Stochastic threshold in cell size control

Abstract

Classic models of cell size control consider that cells divide when reaching a threshold, e.g., size, age, or size extension. The molecular basis of the threshold involves multiple layers of regulation as well as gene noise. In this paper, we study the cell cycle as a first-passage problem with a stochastic threshold and discover that such stochasticity affects the intergeneration statistics, which bewilders the criteria to distinguish the types of size control models. The analytic results show that the autocorrelation in the threshold can drive a sizer model to the adderlike and even timerlike intergeneration statistics, which is supported by simulations. Following the picture that the autocorrelation in the threshold can propagate to the intergeneration statistics, we further show that the adder model can be driven to the timerlike one by a positively autocorrelated threshold, and even to the sizerlike one when the threshold is negatively autocorrelated. This work highlights the importance of examining gene noise in size control.