The Three‐dimensional Shape of Plant Cells and Its Relationship to Pattern of Tissue Growth

Abstract

SUMMARYTwo geometric models were devised for the shape of plant cells, one for those cells undergoing three-dimensional expansion and the other for cells enlarging in one dimension (elongation). Probability distributions for the number and shape of wall facets were generated from the models and compared favourably with those found for real cells by other investigators. The i-D growth model gave averages for the facet number and geometry of cells at interphase, division and daughter cell formation that closely approximated the averages from data collected by previous workers. These two types of developmental models, that is, ones following the quantitative relationships between cells over several generations, have two advantages over the standard interpretation of cell shape as the expression of packing forces. First, shape is explicitly explained from defined positions of cell plates during divisions. Second, subtle features of cell shape have morphogenetic importance in revealing the recent history of a cell with respect to its growth and its ontogenetic relationship to neighbouring cells.

Concerning the Sinuous Shape of Leaf Epidermal Cells

“…It would also seem that the sinuous growth pattern would provide more secure attachment between epidermal and mesophyll cells. The number of palisade cells in contact with an epidermal cell varies from one to nine and averages four (Korn, 1974a) but some of these contacts involve small areas. By regional expansion of the basal periclinal walls in accommodation to lobe growth more contact space with mesophyll cells is possible than by uniform growth alone and, also, a more uniform spacing between mesophyll cells becomes possible (Figs.…”

“…Cultures of gametophytes of Dryopteris thelypteris were used for growth studies (Korn, 1974a) within which a low frequency (io~^) of atypical plants were found. These thalli are characterized by the replacement of the single apical cell by an elongated group of cells usually containing some xylem cells (Plate i, Nos.…”

“…Recently the author (Korn and Spalding, 1973;Korn, 1974a) has suggested several methods by which the two-and three-dimensional geometries of cells can be quantitatively portrayed. The assumptions on which these descriptive methods were based are (i) no two cells of a tissue are morphologically identical although all cells are derived from the same developmental processes, (2) these processes have distinct indeterministic elements which in model construction are stated as probabilistic rules and (3) the joint treatment of these rules will then describe all cells by a statistical statement about a population of cells.…”

ORIGIN OF INTERNODAL AIR SPACES IN HIPPURIS VULGARIS L.

“…A vertex can open to form an air space, can deposit additional wall material and also prevent new cell plates from becoming attached (Sinnott and Bloch, 1941;Korn, 1974). Also, in considering an edge as a morphogenetic region it becomes possible to understand how one may influence another through some spreading effect along its surface, much in the same manner as wall thickenings extend over increasingly greater areas during collenehyma maturation.…”

“…Although Barratt (1916) carefully followed the history of cell patterns in the relationship to the locations of air spaces, she did not identify the important ordering process(es) which determine the initial arrangement of air spaces. This study is an attempt to characterize this ordering feature through model construction that simulates several statistical, and therefore quantitative, features of the adult tissue in a manner carried out previously on other tissues (Korn, 1972(Korn, , 1974Korn and Spalding, 1973;Korn and Fredrick, 1973). v.'-5ri.fi iHciU''.…”