Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties

0568675 - ÚTIA 2024 RIV CZ eng C - Conference Paper (international conference)
Papáček, Štěpán - Matonoha, Ctirad - Duintjer Tebbens, Jurjen
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties.
Proceedings of the Seminar on Numerical Analysis & Winter School /SNA' 23/. Ostrava: Institute of Geonics of the Czech Academy of Sciences, 2023 - (Starý, J.; Sysala, S.; Sysalová, D.), s. 56-59. ISBN 978-80-86407-85-2.
[SEMINAR ON NUMERICAL ANALYSIS - SNA'23 In memoriam of professor Radim Blaheta. Ostrava (CZ), 23.01.2023-27.01.2023]
R&D Projects: GA ČR(CZ) GA21-03689S
Institutional support: RVO:67985556 ; RVO:67985807
Keywords : Mathematical modeling * Biochemical network * Pharmacokinetic (PBPK) models
OECD category: Applied mathematics; Pure mathematics (UIVT-O)
http://library.utia.cas.cz/separaty/2023/TR/papacek-0568675.pdf

This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the drug-induced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzyme-catalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the above-sketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasi-linear' Bohl-Marek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.
Permanent Link: https://hdl.handle.net/11104/0339944