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Volumn 51, Issue 3, 2009, Pages 281-307

Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade

Author keywords

Chemical master equation; Krylov subspace approximations; Stochastic simulation algorithm; Systems biology; Total quasi steady state approximation

Indexed keywords


EID: 67349168128     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-008-9239-y     Document Type: Article
Times cited : (9)

References (60)
  • 1
    • 0031879114 scopus 로고    scopus 로고
    • Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells
    • Aug
    • A. Arkin J. Ross H.H. McAdams 1998 Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells Genetics 149 4 1633 1648 Aug
    • (1998) Genetics , vol.149 , Issue.4 , pp. 1633-1648
    • Arkin, A.1    Ross, J.2
  • 2
    • 0242416539 scopus 로고    scopus 로고
    • Noise in eukaryotic gene expression
    • Apr
    • W.J. Blake M. Kaern C.R. Cantor J.J. Collins 2003 Noise in eukaryotic gene expression Nature 422 6932 633 637 Apr
    • (2003) Nature , vol.422 , Issue.6932 , pp. 633-637
    • Blake, W.J.1    Kaern, M.2    Cantor, C.R.3    Collins, J.J.4
  • 3
    • 2442465034 scopus 로고    scopus 로고
    • Prospects for productivity
    • May
    • B. Booth R. Zemmel 2004 Prospects for productivity Nat. Rev. Drug Discov. 3 5 451 456 May
    • (2004) Nat. Rev. Drug Discov. , vol.3 , Issue.5 , pp. 451-456
    • Booth, B.1    Zemmel, R.2
  • 4
    • 0029681614 scopus 로고    scopus 로고
    • Extending the quasi-steady state approximation by changing variables
    • Jan
    • J.A. Borghans R.J. de Boer L.A. Segel 1996 Extending the quasi-steady state approximation by changing variables Bull. Math. Biol. 58 1 43 63 Jan
    • (1996) Bull. Math. Biol. , vol.58 , Issue.1 , pp. 43-63
    • Borghans, J.A.1    De Boer, R.J.2    Segel, L.A.3
  • 5
    • 0015587773 scopus 로고
    • Reducing the retrieval time of scatter storage techniques
    • February
    • R.P. Brent 1973 Reducing the retrieval time of scatter storage techniques Commun. ACM 16 2 105 109 February
    • (1973) Commun. ACM , vol.16 , Issue.2 , pp. 105-109
    • Brent, R.P.1
  • 6
    • 0000292524 scopus 로고
    • A note on the kinetics of enzyme action
    • G.E. Briggs J.B.S. Haldane 1925 A note on the kinetics of enzyme action Biochem. J. 19 338 339
    • (1925) Biochem. J. , vol.19 , pp. 338-339
    • Briggs, G.E.1    Haldane, J.B.S.2
  • 9
    • 2442438819 scopus 로고    scopus 로고
    • A multi-scaled approach for simulating chemical reaction systems
    • K. Burrage T. Tian P. Burrage 2004 A multi-scaled approach for simulating chemical reaction systems Prog. Biophys. Mol. Biol. 85 2-3 217 234
    • (2004) Prog. Biophys. Mol. Biol. , vol.85 , Issue.23 , pp. 217-234
    • Burrage, K.1    Tian, T.2    Burrage, P.3
  • 10
  • 11
    • 0000592564 scopus 로고
    • Iterative methods for overflow queueing models i and II
    • R.H. Chan 1987 Iterative methods for overflow queueing models I and II Numer. Math. 51 2 143 180
    • (1987) Numer. Math. , vol.51 , Issue.2 , pp. 143-180
    • Chan, R.H.1
  • 12
    • 34047240610 scopus 로고    scopus 로고
    • Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation
    • Mar
    • A. Ciliberto F. Capuani J.J. Tyson 2007 Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation PLoS Comput. Biol. 3 3 e45 Mar
