Geometrical constraints on the shape of cultured cells

Previous studies on cultured cells revealed that the values of certain shape descriptors were highly correlated despite the fact that there was little mathematical interdependence (Heckman, CA: In Advances in Cell Culture, Vol. 4, K. Maramorosch, ed, pp 85-156, 1985). The independence of such descriptors was tested by calculating the values of correlations among descriptors for a data set consisting of macroscopic objects. The descriptors were unlinked for this data set, confirming that high correlations reflected specific characteristics of cultured cells. These characteristics were identified by constructing model figures incorporating the geometrical features postulated to be responsible for each correlation. Because the position of the ellipse of concentration depended upon the form in which mass was displaced in figures, the fraction of the figure falling within the area of the ellipse (FINE) and the ratio of the ellipse area to the figure's area (ARAT) became decorrelated from each other in figures with massive projections. Further, correlations between ARAT or FINE and variables measuring cavities and inflections of the perimeter showed a complex dependence on the size, shape, and number of invaginations. Descriptors could become decorrelated due to features present in only a minority of cells of a population. Finally, cell populations that differed with respect to physiological characteristics showed no differences in the value of ARAT:FINE correlation. However, correlations between ARAT and the coefficient of variation of centroid-to-perimeter distances were altered. This suggested that correlation coefficients may be themselves powerful descriptors of the shape characteristics of cell populations.