Inference of circadian regulatory pathways based on delay differential equations

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Higham, Catherine F. ; Husmeier, Dirk (2015)

Inference of circadian regulatory network models is highly challenging due to the number of biological species and non-linear interactions. In addition, statistical methods that require the numerical integration of the data model are computationally expensive.\ud Using state-of-the-art adaptive gradient matching methods which model the data with Gaussian processes, we address these issues through two novel steps. First, we exploit the fact that, when considering gradients, the interacting biological species can be decoupled into sub-models which contain fewer parameters and are individually quicker to run. Second, we substantially reduce the complexity of the network by introducing time delays to simplify the modelling of the intermediate protein dynamics. A Metropolis-Hastings scheme is used to draw samples from the posterior distribution in a Bayesian framework. Using a recent delay differential equation model describing circadian regulation affecting physiology in the mouse liver, we investigate the extent to which deviance informa- tion criterion can distinguish between under-specified, correct and over- specified models.
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