Neural dynamics for landmark orientation and angular path integration

Abstract

Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed Drosophila melanogaster walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body, a toroidal structure in the centre of the fly brain. The neural population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity, a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors, network structures that have been proposed to support the function of navigational brain circuits.

Extended Data Figure 1. Visual stimuli, walking velocities and fraction of time walking across flies and conditions

a, Single stripe pattern. b, Pattern with multiple features. c, Pattern with two identical stripes positioned symmetrically on the 270° visual display. In all closed-loop experiments, visual stimuli wrapped around the 270° arena, going directly from 0° to 270° and vice versa. d-g, Walking performance during closed-loop walking with a single stripe: d, Forward velocity; e, Magnitude of sideslip velocity; f, Magnitude of rotational velocity; g, Fraction of time walking across all trials. h-k, Same as d-g for the pattern with multiple features. l-o, Same as d-g for pattern with two stripes. p-s, Same as d-g for walking in the dark on a 6 mm diameter ball. t-w, Same as d-g for walking in the dark on a 10 mm diameter ball. x-aa, same as d-g for experiments with trials that combined epochs of closed-loop walking with epochs of walking in darkness (Extended Data Fig. 9).

Extended Data Figure 2. Closed-loop walking in visual environment with single stripe pattern

a, Mean and S.D. of the number of activity bumps as measured by Method 2 (see Methods) during all trials of all flies shown in Fig. 1. b, Mean and S.D. of the number of successive calcium imaging frames (recorded at 8.507 Hz) with more than one bump, measured using Method 1 (see Methods), for all flies shown in Fig. 1. c, Same as b, but computed using Method 2. d, Histogram of slopes of the linear fit between PVA estimate and pattern position during walking epochs, i.e., the gain between unwrapped PVA estimate and unwrapped pattern position. The pattern was mapped from 0°-to-270° to 0°-to-360° for PVA calculations (see Methods). Thus, a slope of 1 corresponds to a visual pattern on the 270° arena that maps to the entire ring of the ellipsoid body. Only those walking epochs during which the pattern moved over at least half of the visual display were included so as to obtain an accurate estimate of the slope (mean slope = 0.92 ± 0.32, n = 172 walking epochs, see Methods). e, Mean and S.D. of angular offsets between PVA position and pattern position for each trial (140 s, see Methods) for all flies. f, Mean and S.D. of S.D. of angular offset between PVA position and pattern position.

Extended Data Figure 3. Closed-loop walking in visual environment with multiple features

a, Mean and S.D. of the number of activity bumps as measured by Method 2 (see Methods) during all trials of all flies shown in Fig. 2. b, Mean and S.D. of the number of successive calcium imaging frames with more than one bump, measured using Method 1 (see Methods), for all flies shown in Fig. 2. c, Same as b, but computed using Method 2. d, Same as Extended Data Fig. 2d for the pattern with multiple features (mean slope = 0.97 ± 0.43, n = 74 walking epochs). e, Mean and S.D. of angular offsets between PVA position and pattern position for each trial (140s) for all flies. f, Mean and S.D. of S.D. of angular offset between PVA position and pattern position.

Extended Data Figure 4. Single activity bump during closed-loop walking in visual environment with two stripes

a, Closed-loop experiment in visual environment with two identical and symmetrically placed stripes. b, Mean and S.D. of number of bumps in EBw.s population activity across trials for each of 7 flies. c, Mean and S.D. of FWHM of bump. Distribution of bump widths is significantly different from that for single stripe stimulus (Fig. 1k); p = 4.5×.5⁻⁶ (see Methods), mean width = 78.7° ± 15.6° for two-stripe trials versus 82.3° ± 11.5° for single stripe trials. d, Mean and S.D. of the number of activity bumps as measured by Method 2 (see Methods) during all trials for all flies. e, Mean and S.D. of the number of successive calcium imaging frames with more than one bump, measured using Method 1 (see Methods). f, Same as e, but computed using Method 2. g, Same as Extended Data Fig. 2d for the pattern with two stripes (mean slope = 1.08 ± 0.41, n = 96 walking epochs). h, EBw.s fluorescence transients during trial with two-stripe pattern (Fly 2 in b). i, PVA estimate of fly's angular orientation compared to actual orientation. j, Mean and S.D. of angular offsets between PVA position and pattern position in all flies. k, Correlation between PVA estimate and actual orientation of original left stripe for all flies. l, Mean and S.D. of angular offsets between PVA position and pattern position for each trial for all flies. m, Mean and S.D. of S.D. of angular offset between PVA position and pattern position.

