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Neural dynamics for landmark orientation and angular path integration

Nature volume 521, pages 186–191 (2015)Cite this article

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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.

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Figure 1: Ellipsoid body activity tracks azimuth of visual cue.
Figure 2: Ellipsoid body is not a retinotopic map of visual scene, but represents the fly's orientation relative to visual landmarks.
Figure 3: EBw.s activity tracks landmark orientation cues over angular rotation when these cues are in conflict.
Figure 4: Path integration, drift and persistence in EBw.s activity in total darkness.

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Acknowledgements

We thank T. Wolff and G. Rubin for sharing information about CX neuron morphology. We thank Janelia Fly Core, and in particular K. Hibbard and S. Coffman, for support, J. Liu for technical support, and V. Iyer for ScanImage support. We are grateful to A. Karpova, A. Leonardo, S. S. Kim, H. Haberkern, D. Turner-Evans, C. Dan, S. Wegener and R. Franconville for discussions and comments on the manuscript. We thank W. Denk, S. Druckmann, J. Dudman, A. Lee, K. Longden, M. Reiser, S. Romani, G. Rubin, Y. Sun, and T. Wolff for feedback on the manuscript. This work was supported by the Howard Hughes Medical Institute.

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Authors and Affiliations

  1. Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, 20147, Virginia, USA

    Johannes D. Seelig & Vivek Jayaraman

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  1. Johannes D. Seelig
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  2. Vivek Jayaraman
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Contributions

Both authors designed the study, performed data analysis and wrote the manuscript. J.D.S. carried out all experiments.

Corresponding author

Correspondence to Vivek Jayaraman.

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The authors declare no competing financial interests.

Extended data figures and tables

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, that is, 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 (140 s) 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 × 10−6 (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 the 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 4-s 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 coloured based on the strength of the PVA during that epoch. Three features are prominent: (1) 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 Fig. 7f, i). (2) 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). (3) Most cases of EB activity drift seem 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: gainDarkAfterHighGain vs gainDarkAfterLowGain: P = 0.04; gainDarkNaive vs gainDarkAfterHighGain: P = 0.01; gainStripeHighGain vs gainStripeLowGain: P = 4 × 10−8; gainStripeHighGain vs gainDarkAfterHighGain: P = 3 × 10−7; gainStripeLowGain vs gainDarkAfterLowGain: P = 0.05; gainStripeLowGain vs gainDarkNaive: P = 0.001; gainStripeHighGain vs gainDarkNaive: P = 1 × 10−15. It cannot be rejected for: gainDarkNaive vs gainDarkAfterLowGain: 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, tmean = 6.6 ± 5.1 s, mean PVA difference, ΔPVAmean = 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 (tmean = 6.2 ± 4.5 s, ΔPVAmean = 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 (tmean = 6.1 ± 4.47 s, ΔPVAmean = 0.04 ± 0.9). g, PVA estimate before stop compared to PVA estimate before restart during closed-loop behaviour 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 (tmean = 4.85 ± 3.0 s, ΔPVAmean = 0.04 ± 0.74). i, PVA estimate before stop compared to PVA estimate at restart during closed-loop behaviour 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 behaviour with a single stripe (tmean = 4.97 ± 3.0 s, ΔPVAmean = 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, tmean = 6.3 ± 7.4 s, ΔPVAmean = −0.1 ± 0.8. j, tmean = 6.4 ± 7.4 s, ΔPVAmean = −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, tmean = 5.6 ± 5.8 s, ΔPVAmean = 0.01 ± 0.7. r, tmean = 5.8 ± 5.8 s, ΔPVAmean = 0.1 ± 0.66.

Supplementary information

EBw.s population activity tracks the fly’s orientation relative to visual landmark

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball is presented with a bright vertical stripe in a closed-loop experiment that allows the fly to control the position of the stripe by turning the ball. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; top right, the visual stimulus presented to the fly on a 270° circular arena (shown here as a rectangle); bottom left, the head-fixed fly walking on the ball; bottom right, the population vector average (PVA, red) and visual cue position (blue) plotted against time (see Methods). PVA and cue position wrap around the extent of the ellipsoid body and visual display respectively, as marked by lines disappearing at -π and reappearing at π or vice versa. PVA estimate and visual cue position are filtered with a 3rd order Savitzky-Golay filter over 7 frames (822 ms) in all videos. Size of calcium video frames: 64 m × 64 m. Video playback at 2X normal speed. (MP4 12390 kb)

