The timing of cellular events: a stochastic vs deterministic perspective

Abstract

Changes in cell state are driven by key molecular events whose timing can often be measured experimentally. Of particular interest is the time taken for the levels of RNA or protein molecules to reach a critical threshold defining the triggering of a cellular event. While this mean trigger time can be estimated by numerical integration of deterministic models, these ignore intrinsic noise and hence their predictions may be inaccurate. Here we study the differences between deterministic and stochastic model predictions for the mean trigger times using simple models of gene expression, post-transcriptional feedback control, and enzyme-mediated catalysis. By comparison of the two predictions, we show that when promoter switching is present there exists a transition from a parameter regime where deterministic models predict a longer trigger time than stochastic models to a regime where the opposite occurs. Furthermore, the ratio of the trigger times of the two models can be large, particularly for auto-regulatory genetic feedback loops. Our theory provides intuitive insight into the origin of these effects and shows that deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells.