Diffusion and diffusion-osmosis models of the transfer of charged molecules across biological barriers

Abstract

Mathematical models of the transfer of large enough charged molecules (macroions) have been constructed on the basis of the classical equations of electromigration diffusion (Helmholtz-Smoluchowski, Goldman, and Goldman-Hodgkin-Katz). It is shown that ion transfer in placental barriers (mimicking lipid-protein membrane barriers) and in muscle barriers proceeds by different mechanisms. In placental barriers, the electromigration diffusion takes place through lipid-protein channels formed by conformational alteration of phospholipid and protein molecules, with diffusion coefficients D = (2.6–3.6) × 10⁻⁸ cm²/s. The transfer in muscle barriers is due to migration via charged interfibrillar channels with negative diffusion activation energy (explained by changes in the structure of muscle fibers and expenditures of thermal energy for the displacement of Cl⁻ from channel walls), and D = (6.0–10.0) × 10⁻⁶ cm²/s.