Many animals rely on an internal heading representation when navigating in varied environments1,2,3,4,5,6,7,8,9,10. How this representation is linked to the sensory cues that define different surroundings is unclear. In the fly brain, heading is represented by ‘compass’ neurons that innervate a ring-shaped structure known as the ellipsoid body3,11,12. Each compass neuron receives inputs from ‘ring’ neurons that are selective for particular visual features13,14,15,16; this combination provides an ideal substrate for the extraction of directional information from a visual scene. Here we combine two-photon calcium imaging and optogenetics in tethered flying flies with circuit modelling, and show how the correlated activity of compass and visual neurons drives plasticity17,18,19,20,21,22, which flexibly transforms two-dimensional visual cues into a stable heading representation. We also describe how this plasticity enables the fly to convert a partial heading representation, established from orienting within part of a novel setting, into a complete heading representation. Our results provide mechanistic insight into the memory-related computations that are essential for flexible navigation in varied surroundings.
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We thank A. Jenett, T. Wolff and G. Rubin for sharing the split line SS00096; B. Pfeiffer, A. Wong, D. Anderson and G. Rubin for sharing codon-optimized GCaMP6f DNA; C. Dan for codon-optimized GCaMP6f flies; Janelia Fly Core and, in particular K. Hibbard and S. Coffman, for fly husbandry; J. Liu for virtual-reality support; V. Goncharov and C. McRaven for microscope support; J. Arnold for fly holder design; Vidrio for ScanImage support; T. Kawase for animation; and E. Nielson and S. Houck for operational support. We are grateful to A. Karpova and members of V.J.’s and A.M.H.’s laboratories for useful discussions and comments on the manuscript. S.S.K., A.M.H., S.R. and V.J. are supported by Howard Hughes Medical Institute; L.F.A. is supported by NSF NeuroNex Award DBI-1707398, the Gatsby Charitable Foundation and the Simons Collaboration for the Global Brain.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Peer review information Nature thanks Holger G. Krapp and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
Extended Data Fig. 1 Manipulation of pinning offset of heading representation relative to visual scene.
a, Schematic shows simultaneous calcium imaging and localized optogenetic stimulation. b–d, Snapshots of compass-neuron population activity before, during and after optogenetic manipulation in open loop (orientations of imposed single-stripe visual scene are shown at the top). b, A bump offset of close to zero before optogenetic manipulation (arrow in e shows the time of this snapshot). c, Optogenetic imposition of the new offset. Left, when the vertical stripe is in front of the fly, the bump was imposed on the right side of the ellipsoid body (rectangle). Right, 45° rotated scene and bump with the same offset as shown on the left. This offset was sequentially imposed across eight positions of the visual scene and ellipsoid body for approximately 2 s per position for 5 min (e middle). d, Snapshot of compass-neuron calcium transients after manipulation (e bottom). The bump position relative to same visual scene as in b is now shifted by the offset imposed in c. e, Segments (60 s) of imaging before (top), during (middle) and after (bottom) a 5-min optogenetic manipulation. Conventions are the same as in Fig. 1. f, Bootstrapped distribution of the mean difference between the imposed and actual offset shifts in Fig. 2 (natural scene), which was not significantly different from 0 (19 trials from 10 flies, bootstrapped mean difference test, two-sided, P = 0.6276). g, Bootstrapped distribution of the mean difference between the imposed and actual offset shifts in b–d (single stripe), which was not significantly different from 0 (25 trials from 14 flies, two-sided, P = 0.8932). h–k, Distribution of imposed (x axis) versus actual (y axis) offset shifts across flies. The distribution is significantly linear along the identity line (circular linearity test. h, Natural scene, 19 trials from 10 flies, P < 0.0001. i, Single stripe, 25 trials from 14 flies, P < 0.0001. j, No CsChrimson, 14 trials from 10 flies, P = 0.0934. k, In darkness, 17 trials from 10 flies, P = 0.6064). l–o, Absolute change in offset across two trials before manipulation (blue) and across two trials after manipulation (yellow), and absolute change in offset induced by manipulation (red). Bootstrapped mean difference tests, one-sided. n values are the same as in h–k. l, Natural scene, bootstrapped mean difference test between epochs before and during manipulation, P = 0.0464; and between epochs during and after manipulation, P = 0.0024. m, Single stripe, bootstrap tests of the mean difference showed a significant difference between the baseline offset shifts and manipulated offset shifts (P = 0.0207 between epochs before and during manipulation; and P = 0.0252 between epochs during and after manipulation). n, No CsChrimson control, bootstrap tests of the mean difference did not show any significant difference; P > 0.05 for all pairs. o, Darkness control, bootstrap tests of the mean difference did not show any significant difference; P > 0.05 for all pairs. Baseline offset shifts were comparable to the experimental group (m), but greater than the control group without CsChrimson (n). This suggests that the baseline offset variance in the experimental group might be due to a higher baseline activity of the compass-neuron population, induced by weak activation of CsChrimson during two-photon imaging.
