Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.
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 th...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2017-07-01
|
| Series: | PLoS Computational Biology |
| Online Access: | https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005676&type=printable |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849695270151913472 |
|---|---|
| author | Giorgos Minas David A Rand |
| author_facet | Giorgos Minas David A Rand |
| author_sort | Giorgos Minas |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-42bfbd338cf346e9ba082b33eba7eb8e |
| institution | DOAJ |
| issn | 1553-734X 1553-7358 |
| language | English |
| publishDate | 2017-07-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj-art-42bfbd338cf346e9ba082b33eba7eb8e2025-08-20T03:19:50ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582017-07-01137e100567610.1371/journal.pcbi.1005676Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.Giorgos MinasDavid A RandIn 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.https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005676&type=printable |
| spellingShingle | Giorgos Minas David A Rand Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. PLoS Computational Biology |
| title | Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. |
| title_full | Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. |
| title_fullStr | Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. |
| title_full_unstemmed | Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. |
| title_short | Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference. |
| title_sort | long time analytic approximation of large stochastic oscillators simulation analysis and inference |
| url | https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005676&type=printable |
| work_keys_str_mv | AT giorgosminas longtimeanalyticapproximationoflargestochasticoscillatorssimulationanalysisandinference AT davidarand longtimeanalyticapproximationoflargestochasticoscillatorssimulationanalysisandinference |