Extended Data Figure 5. Example of EBw.s activity bump transitioning between locking to one of two identical visual cues placed symmetrically on LED arena

a, Sample frames from a calcium imaging time series showing single bump of EBw.s activity as the two-stripe pattern moved around the arena in a trial in which correlation between EBw.s activity and PVA estimate changes over a 4s period (Fly 6 in Extended Data Fig. 4b). Frames during jump indicated by red time stamps. Scale bar: 20 μm. b, EBw.s fluorescence transients during trial displayed in a. c, Decoding of fly's angular orientation using unwrapped PVA of EBw.s activity plotted against the fly's unwrapped orientation with respect to stripe 1 and stripe 2 in the visual scene with two stripes. Red box corresponds to period when the EB activity bump switches from locking to one stripe to locking to the other (identical) stripe.

Extended Data Figure 6. Competing influences of visual cue and self-motion on EBw.s activity

a, Fluorescence transients during cue shift trial (Fly 9 from Fig. 1j). Red box highlights epochs during which cue abruptly shifted to new position. b, Comparison of PVA estimate versus actual orientation. c, Correlations between PVA estimates and actual orientation relative to visual cue across trials and flies for different closed-loop gain values. d, Fluorescence transients in the EB during closed-loop trial with a low gain of 0.58 (Fly 6 in Fig. 1j-m). Superimposed brown line indicates PVA estimate of orientation. e, Decoding of fly's angular orientation using PVA of EBw.s activity plotted along with the pattern position and the fly's walking rotation. PVA closely matches walking rotation rather than visual cue rotation. Note that walking rotation exceeds visual cue angular rotation in this low gain trial. f, Comparison of PVA estimate versus accumulated rotation of visual cue and accumulated walking rotation on the ball shows PVA estimate more closely matches walking rotation than visual cue rotation.

Extended Data Figure 7. EBw.s activity when flies walk in darkness on balls of two different diameters

a, Mean and S.D. of FWHM of bump when walking in darkness on 6 mm ball. Distribution of bump widths is significantly different from that for single stripe stimulus (Fig. 1k); p = 8×10⁻⁹ (see Methods), mean width = 90.9° ± 11.2° for walking in darkness versus 82.3° ± 11.5° for single stripe. b, Correlations between accumulated PVA and walking rotation in the dark across flies for walking on 6 mm diameter ball. c, Mean and S.D. of the number of activity bumps as measured by Method 2 (see Methods) during all trials (6 mm ball). d, Mean and S.D. of the number of successive calcium imaging frames with more than one bump, measured using Method 1 (see Methods, 6 mm ball). e, Same as d, but computed using Method 2 (6 mm ball). f, Gain between accumulated PVA estimates of orientation and accumulated walking rotation across flies for 6 mm ball. g, Sliding window correlations (200 frames with a step size of 25 frames) between accumulated PVA estimate and accumulated walking rotation for different levels of S.D. of walking rotation for 6 mm ball (S.D. cutoff shown included 97% of epochs). Brown line connects highest-frequency bins. h, Correlations between accumulated PVA and walking rotation across flies when walking in the dark on 10 mm diameter ball. i, Same as f for 10 mm ball. j, Same as g for 10 mm ball.

Extended Data Figure 8. Low rotational velocities during walking in darkness are not well captured by EBw.s activity

Comparison of angular velocity against PVA-estimated angular velocity for all flies walking in darkness on 6 mm ball (Fig. 4, see Methods). Each point is computed across a 20-frame window, and colored based on the strength of the PVA during that epoch. Three features are prominent: (i) Rotational velocity and PVA-estimated angular velocity are correlated, but with some spread and with different slopes for different flies, that is, effective walking-rotation-to-PVA gains can be different for different flies (see Extended Data Figure 7f, i). (ii) Low rotational velocities are not always well captured by EB activity which can drift under such conditions (see points near 0 of the y-axis). (iii) Most cases of EB activity drift appear to occur in phases when the PVA strength is low (as marked by dark blue points arranged in a horizontal line for low velocities).

