Fitting the Michaelis–Menten model

The target of this paper is to introduce and investigate different methods for the solution of the Michaelis–Menten (M–M) parameters. One of the main results is that the estimation provides no unique estimators. Two main approaches for parameter estimation of the M–M model are discussed: The analytic one, and the iterative one. The former regards the linearization or Linear Least Squares (LSS), as well as the actual Non-Linear Least Squares (NLLS) evaluation, while the latter regards certain iterative methods for the NLLS estimation. The iterative methods are: An optimized Gauss–Newton (GN) approach, a quadratic and linear expansion approaches for the M–M model, as well as a Batch Sequential approach. All these methods are investigated, evaluated and compared through examples using certain datasets, in which the M–M is the assumed model.