Figure 4.

Increasing grid scale reduces long-term place cell stability in a winner-take-all model of place field formation. (a) Individual examples of place cells simulated from small and large-scale grid inputs (left: smallest grid module = 30 cm, right: smallest grid module = 60 cm). For each cell, the activity map resulting from grid input (left), unstable spatial input (middle) and the combination of grid and unstable spatial inputs (right) are shown, with warmer colors indicating regions of stronger input. The units of activity are a measure proportional to firing rate. Minimum and maximum activity values are reported below each map. The place maps resulting after winner-take-all dynamics are shown at right, with the Pearson’s correlation coefficient between the two maps indicated. Scale bar = 25 cm. (b) Across 9 simulation conditions, in which the number of grid and unstable spatial inputs received by each place cell varied, the correlation coefficients for place maps across days declined with as the spacing of the smallest grid module increased. Each colored line shows the average of ten iterations for one condition (for each of the 9 conditions tested separately, all r(78) < −0.74, p < 2.51e-15, Pearson’s correlations). (c) Place cell correlations observed in individual animals compared to correlations predicted by the model. Each circle represents the average correlation between place cells recorded across days in an individual animal (iWT shown in blue, n = 5 mice, iCre-KO shown in red, n = 6 mice). Each asterisk represents the average correlation obtained in one iteration of the model (n = 5 iterations), using parameters chosen to best match the experimental data (minimum grid spacings: 27 cm for iWT, 37 cm for iWT; number of grid inputs: 1000; number of LEC inputs: 200). There was not a significant difference between the stability values for the experimental and simulated iWT data (p = 0.15, two-tailed WRS test) or the stability values for the experimental and simulated iCre-KO data (p = 0.18, two-tailed WRS test). However, there was a significant decrease in the stability values between simulated iWT and simulated iCre-KO data (p = 0.0079, two-tailed WRS test). (d) The p-value for the Pearson’s correlation between grid scale and the correlation coefficient between place maps across days (n = 9 simulation conditions). Each color represents a different simulation condition, as in (b). Dashed line indicates p = 0.001. (e) The slope between grid scale and the correlation coefficient between place maps across days becomes significantly steeper as the ratio of grid to unstable spatial inputs increases (r(7) = −0.91, p = 6.73e-04; Pearson’s correlation; n = 9 simulation conditions). Mean ± SEM of 10 iterations is shown for each condition. (f) Peak total grid input decreases as the spacing of the smallest grid module increases (r(22) = −0.51, p = 0.011; Pearson’s correlation; n = 3 conditions [each with a different number of grid inputs], 8 grid scales). For each condition, the mean of 10 iterations is shown. Each of the 3 conditions tested individually also showed a significant correlation (n = 2000 place cells, 10 iterations, 8 grid scales; all r(159998) < −0.34, p ≪ 0.0001). (g) The correlation coefficient for place maps across days increases with peak total grid input, a finding that was consistent over all conditions and grid scales tested. Each line represents the average for one condition across all active place cells, 8 grid scales, and 10 iterations per scale (all r > 0.25, all p << 0.0001; Pearson’s correlation). A significant, positive correlation was also observed for all grid scales (all r > 0.20, all p < 3.5e-38). (h) The correlation between the activity maps of summed grid input, as in (a), and the place map resulting after winner-take-all dynamics decreased with the spacing of the smallest grid module (r(70) = −0.44, p = 9.4e-05, Pearson’s correlation). For each of the 9 simulation conditions, the average of 10 iterations is shown. For each condition tested separately, all r < −0.012, all p < 0.0090.