Noise Treatment in Models of Genetic Switches

Abstract

Mathematical modeling plays a key role in understanding and characterization of critical chemical processes underlying the dynamics of cellular decision-making. Deterministic modeling of relevant processes in complex genetic networks through a set of biochemical reactions is generally thought to predict an average kinetic behavior. Stochastic kinetic methods, accounting for random fluctuations, become essential to characterize intrinsic heterogeneity due to low copy numbers and noisy environments present in these systems. While in certain regulatory constructs, it has been shown that a fully discrete stochastic treatment of fluctuations through the Chemical Master Equation yields multi-stability when deterministic treatment predicts monostability; deterministic or continuous approaches continues to be the most widespread method for modeling the behavior of cell populations. We explore stochastic variability in cellular dynamics through a varied treatment of intrinsic noise, the randomness arising either at the level of a single reaction, single molecule or as a drift in concentration of the involved species. Our study involves modeling of a genetic toggle switch which is a set of two mutually repressing genes, acting as a cellular “memory device” during cell differentiation process, deciding the final cell fate. We simulate the complex switching dynamics between the multi-attractor states in these systems through direct sampling using continuous stochastic approaches Langevin dynamics and Fokker Plank equation as well as discrete stochastic methods Gillespie's Stochastic Simulation Algorithm and numerical solution of the Chemical Master Equation. The stochastic trajectories obtained through numerical simulations not only unveil the complex dynamics leading to multi-stability, they also help explore rigorously the variations, if any, in the dynamics of transitions. Our results can further be used to compare the statistics of switching events and hence to benchmark the various computational methods available to model stochasticity in such systems.