Kosmidis Kosmas, Karalis Vangelis, Argyrakis Panos, Macheras Panos
Department of Physics, University of Thessaloniki, Thessaloniki, Greece.
Biophys J. 2004 Sep;87(3):1498-506. doi: 10.1529/biophysj.104.042143.
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.
采用了两种不同的方法来研究非均相条件下酶促反应的动力学，以解释米贝拉地尔异常的非线性药代动力学。首先，提出了一个基于动力学微分方程的详细模型来研究空间限制和体内条件下的酶促反应。其次，应用二维方形晶格中酶反应的蒙特卡罗模拟，特别强调底物的输入和输出，以模拟体内条件。酶促反应的数学模型和蒙特卡罗模拟在均相介质中重现了经典的米氏（MM）动力学，在分形介质中重现了异常动力学。基于这些发现，针对无序介质中底物浓度的变化率，开发了经典MM方程的时间依赖性版本，并成功用于描述米贝拉地尔的实验血浆浓度-时间数据，并推导模型参数的估计值。米贝拉地尔异常的非线性药代动力学源于酶促反应反应空间中的非均相条件。修正后的MM方程能够捕捉无序介质中酶促反应的异质性，从而可以描述米贝拉地尔的药代动力学。
