  Mathematical models for the generation of the action potential can improve
the understanding of physiological mechanisms that are consequence of the
electrical activity in neurons. In such models, some equations involving
empirically obtained functions of the membrane potential are usually defined.
The best known of these models, the Hodgkin-Huxley model, is an example of this
paradigm since it defines the conductances of ion channels in terms of the
opening and closing rates of each type of gate present in the channels. These
functions need to be derived from laboratory measurements that are often very
expensive and produce little data because they involve a time-space-independent
measurement of the voltage in a single channel of the cell membrane. In this
work, we investigate the possibility of finding the Hodgkin-Huxley model's
parametric functions using only two simple measurements (the membrane voltage
as a function of time and the injected current that triggered that voltage) and
applying Deep Learning methods to estimate these functions. This would result
in an hybrid model of the action potential generation composed by the original
Hodgkin-Huxley equations and an Artificial Neural Network that requires a small
set of easy-to-perform measurements to be trained. Experiments were carried out
using data generated from the original Hodgkin-Huxley model, and results show
that a simple two-layer artificial neural network (ANN) architecture trained on
a minimal amount of data can learn to model some of the fundamental proprieties
of the action potential generation by estimating the model's rate functions.
