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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.
Date of Conference: 4-6 Dec. 2011