Parameter estimation in kinetic models for large scale biotechnological systems with advanced mathematical programming techniques

Abstract

In the present work, we formulate parameter estimation problems for kinetic models of large-scale dynamic biotechnological systems. We propose dynamic models of increasing complexity for metabolic networks and continuous bioreactors. The differential algebraic equations (DAE) system for the metabolic network represent the glycolysis, the phosphotransferase system and the pentose-phosphate pathway of Escherichia coli, with modifications proposed for several enzyme kinetics. The most sensitive parameters have been ranked by performing global sensitivity analysis on the dynamic metabolic network. Since the kinetic parameters for the enzymes have been obtained from in vitro experiments, the formulation of a detailed kinetic model for the metabolic network allows parameter adjustment for in vivo conditions. We formulate an unstructured non-segregated model for a chemostat to study the dynamic response to a glucose pulse in a continuous culture of E. coli. Moreover, we perform parameter estimation by formulating a maximum likelihood problem, subject to the DAE systems, within a control vector parameterization approach. Nine kinetic parameters in the metabolic network model have been estimated with good agreement with published experimental data. For the bioreactor model, seven parameters have been tuned based on experimental data obtained in this work. Numerical results show a good agreement between the observed data and the predicted profiles.