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Inference for stochastic oscillators with distributed delays

Banff International Research Station for Mathematical Innovation and Discovery

The time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops (TTFLs) by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here. We develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus (SCN).

Mathematics; Biology and other natural sciences; Probability theory and stochastic processes; Applied statistics

video/mp4

Author affiliation: University of Warwick

2020-12-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76692

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/