Extended Data Figure 9. Gain and correlation coefficients for flies walking with a bright stripe and after the stripe has disappeared

a, Distribution of gains between accumulated walking rotation and accumulated PVA estimate for flies walking in the dark before exposure to visual stimulus in closed-loop experiment (mean = 0.47 ± 1.2, n = 397 walking bouts). b, Distribution of gains between accumulated walking rotation and PVA estimate of flies walking with a bright stripe with high (light red, mean = 0.86 ± 0.64, n = 147 walking bouts) or low (light blue, mean = 0.54 ± 0.5, n = 132) closed-loop gain. All gains used were close to the likely ‘natural’ gain. c, Distribution of gains between accumulated walking rotation and PVA estimate of flies walking in darkness after walking with a stripe under closed-loop control in high (red, mean = 0.57 ± 0.84, n = 150) or low (blue, mean = 0.46 ± 0.7, n = 134) gain conditions. d, Distribution of correlation coefficients between accumulated walking rotation and accumulated PVA estimate for flies walking in darkness before visual experience in the closed-loop setup (mean = 0.6 ± 0.42). e, Distribution of correlation coefficients between accumulated walking rotation and accumulated PVA estimate for flies walking with a stripe under closed-loop control with high (light red, mean = 0.79 ± 0.34) or low (light blue, mean = 0.85 ± 0.18) closed-loop gain. f, Distribution of correlation coefficients between accumulated walking rotation and accumulated PVA estimate for flies walking in darkness after walking with a stripe under closed-loop control with high (red, mean = 0.48 ± 0.43) or low (blue, mean = 0.49 ± 0.49) gain. P-values (Kolmogorov-Smirnov two-sample test) for tests of the null hypothesis that the correlations from two different conditions are drawn from the same distribution are as follows. The null hypothesis can be rejected at p < 0.05 for: gain_{DarkAfterHighGain} vs gain_{DarkAfterLowGain}: p = 0.04; gain_DarkNaive vs gain_{DarkAfterHighGain}: p = 0.01; gain_{StripeHighGain} vs gain_{StripeLowGain}: p = 4×10⁻⁸; gain_{StripeHighGain} vs gain_{DarkAfterHighGain}: p = 3×10⁻⁷; gain_{StripeLowGain} vs gain_{DarkAfterLowGain}: p = 0.05; gain_{StripeLowGain} vs gain_DarkNaive: p = 0.001; gain_{StripeHighGain} vs gain_DarkNaive: p = 1×10⁻¹⁵. It cannot be rejected for: gain_DarkNaive vs gain_{DarkAfterLowGain}: p = 0.2. Subscripts indicate conditions of the relevant experiments. DarkNaive: in darkness without previous exposure to closed-loop visual stimulus; DarkAfterLowGain: walking in darkness after a period of walking in closed loop with a single stripe stimulus under low closed-loop gain conditions; DarkAfterHighGain: walking in darkness after a period of walking in closed loop with a single stripe stimulus under high closed-loop gain conditions; StripeHighGain: walking with a single stripe under high closed-loop gain; StripeLowGain: walking with a single stripe under low closed-loop gain.

Extended Data Figure 10. Maintenance of EB representation of orientation with persistent activity when the fly is standing

