Application of modified Michaelis – Menten equations for determination of enzyme inducing and inhibiting drugs

Abstract

Background Pharmacokinetics (PK) is the process of absorption, distribution, metabolism and elimination (ADME) of drugs. Some drugs undergo zero-order kinetics (ethyl alcohol), first order kinetics (piroxicam) and mixed order kinetics (ascorbic acid). Drugs that undergo Michaelis-Menten metabolism are characterized by either increased or decreased metabolism constant (Km) and maximum velocity (Vmax) of enzyme reaction. Hence literatures were searched with a view to translating in vitro-in vivo enzyme kinetics to pharmacokinetic/pharmacodynamic parameters for determination of enzyme inducing and inhibiting drugs, in order to achieve optimal clinical efficacy and safety. Methods A narrative review of retrospective secondary data on drugs, their metabolites, Vmax and Km, generated in the laboratory and clinical environments was adopted, using inclusion and exclusion criteria. Key word search strategy was applied, to assess databases of published articles on enzyme inducing and inhibiting drugs, that obey Michaelis-Menten kinetics. In vitro and in vivo kinetic parameters, such as concentration of substrate, rate of endogenous substrate production, cellular metabolic rate, initial velocity of metabolism, intrinsic clearance, percent saturation and unsaturation of the enzyme substrate, were calculated using original and modified formulas. Years and numbers of searched publications, types of equations and their applications were recorded. Results A total of fifty-six formulas both established and modified were applied in the present study. Findings have shown that theophylline, voriconazole, phenytoin, thiopental, fluorouracil, thyamine and thymidine are enzyme inducers whereas, mibefradil, metronidazole, isoniazid and puromicin are enzyme inhibitors. They are metabolized and eliminated according to Michaelis-Menten principle. The order could be mixed but may change to zero or first order, depending on drug concentration, frequency and route of drug administration. Conclusion Hence, pharmacokinetic-pharmacodynamic translation can be optimally achieved by incorporating, newly modified Michaelis-Menten equations into pharmacokinetic formulas for clinical efficacy and safety of the enzyme inducing and inhibiting therapeutic agents used in laboratory and clinical settings.

MIWE: detecting the critical states of complex biological systems by the mutual information weighted entropy

“…We use a theoretical model to validate the robustness of MIWE method, and construct a 10-node monitoring network based on the Michaelis–Menten equation [ 9 ], which is mainly used to study transcription and translation processes [ 10 ], nonlinear biological processes [ 11 , 12 ]. The 10-node monitoring network can generate datasets for numerical simulation, and as the parameter p varies from − 0.5 to 0.25, the system experiences the critical transition when the parameter value is p = 0.…”