Mathematical Biosciences and Engineering, 2013, 10(5&6): 1541-1560. doi: 10.3934/mbe.2013.10.1541.

Primary: 92C45, 93E24; Secondary: 34C12, 34D15.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches

1. Mathematics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen

The Michaelis-Menten (MM) function is a fractional linear function depending on two positive parameters.These can be estimated by nonlinear or linear least squares methods.The non-linear methods, based directly on the defect of the MM function, can fail and not produce any minimizer.The linear methods always produce a unique minimizer which, however, may not be positive. Here we give sufficient conditions on thedata such that the nonlinear problem has at least one positive minimizer and also conditions for the minimizer of the linearproblem to be positive.
    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.Thearrangement of the sufficient conditions exhibits the important role of data that have aconcavity property (chemically feasible data).
  Figure/Table
  Supplementary
  Article Metrics

Keywords enzyme kinetics; nonlinear least squares; Parameter identification; operator repressor kinetics.

Citation: Karl Peter Hadeler. Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1541-1560. doi: 10.3934/mbe.2013.10.1541

References

  • 1. Biochem. J., 19 (1925), 338-339.
  • 2. Math. Meth. Appl. Sci., 30 (2007), 1231-1241.
  • 3. in "Handbook of Differential Equations, Vol. 2," Elsevier B. V., Amsterdam, (2006), 239-357
  • 4. J. Theoretical Biology, 274 (2011), 84-96.
  • 5. Biochem. Z., 49 (1913), 333-369.
  • 6. Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 945-961.
  • 7. Thermochim. Acta, 31 (1989), 446-477.
  • 8. Biophysical Journal, 11 (1971), 11-27.

 

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, Karl Peter Hadeler, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved