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Volumn 23, Issue 2, 2013, Pages 529-583

Separation of time-scales and model reduction for stochastic reaction networks

Author keywords

Averaging; Cellular processes; Chemical reactions; Markov chains; Multiple time scales; Quasi steady state assumption; Reaction networks; Scaling limits

Indexed keywords


EID: 84879422004     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AAP841     Document Type: Article
Times cited : (168)

References (32)
  • 1
    • 33744775760 scopus 로고    scopus 로고
    • Asymptotic analysis ofmultiscale approximations to reaction networks
    • MR2288709
    • BALL, K., KURTZ, T. G., POPOVIC, L. and REMPALA, G. (2006). Asymptotic analysis ofmultiscale approximations to reaction networks. Ann. Appl. Probab. 16 1925-1961. MR2288709
    • (2006) Ann. Appl. Probab. , vol.16 , pp. 1925-1961
    • Ball, K.1    Kurtz, T.G.2    Popovic, L.3    Rempala, G.4
  • 2
    • 22944480262 scopus 로고    scopus 로고
    • The slow-scale stochastic simulation algorithm
    • CAO, Y., GILLESPIE, D. T. and PETZOLD, L. R. (2005). The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122 014116. Available at http://link.aip.org/link/?JCP/122/014116/1.
    • (2005) J. Chem. Phys. , vol.122 , pp. 014116
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.R.3
  • 3
    • 70449514562 scopus 로고    scopus 로고
    • Hybrid stochastic simplifications for multiscale gene networks
    • CRUDU, A., DEBUSSCHE, A. and RADULESCU, O. (2009). Hybrid stochastic simplifications for multiscale gene networks. BMC Syst. Biol. 3 89.
    • (2009) BMC Syst. Biol. , vol.3 , pp. 89
    • Crudu, A.1    Debussche, A.2    Radulescu, O.3
  • 4
    • 84879765389 scopus 로고
    • A pseudo-steady state approximation for stochastic chemical kinetics
    • MR0517973
    • DARDEN, T. (1979). A pseudo-steady state approximation for stochastic chemical kinetics. Rocky Mountain J. Math. 9 51-71. MR0517973
    • (1979) Rocky Mountain J. Math. , vol.9 , pp. 51-71
    • Darden, T.1
  • 5
    • 84879772305 scopus 로고
    • Enzyme kinetics: Stochastic vs. deterministic models
    • Austin, Tex., 1980, Univ. Texas Press, Austin, TX. MR0774792
    • DARDEN, T. A. (1982). Enzyme kinetics: Stochastic vs. deterministic models. In Instabilities, Bifurcations, and Fluctuations in Chemical Systems (Austin, Tex., 1980) 248-272. Univ. Texas Press, Austin, TX. MR0774792
    • (1982) Instabilities, Bifurcations, and Fluctuations in Chemical Systems , pp. 248-272
    • Darden, T.A.1
  • 7
    • 27744516835 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
    • E, W., LIU, D. and VANDEN-EIJNDEN, E. (2005). Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys. 123 194107. Available at http://link.aip.org/link/?JCP/123/194107/1.
    • (2005) J. Chem. Phys. , vol.123 , pp. 194107
    • Liu D, E.W.1    Vanden-Eijnden, E.2
  • 8
    • 33846123314 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
    • MR2290567
    • E, W., LIU, D. and VANDEN-EIJNDEN, E. (2007). Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J. Comput. Phys. 221 158-180. MR2290567
    • (2007) J. Comput. Phys. , vol.221 , pp. 158-180
    • Liu D, E.W.1    Vanden-Eijnden, E.2
  • 10
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • GILLESPIE, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 2340-2361.
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 11
    • 18844402156 scopus 로고    scopus 로고
    • Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
