메뉴 건너뛰기




Volumn 31, Issue 3, 2009, Pages 1774-1797

Simulation of stochastic reaction-diffusion processes on unstructured meshes

Author keywords

Diffusion; Finite element method; Hybrid method; Master equation; Reaction rate equations; Unstructured mesh

Indexed keywords

BROWNIAN MOVEMENT; DIFFUSION IN LIQUIDS; LINEAR EQUATIONS; MESH GENERATION; MOLECULAR BIOLOGY; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

EID: 61849164660     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080721388     Document Type: Article
Times cited : (112)

References (51)
  • 1
    • 33748520215 scopus 로고    scopus 로고
    • Stochastic simulation of chemical reactions with spatial resolution and single molecule detail
    • S. S. ANDREWS AND D. BRAY, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail, Phys. Biol., 1 (2004), pp. 137-151.
    • (2004) Phys. Biol , vol.1 , pp. 137-151
    • ANDREWS, S.S.1    BRAY, D.2
  • 2
    • 0021905844 scopus 로고
    • Diffusion-controlled macromolecular interactions
    • O. G. BERG AND P. H. VON HIPPEL, Diffusion-controlled macromolecular interactions, Ann. Rev. Biophys. Chem., 14 (1985), pp. 131-160.
    • (1985) Ann. Rev. Biophys. Chem , vol.14 , pp. 131-160
    • BERG, O.G.1    VON HIPPEL, P.H.2
  • 3
    • 41349099680 scopus 로고    scopus 로고
    • Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
    • D. BERNSTEIN, Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm, Phys. Rev. E, 71 (2005), p. 041103.
    • (2005) Phys. Rev. E , vol.71 , pp. 041103
    • BERNSTEIN, D.1
  • 6
    • 18144386494 scopus 로고    scopus 로고
    • Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
    • Y. CAO, D. GILLESPIE, AND L. PETZOLD, Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems, J. Comput. Phys., 206 (2005), pp. 395-411.
    • (2005) J. Comput. Phys , vol.206 , pp. 395-411
    • CAO, Y.1    GILLESPIE, D.2    PETZOLD, L.3
  • 7
    • 61849139307 scopus 로고    scopus 로고
    • COMSOL MULTIPHASICS REFERENCE GUIDE VERSION 3.4, Comsol Inc., Stockholm, Sweden, 2008.
    • COMSOL MULTIPHASICS REFERENCE GUIDE VERSION 3.4, Comsol Inc., Stockholm, Sweden, 2008.
  • 8
    • 61849161955 scopus 로고    scopus 로고
    • J. CULLHED, S. ENGBLOM, AND A. HELLANDER, The URDME Manual Version 1.0, Technical report 2008-022, Dept. of Information Technology, Uppsala University, Uppsala, Sweden, 2008; also available online at http://www.it.uu.se/research.
    • J. CULLHED, S. ENGBLOM, AND A. HELLANDER, The URDME Manual Version 1.0, Technical report 2008-022, Dept. of Information Technology, Uppsala University, Uppsala, Sweden, 2008; also available online at http://www.it.uu.se/research.
  • 9
    • 34548141875 scopus 로고    scopus 로고
    • Computational methods for diffusion-influenced biochemical reactions
    • M. DOBRZYŃSKI, J. V. RODRÍGUEZ, J. A. KAANDORP, AND J. G. BLOM, Computational methods for diffusion-influenced biochemical reactions, Bioinform., 23 (2007), pp. 1969-1977.
    • (2007) Bioinform , vol.23 , pp. 1969-1977
    • DOBRZYŃSKI, M.1    RODRÍGUEZ, J.V.2    KAANDORP, J.A.3    BLOM, J.G.4
  • 10
    • 22344445928 scopus 로고    scopus 로고
    • Stochastic model for Soj relocation dynamics in Bacillus subtilis
    • K. DOUBROVINSKI AND M. HOWARD, Stochastic model for Soj relocation dynamics in Bacillus subtilis, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 9808-9813.
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 9808-9813
    • DOUBROVINSKI, K.1    HOWARD, M.2
  • 11
    • 27744516835 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
    • W. E, D. LIU, AND E. VANDEN-EIJNDEN, Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates, J. Chem. Phys., 123 (2005), p. 194107.
    • (2005) J. Chem. Phys , vol.123 , pp. 194107
    • LIU, W.E.D.1    VANDEN-EIJNDEN, E.2
  • 12
    • 20844455677 scopus 로고    scopus 로고
    • Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases
