Continuous Rate Modelling of bacterial stochastic size dynamics

Bacterial division is an inherently stochastic process. However, theoretical tools to simulate and study the stochastic transient dynamics of cell-size are scarce. Here, we present a general theoretical approach based on the Chapman-Kolmogorov formalism to describe these stochastic dynamics including continuous growth and division events as jump processes. Using this approach, we analyze the effect of different sources of noise on the dynamics of the size distribution. Oscillations in the distribution central moments were found as consequence of the discrete translation invariance of the system with period of one doubling time, these oscillations are found in both the central moments of the size distribution and the auto-correlation function and do not disappear including stochasticity on division times or size heterogeneity on the population but only after include noise in either growth rate or septum position.