Fig. 2: Population coding of rotational symmetry.

A Normalized HD tuning curves for all POR egocentric bearing (EB) cells (top left) and RSC EB cells (right) recorded in the square environment, shifted for each cell such that the maximum firing rate lies at 0° (‘shifted head direction’). Bottom left, mean tuning curve for each brain area. B One-fold, two-fold, three-fold, and four-fold symmetry scores for the HD tuning curves of all RSC (N = 210) and POR EB (N = 85) cells. Red lines indicate the 95th percentile of a shuffle distribution. C Mean HD x location correlation matrix for all POR EB cells (left; N = 85) and RSC EB cells (right; N = 210) recorded in the square environment. D Same as (B) but based on HD x location correlation matrices (N = 85 POR cells, 210 RSC cells). E Normalized detrended GLM-derived rotation functions for all POR EB cells (top left; N = 85) and RSC EB cells (right; N = 210) recorded in the square environment. Bottom left, mean detrended rotation function for each brain area. F Same as (B) but based on GLM-derived rotation functions (N = 85 POR cells, 210 RSC cells). G Aggregate symmetry scores based on summing individual scores from (B, D, F) (N = 85 POR cells, 210 RSC cells). H Histogram of four-fold symmetry scores for RSC and POR EB cells that did not pass threshold for significant four-fold symmetry (N = 79 POR cells, 101 RSC cells). Note that the RSC population is still significantly rightward-shifted compared to the POR population (dark purple color shows overlap between the distributions; two-sided Wilcoxon rank-sum test, Z = 5.41, P = 6.14e-8). Source data are provided as a Source Data file.