Calculation of Permeability Coefficients from Solute Equilibration Dynamics: An Assessment of Various Methods

Predicting the rate at which substances permeate membrane barriers in vivo is crucial for drug development. Permeability coefficients obtained from in vitro studies are valuable for this goal. These are normally determined by following the dynamics of solute equilibration between two membrane-separated compartments. However, the correct calculation of permeability coefficients from such data is not always straightforward. To address these problems, here we develop a kinetic model for solute permeation through lipid membrane barriers that includes the two membrane leaflets as compartments in a four-compartment model. Accounting for solute association with the membrane allows assessing various methods in a wide variety of conditions. The results showed that the often-used expression P_app = β × r/3 is inapplicable to very large or very small vesicles, to moderately or highly lipophilic solutes, or when the development of a significant pH gradient opposes the solute's flux. We establish useful relationships that overcome these limitations and allow predicting permeability in compartmentalised in vitro or in vivo systems with specific properties. Finally, from the parameters for the interaction of the solute with the membrane barrier, we defined an intrinsic permeability coefficient that facilitates quantitative comparisons between solutes.