Construction and evaluation of "global" Micahelis-Menten reduced models
Dimitris G. Patsatzis (1) and Dimitris A. Goussis (1)
(1) Department of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 157 80 Athens, Greece
Objectives: Multi-compartmental models in non-linear pharmacokinetics are largely based on the enzyme kinetics of Michaelis-Menten mechanism, which is characterized by multi-scale dynamics. The traditional approaches for the analysis of this mechanism fail from constructing reduced models that reproduce the dynamics of the full mechanism in a wide parametric domain. The aim of this work is to construct and evaluate, stable and accurate reduced models with global validity and compare them with the existing Quasi Steady-State (QSSA) and Partial Equilibrium (PEA) approximations. In addition, validity criteria will be presented for the stability and the accuracy of the QSSA and PEA approximations.
Methods: The analysis is based on the algorithmic Computational Singular Perturbation (CSP) methodology [1]. Among others, CSP identifies the variables and reactions that relate the most with the fast timescales in the dynamics of the multi-scale model. Reduced models are constructed that guarantee stability and accuracy, by the use of CSP. The traditional QSSA and PEA approaches are studied in the context of CSP [2]. Algebraic criteria of the validity of each reduced model are derived, regarding the stability and the accuracy of the traditional approaches QSSA and PEA.
Results: The validity of the CSP-generated reduced models is examined for a wide range of values for the initial enzyme/substrate concentrations and for kinetic constants. The QSSA/PEA-generated reduced models are shown less accurate and stable, when compared to the CSP-generated ones, in a large number of cases. New criteria for the validity of QSSA and PEA were produced, which are shown more valid than the existing ones.
Conclusions: The availability of trustworthy reduced Michaelis-Menten models is very important for the experimental investigator in the fields of biology/pharmacokinetics, especially of parameter estimations purposes. CSP provides such models, which are more robust than the existing ones. Regarding the qualitative understanding of the process, the present analysis systematizes the findings in the literature and provides some new insights.
References:
[1] Lam, S. H., & Goussis, D. A. The CSP method for simplifying kinetics. International Journal of Chemical Kinetics, 26(4), 461-486, 1994.
[2] Goussis, D. A. Quasi steady state and partial equilibrium approximations: their relation and their validity. Combustion Theory and Modelling, 16(5), 869-926, 2012.
