Mass, length and growth rate in single cells

Abstract

A heuristic model for the time course of elongation and mass increase of a population of single cells with generation times different from the mean is considered. The fundamental assumption is that the dynamics governing the fluctuations around the mean are the same as those describing the mean itself. Cell length is assumed to depend on cell mass by a 1 3 power law. The final cell length and mass are obtained by demanding that a daughter cell's initial length and mass obey the same equation as those of the mother cell when the mother cell was born. An exponential time course is assumed for simplicity, although most of the results depend only on the initial and final values, not the actual time behavior. The aspect ratio (length/radius) is found to be a constant for all cells at birth, and twice that value at maturity. Thus the individual generation time is a doubling time for the aspect ratio, even though neither mass nor length double in general. Oscillations in ancestor/progeny generation times are derived, and their stability considered. The model yields a non-hereditary determinant of individual generation time. The well-known skewness in the distribution of individual generation times and the “β-plots” of the transition probability model find a natural explanation in the inequality of cell division.