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

Neveen Ali Eshtewy (), Lena Scholz () and Andreas Kremling
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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

Mathematics, 2023, vol. 11, issue 3, 1-15

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.

Keywords: model order reduction; proper orthogonal decomposition; singular value decomposition; inverse problem; parameter estimation; kinetic model; Latin hypercube sampling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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