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

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Author(s)

Giorgos Minas, David A. Rand

School/Research organisations

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 algorithms 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 maintaining 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 statistical 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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Details

Original languageEnglish
Article numbere1005676
Number of pages23
JournalPLoS Computational Biology
Volume13
Issue number7
DOIs
Publication statusPublished - 24 Jul 2017

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