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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. 
[2] 
O. Radulescu, A. N. Gorban, A. Zinovyev and A. Lilienbaum, Robust simplifications of multiscale biochemical networks,, BMC systems biology, 2 (2008), 86. 
[3] 
A. N. Gorban, O. Radulescu and A. Y. Zinovyev, Asymptotology of chemical reaction networks,, Chemical Engineering Science, 65 (2010), 2310. 
[4] 
R. HannemannTamás, A. Gábor, G. Szederkényi and K. M. Hangos, Model complexity reduction of chemical reaction networks using mixedinteger quadratic programming,, Computers and Mathematics with Applications, 65 (2013), 1575. 
[5] 
G. S. Yablonskii, V. I. Bykov, A. N. Gorban, V. I. Elohin, Kinetic Models of Catalytic Reactions,, Elsevier, (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. 
[7] 
J. Choi, K. Yang, T. Lee and S. Y. Lee, New timescale criteria for model simplification of bioreaction systems,, BMC Bioinformatics, 9 (2008), 338. 
[8] 
Z. Huang, Y. Chu and J. Hahn, Model simplification procedure for signal transduction pathway models: An application to IL6 signaling,, Chemical Engineering Science, 65 (2010), 1964. 
[9] 
M. S. Okino and M. L. Mavrovouniotis, Simplification of Mathematical Models of Chemical Reaction Systems,, Chemical Reviews, 98 (1998), 391. 
[10] 
L. Petzold, Model reduction for chemical kinetics: An optimization approach,, AIChE Journal, 45 (1999), 869. 
[11] 
K. R. Schneider and T. Wilhelm, Model reduction by extended quasisteady state approximation,, J. Math. Biol., 40 (2000), 443. 
[12] 
N. Vora and P. Daoutidis, Nonlinear model reduction of chemical reaction systems,, AIChE Journal, 47 (2001), 2320. 
[13] 
E. Kutumova, A. Zinovyev, R. Sharipov and F. Kolpakov, Model composition through model reduction: a combined model of CD95 and NFkappaB signaling pathways,, BMC Systems Biology, 7 (2013), 13. 
[14] 
M. Bodenstein, Eine Theorie der Photochemischen Reaktionsgeschwindigkeiten,, Z. Phys. Chem., 85 (1913), 329. 
[15] 
G. E. Briggs and J. B. Haldane, A Note on the Kinetics of Enzyme Action,, Biochemical Journal, 19 (1925), 338. 
[16] 
L. A. Segel and M. Slemrod, The quasisteadystate assumption: A case study in perturbation,, SIAM Rev., 31 (1989), 446. 
[17] 
A. N. Gorban and M. Shahzad, The MichaelisMenten Stueckelberg Theorem,, Entropy, 13 (2011), 966. 
[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 quasisteady state analyses,, Combustion and Flame, 91 (1992), 107. 
[19] 
T. Turányi, Sensitivity analysis of complex kinetic systems, Tools and Applications,, Journal of mathematical chemistry, 5 (1990), 203. 
[20] 
Z. Zi, Sensitivity analysis approaches applied to systems biology models,, IET systems biology, 5 (2011), 336. 
[21] 
H. Rabitz, M. Kramer and D. Dacol, Sensitivity Analysis in Chemical Kinetics,, Annual Reviews Physics Chemistry, 34 (1983), 419. 
[22] 
SimBiology., Available from: http://usingsimBiologyforpharmacokineticandmechanisticmodeling &, 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, SBMLSAT: A systems biology markup language (SBML) based sensitivity analysis tool,, BMC Bioinf., 9 (2008), 342. 
[25] 
H. Schmidt and M. Jirstrand, Systems biology toolbox for MATLAB: A computational platform for research in systems biology,, Bioinformatics, 22 (2006), 514. 
[26] 
M. RodriguezFernandez and J. R. Banga, SensSB: A software toolbox for the development and sensitivity analysis of systems biology models,, Bioinformatics, 26 (2010), 1675. 
[27] 
D. Chandran, F. T. Bergmann and H. M. Sauro, TinkerCell: modular CAD tool for synthetic biology,, J. Biol. Eng., 3 (2009), 19. 
[28] 
I. Segal, Nonlinear semigroups,, The Annals of Mathematics, 78 (1963), 339. 
[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. 
