Interplay of activation kinetics and the derivative conductance determines resonance properties of neurons

TL;DR

This paper investigates how the activation kinetics and derivative conductance of the $I_h$ current influence the resonance properties of neurons, providing a biophysical understanding of frequency response behavior.

Contribution

It derives equations linking resonance frequency and existence to $I_h$ biophysical parameters, highlighting the roles of derivative conductance and activation kinetics.

Findings

Both $G_h^{Der}$ and $ au_h$ significantly influence resonance.

Resonance is voltage-dependent due to $G_h^{Der}$.

The model predicts resonance behavior based on biophysical properties.

Abstract

In a neuron with hyperpolarization activated current ($I_h$), the correct input frequency leads to an enhancement of the output response. This behavior is known as resonance and is well described by the neuronal impedance. In a simple neuron model we derive equations for the neuron's resonance and we link its frequency and existence with the biophysical properties of $I_h$. For a small voltage change, the component of the ratio of current change to voltage change ($dI/dV$) due to the voltage-dependent conductance change ($dg/dV$) is known as derivative conductance ($G_h^{Der}$). We show that both $G_h^{Der}$ and the current activation kinetics (characterized by the activation time constant $\tau_h$) are mainly responsible for controlling the frequency and existence of resonance. The increment of both factors ($G_h^{Der}$ and $\tau_h$) greatly contributes to the appearance of resonance. We also demonstrate that resonance is voltage dependent due to the voltage dependence of $G_h^{Der}$. Our results have important implications and can be used to predict and explain resonance properties of neurons with the $I_h$ current.