Abstract
MotivationThe 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 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.ResultsWe 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.Availability and implementationProgrammes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD.Supplementary information Supplementary data are available at Bioinformatics online.
Highlights
The time evolution of molecular counts of chemical species in a reaction network is formally described by a Markov jump process (MJP)
We focus on systems where a set of intermediate transformations of the species of interest can be well approximated by the Goodwin oscillator ordinary differential equations (ODEs) (Goodwin, 1965), which can be explicitly solved
3.2.2 Inference performance We study the performance of the proposed filter for the purpose of Bayesian inference by designing a Markov chain Monte Carlo (MCMC) algorithm and applying it to the last five cycles of the simulated data (Fig. 1) with the aim of retrieving the values of the parameters used for the simulations
Summary
The time evolution of molecular counts of chemical species in a reaction network is formally described by a Markov jump process (MJP). Fearnhead et al (2014) find that in cases where the dynamics are non-linear, parameter inference via the LNA is improved by filtering, i.e. by replacing the mean and variance estimates of the process with their predicted value given the past observations. We develop a novel filtering algorithm that is based on the LNA and is generally applicable to stochastic systems comprising distributed delays, with a focus on dynamic state-space models for chemical reaction networks. We first introduce biochemical reaction networks, their exact mathematical description and the CLE and LNA approximations We consider their CLE and LNA approximation in the broader framework of state-space models, and illustrate the LNA updating algorithm in the context of non-delayed systems. The methodology is used to infer parameters of the TTFL of Cry from experimental time-series data observed in a mouse suprachiasmatic nucleus (SCN) tissue (Brancaccio et al, 2013)
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