Reduction of a Structured Model to an Equivalent Unstructured Model.

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A new modeling approach that employs a time-lag kernel can be used to transform a complicated structured model to an equivalent unstructured model. It can be shown that the connection between the two types of models is provided by the timelag kernel, as a natural consequence of reducing a larger set of dynamic equations of a structured model to a smaller set of dynamic equations of an unstructured model. The time-lag kernel compacts the process of a cell's response to the external stimuli into a simple functional form. This modeling approach retains the general form of an unstructured model so as to facilitate simple physical interpretation of the variables. Yet, it retains the predictive power of a structured model by incorporating only those metabolic intermediates that are important to the dynamics of the system. The order of a structured model is reduced through the judicious process of lumping and modal analysis of the eigenvalue- eigenvector of a quasi-linearized system. By identifying the first few most important modes, such an analysis yields useful information on the relative time scales of various processes and clarifies the main feature of the model. The application of the approach is demonstrated with different structured models. Since a model is to be judged based on its intended purpose, in many applications a time-lag kernel approach is a viable, attractive alternative to either an oversimplified unstructured model whose detailed description is unnecessary, or a purely black box approach that has little appeal due to the total lack of process structures. The use of the time-lag model in the fermentation control's environment will be discussed.