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Volumn 8, Issue 1, 2009, Pages 30-45

Switching and diffusion models for gene regulation networks

Author keywords

Diffusion; Gillespie's algorithm; Hybrid model; It ; Lemma; Markov chain; Slow scale simulation; Stochastic simulation algorithm; Transcription; Transition rate; Translation

Indexed keywords

GILLESPIE'S ALGORITHM; HYBRID MODEL; LEMMA; MARKOV CHAIN; SLOW SCALE SIMULATION; STOCHASTIC SIMULATION ALGORITHM; TRANSITION RATE; TRANSLATION;

EID: 70350294369     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/080735412     Document Type: Article
Times cited : (7)

References (37)
  • 2
    • 22144443131 scopus 로고    scopus 로고
    • Nonlinear protein degradation and the function of genetic circuits
    • N. E. BUCHLER, U. GERLAND, AND T. HWA, Nonlinear protein degradation and the function of genetic circuits, Proc. Natl. Acad. Sci. U. S. A., 102 (2005), pp. 9559-9564.
    • (2005) Proc. Natl. Acad. Sci. U.S.A. , vol.102 , pp. 9559-9564
    • Buchler, N.E.1    Gerland, U.2    Hwa, T.3
  • 3
    • 0037217334 scopus 로고    scopus 로고
    • The role of dimerization in noise reduction of simple genetic networks
    • R. BUNDSCHUH, F. HAYOT, AND C. JAYAPRAKASH, The role of dimerization in noise reduction of simple genetic networks, J. Theoret. Biol., 220 (2003), pp. 261-269.
    • (2003) J. Theoret. Biol. , vol.220 , pp. 261-269
    • Bundschuh, R.1    Hayot, F.2    Jayaprakash, C.3
  • 4
    • 70350299873 scopus 로고    scopus 로고
    • The slow-scale stochastic simulation algorithm
    • Y. CAO, D. T. GILLESPIE, AND L. PETZOLD, The slow-scale stochastic simulation algorithm, J. Chomput. Phys., 221 (2007), pp. 58-180.
    • (2007) J. Chomput. Phys. , vol.221 , pp. 58-180
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.3
  • 5
    • 31544465969 scopus 로고    scopus 로고
    • Efficient stepsize selection for the tau-leaping method
    • Y. CAO, D. T. GILLESPIE, AND L. PETZOLD, Efficient stepsize selection for the Tau-leaping method, J. Chem. Phys., 124 (2006), 044109.
    • (2006) J. Chem. Phys. , vol.124 , pp. 044109
    • Cao, Y.1    Gillespie, D.T.2    Petzold, L.3
  • 6
    • 0036207347 scopus 로고    scopus 로고
    • Modeling and simulation of genetic regulatory systems: A literature review
    • H. D. JONG, Modeling and simulation of genetic regulatory systems: A literature review, J. Comput. Biol., 9 (2002), pp. 69-105.
    • (2002) J. Comput. Biol. , vol.9 , pp. 69-105
    • Jong, H.D.1
  • 7
    • 33846123314 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
    • W. E, D. LIU, AND E. VANDEN-EUNDEN, Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales, J. Comput. Phys., 221 (2007), pp. 158-180.
    • (2007) J. Comput. Phys. , vol.221 , pp. 158-180
    • Weinan, E.1    Liu, D.2    Vanden-Eunden, E.3
  • 8
    • 21444438810 scopus 로고    scopus 로고
    • A stochastic analysis of first-order reaction networks
    • C. GADGIL, C. H. LEE, AND H. G. OTHMER, A stochastic analysis of first-order reaction networks, Bull. Math. Biol., 67 (2005), pp. 901-946.
    • (2005) Bull. Math. Biol. , vol.67 , pp. 901-946
    • Gadgil, C.1    Lee, C.H.2    Othmer, H.G.3
  • 9
    • 0001144902 scopus 로고    scopus 로고
    • Efficient exact stochastic simulation of chemical systems with many species and many channels
    • M. GIBSON AND J. BRUCK, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A, 104 (2000), pp. 1876-1889.
    • (2000) J. Phys. Chem. A , vol.104 , pp. 1876-1889
    • Gibson, M.1    Bruck, J.2
  • 10
    • 0002004235 scopus 로고
    • Stochastic differential equations
    • Band 72, translated from the Russian by K. Wickwire, Springer-Verlag, New York
