Towards an Hybrid Hodgkin-Huxley Action Potential Generation Model

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.