    • J. ELF AND M. EHRENBERG, Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases, Syst. Biol., 1 (2004), pp. 230-236.
    • (2004) Syst. Biol , vol.1 , pp. 230-236
    • ELF, J.1    EHRENBERG, M.2
  • 13
    • 0037119587 scopus 로고    scopus 로고
    • Stochastic gene expression in a single cell
    • M. B. ELOWITZ, A. J. LEVINE, E. D. SIGGIA, AND P. S. SWAIN, Stochastic gene expression in a single cell, Science, 297 (2002), pp. 1183-1186.
    • (2002) Science , vol.297 , pp. 1183-1186
    • ELOWITZ, M.B.1    LEVINE, A.J.2    SIGGIA, E.D.3    SWAIN, P.S.4
  • 14
    • 33748962544 scopus 로고    scopus 로고
    • Computing the moments of high dimensional solutions of the master equation
    • S. ENGBLOM, Computing the moments of high dimensional solutions of the master equation, Appl. Math. Comput., 180 (2006), pp. 498-515.
    • (2006) Appl. Math. Comput , vol.180 , pp. 498-515
    • ENGBLOM, S.1
  • 15
    • 33645741503 scopus 로고    scopus 로고
    • A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension
    • R. EYMARD, T. GALLOUËT, AND R. HERBIN, A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension, IMA J. Numer. Anal., 26 (2006), pp. 326-353.
    • (2006) IMA J. Numer. Anal , vol.26 , pp. 326-353
    • EYMARD, R.1    GALLOUËT, T.2    HERBIN, R.3
  • 16
    • 33745591124 scopus 로고    scopus 로고
    • Noise-induced min phenotypes in E. coli
    • D. FANGE AND J. ELF, Noise-induced min phenotypes in E. coli, PLoS Comput. Biol., 2 (2006), pp. 637-648.
    • (2006) PLoS Comput. Biol , vol.2 , pp. 637-648
    • FANGE, D.1    ELF, J.2
  • 17
    • 38349133325 scopus 로고    scopus 로고
    • A hierarchy of approximations of the master equation scaled by a size parameter
    • L. FERM, P. LÖTSTEDT, AND A. HELLANDER, A hierarchy of approximations of the master equation scaled by a size parameter, J. Sci. Comput., 34 (2008), pp. 127-151.
    • (2008) J. Sci. Comput , vol.34 , pp. 127-151
    • FERM, L.1    LÖTSTEDT, P.2    HELLANDER, A.3
  • 18
    • 0004300111 scopus 로고    scopus 로고
    • Handbook of Stochastic Methods
    • 3rd ed, Springer, Berlin
    • C. W. GARDINER, Handbook of Stochastic Methods, 3rd ed., Springer Ser. Synergetics, Springer, Berlin, 2004.
    • (2004) Springer Ser. Synergetics
    • GARDINER, C.W.1
  • 19
    • 70350511699 scopus 로고    scopus 로고
    • Automatic mesh generation and finite element computation
    • IV, P. G. Ciarlet and J. L. Lions, eds, Elsevier, Amsterdam
    • P. L. GEORGE, Automatic mesh generation and finite element computation, in Handbook of Numerical Analysis, Vol. IV, P. G. Ciarlet and J. L. Lions, eds., Elsevier, Amsterdam, 1996, pp. 149-190.
    • (1996) Handbook of Numerical Analysis , pp. 149-190
    • GEORGE, P.L.1
  • 20
    • 0001144902 scopus 로고    scopus 로고
    • Efficient exact stochastic simulation of chemical systems with many species and many channels
    • M. A. GIBSON AND J. BRUCK, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem., 104 (2000), pp. 1876-1889.
    • (2000) J. Phys. Chem , vol.104 , pp. 1876-1889
    • GIBSON, M.A.1    BRUCK, J.2
  • 21
    • 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
  • 23
    • 0029394767 scopus 로고
    • Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli?
    • P. GUPTASARAMA, Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli?, Bioessays, 17 (1995), pp. 987-997.
    • (1995) Bioessays , vol.17 , pp. 987-997
    • GUPTASARAMA, P.1
  • 24
    • 0037109565 scopus 로고    scopus 로고
    • Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
    • E. L. HASELTINE AND J. B. RAWLINGS, Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics, J. Chem. Phys., 117 (2002), pp. 6959-6969.
    • (2002) J. Chem. Phys , vol.117 , pp. 6959-6969
    • HASELTINE, E.L.1    RAWLINGS, J.B.2
  • 25
    • 20844432892 scopus 로고    scopus 로고
    • Stochastic reaction-diffusion simulation with MesoRD
