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Santos-Pata, Diogo, Zucca, Riccardo, López-Carral, Héctor, Verschure, P., (2019). Modulating grid cell scale and intrinsic frequencies via slow high-threshold conductances: A simplified model Neural Networks 119, 66-73

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.

Keywords: Grid cells, Entorhinal, Hyperpolarization, Navigation, Space


Santos-Pata, D., Zucca, R., Low, S. C., Verschure, P. F. M. J., (2017). Size matters: How scaling affects the interaction between grid and border cells Frontiers in Computational Neuroscience , 11, Article 65

Many hippocampal cell types are characterized by a progressive increase in scale along the dorsal-to-ventral axis, such as in the cases of head-direction, grid and place cells. Also located in the medial entorhinal cortex (MEC), border cells would be expected to benefit from such scale modulations. However, this phenomenon has not been experimentally observed. Grid cells in the MEC of mammals integrate velocity related signals to map the environment with characteristic hexagonal tessellation patterns. Due to the noisy nature of these input signals, path integration processes tend to accumulate errors as animals explore the environment, leading to a loss of grid-like activity. It has been suggested that border-to-grid cells' associations minimize the accumulated grid cells' error when rodents explore enclosures. Thus, the border-grid interaction for error minimization is a suitable scenario to study the effects of border cell scaling within the context of spatial representation. In this study, we computationally address the question of (i) border cells' scale from the perspective of their role in maintaining the regularity of grid cells' firing fields, as well as (ii) what are the underlying mechanisms of grid-border associations relative to the scales of both grid and border cells. Our results suggest that for optimal contribution to grid cells' error minimization, border cells should express smaller firing fields relative to those of the associated grid cells, which is consistent with the hypothesis of border cells functioning as spatial anchoring signals.

Keywords: Border cells, Error minimization, Grid cells, Navigation, Path integration