Extended Data Fig. 2 Simulation showing the mapping of a complex scene onto a stable heading representation and optogenetic bump offset shifting.
a, A complex one-dimensional scene was generated via a mixture of four von Mises functions with random mean directions and random concentration parameters, shown for t = 0. b, c, Model simulation. Ring-neuron population activity (b, top) serves as the assumed source of visual input. A time series of angular velocity obtained from tethered flight data was used to compute movement of the visual scene. b, Bottom, compass-neuron population activity during simulated orientation. c, Time-varying synaptic weights between ring and compass neurons. The simulation began with random synaptic weights (left) and random initial activity of compass-neuron population. Ring attractor dynamics ensures a stable bump, albeit with a random offset. The initial turning of bump is not enforced by visual cues but by the angular velocity signal from tethered flight data. The same 400-s turning signal was repeated 3 times (Supplementary Information). Synaptic weights stabilize over time (c, right). After learning, a vertical cross-section of the stabilized synaptic weight matrix resembles the model ring-neuron activity profile shown in a. d, Simulation of optogenetic shift in offset. The simulation began with the stable mapping shown in c. e, During the probe trial, the newly mapped offset was consolidated. All simulation results shown are based on a post-synaptically gated plasticity rule, unless otherwise stated. Extended Data Figures 5, 6 and Supplementary Information provide the differences in predictions made by post- and pre-synaptically gated plasticity rules.
a–c, Simulation of the time evolution of the synaptic weight matrix, induced by a visual scene with two vertical stripes. Conventions are the same as in Extended Data Fig. 2. a, The simulation began with the stabilized synaptic weight matrix shown in Fig. 2e. Visual input provided was two narrow von Mises functions, separated by 180°. Ring attractor dynamics ensured that the compass-neuron population maintained a single bump. Over time, the synaptic weight matrix develops two distinct bands of weak synapses (right), representing weakened connections from two active sets of ring neurons to a compass-neuron bump. b, c, When the system is then presented with a visual scene that has only one vertical stripe, there are two possible outcomes: ring attractor dynamics stabilizes an offset that is either shifted 180° from the original offset (b) or the same as the original offset (c). d–i, Natural bump-offset shifting with two identical vertical stripes (no optogenetic manipulation) separated by 165° in a 330° arena. d–f, Segments (60 s) of compass-neuron calcium transients before (d), during (e) and after (f) manipulation. Conventions are the same as in Fig. 2d, except that the red line represents the position of either one (d, f) or two (e) stripes. Imaging snapshots shown in the left panels were taken at times indicated with arrows beneath right panels. The bump offset is shifted by 180° in f, relative to its position in e (Supplementary Video 4). g, Distribution of the absolute shift in offset measured across trials from all flies. Left, baseline variance; change in offset across two trials before manipulation. Right, baseline variance; change in offset across two trials after manipulation. Centre, change in offset across two trials separated by a manipulation trial. In three cases (n = 19), the shift in offset was close to 180°. Unlike in simulations, in most two-stripe trials the bump position covers only half of the ellipsoid body because of the circular symmetry of the stimulus, which may underlie the apparently low yield of shifting (but see h and i; see Supplementary Information for further discussion). h, The number of bumps during the initial 15 s of 16 trials that did not exhibit a shift of 180° was significantly greater in trials that immediately followed a manipulation trial (red) than in a subsequent trial (blue) (bootstrap test of the mean difference, one-sided, P = 0.0004), indicating that initial competition between two bumps eventually stabilizes to a single bump. This implies that the manipulation trial generated two competing offsets. i, The deviation of the bump offset during the initial 15 s relative to the average bump offset during final 30 s of the same trial was also significantly greater in the trial immediately following a manipulation trial than in a subsequent trial (bootstrap test of mean difference, one-sided, P = 0.0036), which is a natural consequence of competition between two alternating bumps before one stabilizes.
