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Reduction of a kinetic model of active export of importins
1. | Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom |
References:
[1] |
A. N. Kolodkin, H. V. Westerhoff, F. J. Bruggeman, N. Plant, M. J. Moné, B. M. Bakker, M. J. Campbell, V. Leeuwen, P. T. M. Johannes, C. Carlberg and J. L. Snoep, Design principles of nuclear receptor signaling: how complex networking improves signal transduction, Molecular Systems Biology, 6 (2010) 446-460. |
[2] |
O. Radulescu, A. N. Gorban, A. Zinovyev and A. Lilienbaum, Robust simplifications of multiscale biochemical networks, BMC systems biology, 2 (2008) 86-86. |
[3] |
A. N. Gorban, O. Radulescu and A. Y. Zinovyev, Asymptotology of chemical reaction networks, Chemical Engineering Science, 65 (2010) 2310-2324. |
[4] |
R. Hannemann-Tamás, A. Gábor, G. Szederkényi and K. M. Hangos, Model complexity reduction of chemical reaction networks using mixed-integer quadratic programming, Computers and Mathematics with Applications, 65 (2013) 1575-1595. |
[5] |
G. S. Yablonskii, V. I. Bykov, A. N. Gorban, V. I. Elohin, Kinetic Models of Catalytic Reactions, Elsevier, R. G. Compton (Ed.) Series omprehensive Chemical Kinetics, New York, 32( 1991). |
[6] |
O. Radulescu, A. N. Gorban, A. Zinovyev and V. Noel, Reduction of dynamical biochemical reactions networks in computational biology, Frontiers in genetics, 3 (2012) 131-148. |
[7] |
J. Choi, K. Yang, T. Lee and S. Y. Lee, New time-scale criteria for model simplification of bio-reaction systems, BMC Bioinformatics, 9 (2008) 338-346. |
[8] |
Z. Huang, Y. Chu and J. Hahn, Model simplification procedure for signal transduction pathway models: An application to IL-6 signaling, Chemical Engineering Science, 65 (2010) 1964-1975. |
[9] |
M. S. Okino and M. L. Mavrovouniotis, Simplification of Mathematical Models of Chemical Reaction Systems, Chemical Reviews, 98 (1998) 391-408. |
[10] |
L. Petzold, Model reduction for chemical kinetics: An optimization approach, AIChE Journal, 45 (1999) 869-886. |
[11] |
K. R. Schneider and T. Wilhelm, Model reduction by extended quasi-steady state approximation, J. Math. Biol., 40 (2000) 443-450. |
[12] |
N. Vora and P. Daoutidis, Non-linear model reduction of chemical reaction systems, AIChE Journal, 47 (2001) 2320-2332. |
[13] |
E. Kutumova, A. Zinovyev, R. Sharipov and F. Kolpakov, Model composition through model reduction: a combined model of CD95 and NF-kappaB signaling pathways, BMC Systems Biology,7 (2013) 13-34 & preprint, arXiv:1310.6314. |
[14] |
M. Bodenstein, Eine Theorie der Photochemischen Reaktionsgeschwindigkeiten, Z. Phys. Chem., 85 (1913) 329-397. |
[15] |
G. E. Briggs and J. B. Haldane, A Note on the Kinetics of Enzyme Action, Biochemical Journal, 19 (1925) 338-339. |
[16] |
L. A. Segel and M. Slemrod, The quasi-steady-state assumption: A case study in perturbation, SIAM Rev., 31 (1989) 446-477. |
[17] |
A. N. Gorban and M. Shahzad, The Michaelis-Menten Stueckelberg Theorem, Entropy, 13 (2011) 966-1019. |
[18] |
A. S. Tomlin, M. J. Pilling, T. Turányi, J. H. Merkin and J. Brindley, Mechanism reduction for the oscillatory oxidation of hydrogen: sensitivity and quasi-steady state analyses, Combustion and Flame, 91 (1992) 107-130. |
