Stochastic Hybrid Models of Gene Regulatory Networks - A PDE Approach

Abstract

A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance. We show that the hybrid approach yields accurate results for sufficiently large molecule counts, while reducing the computational effort from one ordinary differential equation for each state to one partial differential equation for each mode of the system. Furthermore, we give an analytical steady-state solution of the hybrid model for the case of a self-regulatory gene.

arXiv comment16 pages, 3 figures, 2 tables, V3: added performance comparison for numerical solution + 1 reference

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Cited by in corpus (5)

• Stochastic modeling of auto-regulatory genetic feedback loops: a review and comparative study
• Analytic solutions for stochastic hybrid models of gene regulatory networks
• Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
• Efficient stochastic simulation of gene regulatory networks using hybrid models of transcriptional bursting
• Push-forward method for piecewise deterministic biochemical simulations