# Grid cells : Between what is the correlation of autocorrelogram measured?

In their seminal paper Hafting, Torkel, et al. "Microstructure of a spatial map in the entorhinal cortex." Nature 436.7052 (2005): 801-806.‏ the Mosers have discovered the grid cells.

To show the existence of these cells, they have counted spikes as a function of location, plotted (figure 1.b) a rate map and finally the most known figures of autocorrelogram which beautifully visualize the grid response pattern of these cells.

Auto-correlation is measured between a signal and itself (e.g. when one of the signals is shifted in time). My question is, what is the signal from which the autoelectrogram is calculated and what are the different states of that signal, between which the correlation is calculated (explanation is given at the paper's methods section, but it still didn't help me much).

Autocorrelation is calculated between the spikes-histogram and itself.

The experiment is carried out while the activity of a specific neuron is recorded.

1. Histogram - An animal runs in a circular arena which we divide into multiple squared bins, whenever the cell fires (i.e. generate an action potential) 1 counter is added to the location (the bin) in which the animal is currently located.

2. Autocorrelation - Two instances of the spikes histogram are observed such that one is "placed on-top of the other" and the correlation between the two instances is calculated.

• When the two instances are perfectly aligned, their autocorrelation is 1 (they perfectly match).
• Now we start moving one of the instances. The match between the two instances is not perfect (the autocorrelation is smaller than 1) but because there are peaks (at the spikes-histogram) all across the arena, if we shift one of the instances such that it would be "on top" of another peak (e.g. each peak is aligned with the peak directly to its right) the autocorrelation would, once again, equal 1.
• (τX,τY) - The shift of one of the instances is carried out for every value of x and y of the arena (i.e. for every phase) and the value of autocorrelation for each (τX,τY) shift of the first instance relative to the stationary second instance is plotted - this is what the autocorrelation figure shows.
3. What should we learn from the autocorrelation figure - That the cell response is indeed represented by a grid. The figure exemplifies that when the spikes histogram is shifted in a single full period (i.e. to the next peak) it fully matches itself, so the grid pattern indeed characterize similarly the whole arena (tessellating it).

The recorded signal are spike responses (action potentials) (p.2 Method section), the different states are spike rates (p.4), and the calculated correlation is determined between spike rates and maze coordinates (p.5).

• autocorrelogram figures are plotted in 'r' values. The relevant supplementary section states that r is indeed (some function which reflects) similarity of spike rates of the same cell with spatial lag (TAUx,TAUy). What are the spatial lags used for plotting the figures? What should we learn from this figure - that all hexagon's vertices (of firing fields) have the same firing rate, hexagon centers have the same firing rate and areas in the middle are not so correlated to each other? – Ohad Dan Dec 11 '14 at 9:52