[19] |
T. Turányi, Sensitivity analysis of complex kinetic systems, Tools and Applications, Journal of mathematical chemistry, 5 (1990) 203-248. |
[20] |
Z. Zi, Sensitivity analysis approaches applied to systems biology models, IET systems biology, 5 (2011) 336-346. |
[21] |
H. Rabitz, M. Kramer and D. Dacol, Sensitivity Analysis in Chemical Kinetics, Annual Reviews Physics Chemistry, 34 (1983) 419-461. |
[22] |
SimBiology., Available from: http://using-simBiology-for-pharmacokinetic-and-mechanistic-modeling & http://www.mathworks.co.uk/products/simbiology/. |
[23] |
BioSens, Available from: http://www.chemengr.ucsb.edu/ceweb/faculty/doyle/biosens/ BioSens.htm. |
[24] |
Z. Zi, Y. Zheng, A. E. Rundell and E. Klipp, SBML-SAT: A systems biology markup language (SBML) based sensitivity analysis tool, BMC Bioinf., 9 (2008) 342-356. |
[25] |
H. Schmidt and M. Jirstrand, Systems biology toolbox for MATLAB: A computational platform for research in systems biology, Bioinformatics, 22 (2006) 514-515. |
[26] |
M. Rodriguez-Fernandez and J. R. Banga, SensSB: A software toolbox for the development and sensitivity analysis of systems biology models, Bioinformatics, 26 (2010) 1675-1676. |
[27] |
D. Chandran, F. T. Bergmann and H. M. Sauro, TinkerCell: modular CAD tool for synthetic biology, J. Biol. Eng., 3 (2009) 19-36. |
[28] |
I. Segal, Non-linear semi-groups, The Annals of Mathematics, 78 (1963) 339-364. |
[29] |
T. Tao, Nonlinear dispersive equations: local and global analysis, CBMS Regional Conference Series in Mathematics, 106 (2006). |
show all references
References:
[1] |
A. N. Kolodkin, H. V. Westerhoff, F. J. Bruggeman, N. Plant, M. J. Moné, B. M. Bakker, M. J. Campbell, V. Leeuwen, P. T. M. Johannes, C. Carlberg and J. L. Snoep, Design principles of nuclear receptor signaling: how complex networking improves signal transduction, Molecular Systems Biology, 6 (2010) 446-460. |
[2] |
O. Radulescu, A. N. Gorban, A. Zinovyev and A. Lilienbaum, Robust simplifications of multiscale biochemical networks, BMC systems biology, 2 (2008) 86-86. |
[3] |
A. N. Gorban, O. Radulescu and A. Y. Zinovyev, Asymptotology of chemical reaction networks, Chemical Engineering Science, 65 (2010) 2310-2324. |
[4] |
R. Hannemann-Tamás, A. Gábor, G. Szederkényi and K. M. Hangos, Model complexity reduction of chemical reaction networks using mixed-integer quadratic programming, Computers and Mathematics with Applications, 65 (2013) 1575-1595. |
[5] |
G. S. Yablonskii, V. I. Bykov, A. N. Gorban, V. I. Elohin, Kinetic Models of Catalytic Reactions, Elsevier, R. G. Compton (Ed.) Series omprehensive Chemical Kinetics, New York, 32( 1991). |
[6] |
O. Radulescu, A. N. Gorban, A. Zinovyev and V. Noel, Reduction of dynamical biochemical reactions networks in computational biology, Frontiers in genetics, 3 (2012) 131-148. |
[7] |
J. Choi, K. Yang, T. Lee and S. Y. Lee, New time-scale criteria for model simplification of bio-reaction systems, BMC Bioinformatics, 9 (2008) 338-346. |
[8] |
Z. Huang, Y. Chu and J. Hahn, Model simplification procedure for signal transduction pathway models: An application to IL-6 signaling, Chemical Engineering Science, 65 (2010) 1964-1975. |
