A simplified spiking model of grid-cell scale and intrinsic frequencies

The hexagonal tessellation pattern of grid cells scales up progressively along the dorsal-to-ventral axis of the medial entorhinal cortex (MEC) layer II. This scaling gradient has been hypothesized to originate either from inter-population synaptic dynamics as postulated by attractor networks, from projected theta frequencies to different axis levels, as in oscillatory models, or from cellular dynamics dependent on hyperpolarization-activated cation currents. To test the hypothesis that intrinsic cellular properties account for the scale gradient as well as the different 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. To investigate the causal relationship between oscillatory frequencies and grid-scale increase, we analyzed the dominant frequencies of the membrane potential for cells with distinct after-spike dynamics. We observed that the intrinsic neuronal membrane properties of simulated cells could induce an increase of grid-scale when modulated by after-spike reset values. Differences in the membrane potential oscillatory frequency were observed along the simulated dorsal-to-ventral axis, suggesting that, rather than driving to the increase of grid-scale as proposed by interference models of grid cells, they are the result of intrinsic cellular properties of neurons at each axis level. 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.