Assessing the role of feedback in spatially patterned grid cell responses
We analyze the spike trains of multiple simultaneously recorded grid cells obtained in di erent conditions, to help determine the role of recurrent network feedback in generating grid responses. An important class of models of grid cell activity is based on low dimensional continuous attractor dynamics arising from recurrent connections within the grid system. A necessary prediction of these models is that the strong recurrent connections force the grid responses of di erent cells to maintain fi xed relative spatial phases over long periods of time, even if the response patterns of each neuron change. The observation that grid cells maintain their relative spatial phase relationships across di erent familiar environments supports the presence of recurrent connections, but does not rule out the possibility that these relationships persist due to feed-forward input. We analyze the stability of pairwise neural correlations for experiments in which the spatial responses of single neurons change over time. The first such experiment involves resizing of a familiar enclosure, with the result that spatial grid responses rescale along the resized dimension. We show that the relative spatial phase of ring between pairs of cells remains stable over time even as the absolute spatial phase of ring in these same cells changes greatly through rescaling. This result is again consistent with recurrent connectivity, but it remains possible that common external sensory cues (e.g. border information arriving from boundary cells) somehow register the rescaled grids of all cells to display the same relative phases as before rescaling. In an attempt to address this, we analyze responses from animals first exposure to novel environments. Grid ring becomes more noisy and the spatial ring pattern expands, then relaxes back to the periodicity seen in familiar enclosures. During the relaxation, external sensory cues are static and thus likely not responsible for the changing grid responses. We show that the constant phase relationships seen across familiar environments are present from first exposure as well. Finally, we illustrate a generative model to predict grid cell spikes. The aim is to obtain the key determinants of grid cell ring, including animal location, velocity modulation, neural adaptation, and recurrent feedback in a Bayesian framework, and thus assess network contributions to grid cell activity.