[9] |
M. S. Okino and M. L. Mavrovouniotis, Simplification of Mathematical Models of Chemical Reaction Systems, Chemical Reviews, 98 (1998) 391-408. |
[10] |
L. Petzold, Model reduction for chemical kinetics: An optimization approach, AIChE Journal, 45 (1999) 869-886. |
[11] |
K. R. Schneider and T. Wilhelm, Model reduction by extended quasi-steady state approximation, J. Math. Biol., 40 (2000) 443-450. |
[12] |
N. Vora and P. Daoutidis, Non-linear model reduction of chemical reaction systems, AIChE Journal, 47 (2001) 2320-2332. |
[13] |
E. Kutumova, A. Zinovyev, R. Sharipov and F. Kolpakov, Model composition through model reduction: a combined model of CD95 and NF-kappaB signaling pathways, BMC Systems Biology,7 (2013) 13-34 & preprint, arXiv:1310.6314. |
[14] |
M. Bodenstein, Eine Theorie der Photochemischen Reaktionsgeschwindigkeiten, Z. Phys. Chem., 85 (1913) 329-397. |
[15] |
G. E. Briggs and J. B. Haldane, A Note on the Kinetics of Enzyme Action, Biochemical Journal, 19 (1925) 338-339. |
[16] |
L. A. Segel and M. Slemrod, The quasi-steady-state assumption: A case study in perturbation, SIAM Rev., 31 (1989) 446-477. |
[17] |
A. N. Gorban and M. Shahzad, The Michaelis-Menten Stueckelberg Theorem, Entropy, 13 (2011) 966-1019. |
[18] |
A. S. Tomlin, M. J. Pilling, T. Turányi, J. H. Merkin and J. Brindley, Mechanism reduction for the oscillatory oxidation of hydrogen: sensitivity and quasi-steady state analyses, Combustion and Flame, 91 (1992) 107-130. |
[19] |
T. Turányi, Sensitivity analysis of complex kinetic systems, Tools and Applications, Journal of mathematical chemistry, 5 (1990) 203-248. |
[20] |
Z. Zi, Sensitivity analysis approaches applied to systems biology models, IET systems biology, 5 (2011) 336-346. |
[21] |
H. Rabitz, M. Kramer and D. Dacol, Sensitivity Analysis in Chemical Kinetics, Annual Reviews Physics Chemistry, 34 (1983) 419-461. |
[22] |
SimBiology., Available from: http://using-simBiology-for-pharmacokinetic-and-mechanistic-modeling & http://www.mathworks.co.uk/products/simbiology/. |
[23] |
BioSens, Available from: http://www.chemengr.ucsb.edu/ceweb/faculty/doyle/biosens/ BioSens.htm. |
[24] |
Z. Zi, Y. Zheng, A. E. Rundell and E. Klipp, SBML-SAT: A systems biology markup language (SBML) based sensitivity analysis tool, BMC Bioinf., 9 (2008) 342-356. |
[25] |
H. Schmidt and M. Jirstrand, Systems biology toolbox for MATLAB: A computational platform for research in systems biology, Bioinformatics, 22 (2006) 514-515. |
[26] |
M. Rodriguez-Fernandez and J. R. Banga, SensSB: A software toolbox for the development and sensitivity analysis of systems biology models, Bioinformatics, 26 (2010) 1675-1676. |
[27] |
D. Chandran, F. T. Bergmann and H. M. Sauro, TinkerCell: modular CAD tool for synthetic biology, J. Biol. Eng., 3 (2009) 19-36. |
[28] |
I. Segal, Non-linear semi-groups, The Annals of Mathematics, 78 (1963) 339-364. |
[29] |
T. Tao, Nonlinear dispersive equations: local and global analysis, CBMS Regional Conference Series in Mathematics, 106 (2006). |
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