Stochastic fluctuations in gene expression far from equilibrium: Omega expansion and linear noise approximation

The Omega expansion of the master equation is used to investigate the intrinsic noise in an autoregulatory gene expression system. This Omega expansion provides a mesoscale description of the system and is used to analyze the effect of feedback regulation on intrinsic noise when the system state is far from equilibrium. Using the linear noise approximation, analytic results are obtained for a single gene system with linear feedback that is far from equilibrium. Additionally, analytic expressions are obtained for nonlinear systems near equilibrium. Simulations of such autoregulatory reaction schemes with nonlinear feedback show that during the approach to equilibrium the noise is not always reduced by the strength of the feedback. This is contrary to results seen in the equilibrium limit which show decreased noise with feedback strength. These results demonstrate that the behavior of linearized systems near equilibrium cannot be readily applied to systems far from equilibrium and highlight the need to explore nonequilibrium domains in mesoscopic systems.