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Long-time analytic approximation of large stochastic oscillators : simulation, analysis and inference
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Minas, Giorgos and Rand, D. A. (David A.) (2017) Long-time analytic approximation of large stochastic oscillators : simulation, analysis and inference. PLoS Computational Biology, 13 (7). e1005676. doi:10.1371/journal.pcbi.1005676
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Official URL: http://dx.doi.org/10.1371/journal.pcbi.1005676
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QH Natural history > QH301 Biology | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Systems biology, Stochastic models | ||||||
| Journal or Publication Title: | PLoS Computational Biology | ||||||
| Publisher: | Public Library of Science | ||||||
| ISSN: | 1553-7358 | ||||||
| Official Date: | 24 July 2017 | ||||||
| Dates: |
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| Date of first compliant deposit: | 5 October 2017 | ||||||
| Volume: | 13 | ||||||
| Number: | 7 | ||||||
| Article Number: | e1005676 | ||||||
| DOI: | 10.1371/journal.pcbi.1005676 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), Seventh Framework Programme (European Commission) (FP7) | ||||||
| Grant number: | BB/K003 097/1 (BBSRC), Grant agreement n ̊ 305564 (FP7) |
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