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The subtle business of model reduction for stochastic chemical kinetics
J. Chem. Phys. 130, 064103 (2009); doi:10.1063/1.3072704
Published 10 February 2009
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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![[r harp over l]](http://scitation.aip.org/stockgif3/rlhar2.gif)
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.
©2009 American Institute of Physics
S2S3, 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.
©2009 American Institute of Physics
| History: | Received 14 July 2008; accepted 28 December 2008; published 10 February 2009 |
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http://link.aip.org/link/?JCPSA6/130/064103/1 |
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REFERENCES (14)
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- If c2=0 and c3
c1, Eq. (8) gives 
+=c3 and −=c1. Setting those results into Eq. (9) gives a formula that is indeterminate when c3=c1. But applying L'Hospital's rule to that indeterminate form, taking derivatives with respect to c3 yields the pdf cte−c1t. This nonexponential form, which goes to zero as t
0, is the pdf of the gamma random variable 
(c1,2), which is defined as the sum of two statistically independent exponentials with the same mean c. And this is exactly what we should expect for the time for an S1–S3 conversion via reactions (1) when c2=0 and c3=c1.
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c1c3x12. That is incorrect, as it arises from comparing a single-walker timescale with a many-walker timescale. The correct condition is simply c2c3, as can be seen not only from the result (3) but also from the argument at Eq. (29). The reason why it is not necessary to supplement the condition c2c3 with the condition c1c3 is explained in the second paragraph of Sec. VI. - D. A. McQuarrie, J. Chem. Phys. 38, 433 (1963)
