摘要
Mathematical modelling of cellular metabolism plays an important role in understandingbiological functions and providing identification of targets for biotechnological modification.This paperproposes a nonlinear bilevel programming(NBP)model to infer the objective function of anaerobicglycerol metabolism in Klebsiella Pneumoniae(K.Pneumoniae)for 1,3-propanediol(1,3-PD)production.Based on the Kuhn-Tucker optimality condition of the lower level problem,NBP is transformedinto a nonlinear programming with complementary and slackness conditions.The authors give the existencetheorem of solutions to NBP.An efficient algorithm is proposed to solve NBP and its convergenceis also simply analyzed.Numerical results reveal some interesting conclusions,e.g.,biomass productionis the main force to drive glycerol metabolism,and the objective functions,which are obtained in termof several different groups of flux distributions,are similar.
Mathematical modelling of cellular metabolism plays an important role in understanding biological functions and providing identification of targets for biotechnological modification. This paper proposes a nonlinear bilevel programming （NBP） model to infer the objective function of anaerobic glycerol metabolism in Klebsiella Pneumoniae （K. Pneumoniae） for 1, 3-propanediol （1, 3-PD） produc- tion. Based on the Kuhn-Tucker optimality condition of the lower level problem, NBP is transformed into a nonlinear programming with complementary and slackness conditions. The authors give the exis- tence theorem of solutions to NBP. An efficient algorithm is proposed to solve NBP and its convergence is also simply analyzed. Numerical results reveal some interesting conclusions, e.g., biomass production is the main force to drive glycerol metabolism, and the objective functions, which are obtained in term of several different groups of flux distributions, are similar.
基金
supported by the National Natural Science Foundation of China under Grant Nos.10871033 and 10671126
