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Volumn 130, Issue 6, 2009, Pages

The subtle business of model reduction for stochastic chemical kinetics

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL REACTIONS; RANDOM PROCESSES; REDUCTION;

EID: 60349124931     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3072704     Document Type: Article
Times cited : (25)

References (14)
  • 8
    • 34249950625 scopus 로고    scopus 로고
    • For a review of the stochastic simulation algorithm, the chemical master equation, and related topics, see, 0066-426X 10.1146/annurev.physchem.58.032806. 104637.
    • For a review of the stochastic simulation algorithm, the chemical master equation, and related topics, see D. T. Gillespie, Annu. Rev. Phys. Chem. 0066-426X 10.1146/annurev.physchem.58.032806.104637 58, 35 (2007).
    • (2007) Annu. Rev. Phys. Chem. , vol.58 , pp. 35
    • Gillespie, D.T.1
  • 9
    • 33846417230 scopus 로고    scopus 로고
    • Effect of excluded volume on 2D discrete stochastic chemical kinetics
    • 0021-9606 10.1063/1.2424461, ();, "," J. Comput. Phys. (in press).
    • D. T. Gillespie, S. Lampoudi, and L. R. Petzold, J. Chem. Phys. 0021-9606 10.1063/1.2424461 126, 034302 (2007); S. Lampoudi, D. T. Gillespie, and L. R. Petzold, " Effect of excluded volume on 2D discrete stochastic chemical kinetics.," J. Comput. Phys. (in press).
    • (2007) J. Chem. Phys. , vol.126 , pp. 034302
    • Gillespie, D.T.1    Lampoudi, S.2    Petzold, L.R.3    Lampoudi, S.4    Gillespie, D.T.5    Petzold, L.R.6
  • 10
    • 60349096044 scopus 로고    scopus 로고
    • If c2 =0 and c3 c1, Eq. gives λ+ = c3 and λ- = c1. Setting those results into Eq. 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 c12 t e- c1 t. 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 c1 -1. And this is exactly what we should expect for the time for an S1 - S3 conversion via reactions when c2 =0 and c3 = c1.
    • If c2 =0 and c3 c1, Eq. gives λ+ = c3 and λ- = c1. Setting those results into Eq. 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 c12 t e- c1 t. 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 c1 -1. And this is exactly what we should expect for the time for an S1-S3 conversion via reactions when c2 =0 and c3 = c1.
  • 12
    • 0037444724 scopus 로고    scopus 로고
    • 0021-9606 10.1063/1.1545446.
    • C. Rao and A. P. Arkin, J. Chem. Phys. 0021-9606 10.1063/1.1545446 118, 4999 (2003).
    • (2003) J. Chem. Phys. , vol.118 , pp. 4999
    • Rao, C.1    Arkin, A.P.2
  • 13
    • 60349095788 scopus 로고    scopus 로고
    • In Ref., it was stated that the condition for applying the ssSSA to reactions is (c1 + c2) 2 c1 c3 x12. That is incorrect, as it arises from comparing a single-walker timescale with a many-walker timescale. The correct condition is simply c2 c3, as can be seen not only from the result but also from the argument at Eq. The reason why it is not necessary to supplement the condition c2 c3 with the condition c1 c3 is explained in the second paragraph of Sec.
    • In Ref., it was stated that the condition for applying the ssSSA to reactions is (c1 + c2) 2 c1 c3 x12. That is incorrect, as it arises from comparing a single-walker timescale with a many-walker timescale. The correct condition is simply c2 c3, as can be seen not only from the result but also from the argument at Eq. The reason why it is not necessary to supplement the condition c2 c3 with the condition c1 c3 is explained in the second paragraph of Sec.
  • 14
    • 0001596858 scopus 로고
    • 0021-9606 10.1063/1.1733676, ();, J. Chem. Phys. 0021-9606 10.1063/1.1727900 45, 2145 (1966).
    • D. A. McQuarrie, J. Chem. Phys. 0021-9606 10.1063/1.1733676 38, 433 (1963); I. G. Darvey, B. W. Ninham, and P. J. Staff, J. Chem. Phys. 0021-9606 10.1063/1.1727900 45, 2145 (1966).
    • (1963) J. Chem. Phys. , vol.38 , pp. 433
    • McQuarrie, D.A.1    Darvey, I.G.2    Ninham, B.W.3    Staff, P.J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.