Efficient simulation of heterogeneity and stochasticity in microbial processes

Variability and stochasticity are fundamental features of biochemical systems. Heterogeneity of a cell population refers to individual cell state differences determined by various intercellular and extracellural factors (protein abundances, cell viability, cell cycle). The origin of heterogeneity is a complex interplay of intrinsic, external and extrinsic noise, that is poorly understood (Delvigne and Goffin, 2014; Patnaik, 2006). Due to challenges in experimental monitoring and numerical modelling of the temporal evolution of heterogeneous cell populations, the potential for bioprocess design is hard to be exploited by engineers. Therefore, in our contribution we present a hybrid approach for modelling distributed stochastic processes by means of stochastic ordinary differential equations. Our approach is based on a combination of the sigma point method and an approximate version of the stochastic simulation algorithm (Julier et al., 2000; Gillespie, 2007). Whereas the former one allows to efficiently describe extrinsic and external fluctuations as stochastic inputs to the model equations, the latter provides an efficient approximation to the solution of the chemical master equation for describing stochasticity in the biochemical reactions. In this way, we have an efficient simulation and analysis tool to rapidly study and exploit the interplay between intrinsic, extrinsic and external fluctuations for microbial process design. We apply our approach to a simple model of gene expression and benchmark the performance.