Summary

• Accumulating evidence indicates that the foundation of mammalian spatial orientation and learning is based on an internal network that can keep track of relative position and orientation (from an arbitrary starting point) on the basis of integration of self-motion cues derived from locomotion, vestibular activation and optic flow (path integration).
• Place cells in the hippocampal formation exhibit elevated activity at discrete spots in a given environment, and this spatial representation is determined primarily on the basis of which cells were active at the starting point and how far and in what direction the animal has moved since then. Environmental features become associatively bound to this intrinsic spatial framework and can serve to correct for cumulative error in the path integration process.
• Theoretical studies suggested that a path integration system could involve cooperative interactions (attractor dynamics) among a population of place coding neurons, the synaptic coupling of which defines a two-dimensional attractor map. These cells would communicate with an additional group of neurons, the activity of which depends on the conjunction of movement speed, location and orientation (head direction) information, allowing position on the attractor map to be updated by self-motion information.
• The attractor map hypothesis contains an inherent boundary problem: what happens when the animal's movements carry it beyond the boundary of the map? One solution to this problem is to make the boundaries of the map periodic by coupling neurons at each edge to those on the opposite edge, resulting in a toroidal synaptic matrix. This solution predicts that, in a sufficiently large space, place cells would exhibit a regularly spaced grid of place fields, something that has never been observed in the hippocampus proper.
• Recent discoveries in layer II of the medial entorhinal cortex (MEC), the main source of hippocampal afferents, indicate that these cells do have regularly spaced place fields (grid cells). In addition, cells in the deeper layers of this structure exhibit grid fields that are conjunctive for head orientation and movement speed. Pure head direction neurons are also found there. Therefore, all of the components of previous theoretical models for path integration appear in the MEC, suggesting that this network is the core of the path integration system.
• The scale of MEC spatial firing grids increases systematically from the dorsal to the ventral poles of this structure, in much the same way as is observed for hippocampal place cells, and we show how non-periodic hippocampal place fields could arise from the combination of inputs from entorhinal grid cells, if the inputs cover a range of spatial scales rather than a single scale. This phenomenon, in the spatial domain, is analogous to the low frequency 'beats' heard when two pure tones of slightly different frequencies are combined.
• The problem of how a two-dimensional synaptic matrix with periodic boundary conditions, postulated to underlie grid cell behaviour, could be self-organized in early development is addressed. Based on principles derived from Alan Turing's theory of spontaneous symmetry breaking in chemical systems, we suggest that topographically organized, grid-like patterns of neural activity might be present in the immature cortex, and that these activity patterns guide the development of the proposed periodic synaptic matrix through a mechanism involving competitive synaptic plasticity.