First imagine a decoder which considers the animal as localized within the grid fields of the most responsive cell in each module (Coultrip et al., 1992; Maass, 2000).
We directly observed the high-resolution image of the dense aggregates of matured fibers, long/short or single/few scattered matured fibrils, typical branched fibrils, protofibrils, oligomer-like, in some instances, amorphous and other unstructured smaller aggregates of Aβ1 42 in the grid fields of TEM.
Let λ i be the distance between nearest neighbor peaks of grid fields of width l i. Assume in addition that a given cell responds on a lattice whose vertices are located at the points λ i (n u + m v), where n, m are integers and u, v are linearly independent vectors generating the lattice.
We halved these measurements to the ratios between grid period and the diameter of the grid field to facilitate the comparison to our theoretical predictions.
The pairs of neurons at the next two scales have grid field widths of 2 m and 1 m respectively, and proportionally shorter periodicities as well.
We can take the positional accuracy to be proportional to the grid field width of the smallest module.
Such measurements are consistent with the prediction of the simple winner-take-all model, which predicts a ratio between grid period and grid field width of λ i / l i = e ≈ 1.65.
10.7554/eLife.06444.012 Figure 3. Differential sensitivity of gamma oscillations and grid fields to changes in the strength of E and I synapses.
Giocomo et al. (2011a) reported the ratios between the grid period and the radius of grid field (measured as the radius of the circle around the center field of the autocorrelation map of the grid cells) to be 3.26 ± 0.07 and 3.32 ± 0.06 for Wild-type and HCN KO mice, respectively.
Here spikes occur at successively earlier phases of the theta rhythm during a grid field traversal, suggestive of a spike-timing code [11].
