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The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions
BACKGROUND: It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well des...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
BioMed Central
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3532178/ https://www.ncbi.nlm.nih.gov/pubmed/22583770 http://dx.doi.org/10.1186/1752-0509-6-39 |
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author | Thomas, Philipp Straube, Arthur V Grima, Ramon |
author_facet | Thomas, Philipp Straube, Arthur V Grima, Ramon |
author_sort | Thomas, Philipp |
collection | PubMed |
description | BACKGROUND: It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. RESULTS: We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. CONCLUSIONS: A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology. |
format | Online Article Text |
id | pubmed-3532178 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
spelling | pubmed-35321782013-01-03 The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions Thomas, Philipp Straube, Arthur V Grima, Ramon BMC Syst Biol Research Article BACKGROUND: It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. RESULTS: We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. CONCLUSIONS: A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology. BioMed Central 2012-05-14 /pmc/articles/PMC3532178/ /pubmed/22583770 http://dx.doi.org/10.1186/1752-0509-6-39 Text en Copyright ©2012 Thomas et al.; licensee BioMed Central Ltd. http://creativecommons.org/licenses/by/2.0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Thomas, Philipp Straube, Arthur V Grima, Ramon The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title | The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title_full | The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title_fullStr | The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title_full_unstemmed | The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title_short | The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
title_sort | slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3532178/ https://www.ncbi.nlm.nih.gov/pubmed/22583770 http://dx.doi.org/10.1186/1752-0509-6-39 |
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