Bayesian inference for a discretely observed stochastic kinetic model
Statistics and Computing
Local Identification of Piecewise Deterministic Models of Genetic Networks
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Formal Analysis of the Genetic Toggle
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Parameter identification for Markov models of biochemical reactions
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
The Monte Carlo EM method for the parameter estimation of biological models
Electronic Notes in Theoretical Computer Science (ENTCS)
Parameter estimation for stochastic hybrid models of biochemical reaction networks
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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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 non-parametric 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 optimization 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. Contact: tian@maths.uq.edu.au