Abstract
The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Unlike hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low-dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute, using two alternative mathematical models, the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple noncongruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.
Highlights
Grid cells appear to comprise an essential component of the cognitive representation of space in rodents [1] and in other species, e.g. bats [2]
We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map
Given appropriate conditions, a neural population with recurrent connectivity can effectively store and retrieve many hexagonally periodic continuous attractors
Summary
Grid cells appear to comprise an essential component of the cognitive representation of space in rodents [1] and in other species, e.g. bats [2]. A couple of recent studies [15],[16] have shown that the presence of salient features such as goals or rewards affect the entorhinal map, changing field locations and inducing remapping in other space selective cells These observations, refer solely to the position of the peaks of activity, i.e. the place fields of each cell, and do not take into account the fact that they vary reliably in height, independently across peaks, from one environment to the other [17]. We pose this question within two alternative mathematical models, both accepting the idealized assumptions which underlie the universal map hypothesis, that is, of strict periodicity and equal peak rates, depicted in Fig.1D, but allowing for several uncorrelated grid representations Under these assumptions, we analyze an ensemble of grid cells as a Continuous Attractor Neural Network, extending the frameworks developed in [24], [25] and [26] for the description of place cells. We emphasize that the storage capacity we are interested in quantifies the number of different, independent charts (or collective maps) that the network can store, and not the spatial resolution (which may be referred to as information capacity, i.e. the number of different positions that can be decoded from the ensemble activity), as considered for example in [27] and [28]
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