National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán ; Matonoha, Ctirad ; Duintjer Tebbens, Jurjen
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.
Mathematics and Optimal control theory meet Pharmacy: Towards application of special techniques in modeling, control and optimization of biochemical networks
Papáček, Štěpán ; Matonoha, Ctirad ; Duintjer Tebbens, Jurjen
Similarly to other scienti c domains, the expenses related to in silico modeling in pharmacology need not be extensively apologized. Vis a vis both in vitro and in vivo experiments, physiologically-based pharmacokinetic (PBPK) and pharmacodynamic models represent an important tool for the assessment of drug safety before its approval, as well as a viable option in designing dosing regimens. In this contribution, some special techniques related to the mathematical modeling, control and optimization of biochemical networks are presented on a paradigmatic example of enzyme kinetics.

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