccnitiguous bodies. A preliminary study of mixtures including 2 sizes of nonliving bodies (bubbles or shot) showed that, with increase in number of smaller bodies relative to larger, 4and 5-gons decrease and 6-gons increase on both large and small bodies (except for 5-gons on small bubbles). Since the cited papers on cells generally include no volume measurements, cell size was assumed to be proportional to number of faces; therefore, the cells from each sample were pooled in 3 groups of different ranges as to number of faces per cell. This device made evident the 4and 5-gon decreases and the 6-gon increases with increasing size, but only in certain samples; marked exceptions occurred among others. New data from 2 original samples showed, in general, the correlations described above, but again there were exceptions. Discrepancies were found to arise from variable division patterns whieh affect face types both directly, and indirectly through division effects on cell size. It was concluded that relative size is generally less important in determining cell face distributions than are the more direct cell division events, and that size difference effects can be detected only if the other events operate minimally. THE FIRST 2 papers of this series (Wheeler, 1962a, b) dealt with the importance of cell division in maintaining an already existing predominance of a particular face (polygon) type. Published data were used in these investigations, and many of the authors had reported some size variation among the cells of their samples. Nevertheless, size differences were assumed to have effects below the "resolving power" of the technique employed. MVarvin (1944), however, showed conclusively that differences in cell size, if large enough, significantly alter geometric aspects of cell shape. The purpose of this third paper, then, is to examine (1) the relationship of unequal cell size to cell face distributions (particularly to the more abundant face types) and (2) the effect of cell division on this relationship. MATERIALS AND METHODS-The first paper of the series (Wheeler, 1962a) includes a brief discussion of terminology and of other relevant points. The terms "pentagon," "hexagon," etc., are abbreviated to "5-gon," "6-gon," etc. In addition to the literature data, original observations were made on samples of 2 kinds of large cells: differentiating xylem vessel members from the hypocotyl of sprouting Cucurbita maxima ("banana" squash) seeds, and crystal cells from an aerial root of Monstera deliciosa. The organs were prepared by routine procedures. Face types were identified on camera lucida drawings, using a modification of Lier's (1952) method. 1 Received for publication June 26, 1962. DATA AND DISCUSSION OF SPECIFIC POINTSNonliving systems: observations on bubbles and on metal shot-In his studies of soap bubble foams, Matzke (1945, 1946) found no significant differences either in average numbers of faces per bubble or in face type distributions (percentages of 4-, 5-, 6-gons, etc.) between a foam made exclusively of 1 cc bubbles and one made exclusively of -I cc bubbles. Earlier, Marvin (1939) had made similar observations on 2 separate size classes of compressed shot. However, if large and small bubbles are mixed together in the same foam (Matzke, 1945; Matzke and Nestler, 1946) or if large and small shot are compressed together (Matzke, 1939), then the 2 size classes differ significantly both in average numbers of faces per body and in face type distributions. Obviously, the term "size" requires clarification. In this paper, absolute size will not be considered, and the terms "body size" and "cell size" will mean the size of the object, relative to the size of its immediate neighbors. As few as 2 volume classes may differ from each other in the magnitude of the volume difference, in the ratio of the numbers of large to small entities, or in both. Matzke (1939) compressed together 2 sizes of shot (volume ratio of 8/1) in 3 different experiments, each with a different relative number of large to small, i.e., respectively 2, 8, and . He repeated the study using bubbles of similar relative volume, mixed in the same 3 ratios (Matzke, 1945; Matzke and Nestler, 1946). Table 1 gives the face distributions for each [The JOURNAL for August (50: 641-745) was issued August 21, 19631 AMERICAN JOURNAL OF BOTANY, Vol. 50: No. 8, 1963