Approximation scheme based on effective interactions for stochastic gene regulation

TL;DR

This paper introduces an approximation method using effective interactions to analytically solve master equations in stochastic gene regulation, effectively capturing behaviors like bistability in small-molecule systems.

Contribution

The authors develop a novel approximation scheme that simplifies master equations in stochastic gene regulation, enabling analytical solutions for complex systems.

Findings

Successfully recovers bistability in the exclusive switch model

Provides analytical solutions for self-regulating gene systems

Effective in handling systems with small molecule numbers

Abstract

Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme for dealing with the stochasticity of the gene regulatory systems. Using an effective interaction concept, original master equations can be reduced to simpler master equations, which can be solved analytically. We apply the approximation scheme to self-regulating systems with monomer or dimer interactions, and a two-gene system with an exclusive switch. The approximation scheme can recover bistability of the exclusive switch adequately.