Diffusion Models for the Squid Axon Schwann Cell Layer

Abstract

The Schwann cell, basement membrane, and connective tissue layers that surround the squid giant axon and constitute barriers to diffusion, were modeled in a number of ways to analyze various experimental results. The experiments considered are (a) the time-course of the potassium concentration in the space between the Schwann cell and the axon membrane (from now on referred to as the F-H space) after an initial loading, (b) the time-course of sodium concentration in the F-H space after a sudden change in the sodium concentration in the external fluid; (c) the time-course of the concentration of tetrodotoxin (TTX) or saxitoxin (STX) in the F-H space after a sudden change in external concentration, including (or not) the effects of specific binding of TTX or STX to sites on the axon membrane and nonsaturable binding to sites in the F-H space or in the spaces (clefts) between Schwann cells; (d) the effects of the F-H space, clefts, and diffusion into the clefts from the outside (from now on referred to as convergence into the clefts) on the measured series resistance.The analysis shows that (1) in no case is it necessary to include the effects of the convergence into the clefts from the outside; (2) in case a, the basement membrane, connective tissue layers, and the unstirred layer may be neglected, i.e., the clefts are rate limiting; (3) in case b the clefts may be neglected, i.e., the unstirred layer is rate limiting; (4) in most cases the clefts may be replaced by an equivalent thin diffusion barrier.