    • Ǐ. Ī. GIHMAN AND A. V. SKOROHOD, Stochastic Differential Equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 72, translated from the Russian by K. Wickwire, Springer-Verlag, New York, 1972.
    • (1972) Ergebnisse Der Mathematik Und Ihrer Grenzgebiete
    • Gihman, Ǐ.I.1    Skorohod, A.V.2
  • 11
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • D. T. GILLESPIE, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22 (1976), pp. 403-434.
    • (1976) J. Comput. Phys. , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 12
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • D. T. GILLESPIE, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), pp. 2340-2361.
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 13
    • 0034225547 scopus 로고    scopus 로고
    • The chemical langevin equation
    • D. T. GILLESPIE, The chemical Langevin equation, J. Chem. Phys., 113 (2000), pp. 297-306.
    • (2000) J. Chem. Phys. , vol.113 , pp. 297-306
    • Gillespie, D.T.1
  • 14
    • 0035933994 scopus 로고    scopus 로고
    • Approximate accelerated stochastic simulation of chemically reacting systems
    • D. T. GILLESPIE, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115 (2001), pp. 1716-1733.
    • (2001) J. Chem. Phys. , vol.115 , pp. 1716-1733
    • Gillespie, D.T.1
  • 15
    • 34249950625 scopus 로고    scopus 로고
    • Stochastic simulation of chemical kinetics
    • D. T. GILLESPIE, Stochastic simulation of chemical kinetics, Ann. Rev. Phys. Chem., 58 (2007), pp. 35-55.
    • (2007) Ann. Rev. Phys. Chem. , vol.58 , pp. 35-55
    • Gillespie, D.T.1
  • 17
    • 44949114109 scopus 로고    scopus 로고
    • Modeling and simulating chemical reactions
    • D. J. HIGHAM, Modeling and simulating chemical reactions, SIAM Rev., 50 (2008), pp. 347-368.
    • (2008) SIAM Rev. , vol.50 , pp. 347-368
    • Higham, D.J.1
  • 18
    • 70350280479 scopus 로고    scopus 로고
    • Chemical master versus chemical langevin for first-order reaction networks
    • D. J. HIGHAM AND R. KHANIN, Chemical master versus chemical Langevin for first-order reaction networks, Open Appl. Math. J., 2 (2008), pp. 59-79.
    • (2008) Open Appl. Math. J. , vol.2 , pp. 59-79
    • Higham, D.J.1    Khanin, R.2
  • 19
    • 0012279718 scopus 로고    scopus 로고
    • Strong convergence of euler-type methods for nonlinear stochastic differential equations
    • D. J. HIGHAM, X. MAO, AND A. M. STUART, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal., 40 (2002), pp. 1041-1063.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1041-1063
    • Higham, D.J.1    Mao, X.2    Stuart, A.M.3
  • 20
    • 33745780500 scopus 로고    scopus 로고
    • Network motifs: Structure does not determine function
    • paper 108
    • P. J. INGRAM, M. P. STUMPF, AND J. STARK, Network motifs: Structure does not determine function, BMC Genomics, 7 (2006), paper 108.
    • (2006) BMC Genomics , vol.7
    • Ingram, P.J.1    Stumpf, M.P.2    Stark, J.3
  • 21
    • 54449083140 scopus 로고    scopus 로고
    • Chemical master equation and langevin regimes for a gene transcription model
    • R. KHANIN AND D. J. HIGHAM, Chemical master equation and Langevin regimes for a gene transcription model, Theoretical Comput. Sci., 408 (2008), pp. 31-40.
    • (2008) Theoretical Comput. Sci. , vol.408 , pp. 31-40
    • Khanin, R.1    Higham, D.J.2
  • 22
    • 0003271204 scopus 로고
    • Approximation of population processes
    • SIAM, Philadelphia
    • T. G. KURTZ, Approximation of Population Processes, CBMS-NSF Reg. Conf. Ser. Appl. Math. 26, SIAM, Philadelphia, 1981.
    • (1981) CBMS-NSF Reg. Conf. Ser. Appl. Math. , vol.26
    • Kurtz, T.G.1
  • 23
    • 49749098924 scopus 로고    scopus 로고
    • Multiscale modeling of chemical kinetics via the master equation
