This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S1 ↔ S2 → S3, whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S3 -producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.
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The authors thank Sotiria Lampoudi for some helpful discussions, and also the journal’s anonymous reviewer for some pertinent observations. The authors gratefully acknowledge financial support as follows: D.G. was supported by the California Institute of Technology through Consulting Agreement No. 102-1080890 pursuant to Grant No. R01GM078992 from the National Institute of General Medical Sciences, and through Contract No. 82-1083250 pursuant to Grant No. R01EB007511 from the National Institute of Biomedical Imaging and Bioengineering, and also from the University of California at Santa Barbara under Consulting Agreement No. 054281A20 pursuant to funding from the National Institutes of Health. Y.C. was supported by the National Science Foundation under Award No. CCF-0726763, and also the National Institutes of Health under Award Nos. GM073744 and GM078989. K.S. and L.P. were supported by Grant No. R01EB007511 from the National Institute of Biomedical Imaging and Bioengineering, Pfizer Inc., DOE Contract No. DE-FG02-04ER25621, NSF Contract No. IGERT DG02-21715, and the Institute for Collaborative Biotechnologies through Grant No. DFR3A-8-447850-23002 from the U.S. Army Research Office. K.S. was also supported by a National Science Foundation Graduate Research Fellowship.