Pacemaker potentials are easily simulated with the electronic model
without the use of auxiliary networks. This is achieved either by
inserting a large, variable shunt resistor across the simulated
membrane (see Figure 5) or by allowing a small sodium current leakage
at the resting potential. With the remaining parameters of the
model set as close as possible to the values determined by Hodgkin
and Huxley, the leakage current induces low-frequency, spontaneous
spiking. The spike frequency increases monotonically with increasing
leakage current. In addition, if the sodium conductance inactivation
is allowed to accumulate over several spikes, periodic spike pairs
and spike bursts will result. Subthreshold pacemaker potentials have
also been observed in the model, but with parameter values set close
to the Hodgkin-Huxley data these are generally higher in frequency
than pacemaker potentials in real neurons. It is interesting that
a pacemaker mode may exist in the absence of the simulated sodium
conductance. It is a very high-frequency mode (50 cps or more)
and results from the alternating dominance of potassium current
and chloride (or leakage ion) current in determining the membrane
potential. The significance of this mode cannot be assessed until
better data is available for the potassium conductance at low levels
of depolarization in real neurons. In general, as far as the model is
concerned, pacemaker potentials are possible because the potassium
conductance is delayed in both its rise with depolarization and its
fall with repolarization.
Rate sensitive graded response has also been observed in the electronic
model. The rate sensitivity—or accommodation—is due to the sodium
conductance inactivation. The response of the model to an imposed ramp
depolarization was discussed in Reference 18. At this time, several
alternative model parameters could be altered to bring about reduced
electrical excitability. None of the parameter changes was very
satisfying, however, because none of them was in any way justified by
physiological data. We have since found that the membrane capacitance,
a plausible parameter in view of recent physiological findings, can
completely determine the electrical excitability. Thus, with the
capacitance determined by Hodgkin and Huxley (1 microfarad per cm²),
the model exhibits excitability characteristic of the axon. As the
capacitance is increased, the model becomes less excitable until, with
10 or 12 μμf, it is effectively inexcitable. Thus, with an increased
capacitance—but with all the remaining parameters set as close as
possible to the Hodgkin-Huxley values—the electronic model exhibits the
characteristics of Bullock’s graded-response regions.
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