Geometry of abstract learned knowledge in the hippocampus.

Hippocampal neurons encode physical variables1-7 such as space1 or auditory frequency6 in cognitive maps8. In addition, functional magnetic resonance imaging studies in humans have shown that the hippocampus can also encode more abstract, learned variables9-11. However, their integration into existing neural representations of physical variables12,13 is unknown. Here, using two-photon calcium imaging, we show that individual neurons in the dorsal hippocampus jointly encode accumulated evidence with spatial position in mice performing a decision-making task in virtual reality14-16. Nonlinear dimensionality reduction13 showed that population activity was well-described by approximately four to six latent variables, which suggests that neural activity is constrained to a low-dimensional manifold. Within this low-dimensional space, both physical and abstract variables were jointly mapped in an orderly manner, creating a geometric representation that we show is similar across mice. The existence of conjoined cognitive maps suggests that the hippocampus performs a general computation-the creation of task-specific low-dimensional manifolds that contain a geometric representation of learned knowledge.

A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex.

How the topography of neural circuits relates to their function remains unclear. Although topographic maps exist for sensory and motor variables, they are rarely observed for cognitive variables. Using calcium imaging during virtual navigation, we investigated the relationship between the anatomical organization and functional properties of grid cells, which represent a cognitive code for location during navigation. We found a substantial degree of grid cell micro-organization in mouse medial entorhinal cortex: grid cells and modules all clustered anatomically. Within a module, the layout of grid cells was a noisy two-dimensional lattice in which the anatomical distribution of grid cells largely matched their spatial tuning phases. This micro-arrangement of phases demonstrates the existence of a topographical map encoding a cognitive variable in rodents. It contributes to a foundation for evaluating circuit models of the grid cell network and is consistent with continuous attractor models as the mechanism of grid formation.

Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice.

Grid cells, defined by their striking periodic spatial responses in open 2D arenas, appear to respond differently on 1D tracks: the multiple response fields are not periodically arranged, peak amplitudes vary across fields, and the mean spacing between fields is larger than in 2D environments. We ask whether such 1D responses are consistent with the system's 2D dynamics. Combining analytical and numerical methods, we show that the 1D responses of grid cells with stable 1D fields are consistent with a linear slice through a 2D triangular lattice. Further, the 1D responses of comodular cells are well described by parallel slices, and the offsets in the starting points of the 1D slices can predict the measured 2D relative spatial phase between the cells. From these results, we conclude that the 2D dynamics of these cells is preserved in 1D, suggesting a common computation during both types of navigation behavior.

Stimulus-dependent correlations in threshold-crossing spiking neurons.

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with gaussian statistics, we evaluate the cross-correlation of spike trains in pairs of model neurons with different thresholds. This correlation function tends to be asymmetric in time, indicating a preference for the neuron with the lower threshold to fire before the one with the higher threshold, even if their inputs are identical. The relationship between these results and spike statistics in other models of neural activity is explored. In particular, we compare our model with an integrate-and-fire model in which the membrane voltage resets following each spike. The qualitative properties of spike cross-correlations, emerging from the threshold-crossing model, are similar to those of bursting events in the integrate-and-fire model. This is particularly true for generalized integrate-and-fire models in which spikes tend to occur in bursts, as observed, for example, in retinal ganglion cells driven by a rapidly fluctuating visual stimulus. The threshold-crossing model thus provides a simple, analytically tractable description of event onsets in these neurons.