Multimodal transition and stochastic antiresonance in squid giant axons

TL;DR

This paper models squid giant axon responses to periodic stimuli using the Hodgkin-Huxley model, revealing multimodal transitions and stochastic antiresonance phenomena that match experimental observations.

Contribution

It provides a detailed interpretation of experimental data through a Hodgkin-Huxley framework, highlighting multimodal transitions and noise effects in axonal firing.

Findings

Identification of multimodal transition causing minimum firing rate

Maximum coefficient of variation indicating stochastic antiresonance

Model reproduces dominant mode frequencies near transition

Abstract

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.