A vector-based strategy for olfactory navigation in Drosophila

Abstract

Odors serve as essential cues for navigation. Although tracking an odor plume has been modeled as a reflexive process, it remains unclear whether animals can use memories of their past odor encounters to infer the spatial structure of their chemical environment or their location within it. Here we developed a virtual-reality olfactory paradigm that allows head-fixed Drosophila to navigate structured chemical landscapes, offering insight into how memory mechanisms shape their navigational strategies. We found that flies track an appetitive odor corridor by following its boundary, alternating between rapid counterturns to exit the plume and directed returns to its edge. Using a combination of behavioral modeling, functional calcium imaging, and neural perturbations, we demonstrate that this 'edge-tracking' strategy relies on vector-based computations within the Drosophila central complex in which flies store and dynamically update memories of the direction to return them to the plume's boundary. Consistent with this, we find that FC2 neurons within the fan-shaped body, which encode a fly's navigational goal, signal the direction back to the odor boundary when flies are outside the plume. Together, our studies suggest that flies leverage the plume's boundary as a dynamic landmark to guide their navigation, analogous to the memory-based strategies other insects use for long-distance migration or homing to their nests. Plume tracking thus uses components of a conserved navigational toolkit, enabling flies to use memory mechanisms to navigate through a complex shifting chemical landscape.

Extended Data Figure 1:. Characteristics of odor stimulation at the plume’s boundary

(a) Left: Schematic of closed-loop olfactory system highlighting nozzle yoked to the fly’s heading that provides a continuous stream of clean air, infused with odor (apple cider vinegar) when fly is inside the boundary of the fictive plume. Right: odor concentration profiles measured by PID (photoionization detector) over time at the position of the fly. Top panel shows the full duration of an odor pulse with an onset and decay of approximately 500 msec. Bottom panels show zoomed-in views of the PID trace over the first second from odor pulse onset (left) and offset (right). (b) Positional data of a representative fly upon odor onset and offset. Top: the position of the fly for all entries into the plume (red) and exits from the plume (blue). The solid points represent the animal’s position 500 msec after odor onset and offset. Bottom: histogram shows the distribution of crosswind positions of the fly upon exiting the plume (blue) and upon entering the plume (red). Due to the finite time required for the odor to reach the fly as it walks in virtual space shown in (a), the plume’s edge is not perfectly sharp, with a spatial gradient that depends on how fast the fly is walking. (c) Cumulative density functions (CDFs) of crosswind positions for flies in response to plume entry (red) and exit (blue). n=40 flies, 731 inside trajectories and 796 outside trajectories.

Extended Data Figure 2:. Flies readily edge track along the edge of a vertical plume.

(a) Representative trajectories of four naïve flies that had never previously encountered an odor corridor tracking a 1-meter vertical plume. Epochs outside the plume are depicted in blue and epochs inside the plume are depicted in red. (b) Plume distance tracked by 13 naïve flies. Note that for these experiments, the trial was terminated once a fly tracked more than 1 meter upwind, more than 500 mm in the crosswind direction or more than 100 mm downwind after encountering the plume.

Extended Data Figure 3:. Edge tracking does not depend on the concentration gradient along the longitudinal axis of the plume.

(a) Representative trajectories of an individual fly tracking an odor corridor of a constant concentration of 20% apple cider vinegar (ACV) (left), a plume with an increasing ACV concentration gradient in the upwind direction (10-100% ACV over 1-meter, middle) and a plume with a decreasing ACV concentration gradient in the upwind direction (100-10% ACV over 1-meter, right). Start of each trajectory is marked with a circle. (b) Comparison of average behavioral metrics for the three plumes shown in (a). Each fly navigated a constant concentration, increasing gradient and decreasing gradient plume in a randomized order across flies. Each point represents the average metrics for a single fly, with interindividual average and SEM shown (n = 12 flies). Wilcoxon signed rank test. (c) Representative trajectories for two flies that sequentially navigated a constant concentration 90-degree plume (top) and 90-degree plume, in which the fly was positioned at the center and could select to walk up an increasing (10-100% ACV over 1-meter) or decreasing gradient (100-10% ACV over 1-meter, bottom). (d) Comparison of average behavioral metrics for the constant or gradient plumes shown in (c). Each point represents the average metrics for a single fly, with interindividual average and SEM shown (n = 12 flies). n.s. not significant, p > 0.05. Details of statistical analyses and sample sizes are given in Table S1.