a, PVA estimate before stop compared to PVA estimate before restart for the 6 mm ball (r = 0.5, p = 1×10⁻²⁹, n = 449, linear fit slope = 0.96 ± 0.02, p = 0, intercept: 0.2 ± 0.06, p = 0.0006, R² = 0.83). b, Difference in PVA before stop and before restart plotted against duration over which the fly was standing (mean standing time, t_mean = 6.6 ± 5.1 s, mean PVA difference, ΔPVA_mean = 0.09 ± 1). c, Same as a for the 10 mm ball (r=0.56, p=1×10⁻³¹, n = 374, intercept=0.1 ± 0.06, p = 0.09, slope = 0.97 ± 0.016, p = 0, n = 374, R² = 0.903). d, Same as b for the 10 mm ball (t_mean = 6.2 ± 4.5 s, ΔPVA_mean = 0.03 ± 0.8). e, PVA estimate before stop compared to PVA estimate at restart for the 10 mm ball (r=0.48, p = 1×10⁻²², n = 374, slope = 0.96 ± 0.02, p = 0, intercept=0.13 ± 0.06, p = 0.02, R² = 0.91). f, Difference in PVA estimate before stop and at restart for the 10 mm ball and duration over which the fly was standing (t_mean= 6.1 ± 4.47 s, ΔPVA_mean = 0.04 ± 0.9). g, PVA estimate before stop compared to PVA estimate before restart during closed-loop behavior with a single stripe (r = 0.64, p = 1.5×10⁻⁴⁶, n = 388, intercept = 0.03 ± 0.07, p = 0.6, slope=1 ± 0.02, p = 0, R² = 0.85). h, Difference in PVA before stop and before restart in single stripe closed-loop trial plotted against duration for which the fly was not walking (t_mean=4.85 ± 3.0 s, ΔPVA_mean = 0.04 ± 0.74). i, PVA estimate before stop compared to PVA estimate at restart during closed-loop behavior with a single stripe (r = 0.67, p = 5×10⁻⁵², n = 388, intercept = 0.1 ± 0.06, p = 0.1, slope = 0.97 ± 0.02, p = 0, R² = 0.88). j, Difference in PVA estimate before stop and at restart during closed-loop behavior with a single stripe (t_mean = 4.97 ± 3.0 s, ΔPVA_mean = 0.02 ± 0.65). k-n, Same as g-j for closed-loop walking with the pattern with multiple features. g, r = 0.66, p = 2×10⁻¹⁹, n = 146, intercept = 0.2 ± 0.1, p = 0.05, slope = 0.9 ± 0.03, p = 0, R² = 0.85. h, r = 0.6, p = 1.6×10⁻¹⁴, n = 146, intercept = 0.19 ± 0.11, p = 0.07, slope = 0.91 ± 0.03, p = 2.1×10⁻⁶⁴, R² = 0.87. i, t_mean = 6.3±7.4 s, ΔPVA_mean = −0.1 ± 0.8. j, t_mean = 6.4 ± 7.4 s, ΔPVA_mean = −0.04 ± 0. 8. o-r, Same as g-j for closed-loop walking with two stripes. o, r = 0.6, p = 5.1×10⁻¹⁵, n = 139, intercept = 0.19 ± 0.11, p = 0.08, slope = 0.93 ± 0.03, p = 0, R² = 0.88. p, r = 0.7, p = 1.4×10⁻²¹, n = 139, intercept = 0.2 ± 0.1, p = 0.03, slope = 0.95 ± 0.03, p = 0, R² = 0.9. q, t_mean = 5.6 ± 5.8 s, ΔPVA_mean = 0.01 ± 0.7. r, t_mean = 5.8 ± 5.8 s, ΔPVA_mean = 0.1 ± 0.66.

Figure 1. Ellipsoid body activity tracks azimuth of visual cue

a, Schematic of setup. Inset: close-up of fly on air-supported ball (modified from ). b, Schematic of fly central brain and CX: ellipsoid body (EB), fan-shaped body (FB), protocerebral bridge (PB), paired noduli (NO), lateral accessory lobe (LAL) and gall (Gall). MB: mushroom body. c, Each EBw.s neuron receives inputs from an EB wedge and sends outputs to a corresponding PB column, and to the gall^,. The PB has 18 columns, but EBw.s neurons only innervate the central 16. d, GFP-labeled EBw.s neurons in a brain counterstained with nc82 (Maximum intensity projection (MIP), reproduced with permission from Janelia FlyLight Image Database). e, MIP of two-photon imaging stack (5 frames, 5 μm apart, see Methods) showing EB processes of GCaMP6f-labeled EBw.s neurons. f, Top: Closed-loop walking with a vertical stripe. Bottom: EBw.s activity is measured in 16 regions of interest (ROIs). Sample frames from calcium imaging time series (Fly 15) showing MIP of EB activity bump (see Methods) as fly rotates visual cue around arena (top). Arrows at top of h indicate frame times. g, Steps to compute PVA based on EBw.s population activity. EB is unwrapped from Wedge 1 to Wedge 16 to display population time series in h. Superimposed is PVA estimate that incorporates trial-specific offset (m; see Methods). h, EBw.s fluorescence transients during single trial (same trial as f). Color scale at right. Superimposed brown line indicates PVA estimate of angular orientation of visual cue. Top: Horizontal grayscale stripe shows PVA amplitude; intensity scale at left. i, PVA estimate of angular orientation plotted against actual orientation of visual cue (see Methods). j, Mean and standard deviation (S.D.) of number of activity bumps in EBw.s population activity across trials for each of 15 flies (see Methods). k, Mean and S.D. of full width at half maximum (FWHM) of activity bump across trials and flies (see Methods). l, Mean and S.D. of correlation between PVA estimate and actual orientation (pattern position) (see Methods). m, Mean and S.D. of angular offsets between PVA position and pattern position (see Methods, Extended Data Fig. 2e, f). All scale bars: 20 μm.

