A simple parametric representation of the Hodgkin-Huxley model

Abstract

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 simple representation of this signal is presented in this paper. The new proposal is an adapted Frequency Modulated Möbius multicomponent model defined as a signal plus error model in which the signal is decomposed as a sum of waves. The main strengths of the method are the simple parametric formulation, the interpretability and flexibility of the parameters that describe and discriminate the waveforms, the estimators’ identifiability and accuracy, and the robustness against noise. The approach is validated with a broad simulation experiment of Hodgkin-Huxley signals and real data from squid giant axons. Interesting differences between simulated and real data emerge from the comparison of the parameter configurations. Furthermore, the potential of the FMM parameters to predict Hodgkin-Huxley model parameters is shown using different Machine Learning methods. Finally, promising contributions of the approach in Spike Sorting and cell-type classification are detailed.

Functional clustering of neuronal signals with FMM mixture models

“…In VGA, signals from three types of neurons are differentiated: Pvalb-positive neurons, key in learning and memory process, as detailed in [50] ; Vip-positive neurons, related to circadian rhythms [51] ; and Htr3a-positive neurons, related to bladder dysfunction [52] . The reader interested in how the FMM can shed more light on the modeling of neuronal action potential is referred to [27] and [53] . Due to the flexibility of the FMM model for discriminating different waveforms, the MixFMM algorithm would also be suitable for classifying spikes arising in other cells and experimental conditions, as well as in other contexts, such as those from calcium signals; but always after an ad hoc preprocessing to filter and cut the spike segments.…”

From End to End: Gaining, Sorting, and Employing High-Density Neural Single Unit Recordings

“…Regarded as a foundation stone in neurophysiology, recorded extracellular APs (commonly referred to as spikes) are the fingerprints of single neurons' activities, an observation that has been fueling neuroscientific research for almost a century (Carlson and Carin, 2019 ; Zhang and Constandinou, 2021a ). Analyzing spike trains and spatiotemporal properties of extracellular AP waveforms provides us precious evidence of a cell's functional profile and morphology, including dendritic tree architecture, surrounding environment, and relative position of the recording site (Chaure et al, 2018 ; Rodriguez-Collado and Rueda, 2021 ; Soleymankhani and Shalchyan, 2021 ) and sheds light on the meticulously orchestrated functioning of neural networks (Leibig et al, 2016 ; Luan et al, 2018 ). Besides providing insight into brain activity at the highest temporal resolution currently available (Rey et al, 2015 ; Wouters et al, 2021 ), facilitating the “reverse-engineering” of the brain (Petrantonakis and Poirazi, 2017 ), extracellular APs are eagerly sourced in the development of brain-machine interfaces, too (Hammad et al, 2016 ).…”