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Characterization of Biological Membranes by Equivalent Pores

A. K. Solomon

Published 1968 in The Journal of General Physiology

ABSTRACT

The description of the permeability properties of biological membranes in terms of parallel pathways for lipid-insoluble and lipid=soluble molecules has its roots in the studies of Overton (1) and Collander and Barlund (2) and has been presented in detail in several books, such as those of Davson and Danielli (3) and H6ber (4). The concept of the equivalent pore as a description of the path taken by lipid-insoluble molecules grew from the treatments of Koefoed-Johnsen and Ussing (5) and Pappenheimer, Renkin, and Borrero (6) and has been used by Solomon and coworkers (7-11) to characterize the behavior of single cell membranes, particularly those of red cells. More powerful mathematical treatments based on irreversible thermodynamics have been applied to biological systems, and new experimental evidence bearing on the equivalent pore concept has been obtained both from biological systems and from organic membranes. It appears desirable, therefore, to reexamine both the theoretical basis for the equivalent pore concept and the evidence bearing on its validity when applied to single biological membranes. Since a great deal of the discussion will be concerned with diffusion, it is important to understand the nature of this process, which was perhaps best described by Einstein (12) : " the molecular theory of heat affords a . . . point of view from which the process of diffusion can be considered. The process of irregular motion which we have considered as the h e a t . . , content of a substance will operate in such a manner that the single molecules of a liquid will alter their positions in the most irregular manner thinkable. This wandering about of the molecules of the solute--fortuitous to a certain extent--will have as a result that the original non-uniform distribution of concentration of the solute will gradually give place to a uniform one." Diffusion may be contrasted with viscous or bulk flow, in which a number of molecules in a liquid move together in response to a physical force, often a pressure gradient. Account is taken of the attractive forces between neighboring portions of the fluid. As Prandtl and Tietjens (13) point out, " in homogeneous fluids the behavior of individual fluid particles is not of particular interest; one only wants to know the state of motion and its alteration with time at every point." The matter was put very succinctly by Onsager (14), who stated: "viscous flow is a relative motion of adjacent portions of a liquid. Diffusion is a relative motion of its constituents." When solvent passage through a membrane can take place only by dissolution of the molecules in the membrane, solvent transport takes place by diffusion alone. When a pressure gradient is imposed across a pipe whose diameter is greater by orders

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