Extrinsic Noise Enhances Switching in Models of Cellular Decision Making

Abstract

Numerous biological processes do not follow deterministic rules, i.e., genetically identical cells can display different phenotypes even in identical environments. Such processes involve what is termed cellular decision making, where individual cells probabilistically make choices that determine their fate. One view of cellular decision making is that stochastic noise present in the biomolecular interaction networks responsible for the decisions is a major factor in their probabilistic nature. Most previous work has been focused on the intrinsic noise of these networks, but, especially for high copy-number biomolecules, extrinsic noise is likely much more significant. Here we present a theoretical study of switching in such networks and show that extrinsic noise can not only lower (often by multiple orders of magnitude) the escape time from a stable decision state, but can fundamentally change the process of escape.We first develop an analytical theory for studying how a simple self-regulating gene, which is bistable with hi and low states, is affected by extrinsic noise. Studying the system near bifurcation, we use Fokker-Planck and WKB theory along with a novel formulation of the extrinsic noise to predict the deviation in mean switching time due to the extrinsic noise. We use computational simulations to validate our theory and then to study a more relevant biological system, namely the lac genetic switch.The white noise and weak, adiabatic noise regimes are well described by a barrier-crossing model with corrections. In the strong, adiabatic noise regime, however, extrinsic noise changes the behavior of stochastic switching. A large contribution to switching in this regime originates from movement of the dynamical system in parameter space, which changes the number and location of fixed points. These results have implications for studying natural cellular processes and for engineering complex genetic programs.