Hodgkin, Huxley, and Katz (3) and Hodgkin and Huxley (14), (15), (16),
in 1952, published a series of papers describing detailed measurements
of voltage, current, and time relationships in the giant axon of the
squid (_Loligo_). Hodgkin and Huxley (17) consolidated and formalized
these data into a set of simultaneous differential equations describing
the hypothetical time course of events during spike generation and
propagation. The hypothetical system which these equations describe is
the basis of the Modern Ionic Hypothesis.
The system proposed by Hodgkin and Huxley is basically one of dynamic
opposition of ionic fluxes across the axon membrane. The membrane
itself forms the boundary between two liquid phases—the intracellular
fluid and the extracellular fluid. The intracellular fluid is rich in
potassium ions and immobile organic anions, while the extracellular
fluid contains an abundance of sodium ions and chloride ions. The
membrane is slightly permeable to the potassium, sodium, and chloride
ions; so these ions tend to diffuse across the membrane. When the
axon is inactive (not propagating a spike), the membrane is much more
permeable to chloride and potassium ions than it is to sodium ions.
In this state, in fact, sodium ions are actively transported from the
inside of the membrane to the outside at a rate just sufficient to
balance the inward leakage. The relative sodium ion concentrations on
both sides of the membrane are thus fixed by the active transport rate,
and the net sodium flux across the membrane is effectively zero. The
potassium ions, on the other hand, tend to move out of the cell; while
chloride ions tend to move into it. The inside of the cell thus becomes
negative with respect to the outside. When the potential across the
membrane is sufficient to balance the inward diffusion of chloride with
an equal outward drift, and the outward diffusion of potassium with an
inward drift (and possibly an inward active exchange), equilibrium is
established. The equilibrium potential is normally in the range of 60
to 65 millivolts.
The resting neural membrane is thus polarized, with the inside
approximately 60 millivolts negative with respect to the outside.
Most of the Hodgkin-Huxley data is based on measurements of the
transmembrane current in response to an imposed stepwise reduction
(depolarization) of membrane potential. By varying the external
ion concentrations, Hodgkin and Huxley were able to resolve the
transmembrane current into two “active” components, the potassium
ion current and the sodium ion current. They found that while the
membrane permeabilities to chloride and most other inorganic ions
were relatively constant, the permeabilities to both potassium and
sodium were strongly dependent on membrane potential. In response to a
suddenly applied (step) depolarization, the sodium permeability rises
rapidly to a peak and then declines exponentially to a steady value.
The potassium permeability, on the other hand, rises with considerable
delay to a value which is maintained as long as the membrane remains
depolarized. The magnitudes of both the potassium and the sodium
permeabilities increase monotonically with increasing depolarization.
A small imposed depolarization will result in an immediately
increased sodium permeability. The resulting increased influx of
sodium ions results in further depolarization; and the process
becomes regenerative, producing the all-or-none action potential.
At the peak of the action potential, the sodium conductance begins
to decline, while the delayed potassium conductance is increasing.
Recovery is brought about by an efflux of potassium ions, and both
ionic permeabilities fall rapidly as the membrane is repolarized.
The potassium permeability, however, falls less rapidly than that of
sodium. This is basically the explanation of the all-or-none spike
according to the Modern Ionic Hypothesis.
[Illustration: Figure 5—Hodgkin-Huxley representation of small area of
axon membrane]
[Illustration: Figure 6—Typical responses of sodium conductance and
potassium conductance to imposed step depolarization]
By defining the net driving force on any given ion species as the
difference between the membrane potential and the equilibrium potential
for that ion and describing permeability changes in terms of equivalent
electrical conductance changes, Hodgkin and Huxley reduced the ionic
model to the electrical equivalent in Figure 5. The important dynamic
variables in this equivalent network are the sodium conductance
(G{Na}) and the potassium conductance (G{K}). The change in the sodium
conductance in response to a step depolarization is shown in Figure 6B.
This change can be characterized by seven voltage dependent parameters:
1. Delay time—generally much less than 1 msec
2. Rise time—1 msec or less
3. Magnitude of peak conductance—increases
monotonically with increasing depolarization
4. Inactivation time constant—decreases
monotonically with increasing depolarization.
5. Time constant of recovery from
inactivation—incomplete data
6. Magnitude of steady-state conductance—increases
monotonically with increasing depolarization
7. Fall time on sudden repolarization—less than 1 msec.
Figure 6B shows the potassium conductance change in response to
an imposed step depolarization. Four parameters are sufficient to
characterize this response:
1. Delay time—decreases monotonically with
increasing depolarization
2. Rise time—decreases monotonically with increasing
depolarization
3. Magnitude of steady-state conductance—increases
monotonically with increasing depolarization
4. Fall time on sudden repolarization—8 msec
or more, decreases slightly with increasing
depolarization.
In addition to the aforementioned parameters, the transient portion of
the sodium conductance appears to exhibit an accommodation to slowly
varying membrane potentials. The time constants of accommodation appear
to be those of inactivation or recovery from inactivation—depending on
the direction of change in the membrane potential (18). The remaining
elements in the Hodgkin-Huxley model are constant and are listed below:
1. Potassium potential—80 to 85 mv (inside negative)
2. Sodium potential—45 to 50 mv (inside positive)
3. Leakage potential—38 to 43 mv (inside negative)
4. Leakage conductance—approx. 0.23 millimhos/cm²
5. Membrane capacitance—approx. 1 μf/cm²
6. Resting potential—60 to 65 mv
7. Spike amplitude—approx. 100 mv