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Long-time analytic approximation of large stochastic oscillators: simulation, analysis and inference

View ORCID ProfileGiorgos Minas, David A Rand
doi: https://doi.org/10.1101/068148
Giorgos Minas
1Zeeman Institute for Systems Biology and Infectious Epidemiology Research, Coventry CV4 7AL, UK
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David A Rand
1Zeeman Institute for Systems Biology and Infectious Epidemiology Research, Coventry CV4 7AL, UK
2Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
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Abstract

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also al-gorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still main-taining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statisti-cal inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

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Posted November 09, 2016.
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Long-time analytic approximation of large stochastic oscillators: simulation, analysis and inference
Giorgos Minas, David A Rand
bioRxiv 068148; doi: https://doi.org/10.1101/068148
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Long-time analytic approximation of large stochastic oscillators: simulation, analysis and inference
Giorgos Minas, David A Rand
bioRxiv 068148; doi: https://doi.org/10.1101/068148

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