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Infer objective function of glycerol metabolism in klebsiella pneumoniae basing on bilevel programming

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Abstract

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) production. 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 existence 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.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, 264005, China

    Zhaohua Gong & Yongsheng Yu

  2. School of Mathematical Science, Dalian University of Technology, Dalian, 116024, China

    Enmin Feng

Authors
  1. Zhaohua Gong
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  2. Yongsheng Yu
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  3. Enmin Feng
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Correspondence to Zhaohua Gong.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871033 and 10671126.

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Gong, Z., Yu, Y. & Feng, E. Infer objective function of glycerol metabolism in klebsiella pneumoniae basing on bilevel programming. J Syst Sci Complex 23, 334–342 (2010). https://doi.org/10.1007/s11424-010-8235-1

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  • DOI: https://doi.org/10.1007/s11424-010-8235-1

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