Computing at Glasgow University
Paper ID: 8879
DCS Tech Report Number: TR-2008-274

Inference in a Gene Regulatory Network with Transcriptional Time Delay

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2008

Background: Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework. A Markov chain Monte Marlo approach can then be used to sample from the appropriate posterior probability distributions, provided that suitable prior distributions can be found for the unknown parameter values. Choosing these priors is therefore a vital first step in the inference process. We study here a negative feedback loop in gene regulation where an ODE incorporating a time delay has been proposed as a realistic model and where experimental data is available. Our aim is to show that a priori mathematical analysis can be exploited in the choice of priors. Results: By focussing on the onset of oscillatory behaviour through a Hopf Bifurcation, we derive a range of analytical expressions and constraints that link the model parameters to the observed dynamics of the system. Computational tests on both simulated and experimental data emphasise the usefulness of this analysis. Conclusions: Mathematical analysis not only gives insights into the possible dynamical behaviour of gene expression models, but can also be used to inform the choice of priors when parameters are inferred from experimental data in a Bayesian setting.

Keywords: delay differential equations, Hopf Bifurcation, Bayesian Inference

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