Extended Data Fig. 4: FC2 neurons in one column of the fan-shaped body inhibit FC2 neurons in distant columns; an approximately one-to-one mapping exists between the FC2 phase and the goal angle within, but not across, flies; and flies modulate their forward walking velocity as function of their heading relative to an FC2-defined goal heading.

a, Schematic of scan paths for the entire imaging region (black) alongside the stimulation (red) regions of interest (ROI). b, Trial structure for columnar stimulation. Top: 16 fan-shaped body column ROIs (regions delineated by the dotted lines) and the stimulation ROI (red square). Note that the stimulation ROI can overlap with several column ROIs. Middle: average z-projection of the raw fluorescence signal during stimulation in position A (stim. A; blue), the inter-trial period and stimulation at position B (stim. B; orange). c, Left: mean column ROI ΔF/F₀ aligned to the onset of stimulation (pink background) from flies expressing CsChrimson in FC2 neurons for ROIs that overlap with the stimulation ROI (purple) or ROIs that do not overlap with the stimulation ROI (black). Right: same as left, but for control flies that do not express CsChrimson. Mean ± s.e.m. across flies is shown. d, Change in non-stimulated ROI ΔF/F₀ as a function of the ROI’s wrapped distance from the stimulation site for CsChrimson expressing flies. Each grey dot is the mean for an individual fly. Black dots and thick line show mean ± s.e.m. across flies (n = 16). The increase in activity of column ROIs with a distance of 2 or 3 could reflect lateral excitation or alternatively, could simply be due to neurites of stimulated neurons within the stimulation ROI extending into non-stimulated ROIs. e, Distribution of the estimated angular difference—assuming the fan-shaped body left/right extent maps to 360° of azimuthal space—between stimulation location A and B for all flies (see Methods for how stimulation location angle is computed). f, Distribution of the angular difference between the mean FC2 phase position during stimulation A and B for all flies. g, Heading as a function of the FC2 phase position in the fan-shaped body for flies expressing CsChrimson in FC2 neurons. Each dot is a trial, color-coded by the simulation location. In this plot, a phase value of zero signifies that the FC2 bump is in the middle of the fan-shaped body. Note that the same phase position can be reliably associated with a similar heading direction within a fly, but not necessarily across flies (e.g., compare fly 7 to fly 9). The fact that individual flies show a variable offset between the stimulated fan-shaped body location and the stabilized behavioural heading angle is expected if the FC2/PFL3 system signals angles in the same allocentric reference frame set by the EPG heading bump. This is because the EPG bump in the ellipsoid body shows a variable fly-to-fly offset between the fly’s heading in the world and the bump-position in the brain². h, Left: same data as in panel g, but all trials for all flies are shown in the same plot. Note that there is no clear relationship between phase position and bar position across flies. Right: same as left but for control flies that do not express CsChrimson in FC2 neurons. i, Heading relative to predicted goal angle, inferred using the stimulation location (see Methods), for flies expressing CsChrimson in FC2 neurons (left) and no CsChrimson controls (right). Trials are parsed by the fly’s initial distance to the predicted goal angle (different colors). Mean ± s.e.m. across trials is shown. j, Absolute distance to the predicted goal angle over time (bottom) binned by the fly’s forward walking behaviour 1 s before the stimulation onset (top). Mean ± s.e.m. across trials is shown. k, Left: forward walking velocity as a function of flies’ heading relative to their predicted goal angle. Stimulation A and B trials are combined together. Mean ± s.e.m. across flies is shown. Right: same as left but for control flies.

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