Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods

Authors:
Necmettin Yildirim;Fatih Akçay;Hüseyin Okur;Derya Yildirim
Affiliations:
Computer Sciences Application and Research Center, Ataturk University, 25240 Erzurum, Turkey and Department of Physiology, Center for Nonlinear Dynamics in Physiology and Medicine, McGill Universi ...;Faculty of Medicine, Department of Biochemistry, Ataturk University, 25240 Erzurum, Turkey;Faculty of Engineering, Department of Chemistry, Ataturk University, 25240 Erzurum, Turkey;Faculty of Medicine, Department of Pharmacology, Ataturk University, 25240 Erzurum, Turkey
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

The most commonly used numerical optimization techniques include the Simplex method, Brent's algorithm, Levenberg-Marquardt algorithm, direct search complex algorithm and a quasi-Newton method. In the present study, to compare these methods for a nonlinear model from enzyme kinetic theory known as Michaelis Menten equation, we have developed FORTRAN programs for all of these methods and also numerical solution of an initial value problem to compare optimization methods in terms of number of function evaluations, convergences and computation times. According to these factors, we have found that the Simplex method is the best followed by the Direct search algorithm.