Stochastic threshold in cell size control

Classic models of cell size control consider cells divide while 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 noises. In this work, we study cell cycle as first-passage problem with stochastic threshold and discover such stochasticity affects the inter-division statistics, which bewilders the criteria to distinguish the types of size control models. The analytic results show the autocorrelation in the threshold can drive a sizer model to the adder-like and even timer-like inter-division statistics, which is supported by simulations. Following the picture that the autocorrelation in the threshold can propagate to the inter-division statistics, we further show that the adder model can be driven to the timer-like one by positive autocorrelated threshold, and even to the sizer-like one when the threshold is negatively autocorrelated. This work highlights the importance to examine gene noise in size control.