Figure 2. Ellipsoid body is not a retinotopic map of visual scene, but represents fly's orientation relative to visual landmarks

a, Closed-loop experiment in visual environment with multiple features (Fly 1 in b). b, Mean and S.D. of number of bumps across trials for each of 9 flies. c, Mean and S.D. of FWHM of bump. Distribution of bump widths is not significantly different from that for single stripe stimulus (Fig. 1k); p = 0.14 (see Methods), mean width = 84.9° ± 12.6° for multiple feature trials versus 82.3° ± 11.5° for single stripe trials. d, EBw.s fluorescence transients (same trial as a). e, PVA estimate of fly's angular orientation compared to actual orientation. f, Mean and S.D. of angular offsets (see Methods, Extended Data Fig. 3e, f). g, Correlation between PVA estimate and actual orientation. Scale bar: 20 μm.

Figure 3. EBw.s activity tracks landmark orientation cues over angular rotation when these cues are in conflict

a, In cue shift experiments, fly is in closed-loop control of stripe position until cue is abruptly shifted to new position (see Methods). b, Offset between PVA estimate and actual orientation relative to visual cue before and after cue shift. Plot compares actual offsets with those expected if EBw.s activity did not follow cue position (see Methods). N = 50 shifts (n = 6 flies), r = 0.85, p_r = 0. Fit: slope = 0.78 ± 0.07, p_slope = 0, R² = 0.72. c, In closed-loop gain change experiments, ball rotation drives movement of visual stimulus with different closed-loop gains. d, Fluorescence transients during trial with low gain of 0.6 (Fly 15 from Fig. 1j). e, Comparison of PVA estimate versus accumulated rotation of visual cue and walking rotation on ball (trial in d). Walking rotation exceeds visual cue angular rotation in this low gain trial. f, Similar to d, but with high closed-loop gain of 1.3 (Fly 3 from Fig. 1j). g, Similar to e, but with high gain (trial in f). h, Effective gain between walking rotation and PVA estimate for different closed-loop gains (r = 0.69, p_r = 0, Fit: slope = 0.85 ± 0.07, p_slope = 0, n = 172, R² = 0.48, see Methods). i, Effective gain between visual cue rotation and PVA estimate for different closed-loop gains (r = 0, p_r = 15.1×10⁻³, Fit: slope = −0.17 ± 0.07, p_slope = 0.02, n = 172, R² = 0.03, see Methods).

Figure 4. Path integration, drift and persistence in EBw.s activity in total darkness

a, Experiments with flies walking in total darkness. b, Mean and S.D. of number of bumps across trials for each of 11 flies. c, Fluorescence transients during trial in darkness (Fly 9 in b). d, Accumulated ball rotation plotted against accumulated PVA estimate of fly's rotation. e, Sample frames from time series showing that EBw.s activity is maintained in absence of both visual cues and rotation (Fly 3 in b). Scale bar: 20 μm. f, Fluorescence transients during trial in e. g, Representation of fly's angular orientation is maintained in the absence of rotation and resumes from previous wedge after long delay (gray rectangles indicate epochs of fly standing). h, Comparison of PVA estimate of orientation before stop and at restart for different standing bouts across n = 11 flies (r = 0.7, p_r = 0, Fit: slope = 0.96 ± 0.17, p_slope = 0, n = 499, R² = 0.879). i, Durations of standing bouts in l (t_mean = 6.7 ± 5.1 s, ΔPVA_mean = 0.017 ± 0.76 rad).