Pace of diffusion through membranes

Summary Although membranes are often viewed as barriers to diffusing particles, in many cases their presence does not slow down diffusion. Investigations of the transit time (mean diffusion time) for cases where the source and the target of diffusing particles are separated by various arrangements of membranes reveal the following facts: (i) The transit time is composed of the sum of the times to diffuse each of the membrane and aqueous regions separately and terms representing the time spent at the vicinity of the interfaces between these regions. (ii) In cases of one dimensional diffusion between aqueous and membranal phases, the transit time is governed by the parameter whereD _m andD _w are the diffusion coefficients in the membrane and water, respectively, and is the membrane/water partition coefficient of the particles. While the former ratio depends mostly on the viscosities of the two phases, the latter parameter is very strongly dependent on the identity of the particles. The diffusion from water to the membrane is faster than from the membrane to water whenever . The opposite is true when this parameter is smaller than 1. (iii) In case of one dimensional transmembranal diffusion, the transit time shows a minimum when wherel _w1 andl _w2 are the net diffusion distances in the aqueous phases on both sides of the membrane. In this case, if the diffusion proceeds through pores in the membrane, represents the fraction of membrane area that is occupied by the pores.The transit times for three dimensional diffusion into and from a spherical cell are also presented in a simple form. In addition, some of the relations between transit times and other measurable time parameters, such as the course of the decay of gradients and the time lag to establish steady states, are discussed briefly.The conclusions emerging from this analysis, together with the simple expressions for the transit times can make these investigation useful for the understanding of diffusion in systems containing natural or artificial membranes.