Electric Currents, Membranes, and Biological Sources of Electromotive Force **

A description of steady-state material transfer through the barrier of the idealized physiological transfer unit, phase 1, membrane, phase 2,-two homogeneous phases separated by a complex barrier-based upon Newton's laws of motion has been outlined previously.1 The supposition was made that the conservative forces tending to drive the kinetic materials through a barrier b can be derived from differences in the electrochemical potentials of the kinetic substances k that appear across the barrier. The formal relation between the electrochemical potential, A-Akb, and the material currents within the barrier, fIlhb, can be written as follows:-b F, RMb Equation 1 is exact when the velocities of motion are small and when the system is in a steady state, that is, when the accelerations of the centers of mass of the individual kinetic materials within the barrier are zero. The equation may be used for the description of material transfers in many biological systems without great error, for the accelerations of the material substances within the barriers of the majority of biological transfer systems appear to be negligibly small. The Rhk's in equation 1 are members of the resistance matrix of the barrier, and if Newton's third law of motion is presumed valid,"2 Onsager's reciprocal relations,8" that is, Rhk is equal to Rkh, immediately follow. The present report contains elementary derivations of the relationships that exist between A7ikb and certain other pertinent quantities of interest to a discussion of material transfer systems. Especial attention will be paid to those closed circuit systems of biological import in which steady state electric currents can be determined.