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

TL;DR

This paper introduces an algebraic algorithm to determine parameter regions ensuring constrained steady-state distributions in stochastic reaction networks, addressing the limitations of existing deterministic methods.

Contribution

It presents a novel algebraic approach to compute parameter regions for stochastic steady states with inequality constraints, filling a gap in current analysis techniques.

Findings

The method accurately predicts parameter regions consistent with simulation results.

It effectively handles inequality constraints on means and variances.

The approach is validated on three typical chemical reactions.

Abstract

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