Modulating grid cell scale and intrinsic frequencies via slow high-threshold conductances: A simplified model

Abstract 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 frequencies to different axis levels, as in oscillatory models. Alternatively, cellular dynamics, and specifically slow high-threshold conductances, have been hypothesized to have an effect in the scaling of grid cells. To test the hypothesis these intrinsic hyperpolarization-activated cation currents 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.