TY - JOUR

T1 - Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method

AU - Eshtewy, Neveen Ali

AU - Scholz, Lena

AU - Kremling, Andreas

N1 - Publisher Copyright:
© 2023 by the authors.

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Latin hypercube sampling

KW - inverse problem

KW - kinetic model

KW - model order reduction

KW - parameter estimation

KW - proper orthogonal decomposition

KW - singular value decomposition

UR - http://www.scopus.com/inward/record.url?scp=85147889183&partnerID=8YFLogxK

U2 - 10.3390/math11030699

DO - 10.3390/math11030699

M3 - Article

AN - SCOPUS:85147889183

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 3

M1 - 699

ER -