Those who followed

**Kenneth ("Kacy") Cole, in
the 1930s and 1940s, employed both experimental and analytic techniques
to measure and describe cell membranes in terms of : their conductance,
currents,and the voltage across across them. **

**Cole, with Curtis showed with definitively elegance figure that, during an action potential. the membrane conductance increased dramatically as had been postulated by Bernstein.****With an electrode inserted along the axis of a squid giant axon they were able to measure membrane potentials. Their first measurements showed action potentials from 50 to 80 mV in amplitude but their "AC coupled" amplifier could not give a resting potential level. Later with a "DC coupled" amplifier, they confirmed the Hodgkin and Huxley observation that the action potential reversed its polarity, "overshooting" the baseline at the peak of its action potential.**

**Development of the Voltage Clamp: Marmont,
(working with Cole) made a technological leap by developing the "space
clamp", a guarded region of membrane surrounding an axial electrode
in a squid giant axon where the voltage throughout this region was uniform.
Cole made an enormous conceptual break-through. He realized that he could
"break" the normal feedback between current and voltage in generating
an action potential by controlling the membrane potential with an electronic
feedback circuit (instead of the current control employed by Marmont).
Furthermore, a step change in voltage allowed him to separate the ionic
current from the capacitive current flowing in the membrane (Fig 3:16.
in Cole's book, Membranes, Ions, and Impulses). **

** Meanwhile, Alan (later Sir Alan) Hodgkin and Andrew (later Sir Andrew)
Huxley (HH or H&H) were also carrying out experiments and thinking
carefully about how action potentials might be generated. **

**Numerical integration: It was Huxley who initiated
the numerical integration techniques applied to excitable membranes. Prior
to the second World War, Alan and Andrew had considered a carrier
mechanism model for the generation of impulses. Alan's
ideas were recounted in "Chance and design in electrophysiology"
(J. Physiol. 1976. 263: 1-22). Huxley had carried out extensive calculations
and made predictions about how action potential would change with variations
in the concentration of the extracellular sodium. The following summer
he went on a honeymoon and Alan collaborated with Bernard Katz at Plymouth
to carry out the experiments on varying the sodium concentration in the
medium bathing squid giant axons - which bore out the predictions of Huxley's
calculations. **

**After World War II, Hodgkin visited Cole and was shown the current
records with delayed onset upon depolarization and fast exponential decay
upon repolarization. Alan and Andrew had theorized previously that "the sodium conductance was a continuous function of membrane potential multiplied by an inactivation variable that fell with first-order kinetics towards another function of membrane potential". This formulation predicted that a voltage step would cause a jump in the sodium conductance followed by an exponential decay. Alan, fresh from his radar
and electronics experience during World War II, questioned Kacy sharply
about the delayed onset, arguing that the electronics may have been too
slow to follow a fast change - which had worked so well in Huxley action
potential calculations. Hodgkin also was aware of errors introduced by
the resistance of the axial electrode and developed several ways to improve
on Kacy's voltage control of the axon membrane. The fact that the delay
in onset was very obvious in the records which
he made later with Huxley and Katz (using their much improved experimental
setup) may have played an important role in revising his thinking about
the details of the ionic channel kinetics and conductances. **

**Because (as noted above) Alan and Andrew had thought extensively
about the kind of system which might generate an action potential, they
had a clear view of what data they would need to describe the underlying
mechanisms. Perhaps this is why they were able to develop such a monumental
model from the extraordinarily small number of experiments (41 is the largest
number referenced in their figures or tables) carried out on a few squid
giant axons. Many of these were in deteriorated condition (at least by
the end of the experiment), yet they were able to scale and so fully analyze
this data and encapsulate them in an extraordinary set of equations which
are, some 45 years later, still the defacto standard expression for simulations.
Furthermore they also serve as a framework by which equations for other
excitable membranes are described. The remarkable form of the equations,
raising a first order reaction to a power came about for at least two reasons:
**

In addition, a first order reaction can represent a probability function, making intrepretations more convenient.

**Hodgkin and Huxley felt that they could not be sure that they understood
the ionic basis of the action potential until they could reproduce its
shape with these equations. Kacy told me that Alan and/or Andrew had expressed
to him their reservations about whether or not they would achieve this
goal. After having chosen the form of the equations to be used, they consolidated
all of their data to find the appropriate voltage sensitive rate constants.
Then, because the Cambridge Univ. computer was "off the air for 6
months or so, while it underwent major modifications", in the spring
of 1951, Huxley began the slow work of using a Brunsviga 20
manually cranked calculator with numbers entered by a set of
adjusting levers (projecting from the wheels that were rotated by the hand crank). The output was a line of digits
on the wheels to be read and transcribed to paper. First, he found that the
time and voltage-sensitivities of the ionic conductances could be reproduced.
Then the long process of numerical integration of the action potential
began. Tabular records of the rate and state variables were entered into
the the levers and transcribed from the dials for small increments of time.
Huxley used a tedious iterative, error-correcting,
numerical integration method to estimate and correct for numerical integration
errors. The fact that the whole process for calculation of a 5mS interval,
showing the initiation of and recovery following an action potential, could
be accomplished in 8 hours is astonishing. The calculated action potentials
were - with the exception of a small "gratuitous
bump" late in the falling phase - excellent reproductions of the
experimental observations under a variety of conditions. **

**This monumental accomplishment was not only tremendously gratifying
to H & H and won for them a Nobel prize, but has stood as an outstanding
example of how to tackle such problems. It is also a remarkable achievement
that the HH equations have not been replaced in the intervening four & one-half decades
but remain the default standard equations used for simulations of the squid
axon and also the usual form in which equations for other cell membranes
are cast. **

**Even more astonishing than the calculation of a membrane action potential
for a uniform patch was that Andrew was able to use these equations to
extract the velocity of impulse propagation in an axon of uniform diameter.
Although it was essentially impossible to solve the partial differential
equation describing propagation in time and space, he was able to cast
the problem into an ordinary differential equation for a traveling wave
as shown in Cole's Fig 3.49 (in Membranes,
Ions, and Impulses).
The velocity of 18.8 m/sec he found was
very close to that observed experimentally (21.2m/sec) and serves to this
day as a solid known reference standard which one can use to test any program
used to simulate propagation of HH impulses.
Alan and Andrew sent galley proofs of their spectacular papers to Kacy,
then Scientific Director of the Naval Medical Research Institute (NMRI).
As the sole professional in his lab at the time, I made additional calculations
from their equations and plotted them out by hand. Thus I was one of the
first to experience the awe aroused in readers of these papers.**

On to the Settlers who followed