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

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Minas_2018_PLoSCB_Stochasticoscillators_CC.pdf (2.556Mb)
Date
24/07/2017
Author
Minas, Giorgos
Rand, David A.
Keywords
QA Mathematics
QH301 Biology
Ecology, Evolution, Behavior and Systematics
Genetics
Molecular Biology
Computational Theory and Mathematics
Ecology
Modelling and Simulation
Cellular and Molecular Neuroscience
3rd-DAS
BDC
R2C
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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 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.
Citation
Minas , G & Rand , D A 2017 , ' Long-time analytic approximation of large stochastic oscillators : simulation, analysis and inference ' , PLoS Computational Biology , vol. 13 , no. 7 , e1005676 , pp. 1-23 . https://doi.org/10.1371/journal.pcbi.1005676
Publication
PLoS Computational Biology
Status
Peer reviewed
DOI
https://doi.org/10.1371/journal.pcbi.1005676
ISSN
1553-734X
Type
Journal article
Rights
© 2017 Minas, Rand. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Description
This research was funded by the BBSRC Grant BB/K003097/1 (Systems Biology Analysis of Biological Timers and Inflammation). DAR was also supported by funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 305564. BBSRC web site: www.bbsrc.ac.uk Seventh Framework Programme (FP7) website: cordis.europa.eu/fp7/home_en.html.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/15761

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