Channel current fluctuations conclusively explain neuronal encoding of internal potential into spike trains.

Martin N P Nilsson,Henrik Jörntell

doi:10.1103/physreve.103.022407

Martin N P Nilsson, Henrik Jörntell

Open Access

https://doi.org/10.1103/physreve.103.022407

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Journal: Physical review. E	Publication Date: Feb 17, 2021
Citations: 8	License type: CC BY 4.0

Affiliation: RISE Research Institutes of Sweden

Abstract

Hodgkin and Huxley's seminal neuron model describes the propagation of voltage spikes in axons, but it cannot explain certain full-neuron features crucial for understanding the neural code. We consider channel current fluctuations in a trisection of the Hodgkin-Huxley model, allowing an analytic-mechanistic explanation of these features and yielding consistently excellent matches with in vivo recordings of cerebellar Purkinje neurons, which we use as model systems. This shows that the neuronal encoding is described conclusively by a soft-thresholding function having just three parameters.

Highlights

Hodgkin and Huxley developed their neuron model to describe the propagation of voltage spikes in giant squid axons [1]
The importance of spike intervals has been emphasized by experiments using electrical activation of the synaptic input of dendrites, showing that the mean axonal output spike frequency tends to be linear in input [2], down to a limit
The significant congruence between the theoretical and experimental spike distributions means that the receiving neuron cannot reliably determine values of additional parameters beyond the triple (σ∞, τ, σ0), unless the lengths of spike trains are increased beyond a reasonable limit, i.e., the duration of stationarity

Summary

Introduction

Hodgkin and Huxley developed their neuron model to describe the propagation of voltage spikes (action potentials) in giant squid axons [1]. The importance of spike intervals has been emphasized by experiments using electrical activation of the synaptic input of dendrites, showing that the mean axonal output spike frequency tends to be linear in input [2], down to a limit. Such a function performs soft thresholding [max(0, a(x − b)) for input x; a, b constants] and is known as a rectified linear unit (ReLU). It has recently attracted wide attention as a powerful information processing element in the machine learning and statistics communities [3]

Results

Discussion

Conclusion