The conventions are the same as in Extended Data Fig. 2. a–e, Local optogenetic manipulation spanning 180°. a, The simulation begins with a stabilized synaptic weight matrix, shown in Fig. 2e. Over time, a new map spanning 180° replaced approximately half of the original map (right). A portion of the synaptic weight matrix, corresponding to visual orientations that were not presented, was erased over time (top right corner of right panel). b, c, After manipulation, two potential maps (the original map and the newly imposed map) compete. Which map it is that eventually stabilizes and strengthens depends on whether or not the bump and stimulus begin in the newly mapped region of the ellipsoid body in the trial that immediately follows manipulation. d, Compass-neuron calcium transients before (top), during (middle) and after (bottom) optogenetic manipulation spanning 180° of the visual scene and the ellipsoid body. The conventions are the same as in Fig. 2d. Compare the offsets in the top and bottom panels. e, Distribution of the absolute shift in offset, measured across flies. White dots, baseline before manipulation; black dots, offset shift by manipulation (10 flies, bootstrapped mean difference test, one-sided, *P < 0.0001). f–k, Local optogenetic manipulation spanning 60°. f, The simulation begins with the stabilized synaptic weight matrix shown in Fig. 2e. Over time, the newly imposed map replaces a portion of original map, which spans more than 60° because of the non-zero width (118° tail to tail) of the bump (bottom right). g, h, After the manipulation, two potential maps (the original map and the newly imposed map) compete. After the epoch of manipulation, if the bump begins in the manipulated region (g), the new map is likely to dominate and eventually strengthen. i–k, Optogenetic manipulation spanning 60° of the visual scene and the ellipsoid body. i, Segments (60 s) of compass-neuron population activity before (top), during (middle) and after (bottom) manipulation. The position of stripe (bottom) is not in the manipulated domain, yet the bump is shifted to the optogenetically imposed offset (compare the offsets in the top and bottom panels). j, Left, data from 60°-span manipulation, after which a closed-loop probe trial begins with the stripe in the position that was sampled during manipulation. Open dots, baseline variance of the offset around mean, before manipulation. Solid blue dots, shift in offset induced by 60°-span manipulation. Across the population, the shift was significant (bootstrapped mean comparison, one-sided, P < 0.0013). Right, data from 60°-span manipulation, after which closed-loop probe trial begins with the stripe outside the set of positions sampled during manipulation. Open dots, baseline variance. Solid red dots, shift in offset induced by manipulation. The shift was only marginally significant across the population (bootstrapped mean comparison, one-sided, P = 0.012). The global extrapolation of local manipulation was facilitated when the stripe began in manipulated positions in the probe trial (binomial exact test, *P = 0.0059) (Methods). k, Same data as in j but re-categorized. Left, in probe trials, both the bump and stripe began in a position sampled during the manipulation (4 out of 20 flies). All 4 flies showed a greater-than-90° shift during probe trials. Right, all other conditions (16 out of 20 flies). In total, 3 out of 16 flies showed a greater-than-90° shift. The facilitation of global extrapolation when both the bump and stripe began in manipulated positions was significant (binomial exact test, *P = 0.0012) (Methods).
Extended Data Fig. 5 Deterministic offset difference between two artificial scenes with the same local feature but different two-dimensional organization.
The Supplementary Information provides a detailed discussion. a, Compass-neuron calcium transients measured during closed-loop tethered flight in an artificial scene, arrangement A (A). The conventions are the same as in Fig. 1h. b, Calcium transients from the same fly as in a, but with a different artificial scene, arrangement B (B). c, Distribution of the mean offset of each trial, pooled across all flies (Methods). Distributions of offsets relative to scenes A and B were not significantly different from uniform (n = 40 trials from 10 flies, unimodality test by randomization, P = 0.0819 for A, P = 0.1525 for B). Compare with Fig. 1j. d, Distribution of offset shifts between two trials. The distribution of offset shifts between two artificial scenes, measured across flies, was significantly different from uniform distribution (unimodality test by randomization, from A to B, n = 10 flies, P < 0.0001; from B to A, n = 10 flies, P < 0.0001). The shift in offset was similar across different encounters with same scene, indicating that the offset was stable (unimodality test by randomization, from A to A, n = 10 flies, P = 0.0001; from B to B, n = 10 flies, P = 0.0004). Compare with Extended Data Fig. 6e. e, Parameter sweep to explore how two-dimensional Gaussian filters of different s.d., applied to the artificial scenes in a (arrangement A) and b (arrangement B), would affect shifts in offset between the two scenes. Filters represent the simplified effect of ring-neuron filtering of scenes. Shifts in offset should approximately match azimuthal shifts that would produce the best match (that is, maximum two-dimensional cross-correlation) between the filtered scenes. Each axis represents increasing s.d. of the applied two-dimensional Gaussian filter (g). The point marked with a red X is shown in f. f, Two-dimensional cross-correlation between two scenes in a and b after applying two-dimensional Gaussian filtering with 15° s.d. (red X in e). This filter size corresponds to a 30° full-width at half-maximum receptive field, which matches the