    • S. MACNAMARA, K. BURRAGE, AND R. B. SIDJE, Multiscale modeling of chemical kinetics via the master equation, Multiscale Model. Simul., 6 (2008), pp. 1146-1168.
    • (2008) Multiscale Model. Simul. , vol.6 , pp. 1146-1168
    • Macnamara, S.1    Burrage, K.2    Sidje, R.B.3
  • 25
    • 34248171675 scopus 로고    scopus 로고
    • Approximations of euler-maruyama type for stochastic differential equations with Markovian switching, under non-lipschitz conditions
    • X. MAO, C. YUAN, AND G. YIN, Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions, J. Comput. Appl. Math., 205 (2007), pp. 936-948.
    • (2007) J. Comput. Appl. Math. , vol.205 , pp. 936-948
    • Mao, X.1    Yuan, C.2    Yin, G.3
  • 26
    • 34249881396 scopus 로고    scopus 로고
    • Modeling stochasticity in gene regulation: Characterization in the terms of the underlying distribution function
    • P. PASZEK, Modeling stochasticity in gene regulation: Characterization in the terms of the underlying distribution function, Bull. Math. Biol., 69 (2007), pp. 1567-1601.
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1567-1601
    • Paszek, P.1
  • 27
    • 2942718723 scopus 로고    scopus 로고
    • Control of stochasticity in eukaryotic gene expression
    • J. RASER AND E. O'SHEA, Control of stochasticity in eukaryotic gene expression, Science, 304 (2004), pp. 1811-1814.
    • (2004) Science , vol.304 , pp. 1811-1814
    • Raser, J.1    O'Shea, E.2
  • 29
    • 0036790975 scopus 로고    scopus 로고
    • Intrinsic and extrinsic contributions to stochasticity in gene expression
    • P. S. SWAIN, M. ELOWITZ, AND E. SIGGIA, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Nat. Acad. Sci. U.S.A., 99 (2002), pp. 12795-12800.
    • (2002) Proc. Nat. Acad. Sci. U.S.A. , vol.99 , pp. 12795-12800
    • Swain, P.S.1    Elowitz, M.2    Siggia, E.3
  • 31
    • 33744811457 scopus 로고    scopus 로고
    • Stochastic models for regulatory networks of the genetic toggle switch
    • T. TIAN AND K. BURRAGE, Stochastic models for regulatory networks of the genetic toggle switch, Proc. Nat. Acad. Sci. U.S.A., 103 (2006), pp. 8372-8377.
    • (2006) Proc. Nat. Acad. Sci. U.S.A. , vol.103 , pp. 8372-8377
    • Tian, T.1    Burrage, K.2
  • 32
    • 3142577523 scopus 로고    scopus 로고
    • Stochastic approaches for modelling in vivo reactions
    • T. E. TURNER, S. SCHNELL, AND K. BURRAGE, Stochastic approaches for modelling in vivo reactions, Comput. Biol. Chem., 28 (2004), pp. 165-178.
    • (2004) Comput. Biol. Chem. , vol.28 , pp. 165-178
    • Turner, T.E.1    Schnell, S.2    Burrage, K.3
  • 33
    • 33645109045 scopus 로고    scopus 로고
    • Deterministic modelling and stochastic simulation of pathways using MATLAB
    • M. ULLAH, H. SCHMIDT, K.-H. CHO, AND O. WOLKENHAUER, Deterministic modelling and stochastic simulation of pathways using MATLAB, Syst. Biol., 153 (2006), pp. 53-60.
    • (2006) Syst. Biol. , vol.153 , pp. 53-60
    • Ullah, M.1    Schmidt, H.2    Cho, K.-H.3    Wolkenhauer, O.4
  • 34
    • 40749094910 scopus 로고    scopus 로고
    • Bayesian ranking of biochemical system models
    • V. VYSHEMIRSKY AND M. GIROLAMI, Bayesian ranking of biochemical system models, Bioinformatics, 24 (2008), pp. 833-839.
    • (2008) Bioinformatics , vol.24 , pp. 833-839
    • Vyshemirsky, V.1    Girolami, M.2
  • 35
    • 38749133407 scopus 로고    scopus 로고
    • Noise-induced switches in network systems of the genetic toggle switch
    • paper 50
    • J. WANG, J. ZHANG, Z. YUAN, AND T. ZHOU, Noise-induced switches in network systems of the genetic toggle switch, BMC Syst. Biol., 1 (2007), paper 50.
    • (2007) BMC Syst. Biol. , vol.1
    • Wang, J.1    Zhang, J.2    Yuan, Z.3    Zhou, T.4


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