A systematic approach for finding the objective function and active constraints for dynamic flux balance analysis

Dynamic flux balance analysis (DFBA) has become an instrumental modeling tool for describing the dynamic behavior of bioprocesses. DFBA involves the maximization of a biologically meaningful objective subject to kinetic constraints on the rate of consumption/production of metabolites. In this paper, we propose a systematic data-based approach for finding both the biological objective function and a minimum set of active constraints necessary for matching the model predictions to the experimental data. The proposed algorithm accounts for the errors in the experiments and eliminates the need for ad hoc choices of objective function and constraints as done in previous studies. The method is illustrated for two cases: (1) for in silico (simulated) data generated by a mathematical model for Escherichia coli and (2) for actual experimental data collected from the batch fermentation of Bordetella Pertussis (whooping cough).