    • GOUTSIAS, J. (2005). Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122 184102. Available at http://link.aip.org/link/?JCP/122/184102/1.
    • (2005) J. Chem. Phys. , vol.122 , pp. 184102
    • Goutsias, J.1
  • 12
    • 0037109565 scopus 로고    scopus 로고
    • Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
    • HASELTINE, E. L. and RAWLINGS, J. B. (2002). Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 6959-6969.
    • (2002) J. Chem. Phys. , vol.117 , pp. 6959-6969
    • Haseltine, E.L.1    Rawlings, J.B.2
  • 13
    • 74049102425 scopus 로고    scopus 로고
    • Stochastic kinetic modeling of vesicular stomatitis virus intracellular growth
    • MR2544630
    • HENSEL, S. C., RAWLINGS, J. B. and YIN, J. (2009). Stochastic kinetic modeling of vesicular stomatitis virus intracellular growth. Bull. Math. Biol. 71 1671-1692. MR2544630
    • (2009) Bull. Math. Biol. , vol.71 , pp. 1671-1692
    • Hensel, S.C.1    Rawlings, J.B.2    Yin, J.3
  • 14
    • 3042567006 scopus 로고    scopus 로고
    • A non-Skorohod topology on the Skorohod space
    • (electronic). MR1475862
    • JAKUBOWSKI, A. (1997). A non-Skorohod topology on the Skorohod space. Electron. J. Probab. 2 21 pp. (electronic). MR1475862
    • (1997) Electron. J. Probab. , vol.2
    • Jakubowski, A.1
  • 15
    • 0002263301 scopus 로고
    • Weak and strong convergence of distributions of counting processes
    • KABANOV, Y. M., LIPTSER, R. S. and SHIRYAEV, A. N. (1984). Weak and strong convergence of distributions of counting processes. Theory Probab. Appl. 28 303-336.
    • (1984) Theory Probab. Appl. , vol.28 , pp. 303-336
    • Kabanov, Y.M.1    Liptser, R.S.2    Shiryaev, A.N.3
  • 17
    • 84879756175 scopus 로고    scopus 로고
    • Unpublished manuscript. School of Mathematics, Univ. Minnesota, Dept. Mathematics and Statistics, Univ. Wisconsin, Madison and Dept. Mathematics and Statistics, Concordia Univ
    • KANG, H.-W., KURTZ, T. G. and POPOVIC, L. (2012). Diffusion approximations for multiscale chemical reaction models. Unpublished manuscript. School of Mathematics, Univ. Minnesota, Dept. Mathematics and Statistics, Univ. Wisconsin, Madison and Dept. Mathematics and Statistics, Concordia Univ.
    • (2012) Diffusion Approximations for Multiscale Chemical Reaction Models
    • Kang, H.-W.1    Kurtz, T.G.2    Popovic, L.3
  • 18
    • 0001761643 scopus 로고
    • On stochastic processes defined by differential equations with a small parameter
    • KHAS'MINSKIǏ, R. Z. (1966a). On stochastic processes defined by differential equations with a small parameter. Theory Probab. Appl. 11 211-228.
    • (1966) Theory Probab. Appl. , vol.11 , pp. 211-228
    • Khas'Minskiǐ, R.Z.1
  • 19
    • 0001761644 scopus 로고
    • KHAS'MINSKIǏ, R. Z.
    • KHAS'MINSKIǏ, R. Z. (1966b). A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probab. Appl. 11 390-406.
    • (1966) Theory Probab. Appl. , vol.11 , pp. 390-406
  • 20
    • 0001455869 scopus 로고
    • The relationship between stochastic and deterministic models for chemical reactions
    • KURTZ, T. G. (1972). The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57 2976-2978.
    • (1972) J. Chem. Phys. , vol.57 , pp. 2976-2978
    • Kurtz, T.G.1
  • 21
    • 0000660738 scopus 로고
    • Strong approximation theorems for density dependent Markov chains
    • MR0464414
    • KURTZ, T. G. (1977/78). Strong approximation theorems for density dependent Markov chains. Stochastic Process. Appl. 6 223-240. MR0464414
    • (1977) Stochastic Process. Appl. , vol.6 , pp. 223-240
    • Kurtz, T.G.1
  • 22
    • 0010147542 scopus 로고
