Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

Neurons in the hippocampus and adjacent brain areas show a large diversity in their tuning to location and head direction, and the underlying circuit mechanisms are not yet resolved. In particular, it is unclear why certain cell types are selective to one spatial variable, but invariant to another. For example, place cells are typically invariant to head direction. We propose that all observed spatial tuning patterns - in both their selectivity and their invariance - arise from the same mechanism: Excitatory and inhibitory synaptic plasticity driven by the spatial tuning statistics of synaptic inputs. Using simulations and a mathematical analysis, we show that combined excitatory and inhibitory plasticity can lead to localized, grid-like or invariant activity. Combinations of different input statistics along different spatial dimensions reproduce all major spatial tuning patterns observed in rodents. Our proposed model is robust to changes in parameters, develops patterns on behavioral timescales and makes distinctive experimental predictions.