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

Abstract

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 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.