    • J. HATTNE, D. FANGE, AND J. ELF, Stochastic reaction-diffusion simulation with MesoRD, Bioinform., 21 (2005), pp. 2923-2924.
    • (2005) Bioinform , vol.21 , pp. 2923-2924
    • HATTNE, J.1    FANGE, D.2    ELF, J.3
  • 26
    • 35348838418 scopus 로고    scopus 로고
    • A hybrid method for the chemical master equation
    • A. HELLANDER AND P. LÖTSTEDT, A hybrid method for the chemical master equation, J. Comput. Phys., 227 (2007), pp. 100-122.
    • (2007) J. Comput. Phys , vol.227 , pp. 100-122
    • HELLANDER, A.1    LÖTSTEDT, P.2
  • 27
    • 0001072763 scopus 로고    scopus 로고
    • A finite volume method for the approximation of diffusion operators on distorted meshes
    • F. HERMELINE, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., 160 (2000), pp. 481-499.
    • (2000) J. Comput. Phys , vol.160 , pp. 481-499
    • HERMELINE, F.1
  • 28
    • 33751568004 scopus 로고    scopus 로고
    • Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations
    • S. A. ISAACSON AND C. S. PESKIN, Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations, SIAM J. Sci. Comput., 28 (2006), pp. 47-74.
    • (2006) SIAM J. Sci. Comput , vol.28 , pp. 47-74
    • ISAACSON, S.A.1    PESKIN, C.S.2
  • 30
    • 35448980907 scopus 로고    scopus 로고
    • Kinetics in spatially extended systems, in System Modeling in Cellular Biology
    • Z. Szallasi, J. Stelling, and V. Periwal, eds, MIT Press, Cambridge, MA
    • K. KRUSE AND J. ELF, Kinetics in spatially extended systems, in System Modeling in Cellular Biology. From Concepts to Nuts and Bolts, Z. Szallasi, J. Stelling, and V. Periwal, eds., MIT Press, Cambridge, MA, 2006, pp. 177-198.
    • (2006) From Concepts to Nuts and Bolts , pp. 177-198
    • KRUSE, K.1    ELF, J.2
  • 31
    • 33846097600 scopus 로고    scopus 로고
    • Dynamics of single-cell gene expression
    • D. LONGO AND J. HASTY, Dynamics of single-cell gene expression, Mol. Syst. Biol., 2 (2006), p. 64.
    • (2006) Mol. Syst. Biol , vol.2 , pp. 64
    • LONGO, D.1    HASTY, J.2
  • 32
    • 5544250087 scopus 로고
    • A new approximation scheme for the study of fluctuations in nonuniform nonequilibrium systems
    • M. MALEK-MANSOUR AND J. HOUARD, A new approximation scheme for the study of fluctuations in nonuniform nonequilibrium systems, Phys. Lett. A, 70 (1979), pp. 366-368.
    • (1979) Phys. Lett. A , vol.70 , pp. 366-368
    • MALEK-MANSOUR, M.1    HOUARD, J.2
  • 34
    • 0033083733 scopus 로고    scopus 로고
    • It's a noisy business. Genetic regulation at the nanomolar scale
    • H. H. MCADAMS AND A. ARKIN, It's a noisy business. Genetic regulation at the nanomolar scale, Trends Gen., 15 (1999), pp. 65-69.
    • (1999) Trends Gen , vol.15 , pp. 65-69
    • MCADAMS, H.H.1    ARKIN, A.2
  • 35
    • 18044403385 scopus 로고    scopus 로고
    • The future is noisy: The role of spatial fluctuations in genetic switching
    • R. METZLER, The future is noisy: The role of spatial fluctuations in genetic switching, Phys. Rev. Lett., 87 (2001), p. 068103.
    • (2001) Phys. Rev. Lett , vol.87 , pp. 068103
    • METZLER, R.1
  • 36
    • 0027805257 scopus 로고
    • A quasi-Monte Carlo approach to particle simulation of the heat equation
    • W. J. MOROKOFF AND R. E. CAFLISCH, A quasi-Monte Carlo approach to particle simulation of the heat equation, SIAM J. Numer. Anal., 30 (1993), pp. 1558-1573.
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 1558-1573
    • MOROKOFF, W.J.1    CAFLISCH, R.E.2
  • 37
    • 0006037477 scopus 로고
    • A lumped mass finite-element method with quadrature for a nonlinear parabolic problem
    • Y.-Y. NIE AND V. THOMÉE, A lumped mass finite-element method with quadrature for a nonlinear parabolic problem, IMA J. Numer. Anal., 5 (1985), pp. 371-396.
    • (1985) IMA J. Numer. Anal , vol.5 , pp. 371-396
    • NIE, Y.-Y.1    THOMÉE, V.2
  • 38
