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Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method

Author

Listed:
  • Neveen Ali Eshtewy

    (Department of Mathematics, Arish University, Arish 31111, Egypt)

  • Lena Scholz

    (Department of Mathematics, Technische Universität Berlin, 10623 Berlin, Germany)

  • Andreas Kremling

    (School of Engineering and Design, Technische Universität München, 80333 Munich, Germany)

Abstract

Order reduction methods are important tools for systems engineering and can be used, for example, for parameter estimation of kinetic models for systems biology applications. In particular, the Proper Orthogonal Decomposition (POD) method produces a reduced-order model of a system that is used for solving inverse problems (parameter estimation). POD is an intrusive model order reduction method that is aimed to obtain a lower-dimensional system for a high-dimensional system while preserving the main features of the original system. We use a singular value decomposition (SVD) to compute a reduced basis as it is usually numerically more robust to compute the singular values of the snapshot matrix instead of the eigenvalues of the corresponding correlation matrix. The reduced basis functions are then used to construct a data-fitting function that fits a known experimental data set of system substance concentrations. The method is applied to calibrate a kinetic model of carbon catabolite repression (CCR) in Escherichia coli , where the regulatory mechanisms on the molecular side are well understood and experimental data for a number of state variables is available. In particular, we show that the method can be used to estimate the uptake rate constants and other kinetic parameters of the CCR model.

Suggested Citation

  • Neveen Ali Eshtewy & Lena Scholz & Andreas Kremling, 2023. "Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:699-:d:1051210
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    References listed on IDEAS

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    1. Andreas Raue & Marcel Schilling & Julie Bachmann & Andrew Matteson & Max Schelke & Daniel Kaschek & Sabine Hug & Clemens Kreutz & Brian D Harms & Fabian J Theis & Ursula Klingmüller & Jens Timmer, 2013. "Lessons Learned from Quantitative Dynamical Modeling in Systems Biology," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-17, September.
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