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Bioinformatics Advance Access published online on October 26, 2006
Bioinformatics, doi:10.1093/bioinformatics/btl552
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© The Author (2006). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received June 23, 2006
Revised October 5, 2006
Accepted October 23, 2006

Article

Simulated maximum likelihood method for estimating kinetic rates in gene expression

Tianhai Tian 1 *, Sonling Xu 2, Junbin Gao 3, and Kevin Burrage 1

1 Advanced Computational Modelling Centre, University of Queensland, Brisbane, QLD 4072, Australia
2 Advanced Computational Modelling Centre, University of Queensland, Brisbane, QLD 4072, Australia; Department of Mathematics, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China
3 School of Information Technology, Charles Sturt University, Bathurst, NSW 2795, Australia

* To whom correspondence should be addressed.
Tianhai Tian, E-mail: tian{at}maths.uq.edu.au


  Abstract

Motivation: Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment.

Results: In this paper we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of nonparametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimisation algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Associate Editor: Jonathan Wren
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