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Steady state is an essential concept in reaction networks. Its stabilityreflects fundamental characteristics of several biological phenomena such ascellular signal transduction and gene expression. Because biochemical reactionsoccur at the cellular level, they are affected by unavoidable fluctuations.Although several methods have been proposed to detect and analyze the stabilityof steady states for deterministic models, these methods cannot be applied tostochastic reaction networks. In this paper, we propose an algorithm based onalgebraic computations to calculate parameter regions for constrainedsteady-state distribution of stochastic reaction networks, in which the meansand variances satisfy some given inequality constraints. To evaluate ourproposed method, we perform computer simulations for three typical chemicalreactions and demonstrate that the results obtained with our method areconsistent with the simulation results.

An algebraic method to calculate parameter regions for constrained steady-state distribution in stochastic reaction networks