An Accurate Algebraic Closed Form Solution for Drug Transport Kinetics through P-Glycoprotein Expressing Confluent Cell Monolayers by Fitting Our Experimentally Derived Empirical Fitting Function with the Elementary Rate Constants of 370 Virtual P-gp subs

Abstract

The kinetics of transport by P-gp through confluent cell monolayers is typically modelled by a version of the Michaelis-Menten equations within PBPK mechanistic models^1-5. The quasi-steady-state Michaelis-Menten equation was solved by the Lambert W-function, which is an infinite summation series that can only be evaluated in Matlab, Maple and a few other math programs⁶. Our Structural Mass Action Kinetic Model (SMAKM) for P-gp transport through confluent cell monolayers was built from a more accurate set of mass action kinetic equations. Its most significant departure from PBPK mechanistic models was that P-gp can only bind drug that has partitioned from the cytosol into the cytosolic monolayer, according to its molar partition coefficient K_PC, since that is where P-gp’s substrate binding site resides. Our analysis of P-gp transport for many drugs using SMAKM has shown that most, if not all, commonly used P-gp expressing cells also express basolateral and apical uptake transporters for many, if not all, P-gp substrates. An algebraic Closed Form Solution for P-gp transport has been built by fitting the elementary rate constants of 370 Virtual P-gp substrates to an algebraic equation we started building in 2005 to fit our experimental drug transport kinetics through P-gp expressing confluent cell monolayers. The resultant algebraic Closed Form Solution clearly shows how each of P-gp’s elementary rate constants contributes to transport. It is currently used, within Excel, to predict the upper and lower bounds required to fit the elementary rate constants of new experimental drug transport data using Matlab’s Particle Swarm program.