Fig. 5. Population trajectories are more direct, less tangled and have reduced oscillatory dynamics during locomotion.
a We performed factor analysis on smoothed, binned spike counts to obtain latent factors that represent shared population variance. b Example trial-averaged population trajectory responses for stationary and locomotion trials (t = 0 to 0.5 s). Two factors are plotted at a time for visualisation. Arrows indicate direction of travel—trajectories start at triangles and end at circles. Dots represent 10 ms time intervals. c Overview of calculation of distance ratios as a measure of how direct population trajectory paths were. d Scatter plot of distance ratios for trial-averaged population trajectory responses during the stimulus onset period, for stationary and locomotion trials. Different colours indicate different stimulus speeds. LME analysis, two-sided effect of behavioural state. ***p = 3.75 × 10−19. e Box plots of direct distance (left) and distance travelled (right) between baseline and stimulus steady-states for trial-averaged population trajectory responses during stationary (black, ‘S’) and locomotion (red, ‘L’) trials, for the stimulus onset period. Centre white lines indicate medians, box limits indicate upper and lower quartiles and whiskers indicate full range of data. Grey lines represent individual stimulus speeds for each subject. LME analysis (n = 30 paired trial-averaged responses), two-sided effect of behavioural state. ***p = 9.30 × 10−19; ns not significant, p = 0.22. f Same as (d) for the stimulus offset period. ***p = 2.77 × 10−7. g Same as (e) for the stimulus offset period. p = 1.63 × 10−17 for direct distance and p = 2.95 × 10−10 for distance travelled. h Mean trial-averaged trajectory speed (top panel) and acceleration (bottom panel) over the response period for stationary and locomotion trials. Inset: relative power spectrum of trajectory acceleration. Paired two-sided t-test on low frequency band (0–6 Hz). ***p = 7.46 × 10−7. i Population trajectories had less oscillatory approaches to steady-states during locomotion trials. Left panel: illustration of trajectory angle of approach analysis. Right panel: mean trajectory angle of approach over the response period for stationary and locomotion trials. j Population trajectories exhibited reduced neural tangling during locomotion trials. Left panel: examples of trajectories with high and low neural tangling. Mean tangling values are indicated beneath trajectories. Right panel: mean trajectory tangling over the response period for stationary (black) and locomotion (red) trials. Shaded regions indicate mean ± SEM across subjects (n = 5). Source data are provided as a Source Data file.