For reactions using thiamine diphosphate (ThDP)-dependent enzymes many empirically-derived kinetic models exist. However, there is a lack of mechanistic kinetic models. This is especially true for the synthesis of symmetric 2-hydroxy ketones from two identical aldehydes, with one substrate acting as the donor and the other as the acceptor. In this contribution, a systematic approach for deriving such a kinetic model for thiamine diphosphate (ThDP)-dependent enzymes is presented. The derived mechanistic kinetic model takes this donor-acceptor principle into account by containing two K(m)-values even for identical substrate molecules. As example the stereoselective carbon-carbon coupling of two 3,5-dimethoxy-benzaldehyde molecules to (R)-3,3',5,5'-tetramethoxy-benzoin using benzaldehyde lyase (EC 4.1.2.38) from Pseudomonas fluorescens is studied. The model is derived using a model-based experimental analysis method which includes parameter estimation, model analysis, optimal experimental design, in silico experiments, sensitivity analysis and model revision. It is shown that this approach leads to a robust kinetic model with accurate parameter estimates and an excellent prediction capability.

While model-based optimal experimental design (OED) strategies aiming at maximizing the parameter precision are regularly applied in industry and academia, only a little attention has been payed to OED techniques for model discrimination in practical applications. A broader use of these techniques is mainly hindered by two drawbacks: (i) The use of such techniques is desirable in an early model identification phase, where only a little knowledge on the process is available. The known methods, however, rely on good estimates of the parameters of all candidate model structures. (ii) The available methods are tailored to few (ideally two) model candidates and do not work well if numerous candidate structures are taken into account. In this work we propose a novel design criterion for model-based OED for model discrimination in the case of multiple model candidates. The resulting OED method is thus well-suited for designing experiments in an early stage of the model identification process to efficiently reduce the number of model candidates, thereby reducing the overall cost for model identification.

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Estimating the parameters of a dynamical system based on measurements is an important task in industrial and scientific practice. Since a model's quality is directly linked to its parameter values, obtaining globally rather than locally optimal values is especially important in this context. In practice, however, local methods are used almost exclusively. This is mainly due to the high computational cost of global dynamic parameter estimation, which limits its application to relatively small problems comprising no more than a few equations and parameters. In addition, there is still a lack of software packages that allow global parameter estimation in dynamical systems without expert knowledge. Therefore, we propose an efficient computational method for obtaining globally optimal parameter estimates of dynamical systems using well-established, user-friendly software packages. The method is based on the so-called incremental identification procedure, in combination with deterministic global optimization tools for nonlinear programs.