Fig. 1

Heading-direction (HD) modulation. a Firing rate as a function of location for a typical place cell (left). Firing rate range for spatial map in spikes per second (Hz) is 0–13.8. Colors from blue to red indicate low to high firing rates. (right) Percentage of variance explained by location tuning across neurons. b Example of HD tuning in one neuron. Radius of curve is proportional to the firing rate for each angular bin. Maximum firing rate for angular dependency 3.2 (Hz). c Head-direction tuning of firing rates shown as rate-weighted sums of HD vectors within each bin. Place fields are also shown, as in a. Firing rate ranges for each spatial map are 0–9.5, 0–5.2, 0–13.8; 0–5.9, 0.1–28.5, 0–8.8; 0.1–10.4, 0–7.8, and 0–8. Red circles are the centers of mass of the place fields. Light-blue squares denote bins with average firing rates too low to be included in the analysis of directional modulation. d Average tuning strengths of HD modulation across bins for actual and randomly reshuffled data. Green circle denotes the means of each distribution. Neurons that have average HD modulation higher than the 95% confidence of the shuffled data angular modulation are above the dotted green line (dashed green line is the diagonal); 78% of the neurons are above the equality line (dashed line), and 46% are above the 95% confidence line (dotted line). Histogram of neurons with tuning strength for all neurons and for neurons above 95% confidence interval in light and dark blue bars, respectively. e Schematics of preferred HD vectors (left) and average velocity vectors (right) for each spatial bin. f Distribution of the correlation between preferred HDs (pref. HD) and the velocity of the animal’s motion for actual and shuffled data. Only 13.4% of neurons, indicated by green, have significant correlation between neural response and direction of motion (5% is expected)