Extended Data Figure 4:. Flies do not appear to require bilateral signals to localize the plume’s edge or track along its boundary.

(a) Schematic of the experimental setup in closed-loop olfactory stimulation paradigm illustrating the contact timing of an odor wavefront arriving from different angles (+90°, +45°, 0°, −45°, −90°) to each antenna. Given the small spatial distance between the two antennae and the speed of the air flow, the difference in the timing of odor arrival is < 1 ms even when animals are walking in the crosswind direction. (b) Schematic of experimental setup for flies navigating a fictive odor plume generated by optogenetic activation of Orco+ sensory neurons expressing CsChrimson. When a fly is inside the boundaries of the fictive plume (left), both antennae are simultaneously stimulated using 660 nm light. Outside the fictive plume (right), the light is off (grey) and there is no stimulation. Wind is maintained in closed loop throughout. (c) Representative trajectories of a fly presented with a 660 nm light corridor in the absence (left) or presence (right) of wind. Paths inside the corridor are shown in red while paths outside the corridor are shown in black. (d) Probability distributions of the absolute value of flies’ x-positions inside a light corridor (depicted in red) in the presence (blue) or absence of wind (black). n=14 flies (no wind), 15 flies (wind). (e) Left: Average displacement in the y-direction for flies presented with a light corridor in the presence (blue) or absence of wind. Right: Average heading inside the light corridor in the presence (blue) or absence of wind (black). n=14 flies (no wind), 15 flies (wind). ***p < 0.001 Details of statistical analyses and sample sizes are given in Table S1.

Extended Data Figure 5:. Edge tracking is not the result of random exploration outside the plume.

(a) Schematic of random-walk model. Left: individual outside trajectories from 40 flies tracking a vertical plume were decomposed into a series run lengths and turn angles using the Ramer-Dougles-Peucker algorithm to generate a library for generating synthetic trajectories with the same underlying statistics. Right: flowchart of how trajectories were simulated from this library. The fly was initiated at the plume’s edge with an initial heading and run length matching the distribution observed during actual fly exits from the plume. At each step, a run length, turn angle, and turn direction was chosen to update the new position (x,y) of the fly. The procedure was repeated until the simulated trajectories returned to the edge or traveled greater > 500 mm orthogonal to the plume’s edge. The turn direction was biased by the wind direction as shown in the inset graph which compares the heading distributions for different upwind biases ($a=0$ to $a=1.0$). (b) Left: Distribution plots of initial headings for the three different plume geometries: 0-degree (light grey); 45-degree (dark grey) and 90-degree (black). Middle: distribution run lengths derived from the library of trajectories. Right: distribution of turn angles derived from the library of trajectories. (c) Relationship between upwind bias and upwind turn bias ($a$) for simulated and real flies. Upwind bias is defined as the distance traveled in the upwind direction divided by total path length. Note that real flies show an upwind bias of 0.35, which corresponds to an upwind turn bias ($a=1.0$). (d) Top: Average outside trajectories for flies (left) and simulated trajectories (right) tracking a vertical plume with different upwind biases ($a=0$, $a=1.0$). Note that in contrast to real flies, simulations lacking an upwind bias ($a=0$) never progress along the length of the plume. Simulations with $a=1.0$ make progress but lack directed returns. Because only simulated trajectories that successfully returned to the plume are included in these averages, they progressed further upwind than real flies but were less efficient as shown in (e). Bottom: Comparison of the inbound and outbound segments of outside trajectories (see Methods), defined as leading away from (outbound, black) or returning to (inbound, red) the point farthest from the plume in the crosswind direction for real flies (replotted from Fig. 1f), and simulated trajectories lacking an upwind bias ($a=0$) and with an upwind bias ($a=1.0$). (e-h) Comparison of real and simulated trajectories for different plume configurations: vertical plume (e, replotted from Fig. 1g), 45-degree plume (f), 90-degree plume (g), and jumping plume (h). Comparison of total path length as a function of distance in the perpendicular direction away from the plume for real flies (left column), model with $a=0$ (middle-left column), and model with $a=1.0$ (middle-right column). Right column compares the probability of returning for $n$ consecutive outside bouts for real flies in black and random models shown in dark and light blue.

