A Simple Parametric Representation of the Hodgkin-Huxley Model

The Hodgkin-Huxley model, decades after its first presentation, is still a reference model in neuroscience as it has successfully reproduced the electrophysiological activity of many organisms. The primary signal in the model represents the membrane potential of a neuron. A parametric and simple representation of this signal is presented in this paper. The new proposal is an adapted Frequency Modulated Mobius multicomponent model defined as a flexible decomposition in waves that describe the signal morphology. A specific feature of the new model is that the parameters are subject to interpretable restrictions. A broad simulation experiment is conducted to show the new model accurately represents the simulated Hodgkin-Huxley signal. Moreover, the model potential to predict the neurons relevant characteristics, described with parameters of the Hodgkin Huxley model, is shown using different Machine Learning methods. The proposed model is also validated with real data from Squid Giant Axons. The comparison of the parameter configuration between the simulated and real data demonstrated the flexibility of the model as well as interesting differences. Author summaryAlejandro Rodriguez-Collado. I received the double degree in Statistics and Computer Engineering and the Masters degree in Business Intelligence and Big Data from the Universidad de Valladolid in 2019 and 2020, respectively. I work as researcher and Professor for the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include oscillatory signal processing, neuroscience, multivariate data analysis and supervised learning. Cristina Rueda. I received the BS degree in mathematics from the Universidad de Valladolid in 1987 and the PhD degree in statistical science from the Universidad de Valladolid in 1989. I am currently Professor in the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include statistical inference methods under restrictions, circular data, computational biology, and statistical methods for signal analysis.