Identifying the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae under different culture conditions.

This paper addresses the problem of identifying the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae for production of 1,3-propanediol (1,3-PD) under different culture conditions. To achieve this goal, we propose a multi-level programming model. This model includes three optimization problems, where the constraint region of the first level problem is implicitly determined by the other two optimization problems. The optimized objectives of the first and second level problems are to minimize the set of fluxes that are of major importance to glycerol metabolism and the difference between the observed fluxes and those computed by the model, respectively. The third level problem in the proposed multi-level programming simultaneously solves a set of flux balance analysis (FBA) models. A method is proposed to solve efficiently the presented multi-level programming problem. In this method, we first transform the proposed multi-level problem into a bi-level problem by applying the dual theory of linear programming to the FBA models of the third level. Next, the optimal solution of the above bi-level problem is obtained by iteratively solving a sequence of mixed integer programming problems. Optimization results reveal that the proposed method can identify the shared metabolic objectives of glycerol bioconversion in Klebsiella pneumoniae under three groups of experimental data.