Modeling and parameter identification of microbial bioconversion in fed-batch cultures

In this study, the nonlinear dynamical system of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae in fed-batch cultures is investigated. Because of the abrupt changes of reactant concentrations in fed-batch cultures, the continuous dynamical system previously used is inappropriate to describe the process of fed-batch cultures. In this respect we present a nonlinear impulsive dynamical system of glycerol bioconversion to 1,3-propanediol in fed-batch cultures based on the dynamical system of batch cultures. Then we study some properties of the piecewise continuous solutions to the proposed impulsive system. More important, observing the bigger errors between the experimental results and computational ones obtained from the initial parameters of the dynamical system of batch cultures which was derived from hundreds of practical chemical experiments, we establish a parameter identification model for the impulsive system. Subsequently the existence of the optimal solutions of model is demonstrated by using the compactness of the set of the system solutions and an optimization algorithm is constructed to seek to the optimal parameters of the proposed system by means of the genetic optimization. Finally an illustrative numerical example shows the appropriateness of the nonlinear impulsive system and the validity of optimization algorithm.