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Michaelis-Menten Kinetics under Spatially Constrained Conditions: Application to Mibefradil Pharmacokinetics

Kosmas Kosmidis ^*, Vangelis Karalis , Panos Argyrakis ^* and Panos Macheras 

^* Department of Physics, University of Thessaloniki, Thessaloniki, Greece; and Laboratory of Biopharmaceutics-Pharmacokinetics, School of Pharmacy, University of Athens, Athens, Greece

Correspondence: Address reprint requests to Panos Argyrakis, E-mail: panos{at}physics.auth.gr.

Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.