EBw.s responses track the fly’s orientation within a complex visual scene

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball with a pattern with multiple features in a closed-loop experiment. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; top right, the visual stimulus presented to the fly on a 270° circular arena (shown here as a rectangle); bottom left, the head-fixed fly walking on the ball; bottom right, the population vector average (PVA, red) and pattern position (blue, see Methods) plotted against time. PVA and pattern position wrap around the extent of the ellipsoid body and visual display respectively, as marked by lines disappearing at -π and reappearing at π or vice versa. Size of calcium video frames: 64 m × 64 m. Video playback at 2X normal speed. (MP4 11350 kb)

Single EBw.s activity bump in a visual scene with two symmetrically placed identical visual landmarks

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball with a pattern with two symmetrically positioned identical bright stripes in a closed-loop experiment. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; top right, the visual stimulus; bottom left, the fly walking on the ball; bottom right, the population vector average (PVA, red) and visual cue position (blue) plotted against time. PVA and pattern position (see Methods) wrap around the extent of the ellipsoid body and visual display respectively, as marked by lines disappearing at -π and reappearing at π or vice versa. Size of calcium video frames: 64 m × 64 m. Video playback at 2X normal speed. (MP4 11214 kb)

EBw.s bump locks to one landmark and then another in a visual scene with two symmetrically placed identical visual landmarks

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball with a pattern with two symmetrically positioned identical bright stripes in a closed-loop experiment. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; top right, the visual stimulus; bottom left, the fly walking on the ball; bottom right, the population vector average (PVA, red) and visual cue position (blue) against time. Activity in EB switches from being locked to one cue to being locked to the other (see Extended Data Fig. 5). PVA and cue position are plotted as wrapping around, marked by lines disappearing at -π and reappearing at π or vice versa. Size of calcium video frames: 64 m × 64 m. Video playback at 2X normal speed. (MP4 11667 kb)

EBw.s population activity tracks visual cue even when the cue discontinuously shifts position

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball with a single stripe under closed-loop control. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; top right, the visual stimulus; bottom left, the fly walking on the ball; bottom right, the population vector average (PVA, red) and visual cue position (blue) against time. The green line that appears in the lower right panel at 52.8 s and 102.8 s indicates the time at which the cue is shifted by 120° and -120°, respectively. PVA and cue position are plotted as wrapping around, marked by lines disappearing at -π and reappearing at π or vice versa. Size of calcium video frames: 62 m × 62 m. Video playback at 2X normal speed. (MP4 11287 kb)

EBw.s activity tracks the fly’s orientation in the dark using angular path integration

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking on an air-supported ball in the dark. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; bottom left, the fly walking on the ball; bottom right, the accumulated population vector average (PVA, red) and accumulated ball rotation (blue) plotted against time. Note the different scales for PVA and ball rotation. Size of calcium video frames: 65 m × 65 m. Video playback at 2X normal speed. (MP4 10952 kb)

Persistent activity maintains EBw.s representation of orientation in the absence of both visual and self-motion cues

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking and standing on an air supported ball in darkness. The panels show: top left, the calcium response of EBw.s dendrites in the ellipsoid body; bottom left, the fly walking on the ball, bottom right; the accumulated population vector average (PVA, red) and accumulated ball rotation (blue) plotted against time. Note the different scales for PVA and ball rotation. Although activity appears to decay slowly when the fly stops walking, it resumes in the same EB wedges when the fly resumes walking. Size of calcium video frames: 65 m × 65 m. Video playback at 2X normal speed. (MP4 15069 kb)

Persistent activity during walking in darkness on a 10 mm ball

A fly expressing GCaMP6f under the driver R60D05-GAL4 walking and standing on a 10 mm ball in darkness. The fly’s eyes were covered with black paint. The panels show: top left, the calcium response in the ellipsoid body; bottom left, the fly walking on the ball; bottom right, the accumulated population vector average (PVA, red) and accumulated ball rotation (blue) over time. Note the different scales for PVA and ball rotation. Size of calcium video frames: 64 m × 64 m. Video playback at 2X normal speed. (MP4 15265 kb)

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Seelig, J., Jayaraman, V. Neural dynamics for landmark orientation and angular path integration. Nature 521, 186–191 (2015). https://doi.org/10.1038/nature14446

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