Approximate Bayesian computation for estimating rate constants in biochemical reaction systems

To study the dynamic properties of complex biological systems, mathematical modeling has been used widely in systems biology. Apart from the well-established knowledge for modeling techniques, there are still some difficulties while understanding the dynamics in system biology. One of the major challenges is how to infer unknown parameters in mathematical models based on the experimentally observed data sets. This is extremely difficult when the experimental data are sparse and the biological systems are stochastic. To tackle this problem, in this work we revised one computation method for inference called approximate Bayesian computation (ABC) and conducted extensive computing tests to examine the influence of a number of factors on the performance of ABC. Based on simulation results, we found that the number of stochastic simulations and step size of the observation data have substantial influence on the estimation accuracy. We applied the ABC method to two stochastic systems to test the efficiency and effectiveness of the ABC and obtained promising approximation for the unknown parameters in the systems. This work raised a number of important issues for designing effective inference methods for estimating rate constants in biochemical reaction systems.

[1]  Mark M. Tanaka,et al.  Sequential Monte Carlo without likelihoods , 2007, Proceedings of the National Academy of Sciences.

[2]  D. Wilkinson,et al.  Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation , 2005, Biometrics.

[3]  M. Feldman,et al.  Population growth of human Y chromosomes: a study of Y chromosome microsatellites. , 1999, Molecular biology and evolution.

[4]  Linda R. Petzold,et al.  Accelerated maximum likelihood parameter estimation for stochastic biochemical systems , 2012, BMC Bioinformatics.

[5]  Xiaohui Xie,et al.  Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent , 2010, BMC Systems Biology.

[6]  Darren J. Wilkinson,et al.  Bayesian methods in bioinformatics and computational systems biology , 2006, Briefings Bioinform..

[7]  Chris A. Glasbey,et al.  A latent Gaussian model for compositional data with zeros , 2008 .

[8]  S. Tavaré,et al.  Modern computational approaches for analysing molecular genetic variation data , 2006, Nature Reviews Genetics.

[9]  David Welch,et al.  Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems , 2009, Journal of The Royal Society Interface.

[10]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[11]  J. Arnold,et al.  An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  J Timmer,et al.  Parameter estimation in stochastic biochemical reactions. , 2006, Systems biology.

[13]  Choujun Zhan,et al.  Parameter estimation in systems biology models using spline approximation , 2011, BMC Systems Biology.

[14]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[15]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Feng-Sheng Wang,et al.  Evolutionary optimization with data collocation for reverse engineering of biological networks , 2005, Bioinform..

[17]  Kevin R. Thornton,et al.  Approximate Bayesian Inference Reveals Evidence for a Recent, Severe Bottleneck in a Netherlands Population of Drosophila melanogaster , 2006, Genetics.

[18]  Masaru Tomita,et al.  Dynamic modeling of genetic networks using genetic algorithm and S-system , 2003, Bioinform..

[19]  A. Arkin,et al.  It's a noisy business! Genetic regulation at the nanomolar scale. , 1999, Trends in genetics : TIG.

[20]  Maksat Ashyraliyev,et al.  Systems biology: parameter estimation for biochemical models , 2009, The FEBS journal.

[21]  Junbin Gao,et al.  Simulated maximum likelihood method for estimating kinetic rates in gene expression , 2007, Bioinform..

[22]  Andrew R. Francis,et al.  Using Approximate Bayesian Computation to Estimate Tuberculosis Transmission Parameters From Genotype Data , 2006, Genetics.