Design of a fast voltage clamp for biological membranes, using discontinuous feedback.
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Biomedical subjects
Publications and source records attributed to B Lindemann.
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We propose a physical model for voltage-dependent conductance changes of excitable cell membranes. It is based on competition of uni- and bivalent ions for chains of stable sites extending through the membrane. These one-dimensional pathways (pores) have different profiles of chemical potential for the two ionic species so that bivalent ions can block the passage of univalent ions at large membrane potentials. We treat the special case that each pore is either empty or, because of electrostatic repulsion, contains no more than one uni- or bivalent ion at a time. A system of linear differential equations describes the time-dependent probabilities of the various possible pore states. The states are limited by transition rate constants involving the profile of the chemical potential, the membrane voltage, the ionic concentrations in the adjacent baths, and electrostatic interactions between the ions. The steady-state solutions (Kirchhoff-Hill theorem) yield expressions for the relationship between the small signal conductance of univalent ions and the concentration of these ions in the external bathing medium (a saturation curve) and for the ionic currents and the steady-state current-voltage curve (N-shaped). From the latter curve we compute the shift of theshold potential caused by concentration changes of the external bathing medium. The model yields a number of predictions which can be tested experimentally.
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Experiments were performed to test which structure of frog skin epithelium is responsible for the electrical excitation (fast, all-or-none potential spike) displayed by this tissue during stimulation with a current pulse. Preselected cells of the outer epithelial surface were punctured by microelectrodes under microscopical observation. The major part of the transepithelia resting resistance and the major part of the spike were recorded between microelectrode tip and outside bathing solution. A leak between microelectrode and punctured membrane is made responsible for the attenuation of spike amplitude observed under these recording conditions. It is shown that if the spike is generated at but one of the series membranes of the epithelium, this membrane must be at the outermost border of the tissue.
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