The Role of Time Variant Resistance and Electromotive Force in Ionic Systems Related to Cell Membranes: The Excitability Properties of Frog Skin and Toad Bladder
Central to the modern theory of the electrical properties of cells is the permeability of the plasma membrane to the ions passing across this structure; it has been our purpose to explore, both theoretically and experimentally, the physical implications of this point-of-view. The cornerstone of our analysis has been the fundamental flux equations of Nernst and Planck, which describe the movement of ions in solution subject to gradients of electrochemical potential. As a direct consequence of these equations, we have seen that the potential difference between two points in a solution is the sum of two terms: an intrinsic electromotive force (emf.) associated with the gradients of ionic concentrations, and an ohmic potential difference (IR drop) arising when current flows through the system. In order to illustrate the meaning and significance of these two terms, we have considered the voltage-current relationships in certain synthetic membrane systems; namely, the homogeneous uncharged membrane, the homogeneous fixed-charge membrane, and the two-layer a "sandwich" membrane consisting of a positive and negative fixed-charge lattice in series. Our analysis of these systems enabled us to bring up for discussion the important concepts of non-linear voltage characteristics, slope and chord resistance, time-variant resistance and emf., and rectification. We have noted that in the sandwich membrane of high fixed charge density, the membrane "resistance" is primarily the result of emf.'s generated in the face of current flow, and we have demonstrated the behavior of such membranes experimentally. We then turned our attention to a more direct consideration of the ionic theory of electrical events in cells, and in particular we focused upon the equivalent circuit used to describe the electrical characteristics of the plasma membrane. In order to determine what such an equivalent circuit representation can mean physically, we returned to the basic flux equations and have considered how these equations can be interpreted in electrical language. From these considerations, we have seen that two, quite different equivalent circuits can be written for a homogeneous membrane separating ionic solutions. Of particular significance is the fact that one of these circuits, which has the same form as that used for the plasma membrane, can also pertain to a mosaic membrane consisting of spatially separate regions of ionic selectivity. We have discussed the point that for a homogeneous membrane the essence of the action potential is a time-variant emf. while for a mosaic membrane it is a time -variant resistance. This ambiguity in the meaning of the equivalent circuit led us to the experimental study of the electrical excitability of isolated frog skin and toad bladder. We have seen that when current of proper polarity and sufficient intensity is passed across these structure, an "all-or-none" action potential with a sharp threshold and a prolonged refractory period is elicited. We emphasized that interruption of the current during any point in the action potential abolishes the response, and we have shown, through appropriate bridge measurements, that this is a consequence of the fact that the action potential results from a modulation of the current flow by a time-variant resistance. We then investigated some of the parameters affecting this active response. The result of varying the ionic composition of the medium was studied in the frog skin, and it was found that the response is relatively insensitive to changes in the solution bathing the inner surface, but rapidly and reversibly affected by changes in the outer solution, particularly with regard to the replacement of sodium by potassium and with respect to variations in the calcium concentration. It was also observed that the resistance of the skin and the action potential across it are reversibly altered by metabolic inhibitors and that these alterations occur independently of any changes in the intrinsic emf. across the system. From the finding that the action potential in frog skin and toad bladder is the result of a time-variant resistance, we have argued that this same phenomenon can be the basis of electrical excitability in general. This necessitates attributing real physical significance to the equivalent circuit representing the plasma membrane; that is, the plasma membrane must be a mosaic structure of spatially separate permselective regions.
plasma membrane, ion permeability, Nernst-Planck equations, equivalent circuit, time-variant resistance, action potential, Life Sciences
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