average size of the minor axis of ellipses that fit ring-neuron receptive fields13,39. Higher filter sizes up to 60° full-width at half-maximum (the average size of the major axis of elliptical fits of ring-neuron receptive fields13,39) require similar azimuthal shifts to obtain a best match between the scenes (not shown in e). The azimuthal shift for the best match for this range of filters is 165°, a half rotation of the scene on the visual arena (as observed in d). g, Scenes in a and b after applying Gaussian filtering with 15° s.d. h, i, Simulation of pre- and post-synaptically gated plasticity rules applied when the model network is exposed to the two different filtered scenes shown in g. h, Evolution of the synaptic weight matrix with a pre-synaptically gated plasticity rule. Top left, initial random synaptic weight matrix from 8 × 32 ring neurons to 1 of 32 compass neurons. Top right, after exposure to scene A. Each compass neuron responds most to a snapshot of the scene at a particular orientation. Second row, after exposure to scene B, a new snapshot is mapped to the compass-neuron heading representation. The locations of the top two horizontal bars in arrangements A and B overlap (red rectangles), which corresponds to a 165° shift in the two-dimensional cross-correlation in e and f (or a 180° shift in the 360° arena in simulations). This deterministic offset shift results in the same pinning offset and a retrieval of the same heading representation as before when the scene is repeated later (bottom two rows). The third and fourth rows show repeated exposure to scenes A and B. Bottom two rows, retrieval of the original offset. i, Evolution of the synaptic weight matrix with post-synaptically gated plasticity rule. The result is almost identical to h, given that all ring neurons and compass neurons are activated during simulation. j, k, Simulated offset shifts with pre-synaptically (j) and post-synaptically (k) gated plasticity rules. For each rule, 100 simulations were performed. Both the pre-synaptic and the post-synaptic rules reproduced the population data in d.
a–d, Simulation of pre- and post-synaptically gated plasticity rules with simple two-dimensional scenes. a, Initial random synaptic weight matrix from 2 × 32 ring neurons to 1 of 32 compass neurons. b, Two simple simulated scenes activate mutually exclusive ring neurons. T, top ring neurons are active; B, bottom ring neurons are active. c, Evolution of synaptic weights for a pre-synaptically gated plasticity rule. Top left, initial random weight matrix before presenting scene T. Top right, after exposure to scene T, only synapses from active ring neurons (top row of ring neurons in e) were updated, while synapses from all other ring neurons (bottom row of ring neurons in e) remained intact. Second row, after exposure to scene B, ring neurons that were previously inactive became activated, and their synapses were updated. Third row, when scene T was presented again, the offset between scene orientation and bump position was the same as when scene T was first presented (f). d, Evolution of synaptic weights for a post-synaptically gated plasticity rule. Synapses from inactive ring neurons are erased upon each encounter with a new scene. This would shift offset across two encounters of the same scene if the fly experiences a different scene between them. e, Population data are from ten flies. Distribution of offset shifts between two trials in Fig. 1h, i. The distribution of offset shifts between two different natural scenes, measured across flies, is not significantly different from uniform distribution (unimodality test by randomization, from F to O, P = 0.489; from O to F, P = 0.1504). Different encounters of the same scene lead to similar, near-zero offset shifts, indicating stability of offset (unimodality test by randomization, from F to F, P = 0.0035; from O to O, P < 0.0001). f, g, Simulated offset shifts with pre-synaptically (f) and post-synaptically (g) gated plasticity rules. For each rule, 100 simulations were performed.
This file contains details of computational models.
| Using optogenetics to change the pinning offset of the visual scene relative to the bump First column from the left, initial bump offset before a manipulation trial. Top, calcium imaging. Middle, behavioral recording of the fly in closed-loop control of natural scene shown in Fig. 1i (open space) positioned in the visual arena. Bottom, a cartoon showing the bump offset relative to an orientation of the scene. Second column, bump was optogenetically-induced with offset to left of scene orientation shown in cartoon. Third column, closed-loop probe trial after manipulation. Fourth column, second optogenetic manipulation for same fly. Bump was optogenetically-induced with offset to right of scene orientation shown in cartoon. Last column, closed-loop probe trial after second manipulation.
| Simulation of plasticity Animation of plasticity model shown in Fig. 2e.
| Forced inverse mapping of visual scene to E-PG bump movement in the EB Convention is the same as in Supplementary Video 1. Direction of movement of optogenetically-induced bump is opposite to direction that it would naturally move based on movement of visual scene.
| Natural bump offset changes when the visual scene comprises two vertical stripes opposite each other Convention is the same as in Supplementary Video 1. Left column, initial bump offset before manipulation trial. Middle column, two vertical stripes were presented to fly in closed-loop control. Right column, bump offset after manipulation trial.
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Kim, S.S., Hermundstad, A.M., Romani, S. et al. Generation of stable heading representations in diverse visual scenes. Nature 576, 126–131 (2019). https://doi.org/10.1038/s41586-019-1767-1