Modeling biological timing and synchronization mechanisms by means of interconnections of stochastic switches

Timing and synchronization mechanisms are ubiquitous in living systems, and in many cases involve switch-like regulators that control complex molecular pathways and cellular functions. The switching of such regulators is often irreversible and controlled by the co-activation of a set of concurrent independent enabling events. Despite the random nature of each individual switch, the timing in the onset of the controlled process has a rather small variability. This note introduces a mathematical framework for the description of the collective behavior of populations of interconnected stochastic switches. The main contribution of this note is to explain how the connecting mode (series/parallel) of switches affects the behavior of the entire switch population and in particular the degree of synchronization. We describe the switch model for the G1/S phase transition in yeast and briefly discuss the general utility of this class of models in systems biology.