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

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 ($τ_m$) of a CA1 pyramidal cell model. Our simulation results show that the $I_{\rm h}$ with fast kinetics decreases $τ_m$ 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 $τ_m$ 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 $τ_m$, we propose a new concept called "time scaling factor". Our main finding is that the $I_{\rm h}$ kinetics influences $τ_m$ by modulating the contribution of the $I_{\rm h}$ derivative conductance to $τ_m$.