Membrane Potential and Peak Ionic Conductance

Hodgkin and Huxley discovered that the peak magnitude of the conductance change produced by a depolarizing voltage-clamp step depended on the size of the step. This established the voltage dependence of the sodium and potassium conductances of the axon membrane. The form of this dependence is shown in Figure 7-7 for both the sodium and potassium conductances. Note the steepness of the curves in both cases. For example, a voltage step to -50 mV barely increases gNa, but a step to -30 mV produces a large increase in gNa. Hodgkin and Huxley suggested a simple model that could account for voltage sensitivity of the sodium and potassium conductances. Their model assumes that many individual ion channels, each with a small ionic conductance, determine the behavior of the whole membrane as measured with the voltage-clamp procedure, and that each channel has two conducting states: an open state in which ions are free to cross through the pore, and a closed state in which the pore is blocked. That is, the channels behave as though access to the pore were controlled by a gate. The effect ofmembrane potential changes in this scheme is to alter the probability that a channel will be in the open, conducting state. With depolarization, the probability that a channel is open increases, so that a larger

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Figure 7-7 Voltage-dependence of peak sodium conductance (a) and potassium conductance (b) as a function of the amplitude of a maintained voltage step.

Figure 7-7 Voltage-dependence of peak sodium conductance (a) and potassium conductance (b) as a function of the amplitude of a maintained voltage step.

fraction ofthe total population of channels is open, and the total membrane conductance to that ion increases. The maximum conductance is reached when all the channels are open, so that further depolarization can have no greater effect.

In order for the conducting state of the channel to depend on transmembrane voltage, some charged entity that is either part of the channel protein or associated with it must control the access of ions to the channel. When the membrane potential is near the resting value, these charged particles are in one state that favors closed channels; when the membrane is depolarized, these charged particles take up a new state that favors opening of the channel. One scheme like this is shown in Figure 7-8. The charged particles are assumed to have a positive charge in Figure 7-8; thus, in the presence of a large, inside-negative electric field across the membrane, most of the particles would likely be near the inner face of the membrane. Upon depolarization, however, the distribution of charged particles within the membrane would become more even, and the fraction of particles on the outside would increase. The channel protein in Figure 7-8 is assumed to have a binding site on the outer edge of the membrane

Figure 7-8 A schematic representation of the voltage-sensitive gating of a membrane ion channel. The conducting state of the channel is assumed in this model to depend on the binding of a charged particle to a site on the outer face of the membrane.

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that controls the conformation of the "gating" portion of the channel. When the binding site is unoccupied, the channel is closed; when the site binds one of the positively charged particles (called gating particles), the channel opens. Thus, upon depolarization, the fraction of channels with a gating particle on the binding site will increase, as will the total ionic conductance of the membrane. It is important to emphasize that the drawings in Figure 7-8 are illustrative only; it is not clear, for example, that the gating particles are positively charged, although evidence from molecular studies suggests so. Negatively charged particles moving in the opposite direction or a dipole rotating in the membrane could accomplish the same voltage-dependent gating function. The molecular mechanism underlying the change in conducting state of the channel protein is unknown at present. It seems likely, however, that a conformation change related to charge distribution within the membrane is involved.

The S-shaped relationship between ionic conductance and membrane potential shown in Figure 7-7 is as expected from basic physical principles for the movement of charged particles under the influence of an electric field, as diagrammed schematically in Figure 7-8. The distribution of charged particles within the membrane will be related to the transmembrane electric field (i.e., the membrane potential) according to the Boltzmann relation:

where Po is the proportion of positive gating particles on the outside of the membrane, z is the valence of the gating charge, £ is the electronic charge, Em is membrane potential, k is Boltzmann's constant, T is the absolute temperature, and W is a voltage-independent term giving the offset of the relation along the voltage axis. The steepness of the rise in Po with depolarization depends on the valence, z, of the gating charge: the larger z becomes, the steeper is the rise of Po (and thus of conductance) with depolarization. As we have noted earlier, the sodium and potassium conductances are steeply dependent on membrane potential, implying that the gating charge that moves in order to open a channel has a large valence. For example, in order to produce a rise in sodium conductance like that observed experimentally, the effective valence of the gating particle must be ~6 [i.e., z ~ 6 in the Boltzmann relation of Equation (7-3)].

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