    • (2007) PLoS Comput. Biol. , vol.3 , Issue.3 , pp. 45
    • Ciliberto, A.1    Capuani, F.2    Tyson, J.J.3
  • 14
    • 27744516835 scopus 로고    scopus 로고
    • Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
    • Nov
    • W.E.D. Liu E. Vanden-Eijnden 2005 Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates J. Chem. Phys. 123 19 194107 Nov
    • (2005) J. Chem. Phys. , vol.123 , Issue.19 , pp. 194107
    • Liu, W.E.D.1    Vanden-Eijnden, E.2
  • 17
    • 0037119578 scopus 로고    scopus 로고
    • Small numbers of big molecules
    • August
    • N. Fedoroff W. Fontana 2002 Small numbers of big molecules Science 297 5584 1129 1131 August
    • (2002) Science , vol.297 , Issue.5584 , pp. 1129-1131
    • Fedoroff, N.1    Fontana, W.2
  • 19
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • D.T. Gillespie 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 25 2340 2361
    • (1977) J. Phys. Chem. , vol.81 , Issue.25 , pp. 2340-2361
    • Gillespie, D.T.1
  • 20
    • 0035933994 scopus 로고    scopus 로고
    • Approximate accelerated stochastic simulation of chemically reacting systems
    • D.T. Gillespie 2001 Approximate accelerated stochastic simulation of chemically reacting systems J. Chem. Phys. 115 4 1716 1733
    • (2001) J. Chem. Phys. , vol.115 , Issue.4 , pp. 1716-1733
    • Gillespie, D.T.1
  • 23
    • 0042761623 scopus 로고    scopus 로고
    • On the preconditioning of matrices with skew-symmetric splittings
    • G.H. Golub D. Vanderstraeten 2000 On the preconditioning of matrices with skew-symmetric splittings Numer. Algorithm 25 223 239
    • (2000) Numer. Algorithm , vol.25 , pp. 223-239
    • Golub, G.H.1    Vanderstraeten, D.2
  • 24
    • 34248187057 scopus 로고    scopus 로고
    • A solver for the stochastic master equation applied to gene regulatory networks
    • (Special issue on evolutionary problems)
    • M. Hegland C. Burden L. Santoso S. MacNamara H. Booth 2006 A solver for the stochastic master equation applied to gene regulatory networks J. Comput. Appl. Math. 205 2 708 724 (Special issue on evolutionary problems)
    • (2006) J. Comput. Appl. Math. , vol.205 , Issue.2 , pp. 708-724
    • Hegland, M.1    Burden, C.2    Santoso, L.3    Booth, H.4
  • 25
    • 0346328093 scopus 로고
    • Ueber das gesetz der wirkung des invertins
    • V. Henri 1901 Ueber das gesetz der wirkung des invertins Z. Phys. Chem. 39 194 216
    • (1901) Z. Phys. Chem. , vol.39 , pp. 194-216
    • Henri, V.1
  • 27
    • 0029790351 scopus 로고    scopus 로고
    • Ultrasensitivity in the mitogen-activated protein kinase cascade
    • Sep
    • C.Y. Huang J.E. Ferrell 1996 Ultrasensitivity in the mitogen-activated protein kinase cascade Proc. Natl. Acad. Sci. U. S. A. 93 19 10078 10083 Sep
    • (1996) Proc. Natl. Acad. Sci. U. S. A. , vol.93 , Issue.19 , pp. 10078-10083
    • Huang, C.Y.1    Ferrell, J.E.2
  • 28
    • 35548973892 scopus 로고    scopus 로고
    • DNA sequencing: Bench to bedside and beyond
    • C.A. Hutchison 2007 DNA sequencing: bench to bedside and beyond Nucleic Acids Res. 35 18 6227 6237
    • (2007) Nucleic Acids Res. , vol.35 , Issue.18 , pp. 6227-6237
    • Hutchison, C.A.1
  • 32
    • 51549101248 scopus 로고    scopus 로고
