The HH model replicates many of the features of spiking of the squid giant axon:
the form, duration and amplitude of a single spike (both for the membrane and
the propagating spike), its sharp threshold, the conduction velocity of the spike
along the axon, the refractory period of the neuron, the impedance changes
during the spike, anode-break excitation, accommodation, subthreshold
response and oscillations. When simulating the response to sustained stimulus
currents, it demonstrates a discontinuous onset of repetitive firing with a high
spiking frequency and a limited bandwidth of the firing frequency.
However, careful studies of the model reveal that it does not provide a good
description of quite a few electrophysiological properties of the axon (Clay,
1998), in particular the refractory behavior of the preparation in response either
to sustained or periodic current pulse stimulation. Also, the model does not
account for after potentials and slow changes in the squid giant axon.
Still, the HH model serves as the 'golden standard' of neuronal excitability, and
with minor changes - as the backbone of most neuronal spiking models. The
main reason is that the HH model does capture the essence of spiking through
ionic currents (Na+ and K+), which enter and leave the cell through voltage
dependent channels. Moreover, the model is compact, and approximates well
many of the features shared by different types of neurons (shape and duration of
spiking, repetitive spiking in response to sustained inputs, refractoriness etc.)
while incorporating biophysical aspects of the neuron. Adding the appropriate
currents for other channel types (usually using similar kinetic schemes) is easily
done. Accordingly, and since the model has been studied mathematically in great
detail (Jack et al., 1975), it is the common choice of conductance based
modeling for computational studies and theoretical ones.
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