Optimal information transmission in a sequential model for cell division
In proliferating cell populations, adaptive changes to biochemical reactions can change a cell's division time, which in turn can change the population size. However, biochemical reactions are subject to noise, and therefore the conditions for optimal information transmission from the molecular to the population scale are poorly understood. Here, we model cell proliferation as a Bellman-Harris branching process with age-dependent division times. We identify 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 feature to characterize the amount of influence that a given reaction step has on the population size via the mutual information. We find that information transmission is optimal for a characteristic number of steps until division: too few and the population size is unpredictable; too many and any given step has vanishing influence on the population size. Our work reveals the potential tradeoffs involved in adaptive decision making at the sub-cellular, cellular and population scales.