Inferring Parameters of Gene Regulatory Networks via Particle Filtering

Xiaohu Shen,Haris Vikalo

doi:10.1155/2010/204612

Abstract

Gene regulatory networks are highly complex dynamical systems comprising biomolecular components which interact with each other and through those interactions determine gene expression levels, that is, determine the rate of gene transcription. In this paper, a particle filter with Markov Chain Monte Carlo move step is employed for the estimation of reaction rate constants in gene regulatory networks modeled by chemical Langevin equations. Simulation studies demonstrate that the proposed technique outperforms previously considered methods while being computationally more efficient. Dynamic behavior of gene regulatory networks averaged over a large number of cells can be modeled by ordinary differential equations. For this scenario, we compute an approximation to the Cramer-Rao lower bound on the mean-square error of estimating reaction rates and demonstrate that, when the number of unknown parameters is small, the proposed particle filter can be nearly optimal.

Highlights

Gene regulatory networks (GRN) are systems comprising biomolecular components that interact with each other and through those interactions determine gene expression levels, that is, determine the rate of gene transcription to mRNA [1,2,3]
We studied the problem of estimating reaction rates in a gene regulatory network modeled by a chemical Langevin equation, that is, a high-dimensional stochastic differential equation
We proposed a solution which employs a particle filtering algorithm with Markov Chain Monte Carlo move step

Summary

Introduction

Gene regulatory networks (GRN) are systems comprising biomolecular components (genes, mRNA, proteins) that interact with each other and through those interactions determine gene expression levels, that is, determine the rate of gene transcription to mRNA [1,2,3]. Dynamic behavior of gene regulatory networks averaged over a large number of cells can be modeled by ordinary differential equations For this scenario, we compute an approximation to the CramerRao lower bound on the mean-square error of estimating reaction rates and demonstrate that, when the number of unknown parameters is small, the proposed particle filter can be nearly optimal. The function hm(X(t)) counts all possible combinations of individual molecules that may lead to a reaction in the mth channel.) The chemical master equation is often used to simulate the Markov process X(t) and enable computational studies of GRN To this end, one may employ various stochastic simulation algorithms, originally proposed by Gillespie [4].

Particle Filter with Markov Chain Monte Carlo Move Step

A Deterministic Model of Gene Regulatory Networks

Conclusions