Kinetics of excitable membranes. Voltage amplification in a diffusion regime.

An understanding of the properties of excitable membranes requires the calculation of ion flow through the membrane, including the effects of nonuniformity in the transverse membrane properties (mobilities, fixed charge, electric field). Permeability is apparently controlled at the external interface. Two factors may be involved here: the statistical blocking of pores by divalent cations, and activation energy. Only the former is included in the present treatment. When the total transmembrane voltage is varied, a redistribution in ionic concentration occurs. This can cause a change in boundary (zeta) potential, large in comparison with the applied voltage change-"voltage amplification." The result is a steep change in membrane conductance. The calculated flow curves are compared with experimental results. The Appendix gives an outline of the numerical method used for solving the boundary value problem with several diffusible ions, across a nonuniform regime.

Positive endocochlear potential: mechanism of production by marginal cells of stria vascularis.

The positive endocochlear potential (EP+) and high K+ concentration of the endolymph in the scala media of the mammalian cochlea are unusual. They have long been assumed to be due to a putative K-pump in the luminal membrane of the marginal cells of the stria vascularis, which were believed to have a negative internal potential. We show that the cell potential is more positive than the EP+, and that the ion pump is conventional Na,K-ATPase, probably in the basolateral membrane. The latter was determined from experiments in which the ionic environment of the strial cells was controlled by perfusion of the perilymphatic space of the cochlea, in the absence of vascular circulation. While the usual EP+ was maintained by normal perfusate, replacement of Na+ by choline resulted in a negative EP, showing that Na,K-ATPase is necessary for the production of EP+. Elimination of K+ as well as Na+ from the perfusate did not change the value of the negative EP, showing that no K-ATPase is involved.

Ion flow through membranes and the resting potential of cells.

A knowledge of the relationship between ion flow, both passive and active, ionic concentration, and membrane potential is essential to the understanding of cellular function. The problem has been analyzed on the basis of elementary physical and biophysical principles, providing a theoretical model of current flow and resting potential of cells, including those in epithelia. The model assumes that the permeability of the ion channels is not voltage dependent, but applies to gated channels when the gates are open. Two sources of nonlinearity of the current-voltage relationship are included in the analysis: ionic depletion and accumulation at the channels' mouths, and channel saturation at higher concentrations. The predictions of the model have been quantitative, validated by comparison with experiment, which has been limited to the only two cases in which adequate data was found. Application of the theory to the scala media of the mammalian cochlea has explained the source of its high positive potential and provided estimates of the Na+ and K+ permeabilities of the membranes of its marginal cells. This analysis provides a theoretically sound alternative to the widely used Goldman equation, the limited validity of which was emphasized by Goldman (D.E. Goldman, 1943, J. Gen. Physiol, 27:37-60), as well as its derivatives, including the Goldman-Hodgkin-Katz equation for resting potentials.

Ion flow through biomembranes. Physical theory explains its high sensitivity.

Numerous biomembranes exhibit a sensitivity to changes in electrical potential greater than predicted as possible from the classical application of the Boltzmann relation, a phenomenon which has long defied explanation, the actual sensitivity of some Na+ channels being many times greater than the classical limit. This paper explains, using a minimum of mathematics, how the very rapid gating effect of adsorbed Ca2+ (or other impermeable divalent cations) can directly affect the conductance of channels, and thus interact with the electric field within the channel to produce a change in the potential across the channel's gate much greater than the change in the membrane potential, with a corresponding change in the fraction of open conformational gates and change in conductance. These results are not in conflict with the Boltzmann relation, the necessary energy being made available from the total potential difference across the membrane by a long unrecognized stochastic process; the full mathematical theory is given in cited references.

The excitable membrane. A physiochemical model.

The model of the excitable membrane assumes common channels for Na(+) and K(+); the two ion species interact within the pores through their electrostatic forces. The electric field varies across the membrane and with time, as a result of ionic redistribution. Ionic flow is primarily controlled by energy barriers at the two interfaces and by Ca(++) adsorption at the external interface. When the membrane is polarized, the high electric field at the external interface acting on the membrane fixed charge keeps the effective channel diameter small, so that only dihydrated ions can cross the interface. The higher energy required to partially dehydrate Na(+) accounts for its lower permeability when polarized. Depolarized, the channel entrance can expand, permitting quadrihydrated ions to pass; the large initial Na(+) flow is the result of the large concentration ratio across the interface. The effect at the internal interface is symmetric; Na(+) crosses with greater difficulty when the membrane is depolarized. Na(+) inactivation occurs when the ion distribution within the membrane has assumed its new steady-state value. Calculations based on parameters consistent with physicochemical data agree generally with a wide range of experiments. The model does not obey the two fundamental Hodgkin-Huxley (HH) postulates (independence principle, ion flow proportional to thermodynamic potential). In several instances the model predicts experimental results which are not predicted by the HH equations.

Sensitivity of membranes to their environment. Role of stochastic processes.

Ionic flow through biomembranes often exhibits a sensitivity to the environment, which is difficult to explain by classical theory, that usually assumes that the free energy available to change the membrane permeability results from the environmental change acting directly on the permeability control mechanism. This implies, for example, that a change delta V in the trans-membrane potential can produce a maximum free energy change, delta V X q, on a gate (control mechanism) carrying a charge q. The analysis presented here shows that when stochastic fluctuations are considered, under suitable conditions (gate cycle times rapid compared with the field relaxation time within a channel), the change in free energy is limited, not by the magnitude of the stimulus, but by the electrochemical potential difference across the membrane, which may be very much greater. Conformational channel gates probably relax more slowly than the field within the channel; this would preclude appreciable direct amplification of the stimulus. It is shown, however, that the effect of impermeable cations such as Ca++ is to restore the amplification of the stimulus through its interaction with the electric field. The analysis predicts that the effect of Ca++ should be primarily to affect the number of channels that are open, while only slightly affecting the conductivity of an open channel.