Cell-division time statistics from stochastic exponential threshold-crossing

Abstract

For cell division to take place, proteins that carry it out need to accumulate to a functional threshold. Most of these divisome proteins are highly abundant in the cell, and accumulate smoothly and approximately exponentially throughout the cell cycle. In this threshold-crossing process, stochastic components arise from variation from one cycle to the next of accumulation rate and division fraction, and from fluctuations of the threshold itself. How these combine to determine the statistical properties of division times is still not well understood. Here we formulate this stochastic process and calculate the statistical properties of cell division times by using first passage time (FPT) techniques. We find that the distribution shape is determined by a ratio between two coefficient of variations (CVs), interpolating between Gaussian-like and long-tailed. Mean, variance and skewness of division times are predicted to follow well-defined relationships with model parameters. Publicly available single-cell data span a broad range of values in parameter space; the measured distribution shape and moment scaling agree well with the theory over the entire range. Because of balanced biosynthesis, the accumulation dynamics of any abundant protein – as well as cell size – predicts division time statistics equally well using our model. These results suggest that cell division is a multi-variable emergent process, which is nevertheless predictable by a single variable thanks to coupling and correlations inside the system.