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dc.contributor.authorKim, Jae Kyoung
Josić, Krešimir
Bennett, Matthew R.
dc.date.accessioned 2016-01-15T19:47:51Z
dc.date.available 2016-01-15T19:47:51Z
dc.date.issued 2015
dc.identifier.citation Kim, Jae Kyoung, Josić, Krešimir and Bennett, Matthew R.. "The relationship between stochastic and deterministic quasi-steady state approximations." BMC Systems Biology, 9, (2015) Springer: http://dx.doi.org/10.1186/s12918-015-0218-3.
dc.identifier.urihttps://hdl.handle.net/1911/87850
dc.description.abstract Background: The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Results: Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. Conclusions: The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.
dc.language.iso eng
dc.publisher Springer
dc.rights This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.title The relationship between stochastic and deterministic quasi-steady state approximations
dc.type Journal article
dc.contributor.funder National Institutes of Health
dc.contributor.funder National Science Foundation/ National Institute of General Medical Sciences
dc.contributor.funder Welch Foundation
dc.contributor.funder National Science Foundation
dc.contributor.funder KAIST Research Allowance
dc.citation.journalTitle BMC Systems Biology
dc.subject.keywordStochastic QSSA
Multi-scale stochastic simulation
Hill function
Michaelis-Menten function
dc.citation.volumeNumber 9
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1186/s12918-015-0218-3
dc.identifier.grantID R01GM104974 (National Science Foundation/ National Institute of General Medical Sciences)
dc.identifier.grantID C-1729 (Welch Foundation)
dc.identifier.grantID DMS-0931642 (National Science Foundation)
dc.identifier.grantID G04150020 (KAIST Research Allowance)
dc.type.publication publisher version


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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and
Except where otherwise noted, this item's license is described as This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and