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Superstar of the Sloan Minority Ph.D. Program
Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches
1. | Mathematics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany |
We discuss in detail the models and equilibrium relations of a classical operator-repressor system, and we extend our approach to the MM problem with leakage and to reversible MM kinetics. The arrangement of the sufficient conditions exhibits the important role of data that have a concavity property (chemically feasible data).
References:
[1] |
G. E. Briggs and J. B. S. Haldane, A note on the kinematics of enzyme action, Biochem. J., 19 (1925), 338-339. |
[2] |
K. P. Hadeler and D. Jukić, K. Sabo, Least squares problems for Michaelis-Menten kinetics, Math. Meth. Appl. Sci., 30 (2007), 1231-1241.
doi: 10.1002/mma.835. |
[3] |
M. W. Hirsch and H. L. Smith, Monotone dynamical systems, in "Handbook of Differential Equations, Vol. 2," Elsevier B. V., Amsterdam, (2006), 239-357 |
[4] |
M. C. Mackey, M. Tyran-Kaminska and R. Yvinec, Molecular distributions in gene regulatory dynamics, J. Theoretical Biology, 274 (2011), 84-96.
doi: 10.1016/j.jtbi.2011.01.020. |
[5] |
L. Michaelis and M. L. Menten, Die kinetik der invertinwirkung, Biochem. Z., 49 (1913), 333-369. |
[6] |
L. Noethen and S. Walcher, Tikhonov's theorem and quasi-steady state, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 945-961.
doi: 10.3934/dcdsb.2011.16.945. |
[7] |
L. A. Segel and M. Slemrod, The quasi-steady-state assumption: A case study in perturbation, Thermochim. Acta, 31 (1989), 446-477.
doi: 10.1137/1031091. |
[8] |
Gad Yail and Ezra Yagil, On the relation between effector concentration and the rate of induced enzyme synthesis, Biophysical Journal, 11 (1971), 11-27. |
show all references
References:
[1] |
G. E. Briggs and J. B. S. Haldane, A note on the kinematics of enzyme action, Biochem. J., 19 (1925), 338-339. |
[2] |
K. P. Hadeler and D. Jukić, K. Sabo, Least squares problems for Michaelis-Menten kinetics, Math. Meth. Appl. Sci., 30 (2007), 1231-1241.
doi: 10.1002/mma.835. |
[3] |
M. W. Hirsch and H. L. Smith, Monotone dynamical systems, in "Handbook of Differential Equations, Vol. 2," Elsevier B. V., Amsterdam, (2006), 239-357 |
[4] |
M. C. Mackey, M. Tyran-Kaminska and R. Yvinec, Molecular distributions in gene regulatory dynamics, J. Theoretical Biology, 274 (2011), 84-96.
doi: 10.1016/j.jtbi.2011.01.020. |
[5] |
L. Michaelis and M. L. Menten, Die kinetik der invertinwirkung, Biochem. Z., 49 (1913), 333-369. |
[6] |
L. Noethen and S. Walcher, Tikhonov's theorem and quasi-steady state, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 945-961.
doi: 10.3934/dcdsb.2011.16.945. |
[7] |
L. A. Segel and M. Slemrod, The quasi-steady-state assumption: A case study in perturbation, Thermochim. Acta, 31 (1989), 446-477.
doi: 10.1137/1031091. |
[8] |
Gad Yail and Ezra Yagil, On the relation between effector concentration and the rate of induced enzyme synthesis, Biophysical Journal, 11 (1971), 11-27. |
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