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Two classes of quasi-steady-state model reductions for stochastic kinetics

Mastny, Ethan A. and Haseltine, Eric L. and Rawlings, James B. (2007) Two classes of quasi-steady-state model reductions for stochastic kinetics. Journal of Chemical Physics, 127 (9). Art. No. 094106. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:MASjcp07

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Abstract

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case.


Item Type:Article
Additional Information:©2007 American Institute of Physics (Received 7 February 2007; accepted 2 July 2007; published online 6 September 2007) Funding was provided by NIH grant 5R21AI071197-02 and NSF DDDAS grant CNS-0540147. One of the authors (E.L.H.) gratefully acknowledges support from the National Institutes of Health under Ruth L. Kirschstein National Research Service Award 5F32CA120055. The authors would like to thank Dr. J.W. Eaton for help preparing this paper. All simulations were performed using Octave (http://www.octave.org). Octave is freely distributed under the terms of the GNU General Public License.
Subject Keywords:chemical reactions; perturbation techniques; reaction kinetics; reduced order systems; sampling methods; stochastic processes
Issue or Number:9
Record Number:CaltechAUTHORS:MASjcp07
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MASjcp07
Alternative URL:http://dx.doi.org/10.1063/1.2764480
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8707
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:07 Sep 2007
Last Modified:26 Dec 2012 09:41

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