Efficient calculation of steady state probability distribution for stochastic biochemical reaction network

Shahriar Karim,David M Umulis,Gregery T Buzzard

doi:10.1186/1471-2164-13-s6-s10

Shahriar Karim, David M Umulis + Show 1 more

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https://doi.org/10.1186/1471-2164-13-s6-s10

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Journal: BMC Genomics	Publication Date: Oct 1, 2012
Citations: 27	License type: CC BY 2.0

Affiliation: Purdue University West Lafayette

Abstract

The Steady State (SS) probability distribution is an important quantity needed to characterize the steady state behavior of many stochastic biochemical networks. In this paper, we propose an efficient and accurate approach to calculating an approximate SS probability distribution from solution of the Chemical Master Equation (CME) under the assumption of the existence of a unique deterministic SS of the system. To find the approximate solution to the CME, a truncated state-space representation is used to reduce the state-space of the system and translate it to a finite dimension. The subsequent ill-posed eigenvalue problem of a linear system for the finite state-space can be converted to a well-posed system of linear equations and solved. The proposed strategy yields efficient and accurate estimation of noise in stochastic biochemical systems. To demonstrate the approach, we applied the method to characterize the noise behavior of a set of biochemical networks of ligand-receptor interactions for Bone Morphogenetic Protein (BMP) signaling. We found that recruitment of type II receptors during the receptor oligomerization by itself doesn't not tend to lower noise in receptor signaling, but regulation by a secreted co-factor may provide a substantial improvement in signaling relative to noise. The steady state probability approximation method shortened the time necessary to calculate the probability distributions compared to earlier approaches, such as Gillespie's Stochastic Simulation Algorithm (SSA) while maintaining high accuracy.

Highlights

Many biological networks exhibit stochasticity due to a combinatorial effect of low molecular concentrations and slow system dynamics
Cv-2 has the ability to regulate the stochastic noise in Bone Morphogenetic Protein (BMP) signaling, and in this example we demonstrate that the role of Cv-2 is heavily dependent on reaction kinetics of the network: for some sets of parameter values, Cv-2 increases the coefficient of variation of the steady state signaling distribution, while for other parameter values it decreases the coefficient of variation
In this study, we illustrate an approach of determining the steady state probability distribution efficiently to carry on continuation in multiple variables within a large-scale parameter screen

Summary

Introduction

Many biological networks exhibit stochasticity due to a combinatorial effect of low molecular concentrations and slow system dynamics. BMPs make up the largest subfamily of the Transforming Growth Factor-b superfamily and are involved in numerous processes including growth, differentiation and diseases [1] Due to their potency at driving development, they are of great value for stem-cell differentiations in cell culture. BMP regulation occurs at many points along the pathway, and a lot of focus has been on identifying and understanding how the ligand activity is regulated in the extracellular environment by secreted binding proteins. These include molecules such as Cv-2, HSPGs, among other reviewed in [1]. A focus of this work is to gain a better understanding of how regulation in the extracellular region impacts cell signaling noise, and eventually cell-to-cell variability

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