  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.
