Extended Data Fig. 1: Characterizing the anatomy and physiology of h∆B cells, showing that sytGCaMP and RGECO1a yield similar EPG phase estimates in the ellipsoid body, quantifying the EPG phase tracking of the closed loop dot, and evidence that the h∆B phase tracks the fly’s traveling direction in walking flies.

a, At least sixteen somas are labeled by the h∆B split-Gal4 line used in this paper. By comparison, the hemibrain connectome (v1.1) reports nineteen h∆B cells²⁰. b, GFP expression of the h∆B split Gal4 in the fan-shaped body. c, Same as panel b, but not showing the anti-nc82 neuropil stain. d, h∆B cells from hemibrain connectome v1.1²⁰. e, Top, h∆B GCaMP7f signal in a tethered, flying fly experiencing optic-flow (in the time window bracketed by the vertical dashed lines) with foci of expansion that simulate the following directions of travel: 180° (backward), −120°, −60°, 0° (forward), 60°, 120°. Bottom, Phase-nulled and averaged h∆B activity patterns in the fan-shaped body, calculated from the above [Ca²⁺] signals in the last 2.5 s of optic flow presentation. Population means with s.e.m. are shown. f, Same as panel e, but with h∆B sytGCaMP7f signal. Note that the single-bump structure in the sytGCaMP7f signal is clearer than the structure in the cytoplasmic GCaMP7f signal, which is consistent with sytGCaMP7f biasing GCaMP to axonal compartments of h∆Bs. g, Probability distributions of the difference between the EPG phase and the bright dot’s angular position, without and with optic flow. h, Circular standard deviation of the EPG phase – dot position distributions, without and with optic flow. Two-tailed unpaired t-test was performed. i, Correlations between the angular velocities of the EPG phase and the visual landmark position under different conditions. The first two columns use the same data as in panels g and h. The third and fourth columns use data from simultaneous GCaMP7f imaging of EPG cells and PFR cells in tethered-flying flies with a closed-loop dot. The fifth column use data from GCaMP6m imaging of EPG cells in tethered-walking flies with a closed-loop bar. Two-tailed one sample t-tests were performed against zero. P values are 1.7e-3, 1.3e-4, 5.3e-4, 1.2e-5 and 3.6e-4 comparing each column (from left to right) to zero, respectively. The relatively low, but significantly different from zero, r values show that the EPG phase tracks, even if poorly, the rotation of the landmark. The EPG phase measured in walking experiments tracks the closed-loop stimulus better than in tethered flight. See Main Text for possible technical reasons for why one would observe this difference. The fact that EPG-phase tracking of the closed loop dot is better when we co-imaged EPG cells and PFR cells compared to when we imaged EPG cells and h∆Bs argues that the flies’ genetic background (and thus how reliably flies perform tethered flight) can also quantitatively impact these measures. j, Angular-velocity correlations of the EPG phase and the visual landmark position under different conditions as a function of the time-lag between the two velocity signals. Same data as in panel i, but data with and without optic flow are lumped together. Correlation is highest at 290 ms, 260 ms and 375 ms for the three panels from left to right, respectively. Thus, we used time lags of 275 ms (mean of 290 and 260) and 375 ms for calculating the correlations in flight and walking experiments in panel i, respectively. k, Probability distribution of the angular position of the dot on the arena. Same data as in panels g and h, but data with and without optic flow are lumped together. We tested the uniformity of the distribution across angles using reduced χ2 test. P value is > 0.995, meaning that we cannot reject the hypothesis that the dot position is not evenly distributed on the arena. l, Circular standard deviation of the EPG phase minus the h∆B phase distributions, without and with optic flow. Same data as in panels g, h. Two-tailed unpaired t-test was performed. P value equals 1.3e-6. m, Correlations between the EPG phase and the h∆B phase. Same data as in panels g, h and l. Two-tailed unpaired t-test was performed. P value equals 3.9e-4. n, Data collected from tethered flies walking on a floating ball in complete darkness are shown in this panel and all subsequent panels in this figure. Sample time series of simultaneously imaged EPG and h∆B Gal4 lines. Top two traces show [Ca²⁺] signals. Third trace shows the phase estimates of the two bumps. Bottom two traces show the forward velocity and sideslip velocity of the fly. Quasi-unidirectional walking bouts are labeled with walking directions indicated. o, Probability distribution of the difference between EPG phase and h∆B phase from time segments where flies were walking in three different general directions (Methods). p, EPG – h∆B phase as a function of the egocentric traveling direction. Gray: individual fly circular means. Black: population circular mean and s.e.m. The sign of EPG – h∆B phase deviations seen here, in walking, are consistent with the signs observed in flight, for the same directions of backward-left and backward-right travel. Watson-Williams multi-sample tests were performed. P values are 1.6e-3 and 2.6e-6 comparing the 1st and 3rd columns (from left to right) to the 2nd column, respectively.