Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches
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 met...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-07-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1541 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590118651691008 |
|---|---|
| author | Karl Peter Hadeler |
| author_facet | Karl Peter Hadeler |
| author_sort | Karl Peter Hadeler |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-63dbdd2570fc4f0998d9c792837dba67 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-63dbdd2570fc4f0998d9c792837dba672025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61541156010.3934/mbe.2013.10.1541Michaelis-Menten kinetics, the operator-repressor system, and least squares approachesKarl Peter Hadeler0Mathematics, University of Tübingen, Auf der Morgenstelle 10, 72076 TübingenThe 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).https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1541enzyme kineticsnonlinear least squaresparameter identificationoperator repressor kinetics. |
| spellingShingle | Karl Peter Hadeler Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches Mathematical Biosciences and Engineering enzyme kinetics nonlinear least squares parameter identification operator repressor kinetics. |
| title | Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches |
| title_full | Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches |
| title_fullStr | Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches |
| title_full_unstemmed | Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches |
| title_short | Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches |
| title_sort | michaelis menten kinetics the operator repressor system and least squares approaches |
| topic | enzyme kinetics nonlinear least squares parameter identification operator repressor kinetics. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1541 |
| work_keys_str_mv | AT karlpeterhadeler michaelismentenkineticstheoperatorrepressorsystemandleastsquaresapproaches |