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Steady state probability approximation applied to stochastic model of biological network

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3 Author(s)
Md. Shahriar Karim ; Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47901, USA ; David M. Umulis ; Gregery T. Buzzard

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.

Published in:

2011 IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS)

Date of Conference:

4-6 Dec. 2011