[2] 
O. Radulescu, A. N. Gorban, A. Zinovyev and A. Lilienbaum, Robust simplifications of multiscale biochemical networks,, BMC systems biology, 2 (2008), 86. 
[3] 
A. N. Gorban, O. Radulescu and A. Y. Zinovyev, Asymptotology of chemical reaction networks,, Chemical Engineering Science, 65 (2010), 2310. 
[4] 
R. HannemannTamás, A. Gábor, G. Szederkényi and K. M. Hangos, Model complexity reduction of chemical reaction networks using mixedinteger quadratic programming,, Computers and Mathematics with Applications, 65 (2013), 1575. 
[5] 
G. S. Yablonskii, V. I. Bykov, A. N. Gorban, V. I. Elohin, Kinetic Models of Catalytic Reactions,, Elsevier, (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. 
[7] 
J. Choi, K. Yang, T. Lee and S. Y. Lee, New timescale criteria for model simplification of bioreaction systems,, BMC Bioinformatics, 9 (2008), 338. 
[8] 
Z. Huang, Y. Chu and J. Hahn, Model simplification procedure for signal transduction pathway models: An application to IL6 signaling,, Chemical Engineering Science, 65 (2010), 1964. 
[9] 
M. S. Okino and M. L. Mavrovouniotis, Simplification of Mathematical Models of Chemical Reaction Systems,, Chemical Reviews, 98 (1998), 391. 
[10] 
L. Petzold, Model reduction for chemical kinetics: An optimization approach,, AIChE Journal, 45 (1999), 869. 
[11] 
K. R. Schneider and T. Wilhelm, Model reduction by extended quasisteady state approximation,, J. Math. Biol., 40 (2000), 443. 
[12] 
N. Vora and P. Daoutidis, Nonlinear model reduction of chemical reaction systems,, AIChE Journal, 47 (2001), 2320. 
[13] 
E. Kutumova, A. Zinovyev, R. Sharipov and F. Kolpakov, Model composition through model reduction: a combined model of CD95 and NFkappaB signaling pathways,, BMC Systems Biology, 7 (2013), 13. 
[14] 
M. Bodenstein, Eine Theorie der Photochemischen Reaktionsgeschwindigkeiten,, Z. Phys. Chem., 85 (1913), 329. 
[15] 
G. E. Briggs and J. B. Haldane, A Note on the Kinetics of Enzyme Action,, Biochemical Journal, 19 (1925), 338. 
[16] 
L. A. Segel and M. Slemrod, The quasisteadystate assumption: A case study in perturbation,, SIAM Rev., 31 (1989), 446. 
[17] 
A. N. Gorban and M. Shahzad, The MichaelisMenten Stueckelberg Theorem,, Entropy, 13 (2011), 966. 
[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 quasisteady state analyses,, Combustion and Flame, 91 (1992), 107. 
[19] 
T. Turányi, Sensitivity analysis of complex kinetic systems, Tools and Applications,, Journal of mathematical chemistry, 5 (1990), 203. 
[20] 
Z. Zi, Sensitivity analysis approaches applied to systems biology models,, IET systems biology, 5 (2011), 336. 
[21] 
H. Rabitz, M. Kramer and D. Dacol, Sensitivity Analysis in Chemical Kinetics,, Annual Reviews Physics Chemistry, 34 (1983), 419. 
[22] 
SimBiology., Available from: http://usingsimBiologyforpharmacokineticandmechanisticmodeling &, 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, SBMLSAT: A systems biology markup language (SBML) based sensitivity analysis tool,, BMC Bioinf., 9 (2008), 342. 
[25] 
H. Schmidt and M. Jirstrand, Systems biology toolbox for MATLAB: A computational platform for research in systems biology,, Bioinformatics, 22 (2006), 514. 
[26] 
M. RodriguezFernandez and J. R. Banga, SensSB: A software toolbox for the development and sensitivity analysis of systems biology models,, Bioinformatics, 26 (2010), 1675. 
[27] 
D. Chandran, F. T. Bergmann and H. M. Sauro, TinkerCell: modular CAD tool for synthetic biology,, J. Biol. Eng., 3 (2009), 19. 
[28] 
I. Segal, Nonlinear semigroups,, The Annals of Mathematics, 78 (1963), 339. 
[29] 
T. Tao, Nonlinear dispersive equations: local and global analysis,, CBMS Regional Conference Series in Mathematics, 106 (2006). 
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