    • 61849117120 scopus 로고    scopus 로고
    • B. ØKSENDAL, Stochastic Differential Equations, Springer, New York, 2005.
    • B. ØKSENDAL, Stochastic Differential Equations, Springer, New York, 2005.
  • 39
    • 0034691214 scopus 로고    scopus 로고
    • Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation
    • J. PAULSSON, O. G. BERG, AND M. EHRENBERG, Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 7148-7153.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 7148-7153
    • PAULSSON, J.1    BERG, O.G.2    EHRENBERG, M.3
  • 41
    • 25444468618 scopus 로고    scopus 로고
    • Noise in gene expression: Origins, consequences and control
    • J. M. RASER AND E. K. O'SHEA, Noise in gene expression: Origins, consequences and control, Science, 309 (2005), pp. 2010-2013.
    • (2005) Science , vol.309 , pp. 2010-2013
    • RASER, J.M.1    O'SHEA, E.K.2
  • 42
    • 61849168743 scopus 로고    scopus 로고
    • Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (pts) pathway in Escherichia coli
    • J. V. RODRÍGUEZ, J. A. KAANDORP, M. DOBRZYŃSKI, AND J. G. BLOM, Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (pts) pathway in Escherichia coli, Bioinform., 23 (2007), pp. 1969-1977.
    • (2007) Bioinform , vol.23 , pp. 1969-1977
    • RODRÍGUEZ, J.V.1    KAANDORP, J.A.2    DOBRZYŃSKI, M.3    BLOM, J.G.4
  • 44
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. STRANG, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.
    • (1968) SIAM J. Numer. Anal , vol.5 , pp. 506-517
    • STRANG, G.1
  • 45
    • 0030211187 scopus 로고    scopus 로고
    • Stochastic simulation of coupled reaction-diffusion processes
    • A. B. STUNDZIA AND C. L. LUMSDEN, Stochastic simulation of coupled reaction-diffusion processes, J. Comput. Phys., 127 (1996), pp. 196-207.
    • (1996) J. Comput. Phys , vol.127 , pp. 196-207
    • STUNDZIA, A.B.1    LUMSDEN, C.L.2
  • 46
    • 44149100025 scopus 로고    scopus 로고
    • An accuracy evaluation of unstructured node-centred finite volume methods
    • M. SVÄRD, J. GONG, AND J. NORDSTROM, An accuracy evaluation of unstructured node-centred finite volume methods, Appl. Numer. Math., 58 (2008), pp. 1142-1158.
    • (2008) Appl. Numer. Math , vol.58 , pp. 1142-1158
    • SVÄRD, M.1    GONG, J.2    NORDSTROM, J.3
  • 48
    • 38849085199 scopus 로고    scopus 로고
    • On the existence of maximum principles in parabolic finite element equations
    • V. THOMÉE AND L. WAHLBIN, On the existence of maximum principles in parabolic finite element equations, Math. Comp., 77 (2008), pp. 11-19.
    • (2008) Math. Comp , vol.77 , pp. 11-19
    • THOMÉE, V.1    WAHLBIN, L.2
  • 49
    • 0033450269 scopus 로고    scopus 로고
    • A monotone finite element scheme for convection-diffusion equations
    • J. XU AND L. ZIKATANOV, A monotone finite element scheme for convection-diffusion equations, Math. Comp., 68 (1999), pp. 1429-1446.
    • (1999) Math. Comp , vol.68 , pp. 1429-1446
    • XU, J.1    ZIKATANOV, L.2
  • 50
    • 41249084112 scopus 로고    scopus 로고
    • A hybrid multiscale kinetic Monte Carlo method for simulation of copper electrodeposition
    • Z. ZHENG, R. M. STEPHENS, R. D. BRAATZ, R. C. ALKIRE, AND L. R. PETZOLD, A hybrid multiscale kinetic Monte Carlo method for simulation of copper electrodeposition, J. Comput. Phys., 227 (2008), pp. 5184-5199.
    • (2008) J. Comput. Phys , vol.227 , pp. 5184-5199
    • ZHENG, Z.1    STEPHENS, R.M.2    BRAATZ, R.D.3    ALKIRE, R.C.4    PETZOLD, L.R.5
  • 51
    • 29244454300 scopus 로고    scopus 로고
    • Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space
    • J. S. VAN ZON AND P. REIN TEN WOLDE, Green's-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space, J. Chem. Phys., 123 (2005), p. 234910.
    • (2005) J. Chem. Phys , vol.123 , pp. 234910
    • VAN ZON, J.S.1    REIN TEN WOLDE, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.