U(1) dynamics in neuronal activities

TL;DR

This paper introduces a U(1) dynamics model for neuronal activities that integrates action potentials and phase information, providing a minimal framework to describe neuron behavior and synaptic interactions beyond traditional rate models.

Contribution

It proposes the U(1) neuron model, capturing neural dynamics through phase and action potential integration, and establishes its relation to existing neuron models like Hodgkin-Huxley and Kinouchi-Copelli.

Findings

The U(1) neuron model describes phase transitions in neural activity.

It maps the Hodgkin-Huxley neuron dynamics within the U(1) framework.

The model highlights phase-dependent synaptic interactions.

Abstract

Neurons convert the external stimuli into action potentials, or spikes, and encode the contained information into the biological nerve system. Despite the complexity of neurons and the synaptic interactions in between, the rate models are often adapted to describe neural encoding with modest success. However, it is not clear whether the firing rate, the reciprocal of the time interval between spikes, is sufficient to capture the essential feature for the neuronal dynamics. Going beyond the usual relaxation dynamics in Ginzburg-Landau theory for statistical systems, we propose the neural activities can be captured by the U(1) dynamics, integrating the action potential and the ``phase" of the neuron together. The gain function of the Hodgkin-Huxley neuron and the corresponding dynamical phase transitions can be described within the U(1) neuron framework. In addition, the phase dependence of the synaptic interactions is illustrated and the mapping to the Kinouchi-Copelli neuron is established. It suggests that the U(1) neuron is the minimal model for single-neuron activities and serves as the building block of the neuronal network for information processing.