Extended Data Fig. 4: Interaction between heading and velocity tuning in PFNd neurons.

a. Firing rate versus v^p for all PFNd recordings. Data are divided into bins based on the proximity of the fly’s heading to the neuron’s preferred heading. Three of these cells are shown in Fig. 2b. b. Linear fits for one example cell. c. Fitted slope values (reproduced from Fig. 2b) and y-intercept values for all cells (n=14 cells in 9 flies). Horizontal lines indicate mean values. For both parameters, there is a statistically significant effect of heading (2-way paired t-tests, Bonferroni-corrected p values). However, the effect of heading on the slope is relatively large and consistent, as compared to the effect on the y-intercept, which is smaller and less consistent. This implies that the effect of heading (θ) on the cell’s firing rate (f) is largely multiplicative, i.e., it controls the slope of the relationship between f and v^p, as in f ∝ (cos(θ – θ^p) + a) v^p + b where θ^p, a, and b are constants. In our computational model (Fig. 4a–d), we use this same relationship, with θ^p=0, a=1, b=0.