Membranes, Tagged Components, and Membrane Transfer Coefficient **

Concepts, introduced into physics in the analysis of the Peltier effect by Thomson in 1854 and generalized by Onsager in 1931, have made it clear that the equations commonly used for the description of membrane transfer processes are incomplete. Kedem and Katchalsky' have recently emphasized the utility of these concepts in removing inconsistencies of interpretation introduced by the use of incomplete equations for the description of the movement of water through membranes. Incomplete equations are also used in present accounts of the behavior of tagged species in transfer systems, which also give rise to interpretive difficulties. A good example of the nature of some of the difficulties encountered is illustrated by the classical investigations of Hevesy, Hofer, and Krogh.' They had occasion to measure the overall transfer coefficient for the absorption of water through the skin of a frog. They found to their surprise that two values of the transfer coefficient of water for which they could not give a satisfactory explanation were obtained. The value of the transfer coefficient depended upon how the experiment was performed. The transfer coefficient estimated from the weight change of the frog in an osmotic experiment was some five-fold greater than that determined from an appropriate experiment with tagged water. Furthermore, they observed that the flux of tagged water appeared to be independent of the flux of normal water. Though they made many suggestions attempting to account for these experimental findings, they concluded that further information was needed before the experimental results could be 'explained.' Similar experimental results have been obtained many times since in investigations conducted on membranes of living systems. Some investigators have regarded the two transfer coefficients to be the result of some biological artifact, such as incomplete mixing when tagged water is used, or "active secretion" through the membrane. The experimental results obtained by Swansone5 and by Mauro7 on artificial membranes rendered