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Mathematica Slovaca

, 59:593 | Cite as

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

  • Anna Siudak
  • Eric von Lieres
  • Christine H. Müller
Article

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.

Keywords

implicitly given nonlinear model differential equations estimation least trimmed squares model discrimination experimental design 

2000 Mathematics Subject Classification

Primary 62J02, 62H12, 62K05, 62P10, 62P30 

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Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Anna Siudak
    • 1
  • Eric von Lieres
    • 2
  • Christine H. Müller
    • 3
  1. 1.Carl von Ossietzky University OldenburgInstitut für MathematikOldenburg i.O.Germany
  2. 2.Research Centre Jülich 2Institute of BiotechnologyJülichGermany
  3. 3.Fachbereich MathematikUniversity KasselKasselGermany

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