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Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs)

Author

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  • Arvind Raghunathan
  • J. PÉRez-Correa
  • Eduardo Agosin
  • Lorenz Biegler

Abstract

Recent years have witnessed a surge in research in cellular biology. There has been particular interest in the interaction between cellular metabolism and its environment. In this work we present a framework for fitting fermentation models that include this interaction. Differential equations describe the evolution of extracellular metabolites, while a Linear Program (LP) models cell metabolism, and piecewise smooth functions model the links between cell metabolism and its environment. We show that the fermentation dynamics can be described using Differential Variational Inequalities (DVIs). Discretization of the system and reformulation of the VIs using optimality conditions converts the DVI to a Mathematical Program with Complementarity Constraints (MPCC). We briefly describe an interior point algorithm for solving MPCCs. Encouraging numerical results are presented in estimating model parameters to fit model prediction and data obtained from fermentation, using cultures of Saccharomyces cerevisiae reported in the literature. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Arvind Raghunathan & J. PÉRez-Correa & Eduardo Agosin & Lorenz Biegler, 2006. "Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs)," Annals of Operations Research, Springer, vol. 148(1), pages 251-270, November.
    • Handle: RePEc:spr:annopr:v:148:y:2006:i:1:p:251-270:10.1007/s10479-006-0086-8
    DOI: 10.1007/s10479-006-0086-8
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    Cited by:

    1. Yirong Jiang & Qiqing Song & Qiongfen Zhang, 2021. "Uniqueness and Hyers-Ulam Stability of Random Differential Variational Inequalities with Nonlocal Boundary Conditions," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 646-665, May.
    2. Xing Wang & Ya-wei Qi & Chang-qi Tao & Yi-bin Xiao, 2017. "A Class of Delay Differential Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 56-69, January.
    3. Heng-you Lan, 2019. "On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 327-344, September.
    4. Xing Wang & Nan-Jing Huang, 2013. "Differential Vector Variational Inequalities in Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 109-129, July.
    5. Sungho Shin & Ophelia S Venturelli & Victor M Zavala, 2019. "Scalable nonlinear programming framework for parameter estimation in dynamic biological system models," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-29, March.

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