Kinetic considerations for the quantitative assessment of efflux activity and inhibition: Implications for understanding and predicting the effects of efflux inhibition

Purpose. Unexpected and complex experimental observations related to efflux transport have been reported in the literature. This work was conducted to develop relationships for efflux activity (PSefflux) as a function of commonly studied kinetic parameters [permeability-surface area product (PS), efflux ratio (ER), degree of efflux inhibition (phi(i)), 50% inhibitory concentration (IC50), and Michaelis-Menten constant (K-m)]. Methods. A three-compartment model (apical, cellular, and basolateral) was used to derive flux equations relating the initial rate of flux and steady-state mass transfer in the presence or absence of active efflux. Various definitions of efflux ratio (ER) were examined in terms of permeability-surface area products. The efflux activity (PSefflux) was expressed in terms of ER and PS. The relationships between PSefflux and PS, ER, phi(i), IC50, and K-m were solved mathematically. Simulations and examples from the literature were used to illustrate the resulting mathematical relationships. Results. The relationships derived according to a three-compartment model differed fundamentally from commonly accepted approaches for determining PSefflux, phi(i), IC50 and K-m. Based on the model assumptions and mathematical derivations, currently used mathematical relationships erroneously imply that efflux activity is proportional to change in PS (i.e., flux or P-app) and thus underestimate PSefflux and phi(i,) and overestimate IC50 and K-m. Conclusions. An understanding of the relationship between efflux inhibition and kinetic parameters is critical for appropriate data interpretation, standardization in calculating and expressing the influence of efflux transport, and predicting the clinical significance of efflux inhibition.