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Least‐squares problems for Michaelis–Menten kinetics
Author(s) -
Hadeler K. P.,
Jukić Dragan,
Sabo Kristian
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.835
Subject(s) - mathematics , monotone polygon , chebyshev filter , michaelis–menten kinetics , least squares function approximation , non linear least squares , nonlinear system , parameter identification problem , identification (biology) , inequality , mathematical analysis , explained sum of squares , statistics , chemistry , model parameter , geometry , biochemistry , physics , quantum mechanics , estimator , enzyme assay , enzyme , botany , biology
The Michaelis–Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for nonlinear and for linear least‐squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behaviour. Copyright © 2007 John Wiley & Sons, Ltd.