, Volume 59, Issue 5, pp 593-610
Date: 27 Oct 2009

Estimation, model discrimination, and experimental design for implicitly given nonlinear models of enzyme catalyzed chemical reactions

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Abstract

Many nonlinear models as e.g. models of chemical reactions are described by systems of differential equations which have no explicit solution. In such cases the statistical analysis is much more complicated than for nonlinear models with explicitly given response functions. Numerical approaches need to be applied in place of explicit solutions. This paper describes how the analysis can be done when the response function is only implicitly given by differential equations. It is shown how the unknown parameters can be estimated and how these estimations can be applied for model discrimination and for deriving optimal designs for future research. The methods are demonstrated with a chemical reaction catalyzed by the enzyme Benzaldehyde lyase.

Dedicated to Professor Andrej Pázman on the occasion of his 70th birthday
Communicated by Gejza Wimmer
Research of third author supported by the SFB/TR TRR 30 Project D6.