Browsing by Author "Biegler, Lorenz T."

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    Fast and reliable calibration of solid substrate fermentation kinetic models using advanced non-linear programming techniques
    (UNIV CATOLICA DE VALPARAISO, 2007) Macarena Araya, M.; Arrieta, Juan J.; Ricardo Perez Correa, J.; Biegler, Lorenz T.; Jorquera, Hector
    Calibration of mechanistic kinetic models describing microorganism growth and secondary metabolite production on solid substrates is difficult due to model complexity given the sheer number of parameters needing to be estimated and violation of standard conditions of numerical regularity. We show how advanced non-linear programming techniques can be applied to achieve fast and reliable calibration of a complex kinetic model describing growth of Gibberella fujikuroi and production of gibberellic acid on an inert solid support in glass columns. Experimental culture data was obtained under different temperature and water activity conditions. Model differential equations were discretized using orthogonal collocations on finite elements while model calibration was formulated as a simultaneous solution/optimization problem. A special purpose optimization code (IPOPT) was used to solve the resulting large-scale non-linear program. Convergence proved much faster and a better fitting model was achieved in comparison with the standard sequential solution/optimization approach. Furthermore, statistical analysis showed that most parameter estimates were reliable and accurate.
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    Parameter estimation in metabolic flux balance models for batch fermentation - formulation & solution using Differential Variational Inequalities (DVIs)
    (SPRINGER, 2006) Raghunathan, Arvind U.; Ricardo Perez Correa, J.; Agosin, Eduardo; Biegler, Lorenz T.
    Recent years have witnessed a surge in research in cellular biology. There has been particular interest in the interaction between cellular metabolism and its environment. In this work we present a framework for fitting fermentation models that include this interaction. Differential equations describe the evolution of extracellular metabolites, while a Linear Program (LP) models cell metabolism, and piecewise smooth functions model the links between cell metabolism and its environment. We show that the fermentation dynamics can be described using Differential Variational Inequalities (DVIs). Discretization of the system and reformulation of the VIs using optimality conditions converts the DVI to a Mathematical Program with Complementarity Constraints (MPCC). We briefly describe an interior point algorithm for solving MPCCs. Encouraging numerical results are presented in estimating model parameters to fit model prediction and data obtained from fermentation, using cultures of Saccharomyces cerevisiae reported in the literature.