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Chapter 2. A Brief history of Computational Neuroscience - - From my

The Pioneers: Cole, Hodgkin, & Huxley
Those who followed

Experimental Methods and Data: Underpinnings for Computational Advances

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 elegant figure that, during
     an action potential. the membrane conductance increased dramatically as
     had been postulated by Bernstein.
   * But they were startled later to find (with an electrode along the axis
     of a squid giant axon) that the membrane potential reversed its
     polarity, "overshooting" the baseline at the peak of its action

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

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 "Chances 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 upon reaching
a threshold membrane depolarization, the sodium conductance would jump
immediately to a high value and then 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

Hodgkin-Huxley equations.

Because (as noted above) Alan and Andrew had thought extensively about the
kind of system which might generate and 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 40
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
*1) No simple ordinary differential equation could describe the delayed
onset of conductances upon step depolarization yet show the fast exponential
decay on reset (return to polarizations near rest).
*2) A first order reaction raised to a power not only provided both the
delayed onset and exponential decay but also offered a simple way to
incorporate the voltage sensitivity of the ionic channels.
In addition, a first order reaction can represent a probability function,
making intrepretations more convenient.

Numerical integration by hand crank calculator

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 manually cranked calculator with keyboard
input and a line of digits (on 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 keyboard 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 decades but are 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.