Linear parameter estimation of rational biokinetic functions.

For rational biokinetic functions such as the Michaelis-Menten equation, in general, a nonlinear least-squares method is a good estimator. However, a major drawback of a nonlinear least-squares estimator is that it can end up in a local minimum. Rearranging and linearizing rational biokinetic functions for parameter estimation is common practice (e.g. Lineweaver-Burk linearization). By rearranging, however, the error is distorted. In addition, the rearranged model frequently leads to a so-called 'errors-in-variables' estimation problem. Applying the ordinary least squares (OLS) method to the linearly reparameterized function ensures a global minimum, but its estimates become biased if the regression variables contain errors and thus bias compensation is needed. Therefore, in this paper, a bias compensated total least squares (CTLS) method, which as OLS is a direct method, is proposed to solve the estimation problem. The applicability of a general linear reparameterization procedure and the advances of CTLS over ordinary least squares and nonlinear least squares approaches are shown by two simulation examples. The examples contain Michaelis-Menten kinetics and enzyme kinetics with substrate inhibition. Furthermore, CTLS is demonstrated with real data of an activated sludge experiment. It is concluded that for rational biokinetic models CTLS is a powerful alternative to the existing least-squares methods.