Eur. Phys. J. Spec. Top. (2021) 230: 2951-2961
https://doi.org/10.1140/epjs/s11734-021-00176-z

Regular Article

Impact of the activation rate of the hyperpolarization- activated current ${\text{I}}_{\mathrm{h}}$ on the neuronal membrane time constant and synaptic potential duration

¹ Vollum Institute, Oregon Health & Science University, Portland, OR, USA
² Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers University, Newark, New Jersey, NJ, USA
³ Department of Physics, School of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, Ribeirão Preto, SP, Brazil

^c antonior@usp.br

Received: 23 November 2020
Accepted: 7 May 2021
Published online: 11 June 2021

Abstract

The temporal dynamics of membrane voltage changes in neurons is controlled by ionic currents. These currents are characterized by two main properties: conductance and kinetics. The hyperpolarization-activated current (${\text{I}}_{\mathrm{h}}$) strongly modulates subthreshold potential changes by shortening the excitatory postsynaptic potentials and decreasing their temporal summation. Whereas the shortening of the synaptic potentials caused by the ${\text{I}}_{\mathrm{h}}$ conductance is well understood, the role of the ${\text{I}}_{\mathrm{h}}$ kinetics remains unclear. Here, we use a model of the ${\text{I}}_{\mathrm{h}}$ current model with either fast or slow kinetics to determine its influence on the membrane time constant (${\tau }_m)$ of a CA1 pyramidal cell model. Our simulation results show that the ${\text{I}}_{\mathrm{h}}$ with fast kinetics decreases ${\tau }_m$ and attenuates and shortens the excitatory postsynaptic potentials more than the slow ${\text{I}}_{\mathrm{h}}$. We conclude that the ${\text{I}}_{\mathrm{h}}$ activation kinetics is able to modulate ${\tau }_m$ and the temporal properties of excitatory postsynaptic potentials (EPSPs) in CA1 pyramidal cells. To elucidate the mechanisms by which ${\text{I}}_{\mathrm{h}}$ kinetics controls ${\tau }_m$, we propose a new concept called “time scaling factor”. Our main finding is that the ${\text{I}}_{\mathrm{h}}$ kinetics influences ${\tau }_m$ by modulating the contribution of the ${\text{I}}_{\mathrm{h}}$ derivative conductance to ${\tau }_m$.