  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 $\tau_m$.
