This is the readme for the model associated with the paper:

Prescott SA, De Koninck Y, Sejnowski TJ (2008) Biophysical Basis for
Three Distinct Dynamical Mechanisms of Action Potential
Initiation. PLoS Comput. Biol. 4(10): e1000198
Abstract: Transduction of graded synaptic input into trains of
all-or-none action potentials (spikes) is a crucial step in neural
coding.  Hodgkin identified three classes of neurons with
qualitatively different analogue-to-digital transduction properties.
Despite widespread use of this classification scheme, a generalizable
explanation of its biophysical basis has not been described.  We
recorded from spinal sensory neurons representing each class and
reproduced their transduction properties in a minimal model.  Using
phase plane and bifurcation analysis, each class of excitability was
shown to derive from distinct spike initiating dynamics.  Excitability
could be converted between all three classes by varying single
parameters; moreover, several parameters, when varied one at a time,
had functionally equivalent effects on excitability.  From this, we
conclude that the spike initiating dynamics associated with each of
Hodgkin's classes represent different outcomes in a nonlinear
competition between oppositely directed, kinetically mismatched
currents.  Class 1 excitability occurs through a saddle-node on
invariant circle bifurcation when net current at perithreshold
potentials is inward (depolarizing) at steady state.  Class 2
excitability occurs through a Hopf bifurcation when, despite net
current being outward (hyperpolarizing) at steady state, spike
initiation occurs because inward current activates faster than outward
current.  Class 3 excitability occurs through a
quasi-separatrix-crossing when fast-activating inward current
overpowers slow-activating outward current during a stimulus
transient, although slow-activating outward current dominates during
constant stimulation.  Experiments confirmed that different classes of
spinal lamina I neurons express the subthreshold currents predicted by
our simulations and, further, that those currents are necessary for
the excitability in each cell class.  Thus, our results demonstrate
that all three classes of excitability arise from a continuum in the
direction and magnitude of subthreshold currents.  Through detailed
analysis of the spike initiating process, we have explained a
fundamental link between biophysical properties and qualitative
differences in how neurons encode sensory input.

Model Notes:

Models demonstrate how action potentials can be generated through
different dynamical mechanisms depending on the direction and
magnitude of subthreshold current. We start with a two-dimensional
Morris-Lecar-type model. Varying parameter Beta_w causes this model to
exhibit class 1, 2, or 3 excitability according to Hodgkin's 1948
classification (see Figure 1 in paper). In this, the simplest model,
dynamical systems analysis shows that each class is associated with a
different spike initiating mechanism (see Figure 2 in paper). Try
varying Beta_w to see how it affects dynamics visualized on the V-w

To increase the biological realism of the model, we split the recovery
variable (w) into two parts (y and z) which each control slightly
different currents (see Figure 4 in paper).  Try varying gsub and

Noise is not included in these models but can be added by following
the notes included in the code.  The code contains numerous other
comments that will help explain the model.

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Novemeber 14th, 2008: smaller sigma instead of sigma_inoise in comments update