Computational simulations to study the kinetics of drug efflux via multidrug resistant membrane proteins expressed in confluent cell monolayers: A critical evaluation of different models employed, data fitting techniques and global optimization strategies

Computational models have often been employed to understand the kinetics of drug efflux via membrane proteins expressed in relevant systems. One such membrane protein extensively studied is P-glycoprotein (P-gp), a multidrug resistance protein expressed in the apical surface of epithelial cells lining several organs and tissues. Several models have been employed to understand the kinetics of drug efflux via P-gp. One such model is the minimal mass action model which is capable of determining the elementary kinetic parameters thereby providing a better understanding of the structure---function relationship of P-gp. One of the limitations of this model is that it gives a small range of possible values for each parameter, rather than a lone vector of fits. One aspect of this study is to determine the basis for the range. We find that the "range" cannot be attributed to inherent experimental error. Rather it can be attributed to the global optimization technique of the model, i.e. determining all the parameters simultaneously. The Michaelis-Menten model is also employed to study P-gp kinetics. This model allows us to determine the maximal rate of drug efflux (Vmax) and the Michaelis-Menten constant (Km). This model was originally designed for enzymes which catalyze reactions in aqueous environments. It is unclear if it is suitable to apply this model to membrane proteins such as P-gp, which directly pick substrate from the membrane. Bentz et al. (2005) using data generated by simulations employing the minimal mass action kinetic model, showed that experimentally determined Vmax values correlates reasonably well with the molecular Vmax, as determined by the elementary rate parameters. However, they found no correlation between the molecular and experimental Km values, even if the data had no error. Recently, Sun and Pang (2008), using data generated by simulations employing the steady state Michaelis-Menten model, obtained the exact opposite result. Our second objective was to compare and contrast the two computational models in their abilities to determine the kinetic parameters and to examine the possible reason for the discrepancies in correlations obtained by the same. We find that the original results of Bentz et al. (2005) hold, irrespective of the model employed. This is subjected to the fact that appropriate substrate concentrations (those capable of saturating at least 70% of P-gp present) are used. We know that P-gp is expressed in the apical membrane of epithelial cells, which are composed of microvilli. Microvilli are dynamic structures. Their expression can be altered thereby altering cellular surface area. This in turn could alter P-gp expression, besides affecting passive transport. The third aspect of my study is to understand how the changing microvilli morphology affects efflux of compounds. We discover that as long as the height of the microvilli is lesser than the distance between two adjacent microvilli, the number of molecules escaping per unit area of the membrane remains constant. If the height becomes greater than the distance between microvilli, the number of escapes per unit area falls considerably.