    • Representations of Markov processes as multiparameter time changes
    • MR0577310
    • KURTZ, T. G. (1980). Representations of Markov processes as multiparameter time changes. Ann. Probab. 8 682-715. MR0577310
    • (1980) Ann. Probab. , vol.8 , pp. 682-715
    • Kurtz, T.G.1
  • 23
    • 0001168654 scopus 로고
    • Random time changes and convergence in distribution under the Meyer-Zheng conditions
    • MR1112405
    • KURTZ, T. G. (1991). Random time changes and convergence in distribution under the Meyer-Zheng conditions. Ann. Probab. 19 1010-1034. MR1112405
    • (1991) Ann. Probab. , vol.19 , pp. 1010-1034
    • Kurtz, T.G.1
  • 24
    • 0004399662 scopus 로고
    • Averaging for martingale problems and stochastic approximation
    • (New Brunswick, NJ, 1991). Lecture Notes in Control and Information Sciences, Springer, Berlin. MR1169928
    • KURTZ, T. G. (1992). Averaging for martingale problems and stochastic approximation. In Applied Stochastic Analysis (New Brunswick, NJ, 1991). Lecture Notes in Control and Information Sciences 177 186-209. Springer, Berlin. MR1169928
    • (1992) Applied Stochastic Analysis , vol.177 , pp. 186-209
    • Kurtz, T.G.1
  • 25
    • 49749098924 scopus 로고    scopus 로고
    • Multiscale modeling of chemical kinetics via the master equation
    • MR2393029
    • MACNAMARA, S., BURRAGE, K. and SIDJE, R. B. (2007). Multiscale modeling of chemical kinetics via the master equation. Multiscale Model. Simul. 6 1146-1168. MR2393029
    • (2007) Multiscale Model. Simul. , vol.6 , pp. 1146-1168
    • MacNamara, S.1    Burrage, K.2    Sidje, R.B.3
  • 26
    • 34548474499 scopus 로고    scopus 로고
    • Two classes of quasi-steadystate model reductions for stochastic kinetics
    • MASTNY, E. A., HASELTINE, E. L. and RAWLINGS, J. B. (2007). Two classes of quasi-steadystate model reductions for stochastic kinetics. J. Chem. Phys. 127 094106. Available at http://link.aip.org/link/?JCP/127/094106/1.
    • (2007) J. Chem. Phys. , vol.127 , pp. 094106
    • Mastny, E.A.1    Haseltine, E.L.2    Rawlings, J.B.3
  • 29
    • 0037444724 scopus 로고    scopus 로고
    • Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
    • RAO, C. V. and ARKIN, A. P. (2003). Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys. 118 4999-5010.
    • (2003) J. Chem. Phys. , vol.118 , pp. 4999-5010
    • Rao, C.V.1    Arkin, A.P.2
  • 30
    • 0024731820 scopus 로고
    • The quasi-steady-state assumption: A case study in perturbation
    • MR1012300
    • SEGEL, L. A. and SLEMROD, M. (1989). The quasi-steady-state assumption: A case study in perturbation. SIAM Rev. 31 446-477. MR1012300
    • (1989) SIAM Rev. , vol.31 , pp. 446-477
    • Segel, L.A.1    Slemrod, M.2
  • 31
    • 0035812883 scopus 로고    scopus 로고
    • Stochastic kinetic analysis of Escherichia coli stress circuit using sigma(32)-targeted antisense
    • SRIVASTAVA, R., PETERSON, M. S. and BENTLEY, W. E. (2001). Stochastic kinetic analysis of Escherichia coli stress circuit using sigma(32)-targeted antisense. Biotechnol. Bioeng. 75 120-129.
    • (2001) Biotechnol. Bioeng. , vol.75 , pp. 120-129
    • Srivastava, R.1    Peterson, M.S.2    Bentley, W.E.3
  • 32
    • 74049117430 scopus 로고    scopus 로고
    • Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes
    • MR2552726
    • ZEISER, S., FRANZ, U. and LIEBSCHER, V. (2010). Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes. J. Math. Biol. 60 207-246. MR2552726
    • (2010) J. Math. Biol. , vol.60 , pp. 207-246
    • Zeiser, S.1    Franz, U.2    Liebscher, V.3


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