12.3. The full Hodgkin–Huxley mechanism and its molecular underpinnings[[Student version, January 17, 2003]] 473
Figure 12.17: (Experimental data.) Patch-clamp recordings of sodium channels in cultured muscle cells of rats,
showing the origin of the inward sodium current from discrete channel-opening events. (a)Time course of a 10mV
depolarizing voltage step, applied across the patch of membrane (b)Nine individual current responses elicited by the
stimulus pulses, showing six individual sodium channel openings (circles). The potassium channels were blocked.
The patch contained 2–3 active channels. (c)Average of 300 individual responses like the ones shown in (b). If
aregion of membrane contains many chanels, all opening independently, we would expect its total conductance to
resemble this curve, and indeed it does (see Figure 12.6c). [Data from Sigworth & Neher, 1980.]
The observation of digital, all-or-nothing, switching in single ion channels may seem puzzling in
the light of our earlier discussion. Didn’t our simple model for voltage-gating require acontinuous
response of the membrane conductance toV (Figure 12.9a)? Didn’t Hodgkin and Huxley find
acontinuous time course for their conductances, with a continuously varying saturation value of
g∞K+(V)? To resolve this paradox, we need to recall that there are many ion channels in each
small patch of membrane (see Problem 12.7), each switching independently. Thus the values of
gimeasured by the space-clamp technique reflect not only the conductances of individual open
channels (a discrete quantity) and their densityσchanin the membrane (a constant), but also the
average fraction of all channels that are open. The last factor mentionedcanchange in a nearly
continuous manner if the patch of membrane being studied contains many channels.
Wecan test the idea just stated by noticing that the fraction of open channels should be a
particular function ofV.Suppose that the channel really is a simple two-state device. We studied
the resulting equilibrium in Section 6.6.1 on page 193, arriving at a formula for the probability of
one state (“channel open”) in terms of the free energy difference ∆Ffor the transition closed→open
(Equation 6.34 on page 199):
Popen=1
1+e∆F/kBT. (12.26)
Wecannot predict the numerical value of ∆Fwithout detailed molecular modeling of the channel.
But we can predict thechangein ∆Fwhen we changeV. Suppose that the channel has enough
structural integrity so that its two states, and their internal energies, are almost unchanged byV.
Then the only change to ∆Fcomes from the fact that a few charges in the voltage-sensing region
move in the external field, as shown in Figure 12.16b.