Can Grid Cell Ensembles Represent Multiple Spaces?

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.

Can grid cell ensembles represent multiple spaces?

The way grid cells represent space in the rodent brain has been a striking discovery, with theoret-ical implications still unclear. Differently from 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, em-bedded 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 po-tential 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 non-congruent metric rela-tionships, 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.

Coding advantage of grid cell orientation under noisy conditions

Grid cells constitute a crucial component of the “GPS” in the mammalian brain. Recent experiments revealed that grid cell activity is anchored to environmental boundaries. More specifically, these results revealed a slight yet consistent offset of 8 degrees relative to boundaries of a square environment. The causes and possible functional roles of this orientation are still unclear. Here we propose that this phenomenon maximizes the spatial information conveyed by grid cells. Computer simulations of the grid cell network reveal that the universal grid orientation at 8 degrees optimizes spatial coding specifically in the presence of noise. Our model also predicts the minimum number of grid cells in each module. In addition, analytical results and a dynamical reinforcement learning model reveal the mechanism underlying the noise-induced orientation preference at 8 degrees. Together, these results suggest that the experimentally observed common orientation of grid cells serves to maximize spatial information in the presence of noise.