A Model for Statistics of the Cell Division Process

Abstract

SUMMARY: A model for the statistics of cell division is proposed. The model assumes: (1) that growth at the cellular level is deterministic; (2) that the mean size of a cell at division is under cellular and environmental control; (3) that the distribution of sizes of cells at division has a small coefficient of variation, and is independent of the size at previous divisions; (4) that the cell divides nearly into equal halves. The observed coefficient of variation of the life-length distributionf f (t) results from a twofold smaller coefficient of variation in the distribution of cellular mass at division, g (c). The magnification of the coefficient of variation results from the fact that the mass variable enters twice, once in determining the size of cell formed at division, and, secondly, in determining the size of the cell when it in turn divides. In the expression for T, these sizes enter as the logarithm of their ratio. These mathematical operations contribute to the increased coefficient of variation of the f (T) distribution over the g (c) distribution. The skewed nature of the f (T) distribution is attributable to a number of causes. We feel that an important source of the skewness is due to deviations from equi-partition of cell constituents at division. In this respect the present model is in disagreement with previous models which presume that the skewness results from the statistics of a small number of molecular events taking place inside each cell. The experimentally observed positive sister-sister life-length correlation and the negative mother-daughter life-length correlation are explained by the model. Deviations from the predicted values of + 0.5 and —0.5, respectively may be explained in part by deviation from equal distribution of cell contents at division. Deviations of the correlations in excess of these, observed in some cases, imply the existence of the other biological processes. The size distribution of cells in balanced growth cultures based on this model is given.