Optimal control of cell proliferation at the molecular level

Molecular noise leads to variability in cell division times, which then leads to variability in population size. Thus, control exerted by a cell at the molecular level can have important consequences at the population level. However, the nature of this control and how it shapes distributions of division times and of population sizes remains poorly understood. In this work, we treat cell proliferation as a Bellman-Harris branching process with age-dependent division times. We discover a class of division time distributions, built from a series of Markovian steps, for which the population size distribution at all times is hierarchically calculable. We use this discovery to characterize the amount of influence that a given step has on the population size using an information-theoretic measure. This measure allows us to investigate optimal control of a population size at the molecular level. We discuss important features of the optimal strategies and make comparisons to experimentally observed division time distributions.