A review of existence criteria for parameter estimation of the Michaelis–Menten regression model |
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Authors: | Dragan Jukić Kristian Sabo Rudolf Scitovski |
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Affiliation: | (1) Department of Mathematics, University J. J. Strossmayer, Gajev trg 6, 31000 Osijek, Croatia |
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Abstract: | In this paper we consider the least squares (LS) and total least squares (TLS) problems for a Michaelis–Menten enzyme kinetic model f(x; a, b) = ax/(b + x), a, b > 0. In various applied research such as biochemistry, pharmacology, biology and medicine there are lots of different applications of this model. We will systematize some of our results pertaining to the existence of the LS and TLS estimate, which were proved in Hadeler et al. (Math Method Appl Sci 30:1231–1241, 2007) and Jukić et al. (J Comput Appl Math 201:230–246, 2007). Finally, we suggest a choice of good initial approximation and give one numerical example. |
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Keywords: | Michaelis– Menten function Nonlinear least squares Least squares estimate Total least squares Existence problem |
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