Grid cells in the medial entorhinal cortex (MEC) have known spatial periodic firing fields which provide a metric for the representation of self-location and path planning. The hexagonal tessellation pattern of grid cells scales up progressively along the MEC’s layer II dorsal-to-ventral axis. This scaling gradient has been hypothesized to originate either from inter-population synaptic dynamics as postulated by attractor networks, or from projected theta frequency waves to different axis levels, as in oscillatory models. Alternatively, cellular dynamics and specifically slow high-threshold conductances have been proposed to have an impact on the grid cell scale. To test the hypothesis that intrinsic hyperpolarization-activated cation currents account for both the scaled gradient and the oscillatory frequencies observed along the dorsal-to-ventral axis, we have modeled and analyzed data from a population of grid cells simulated with spiking neurons interacting through low-dimensional attractor dynamics. We observed that the intrinsic neuronal membrane properties of simulated cells were sufficient to induce an increase in grid scale and potentiate differences in the membrane potential oscillatory frequency. Overall, our results suggest that the after-spike dynamics of cation currents may play a major role in determining the grid cells’ scale and that oscillatory frequencies are a consequence of intrinsic cellular properties that are specific to different levels of the dorsal-to-ventral axis in the MEC layer II.