Membrane structure and passive flows.

The close-packed arrays of microvilli commonly called brush borders create a structured membrane with vastly increased area for the transport of solutes and water. The very geometry of the structured membrane governs the nature of the passive trans-membrane flows, and with system parameters comparable to those found in, say, the proximal tubule of kidney one finds that whereas the increase in salt flow is about the same as the increase in area, the increase in water flow is several hundred percent greater than the increase in area. The permeant salt transverses the structure by flowing down into the solution-filled region between the microvilli, through the membrane of a microvillus, and then down the interior of the microvillus into the second bathing solution (see Fig. 2). Thus we see that the membrane per se separates two small regions in which diffusion gradients are established and faces a continuous distribution of concentrations that may differ significantly from those found in the two bathing solutions. The effect of structure is most pronounced close to the isotonic state and thus may be of some importance in biological systems as they are generally poised in nearly isotonic states. In an earlier paper (Richardson et al., 1973) a structured membrane separating two solutions containing a permeant salt and an impermeant nonelectrolyte was analyzed. Here we shall examine a system of more biological relevance: the solutions contain two mono-monovalent salts having a common anion. In particular, we can think of solutions with NaCl and KCl, where only NaCl can permeate the membrane. In other words, we have NaCl as a permeant salt and KCl as a support electrolyte. Because of the earlier presentation, the analysis here will be abbreviated.