Extended Data Figure 6:. Comparison of edge tracking of plumes with different orientations relative to the wind.

(a) Comparison of aligned average trajectories for flies tracking indicated plume orientations, n=20-40 flies, replotted from Fig. 2e-h to highlight the variation in the inside (red) and outside (blue) trajectories of flies depending on the geometry of the plume they are tracking. (b) Comparison of time spent inside or outside the plume across different plume geometries, with each dot indicating the average of all trajectories for a single fly. n=20-40 flies. Letters denote statistically different groups (p < 0.05). (c-f) Left, entry (red) and exit (blue) angles for two representative individuals tracking the indicated plumes shows that flies use a restricted set of angles as they edge track. Right, comparison of behavioral metrics in clean air outside the plume (blue) and in odor (red) for indicated plumes. (c) 0- degree (with data replotted from Figure 1); (d) 45-degree; (e) 90-degree; (f) jumping plume. Each data point indicates the average for all inside or outside bouts for an individual trajectory. n.s., not significant, *p < 0.05, **p < 0.005, ***p < 0.001, ****p < 0.0001. Details of statistical analyses and sample sizes are given in Table S1.

Extended Data Figure 7:. A switching state space model for edge tracking.

(a) Diagram of the switching state space model used to infer fly navigation states (discrete latent variables) and memories (continuous latent variables). The model also infers transition rates between states and parameters of the memory and velocity update rules. See Methods for details. (b) Representative example of a real fly trajectory with navigation states and memories inferred. Left: trajectory is colored according to when the fly is inside the plume (red) or outside the plume (light blue), with arrows indicating entry direction (red) and exit direction (black) as flies cross the plume’s boundary. Right: The same fly trajectory colored according to leaving state (orange) and returning state (blue) with arrows indicating inferred leaving goal (orange) and returning goal (blue). Note that leaving and returning states are not equivalent to times when the fly is inside or outside the odor plume. (c) Scatter plots showing the distribution of parameters for the 28 trajectories (dots) from flies that made at least 30 returns which were used to train the model, and parameters for the average fly model (stars), see Methods for details. (d) Individual flies display heterogeneity in how closely they track the edge of the plume, reflected in distinct model parameters corresponding to different state transitions and velocity updates. Each box shows the representative trajectory for an individual fly (left, cyan) used to fit model parameters and two simulations (right, blue) for 45- and 90-degree plumes. All bouts inside the odor are shown in red. (e) Example inference of navigational states (right) compared with ground truth (middle) for a simulated trajectory. (f) Example inference of memories (thin lines) compared with ground truth (thick lines) for the simulated trajectory in (e). (g) Parameter distributions across different experiments. The first panel shows the learning rate of 28 training trajectories (trajectories including replay experiment are shown by square markers). The second to last panels show state and velocity parameters for 46 edge tracking trajectories with at least 20 returns. (h) Joint distribution of the memory noise parameter and standard deviation of inferred memories for 28 training trajectories. Inferred memories here are the mean of variational distributions fitted to individual trajectories. Standard deviation of inferred memories is calculated as the geometric mean of crosswind component standard deviation and alongwind component standard deviation.

Extended Data Figure 8:. Model captures the average statistics of edge tracking across different plume geometries.

(a-c) Histograms comparing metrics of real and simulated fly trajectories tracking indicated plume orientations: (a) vertical (0-degree) (28 flies, 25 simulations), (b) 45-degree (24 flies, 25 simulations), and (c) 90-degree (20 flies, 25 simulations). These represent the same set of trajectories as in Figure 5c, d but now divided by plume geometry.

Extended Data Figure 9:. The role of the entry and exit angle memory in the model.

