  Neuronal excitability is the phenomena that describes action potential
generation due to a stimulus input. Commonly, neuronal excitability is divided
into two classes: Type I and Type II, both having different properties that
affect information processing, such as thresholding and gain scaling. These
properties can be mathematically studied using generalised phenomenological
models, such as the Fitzhugh-Nagumo model and the mirrored FHN. The FHN model
shows that each excitability type corresponds to one specific type of
bifurcation in the phase plane: Type I underlies a saddle-node on invariant
cycle bifurcation, and Type II a Hopf bifurcation. The difficulty of modelling
Type I excitability is that it is not only represented by its underlying
bifurcation, but also should be able to generate frequency while maintaining a
small depolarising current. Using the mFHN model, we show that this situation
is possible without modifying the phase portrait, due to the incorporation of a
slow regenerative variable. We show that in the singular limit of the mFHN
model, the time-scale separation can be chosen such that there is a
configuration of a classical phase portrait that allows for SNIC bifurcation,
zero-frequency onset and a depolarising current, such as observed in Type I
excitability. Using the definition of slow conductance, g_s, we show that these
mathematical findings for excitability change are translatable to reduced
conductance based models and also relates to an experimentally measurable
quantity. This not only allows for a measure of excitability change, but also
relates the mathematical parameters that indicate a physiological Type I
excitability to parameters that can be tuned during experiments.
