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Slow manifold reduction of a stochastic chemical reaction: Exploring Keizer's paradox
1. | Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States, United States |
References:
[1] |
L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology,'' Pearson Education, Inc., 2003. |
[2] |
J. Beischke, P. Weber, N. Sarafoff, M. Beekes, A. Giese and H. Kretzschmar, Autocatalytic self-propagation of misfolded prion protein, Proc. Natl. Acad. Sci., 101 (2004), 12207-12211.
doi: 10.1073/pnas.0404650101. |
[3] |
C. W. Gardiner, "Handbook of Stochastic Methods. For Physics, Chemistry and the Natural Sciences,'' Second edition, Springer Series in Synergetics, 13, Springer-Verlag, Berlin, 1985. |
[4] |
B. L. Granovsky and A. I. Zeifman, The decay function of nonhomogeneous birth-death processes, with application to mean-field models, Stoch. Process. Appl., 72 (1997), 105-120.
doi: 10.1016/S0304-4149(97)00085-9. |
[5] |
B. L. Granovsky and A. I. Zeifman, The $N$-limit of spectral gap of a class of birth-death Markov chains, Appl. Stoch. Models Bus. Ind., 16 (2000), 235-248.
doi: 10.1002/1526-4025(200010/12)16:4<235::AID-ASMB415>3.3.CO;2-J. |
[6] |
J. Keizer, "Statistical Thermodynamics of Nonequilibrium Processes,'' Springer-Verlag, 1987. |
[7] |
T. G. Kurtz, Limit theorems for sequences of jump Markov processes approximating ordinary differential processes, J. Appl. Prob., 8 (1971), 344-356. |
[8] |
T. G. Kurtz, The relationship between stochastic and deterministic models for chemical reactions, J. Chem. Phys., 57 (1972), 2976-2978.
doi: 10.1063/1.1678692. |
[9] |
I. Nåsell, Extinction and quasi-stationarity in the Verhulst logistic model, Journal of Theoretical Biology, 211 (2001), 11-27.
doi: 10.1006/jtbi.2001.2328. |
[10] |
H. Qian and L. M. Bishop, The chemical master equation approach to nonequilibrium steady-state of open biochemical systems: Linear single-molecule enzyme kinetics and nonlinear biochemical reaction networks, Int. J. Mol. Sci., 11 (2010), 3472-3500.
doi: 10.3390/ijms11093472. |
[11] |
N. van Kampen, "Stochastic Processes in Physics and Chemistry,'' Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981. |
[12] |
M. Vellela and H. Qian, A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox, Bull. Math. Biol., 69 (2007), 1727-1746.
doi: 10.1007/s11538-006-9188-3. |
show all references
References:
[1] |
L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology,'' Pearson Education, Inc., 2003. |
[2] |
J. Beischke, P. Weber, N. Sarafoff, M. Beekes, A. Giese and H. Kretzschmar, Autocatalytic self-propagation of misfolded prion protein, Proc. Natl. Acad. Sci., 101 (2004), 12207-12211.
doi: 10.1073/pnas.0404650101. |
[3] |
C. W. Gardiner, "Handbook of Stochastic Methods. For Physics, Chemistry and the Natural Sciences,'' Second edition, Springer Series in Synergetics, 13, Springer-Verlag, Berlin, 1985. |
[4] |
B. L. Granovsky and A. I. Zeifman, The decay function of nonhomogeneous birth-death processes, with application to mean-field models, Stoch. Process. Appl., 72 (1997), 105-120.
doi: 10.1016/S0304-4149(97)00085-9. |
[5] |
B. L. Granovsky and A. I. Zeifman, The $N$-limit of spectral gap of a class of birth-death Markov chains, Appl. Stoch. Models Bus. Ind., 16 (2000), 235-248.
doi: 10.1002/1526-4025(200010/12)16:4<235::AID-ASMB415>3.3.CO;2-J. |
[6] |
J. Keizer, "Statistical Thermodynamics of Nonequilibrium Processes,'' Springer-Verlag, 1987. |
[7] |
T. G. Kurtz, Limit theorems for sequences of jump Markov processes approximating ordinary differential processes, J. Appl. Prob., 8 (1971), 344-356. |
[8] |
T. G. Kurtz, The relationship between stochastic and deterministic models for chemical reactions, J. Chem. Phys., 57 (1972), 2976-2978.
doi: 10.1063/1.1678692. |
[9] |
I. Nåsell, Extinction and quasi-stationarity in the Verhulst logistic model, Journal of Theoretical Biology, 211 (2001), 11-27.
doi: 10.1006/jtbi.2001.2328. |
[10] |
H. Qian and L. M. Bishop, The chemical master equation approach to nonequilibrium steady-state of open biochemical systems: Linear single-molecule enzyme kinetics and nonlinear biochemical reaction networks, Int. J. Mol. Sci., 11 (2010), 3472-3500.
doi: 10.3390/ijms11093472. |
[11] |
N. van Kampen, "Stochastic Processes in Physics and Chemistry,'' Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981. |
[12] |
M. Vellela and H. Qian, A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox, Bull. Math. Biol., 69 (2007), 1727-1746.
doi: 10.1007/s11538-006-9188-3. |
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