Impact of the activation rate of the hyperpolarization-activated current $I_{\rm h}$ on the neuronal membrane time constant and synaptic potential duration

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 ($I_{\rm h}$) 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 $I_{\rm h}$ conductance is well understood, the role of the $I_{\rm h}$ kinetics remains unclear. Here, we use a model of the $I_{\rm h}$ 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 $I_{\rm h}$ with fast kinetics decreases $\tau_m$ and attenuates and shortens the excitatory postsynaptic potentials more than the slow $I_{\rm h}$. We conclude that the $I_{\rm h}$ activation kinetics is able to modulate $\tau_m$ and the temporal properties of excitatory postsynaptic potentials (EPSPs) in CA1 pyramidal cells. In order to elucidate the mechanisms by which $I_{\rm h}$ kinetics controls $\tau_m$, we propose a new concept called "time scaling factor". Our main finding is that the $I_{\rm h}$ kinetics influences $\tau_m$ by modulating the contribution of the $I_{\rm h}$ derivative conductance to $\tau_m$.