    • Stochastic chemical kinetics and the total quasi-steady-state assumption: Application to the stochastic simulation algorithm and chemical master equation
    • MacNamara, S., Bersani, A.M., Burrage, K., Sidje, R.B.: Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation. J. Chem. Phys. 129, 95-105 (2008)
    • (2008) J. Chem. Phys. , vol.129 , pp. 95-105
    • MacNamara, S.1    Bersani, A.M.2    Burrage, K.3    Sidje, R.B.4
  • 34
    • 49749098924 scopus 로고    scopus 로고
    • Multiscale modeling of chemical kinetics via the master equation
    • S. MacNamara K. Burrage R.B. Sidje 2008 Multiscale modeling of chemical kinetics via the master equation Multiscale Model. Simul. 6 4 1146 1168
    • (2008) Multiscale Model. Simul. , vol.6 , Issue.4 , pp. 1146-1168
    • Burrage, K.1    Sidje, R.B.2
  • 36
    • 0000870544 scopus 로고
    • Die kinetik der invertinwirkung
    • L. Michaelis M.L. Menten 1913 Die kinetik der invertinwirkung Biochem. Z. 49 333 369
    • (1913) Biochem. Z. , vol.49 , pp. 333-369
    • Michaelis, L.1    Menten, M.L.2
  • 37
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • C. Moler C. Van Loan 1978 Nineteen dubious ways to compute the exponential of a matrix SIAM Rev. 20 801 836
    • (1978) SIAM Rev. , vol.20 , pp. 801-836
    • Moler, C.1    Van Loan, C.2
  • 38
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, 25 years later
    • C. Moler C. Van Loan 2003 Nineteen dubious ways to compute the exponential of a matrix, 25 years later SIAM Rev. 45 1 3 49
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 39
    • 33751347484 scopus 로고    scopus 로고
    • The finite state projection algorithm for the solution of the chemical master equation
    • B. Munsky M. Khammash 2006 The finite state projection algorithm for the solution of the chemical master equation J. Chem. Phys. 124 044104
    • (2006) J. Chem. Phys. , vol.124 , pp. 044104
    • Munsky, B.1    Khammash, M.2
  • 40
    • 33645241165 scopus 로고    scopus 로고
    • Identifying optimal lipid raft characteristics required to promote nanoscale protein-protein interactions on the plasma membrane
    • D.V. Nicolau Jr. K. Burrage R.G. Parton J.F. Hancock 2006 Identifying optimal lipid raft characteristics required to promote nanoscale protein-protein interactions on the plasma membrane Mol. Cell Biol. 26 1 313 323
    • (2006) Mol. Cell Biol. , vol.26 , Issue.1 , pp. 313-323
    • Nicolau, Jr.D.V.1    Burrage, K.2    Parton, R.G.3    Hancock, J.F.4
  • 42
    • 33846543728 scopus 로고    scopus 로고
    • The total quasi-steady-state approximation for fully competitive enzyme reactions
    • Jan
    • M.G. Pedersen A.M. Bersani E. Bersani 2007 The total quasi-steady-state approximation for fully competitive enzyme reactions Bull. Math. Biol. 69 1 433 457 Jan
    • (2007) Bull. Math. Biol. , vol.69 , Issue.1 , pp. 433-457
    • Pedersen, M.G.1    Bersani, A.M.2    Bersani, E.3
  • 43
    • 0037444724 scopus 로고    scopus 로고
    • Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
    • C.V. Rao A.P. Arkin 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
  • 44
    • 0942279178 scopus 로고    scopus 로고
    • Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
    • December
