The identification of metabolic systems such as metabolic pathways, enzyme actions and gene regulations, is a complex task, due to the complexity of the system and limited knowledge about the model. In the past, mathematical equations and ODEs have been used to capture the structure of the model, and conventional optimization techniques have been used to identify the parameters of the model. In general, however, a pure mathematical formulation of the model is difficult, due to parametric uncertainty and incomplete knowledge of mechanisms. In this paper, we propose a modeling approach that uses (1) a fuzzy rule-based model to augment algebraic enzyme models that are incomplete, and (2) a hybrid genetic algorithm (GA) to identify uncertain parameters in the model. The hybrid GA integrates a GA with the simplex method in functional optimization to improve the GA's convergence rate. We have applied this approach to modeling the rate of enzyme reactions in E. coli's central metabolism. The proposed modeling strategy allows (1) easy incorporation of qualitative insights into a pure mathematical model and (2) adaptive identification and optimization of key parameters to fit the system behaviors observed in biochemical experiments.
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