A general mathematical framework to model generation structure in a population of asynchronously dividing cells.

In otherwise homogeneous cell populations, individual cells undergo asynchronous cell cycles. In recent years, interest in this fundamental observation has been boosted by the wide usage of CFSE, a fluorescent dye that allows the precise estimation by flow cytometry of the number of divisions performed by different cells in a population, and thus the generation structure. In this work, we propose two general mathematical frameworks to model the time evolution of generation structure in a cell population. The first modeling framework is more descriptive and assumes that cell division time is distributed in the cell population, due to intrinsic noise in the molecular machinery in individual cells; while the second framework assumes that asynchrony in cell division stems from randomness in the interactions individual cells make with environmental agents. We reduce these formalisms to recover two preexistent models, which build on each of the hypotheses. When confronted to kinetics data on CFSE labeled cells taken from literature, these models can fit precursor frequency distributions at each measured time point. However, they fail to fit the whole kinetics of precursor frequency distributions. In contrast, two extensions of those models, derived also from our general formalisms, fit equally well both the whole kinetics and individual profiles at each time point, providing a biologically reasonable estimation of parameters. We prove that the distribution of cell division times is not Gaussian, as previously proposed, but is better described by an asymmetric distribution such as the Gamma distribution. We show also that the observed cell asynchrony could be explained by the existence of a single transitional event during cell division. Based on these results, we suggest new ways of combining theoretical and experimental work to assess how much of noise in internal machinery of the cell and interactions with the environmental agents contribute to the asynchrony in cell division.