In my previous posts on this topic (1 and 2), I explained how the Cognitive Map literature has been boggled for decades by misuse of the word “map”. A map, I argued, is properly defined as a data structure that associates spatial locations with features. The word is frequently used in the literature to refer to a neural representation of absolute Euclidean space, but that shouldn’t be called a map, because it doesn’t contain any information about the features of any particular environment. A representation of abstract space is better thought of as a sheet of paper on which a map can be drawn.
The grid cell system, in my judgement, looks much more like a representation of absolute space than like a map. Grid cells maintain the same activity patterns and relationships across all environments — thus they don’t encode information about the distinctive features of any particular environment.
A good way of thinking about grid cells is as a coordinate system. Each individual grid cell represents a triangular array of X-Y coordinates; the combined activity of all the grid cells constrains the location to a specific coordinate pair. The representation doesn’t look like the Cartesian numerical coordinates that we are used to, but Ila Fiete has argued in several papers that grid cells do in fact encode numbers in an abstract sense — furthermore the encoding has properties that make it particularly easy for neural networks to perform arithmetic on those numbers. So think of grid cells as a coordinate system, or as a sheet of paper on which a map can be drawn — but don’t think of them as a map.
(Footnote: Some people think that those statements are not true — that grid cells actually do encode information about the features of an environment. They note that in many experiments it is possible to observe distortions and irregularities in the grid, and that in environments that can be decomposed into repeating parts — a hairpin-turn maze, for example — the grid gets broken up in a way that causes it to align identically with each part. That data is certainly valid, but I believe that it indicates flaws in an animal’s ability to keep track of its movements, not a “design feature” of the grid cell system. But this is a complicated issue, and in the end only experiments can resolve it.)
If a map is a data structure that associates places with features, and grid cells encode places, then a map ought to be a structure that associates grid cell activity patterns with neural activity patterns that represent features of the world. Where might we find such a thing? The best candidate — almost the obvious candidate, once the question has been framed this way — is the hippocampus.
Anatomically the hippocampus is structured to associate input from the medial entorhinal cortex (MEC) with input from the lateral entorhinal cortex (LEC). Projections from both areas converge on individual cells in the dentate gyrus, CA3, and CA1.
The MEC contains the grid cells, but it also contains some other types of cells that, in contrast to grid cells, actually do encode features of an environment, most notably border/boundary cells, which respond to walls or other features that constrain the ability of an animal to move freely.
The LEC is more difficult to characterize. Studies by Jim Knierim and others have given us some tantalizing clues, but even so the firing correlates of the cells there are rather poorly understood. As far as I can see, though, the idea that it encodes localized features of the environment seems compatible with everything we know about it.
What I am proposing is that the hippocampus encodes cognitive maps by associating places (represented in MEC) with features (represented mostly in LEC but maybe to some degree also in MEC). Mechanistically the idea is that when a feature-pattern in LEC is active at the same time as a grid-pattern in MEC, it induces activity in a set of hippocampal cells that receive convergent input, which then undergo LTP. This synaptic enhancement forms an indirect link between the MEC and LEC cells. If synapses from hippocampus to EC are also strengthened, then we also get a mechanism for reading out the map.
Let me emphasize the central point: I am proposing that maps — associations between places and features — are stored in the synaptic matrix of the hippocampus
What does this say about place cells? It would not be correct to say that they form a map; the relationship is more subtle than that. I will address that question, and more generally the ways that a synapse-map of this sort could be used, in my next post on this topic.
For the moment, though, I would just like to note that if this proposal is right, there is a certain irony in all this. O’Keefe and Nadel, in The Hippocampus as a Cognitive Map, made essentially the following argument:
- A cognitive map is a representation of absolute Euclidean space.
- The hippocampus implements a representation of absolute Euclidean space.
- Therefore, the hippocampus implements cognitive maps.
I have argued that statement 1 is a conceptual error. Statement 2 is empirically false, though of course O’Keefe and Nadel had no way of knowing it. The net result, though, is that statement 3 might very well turn out to be true.
Sometimes science follows weird paths.