Since gene regulatory systems sometimes contain 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 the bistability of the exclusive switch adequately.

• Received 13 December 2010

DOI:https://doi.org/10.1103/PhysRevE.83.041915