Towards a unified model of passive drug permeation I: origins of the unstirred water layer with applications to ionic permeation

In this work, we provide a unified theoretical framework describing how drug molecules can permeate across membranes in neutral and ionized forms for unstirred in vitro systems. The analysis provides a self-consistent basis for the origin of the unstirred water layer (UWL) within the Nernst-Planck framework in the fully unstirred limit and further provides an accounting mechanism based simply on the bulk aqueous solvent diffusion constant of the drug molecule. Our framework makes no new assumptions about the underlying physics of molecular permeation. We hold simply that Nernst-Planck is a reasonable approximation at low concentrations and all physical systems must conserve mass. The applicability of the derived framework has been examined both with respect to the effect of stirring and externally applied voltages to measured permeability. The analysis contains data for 9 compounds extracted from the literature representing a range of permeabilities and aqueous diffusion coefficients. Applicability with respect to ionized permeation is examined using literature data for the permanently charged cation, crystal violet, providing a basis for the underlying mechanism for ionized drug permeation for this molecule as being due to mobile counter-current flow.