  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.