    • M. Rathinam L.R. Petzold Y. Cao D.T. Gillespie 2003 Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method J. Chem. Phys. 119 12784 12794 December
    • (2003) J. Chem. Phys. , vol.119 , pp. 12784-12794
    • Rathinam, M.1    Petzold, L.R.2    Cao, Y.3    Gillespie, D.T.4
  • 45
    • 0014824563 scopus 로고
    • Time-dependent Michaelis-Menten kinetics for an enzyme-substrate- inhibitor system
    • S.I. Rubinow J.L. Lebowitz 1970 Time-dependent Michaelis-Menten kinetics for an enzyme-substrate-inhibitor system J. Am. Chem. Soc. 92 3888 3893
    • (1970) J. Am. Chem. Soc. , vol.92 , pp. 3888-3893
    • Rubinow, S.I.1    Lebowitz, J.L.2
  • 46
    • 0026818185 scopus 로고
    • Analysis of some krylov subspace approximaitons to the matrix exponential operator
    • February
    • Y. Saad 1992 Analysis of some krylov subspace approximaitons to the matrix exponential operator Siam J. Numer. Anal. 29 1 209 228 February
    • (1992) Siam J. Numer. Anal. , vol.29 , Issue.1 , pp. 209-228
    • Saad, Y.1
  • 48
    • 0024731820 scopus 로고
    • The quasi-steady-state assumption: A case study in perturbation
    • L.A. Segel M. Slemrod 1989 The quasi-steady-state assumption: a case study in perturbation SIAM Rev. 31 3 446 447
    • (1989) SIAM Rev. , vol.31 , Issue.3 , pp. 446-447
    • Segel, L.A.1    Slemrod, M.2
  • 49
    • 0032010619 scopus 로고    scopus 로고
    • Expokit: A software package for computing matrix exponentials
    • R.B. Sidje 1998 Expokit: a software package for computing matrix exponentials ACM Trans. Math. Softw. 24 1 130 156
    • (1998) ACM Trans. Math. Softw. , vol.24 , Issue.1 , pp. 130-156
    • Sidje, R.B.1
  • 51
    • 0033611447 scopus 로고    scopus 로고
    • A numerical study of large sparse matrix exponentials arising in Markov chains
    • R.B. Sidje W.J. Stewart 1999 A numerical study of large sparse matrix exponentials arising in Markov chains Comput. Stat. Data Anal. 29 345 368
    • (1999) Comput. Stat. Data Anal. , vol.29 , pp. 345-368
    • Sidje, R.B.1    Stewart, W.J.2
  • 53
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang 1968 On the construction and comparison of difference schemes SIAM J. Numer. Anal. 5 2 506 517
    • (1968) SIAM J. Numer. Anal. , vol.5 , Issue.2 , pp. 506-517
    • Strang, G.1
  • 56
    • 3142543968 scopus 로고    scopus 로고
    • Binomial leap methods for simulating stochastic chemical kinetics
    • T. Tian K. Burrage 2004 Binomial leap methods for simulating stochastic chemical kinetics J. Chem. Phys. 121 21 10356 10364
    • (2004) J. Chem. Phys. , vol.121 , Issue.21 , pp. 10356-10364
    • Tian, T.1    Burrage, K.2
  • 57
    • 0344395658 scopus 로고    scopus 로고
    • Michaelis-menten kinetics at high enzyme concentrations
    • Nov
    • A.R. Tzafriri 2003 Michaelis-menten kinetics at high enzyme concentrations Bull. Math. Biol. 65 6 1111 1129 Nov
    • (2003) Bull. Math. Biol. , vol.65 , Issue.6 , pp. 1111-1129
    • Tzafriri, A.R.1
  • 60
    • 34848889762 scopus 로고    scopus 로고
    • The thousand-dollar genome. Genetic brinkmanship or personalized medicine?
    • Oct
    • H. Wolinsky 2007 The thousand-dollar genome. Genetic brinkmanship or personalized medicine? EMBO Rep. 8 10 900 903 Oct
    • (2007) EMBO Rep. , vol.8 , Issue.10 , pp. 900-903
    • Wolinsky, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.