12.3. The full Hodgkin–Huxley mechanism and its molecular underpinnings[[Student version, January 17, 2003]] 465
Our result also makes sense in the light of our mechanical analogy (Section 12.2.2). In Your
Turn 12b(c), you found that the wave speed was proportional to the density of stored energy
divided by a friction constant. Examining our expression forθ,wenotice that bothκandgtotare
inverse resistances, and so√κgtotis indeed an inverse “friction” constant. In addition, the formula
E/A=^12 q^2 /(CA)for the electrostatic energy density stored in a charged membrane of areaAshows
that the stored energy is proportional to 1/C.Thusour formula forθhas essentially the structure
expected from the mechanical analogy.
T 2 Section 12.2.5′on page 482 discusses how the nonlinear cable equation determines the speed
of its traveling-wave solution.
12.3 The full Hodgkin–Huxley mechanism and its molecular underpinnings
underpinnings
Section 12.2.5 showed how the hypothesis of voltage-gated conductances leads to a nonlinear cable
equation, with self-sustaining, travelingwaves ofexcitation reminiscent of actual action potentials.
This is an encouraging result, but it should make us want to see whether axon membranes really
do have the remarkable properties of voltage-dependent, ion-selective conductance we attributed
to them. In addition, simple voltage gating has not given us any understanding of how the action
potentialterminates;Figure 12.10 shows the ion channels opening and staying open, presumably
until the concentration differences giving rise to the resting potential have been exhausted. Finally,
while voltage gating may be an attractive idea, we do not yet have any idea how the cell could
implement it using molecular machinery. This section will address all these points.
12.3.1 Each ion conductance follows a characteristic time course when
the membrane potential changes
Hodgkin, Huxley, Katz, and others confirmed the existence of voltage-dependent, ion-selective
conductances in a series of elegant experiments, which hinged on three main technical points.
Space-clamping The conductancesgidetermine the current through a patch of membrane held
at a fixed, uniform potential drop. But during the normal operation of a cell, deviations from
the resting potential are highlynonuniform along the axon—they are localized pulses. Cole and
G. Marmont addressed this problem by developing thespace-clamptechnique. The technique
involved threading an ultrafine wire down the inside of an axon (Figure 12.11). The metallic wire
wasamuch better conductor than the axoplasm, so its presence forced the entire interior to be at
afixed, uniform potential. Introducing a similar long exterior electrode then forcesV(x)itself to
beuniform inx.
Voltage-clamping One could imagine forcing a given current across the membrane, measuring
the resulting potential drop, and attempting to recover a relation like the one sketched in Fig-
ure 12.9b. There are a number of experimental difficulties with this approach, however. For one
thing, the figure shows that a givenjq,rcan be compatible withmultiplevalues ofV. More im-
portantly, we are exploring the hypothesis that the devices regulating conductance are themselves
regulated byV,not by current flux, so thatV is the more natural variable to fix. For these