This discussion reminded me of the “Method of Loci” memorization technique.

Coffee Mug,

Excelent. This is a very nice summary of the literature on the hippocampus, space, and memory. I appreciate how you've managed to make it accessible and compelling to the lay reader without sacrificing too much factual correctness. Given your obvious familiarity with this field, I can imagine what a heroic effort it must have been to suppress your expert skepticism. As for myself, I think that I would be utterly incapable of writing about, say, the cognitive map theory or the notion of "episodic" memory, without falling into an incomprehensible rant.

you said it! i almost did a run through on the water maze and blind rats as well, but i fear tedium.. also have to constantly suppress the desire to try to teach people 20-30 new terms by putting their definitons in parentheses.. thanks for the input..

I didn't know about a lot of this research into the mecahnism of navigation. I had heard of hippocampal place cells, but not of grid cells. I always guessed that the brain presumably has a bunch of neurons that recreate a model of the spatial environment.

What I really wonder about, though, is how all the dynamic switching is accomplished to change between maps. There can't be one cognitive map that contains, for instance, all the information about the inside of every building on my university campus. Therefore, a new cognitive map would need to be retrieved upon entering each one. It appears that it comes down to a fractal problem: I am somewhere in the floorplan of a building, which is somewhere within the city of Berkeley, which in turn is somewhere within the SF Bay Area. Therefore, just as we wouldn't look at the same scale map when planning a cross-country car trip as we would when trying to find a friend's house, there must be levels of progressive coarse-graining of the cognitive map. If a single layer of place cells were used, it would need to somehow dynamically re-scale its coordinate axes depending on the navigation problem at hand, and somehow accomplish this while maintaining the old information, so that if I left my apartment to go to class and then came back, I wouldn't have forgotten how to get to the shower. This seems impossible without something much, much more complex going on than just a grid of cells that are tied to spatial regions.

the grid cells re-scale along the dorsal-ventral axis of the medial entorhinal cortex. smaller grids at the top.. it's suggested that the overlay of these grids provides a unique location, producing place cells.. so that's one part of the solution..

another thing is that there is a lot of theorizng about the role of the different subregions in determining which map.. maybe we'll do that next.. in broad terms the dentate gyrus gets the information first and acts as a pattern separator/sparse coder.. the CA3 is recurrent network and then pattern completes if it can.. and the CA1 can act as a comparator/novely detector..

these are some ideas.. together they might allow unique non-confusing coding..

Ila Fiete has pointed out that the multiplicity of grid scales represented in the entorhinal cortex enables the system to represent very large spaces through a residue number system. With the proper read-out, distances on the scale of the San Francisco Bay area could be mapped even though the largest grid size may only be several tens of meters (I'm flagrantly speculating here: nobody has any idea whether an entorhinal grid-cell system even exists in humans).

the grid cells re-scale along the dorsal-ventral axis of the medial entorhinal cortex. smaller grids at the top.. it's suggested that the overlay of these grids provides a unique location, producing place cells.. so that's one part of the solution..

Ila Fiete has pointed out that the multiplicity of grid scales represented in the entorhinal cortex enables the system to represent very large spaces through a residue number system.

Could either of you point me to a reference where I can read about these theories? They sound interesting, though I can't exactly understand them from these snippets. I'm guessing that you are talking of something like the following: If two cell grids had respective scales 1 cell=1 meter and another had 1 cell=5 meters, then the point (42 m, -31 m) could be represented by coincident firing of the cells in the first grid at (+ 2 cells, -1 cell) from the origin and the second grid at (+8 cells, -6 cells) from the origin (5*8+1*2=42 and 5*(-6)+1(-1)=-31).

if you don't have academic access i'll send these two you.. the first one has some really great figures.. i haven't written about it directly yet because after a few months of study off and on i still don't quite get what happens when you fall off the edge of the map.. my understanding is that the touretzky model treats the edge of the map differently than the moser model.. in a sense your model captures the idea of how to code for a unique place, but recall that grid cells are repeating, so one cell codes for (2x, -1y) where x and y are integers. really it would be a different equation because the grid is triangular.. so the idea is that there is are unique places where all the grids of different scales will happen to have a nodes..

Path integration and the neural basis of the 'cognitive map'

Bruce L. McNaughton1,4, Francesco P. Battaglia2, Ole Jensen3, Edvard I Moser4 and May-Britt Moser4

The hippocampal formation can encode relative spatial location, without reference to external cues, by the integration of linear and angular self-motion (path integration). Theoretical studies, in conjunction with recent empirical discoveries, suggest that the medial entorhinal cortex (MEC) might perform some of the essential underlying computations by means of a unique, periodic synaptic matrix that could be self-organized in early development through a simple, symmetry-breaking operation. The scale at which space is represented increases systematically along the dorsoventral axis in both the hippocampus and the MEC, apparently because of systematic variation in the gain of a movement-speed signal. Convergence of spatially periodic input at multiple scales, from so-called grid cells in the entorhinal cortex, might result in non-periodic spatial firing patterns (place fields) in the hippocampus.

A Spin Glass Model of Path Integration in Rat Medial Entorhinal Cortex

Mark C. Fuhs and David S. Touretzky

Electrophysiological recording studies in the dorsocaudal region of medial entorhinal cortex (dMEC) of the rat reveal cells whose spatial firing fields show a remarkably regular hexagonal grid pattern (Fyhn et al., 2004Go; Hafting et al., 2005Go). We describe a symmetric, locally connected neural network, or spin glass model, that spontaneously produces a hexagonal grid of activity bumps on a two-dimensional sheet of units. The spatial firing fields of the simulated cells closely resemble those of dMEC cells. A collection of grids with different scales and/or orientations forms a basis set for encoding position. Simulations show that the animal’s location can easily be determined from the population activity pattern. Introducing an asymmetry in the model allows the activity bumps to be shifted in any direction, at a rate proportional to velocity, to achieve path integration. Furthermore, information about the structure of the environment can be superimposed on the spatial position signal by modulation of the bump activity levels without significantly interfering with the hexagonal periodicity of firing fields. Our results support the conjecture of Hafting et al. (2005)Go that an attractor network in dMEC may be the source of path integration information afferent to hippocampus.

The Fuhs & Touretzky model has its problems:

Do we understand the emergent dynamics of grid cell activity?
Yoram Burak and Ila Fiete

(By the way, in case anybody is suspicious, I'm not some kind of a sock puppet for Ila Fiete. I've only met talked to her a couple of times. She seems to be one of the better theoreticians, in my opinion.)

Thanks amnestic and ChairmanK. Being a student, I have access to all of these.