Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells proposedly providing a metric for cognitive maps. Here, we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid compared to a square environment; an effect particularly pronounced in the trapezoid’s narrow part. Congruent with spatial frequency changes of eigenvector grid patterns, distance estimates between remembered positions were persistently biased; revealing distorted memory maps that explained behavior better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory similarly to rodent grid cell activity — thus strengthening the putative link between grid cells and behavior along with their cognitive functions beyond navigation.

Entorhinal grid cells, so-called because of their hexagonally tiled spatial receptive fields, are organized in modules which, collectively, are believed to form a population code for the animal’s position. Here, we apply topological data analysis to simultaneous recordings of hundreds of grid cells and show that joint activity of grid cells within a module lies on a toroidal manifold. Each position of the animal in its physical environment corresponds to a single location on the torus, and each grid cell is preferentially active within a single “field” on the torus. Toroidal firing positions persist between environments, and between wakefulness and sleep, in agreement with continuous attractor models of grid cells.

Extensive research has revealed that the hippocampus and entorhinal cortex maintain a rich representation of space through the coordinated activity of place cells, grid cells, and other spatial cell types. Frequently described as a ‘cognitive map’ or a ‘hippocampal map’, these maps are thought to support episodic memory through their instantiation and retrieval. Though often a useful and intuitive metaphor, a map typically evokes a static representation of the external world. However, the world itself, and our experience of it, are intrinsically dynamic. In order to make the most of their maps, a navigator must be able to adapt to, incorporate, and overcome these dynamics. Here I describe three projects where we address how hippocampal and entorhinal representations do just that. In the first project, I describe how boundaries dynamically anchor entorhinal grid cells and human spatial memory alike when the shape of a familiar environment is changed. In the second project, I describe how the hippocampus maintains a representation of the recent past even in the absence of disambiguating sensory and explicit task demands, a representation which causally depends on intrinsic hippocampal circuitry. In the third project, I describe how the hippocampus preserves a stable representation of context despite ongoing representational changes across a timescale of weeks. Together, these projects highlight the dynamic and adaptive nature of our hippocampal and entorhinal representations, and set the stage for future work building on these techniques and paradigms.