Asymmetrical voltage response in resonant neurons shaped by nonlinearities

TL;DR

This paper investigates how nonlinearities in neuron models cause asymmetric voltage responses to oscillatory inputs, revealing mechanisms behind frequency-dependent response patterns and their ionic basis.

Contribution

It introduces a geometrical explanation for voltage asymmetries caused by nonlinearities and identifies frequency-dependent patterns in gating variables.

Findings

Asymmetries arise from nonlinearities in activation curves and nullclines.

High amplitude oscillations emphasize asymmetric responses.

Frequency-dependent gating variable patterns are linked to nonlinearities.

Abstract

The conventional impedance profile of a neuron can identify the presence of resonance and other properties of the neuronal response to oscillatory inputs, such as nonlinear response amplifications, but it cannot distinguish other nonlinear properties such as asymmetries in the shape of the voltage response envelope. Experimental observations have shown that the response of neurons to oscillatory inputs preferentially enhances either the upper or lower part of the voltage envelope in different frequency bands. These asymmetric voltage responses arise in a neuron model when it is submitted to high enough amplitude oscillatory currents of variable frequencies. We show how the nonlinearities associated to different ionic currents or present in the model as captured by its voltage equation lead to asymmetrical response and how high amplitude oscillatory currents emphasize this response. We propose a geometrical explanation for the phenomenon where asymmetries result not only from nonlinearities in their activation curves but also from nonlinearites captured by the nullclines in the phase-plane diagram and from the system's time-scale separation. In addition, we identify an unexpected frequency-dependent pattern which develops in the gating variables of these currents and is a product of strong nonlinearities in the system as we show by controlling such behavior by manipulating the activation curve parameters. The results reported in this paper shed light on the ionic mechanisms by which brain embedded neurons process oscillatory information.