Steady state probability approximation applied to stochastic model of biological network

Abstract

The Steady State (SS) probability distribution for the Chemical Master Equation (CME) is an important quantity used to characterize many biological systems. In this paper, we propose a comparatively easy, yet efficient and accurate, way of finding the SS distribution assuming the existence of a unique deterministic SS (unimodal) of the system. In order to find the approximate SS, we first use the truncated-state space representation to reduce the system to a finite dimension, and subsequently reformulate an eigenvalue problem into a linear system. To demonstrate the utility of the approach, we apply the method and determine the SS probability distribution to quantify the parameter dependency of surface-associated BMP binding proteins (SBPs) in the regulation of BMP mediated signaling and pattern formation.