(a) Simulated trajectories tracking vertical, 45-degree and 90-degree plumes using a model where entry memory is maintained as a null vector. For each plume, two individual representative trajectories are shown (thick lines) along with an overlay of 25 trajectories. (b) Same as (a) but for simulated trajectories using a model that has a constant exit memory in the upwind direction with a random crosswind component. (c) Same as (a) but for simulated trajectories using a model where the exit memory is resampled from the initialization distribution at each exit. (d) Same as (a) but for simulated trajectories using a model with a constant upwind exit memory. (e) Plume progress (distance between first and last exit divided by total path length) for indicated model variants. Letters denote statistically different groups (p < 0.05). Details of statistical analyses and sample sizes are given in Table S1. (f) Changes of the alongwind component of the entry angle memory, entry direction, exit memory and exit direction during olfactory replay after tracking a 90° plume (see Fig 4b,c). Results shown for trajectories with more than 9 entries during replay. Left: Entry and exit direction and inferred entry and exit angle memory for 8 real flies. Inferred memories are the mean of variational distributions fitted to individual trajectories. Dashed gray line indicates average from corresponding model trajectories plotted for comparison. Error bars show standard deviation. Right: Same as at left but plotted for 22 simulated trajectories. For simulations, entry and exit angle memory represent ground truth memory. (g) Changes of the crosswind components of entry memory, entry direction, exit memory and exit direction for alternating plume experiment (see Fig 5e-f) with a single operant training period. Results shown for trajectories with more than 9 entries after tracking the first edge. Left: Entry and exit direction and inferred entry and exit angle memory for 7 real flies. Dashed gray line represents average of the corresponding simulations plotted for comparison. Right: Same as at left but plotted for 28 simulated trajectories.

Extended Data Figure 10:. Model of how flies modify their trajectories with experience.

(a) Plots depicting the change in efficiency of outside bouts (distance perpendicular to edge divided by total path length) for real flies (top) and simulated trajectories (bottom) tracking different plume types (0-degree, 45-degree, 90-degree, and jumping plume). n=11-20 flies; 19-23 simulations. Each point represents the efficiency of a single bout with the lines representing the average value ± standard error. (b) Left: Representative simulation of the olfactory ‘replay’ experiment, showing simulated trajectory during edge tracking of a 90-degree plume (dark blue trace indicates outside the odor, red inside the odor), subsequent replay of the same odor sequence (light blue trace indicates outside the odor, red inside the odor) or replay of the same odor sequence to a naïve model (black trace indicates outside the odor, red inside the odor). Right, top: Polar plots showing the net displacement direction of simulated trajectories outside the odor and entry direction when they encounter the odor during edge tracking (left, dark blue), replay (middle, cyan), or replay to naïve models (right, black). Each point represents a single bout. Solid lines represent the average vector. Right, bottom: changes of the alongwind projection of directions over outside bouts, error bars are standard error across n=21 simulations. For the alongwind projection, 1 denotes straight upwind and −1 denotes straight downwind. n.s., not significant p>0.05,* p <0.05, **p < 0.005. Details of statistical analyses and sample sizes are given in Table S1.

Extended Data Figure 11:. Flies can be operantly trained to track plumes of different orientations.

(a) Schematic of experimental protocol used to operantly train flies to track plumes in different orientations. After a 5-minute baseline period during which flies walked in clean air, they were given a 45° plume to navigate. Animals that edge tracked a plume for at least 250 mm were then subjected to one of four training conditions: No training, in which flies were immediately tested with a −45° plume in the opposite direction without reinforcement; Same training (5X), in which odor delivery was triggered when flies were heading in the same direction that would lead them back to the initial plume segment (e.g. the 90° to 135° sector), and ceased upon entering a 90° upwind exit zone (−45° to 45°) (training was repeated five times); Opposite training (1X), in which odor delivery was triggered when flies traveled in the direction (e.g. −90° to −135° sector) required to enter the second plume segment. Note that to enter the second plume segment flies must travel in the same direction as used for operant conditioning (−90° to −135°) and so effectively have a second operant training epoch; Opposite training (5X), consisting of five bouts of odor reinforcement triggered by entering the −90° to −135° sector required to enter the second plume segment. Plume orientations (e.g. whether the initial plume segment was oriented 45° or −45°) were interleaved across trials for consistency and the type of trial was defined in advance. (b) Comparison of the plume re-encounters per meter for the five conditions for real flies (left) and simulated trajectories (right). n=17 for same training, n=15 for no training and opposite training. n=31 simulations for each condition. (c) Overlaid trajectories for flies tracking the indicated plume segments: initial plume, no training, same training (5X), opposite training (1X), and opposite training (5X). Individual trajectories shown as thin black line with a single representative trajectory shown in red and plume’s edge is depicted as dashed line. (d) Same as in (c) except for simulated trajectories. Letters denote statistically different groups (p < 0.05). Details of statistical analyses and sample sizes are given in Table S1.

Figure 1:. A virtual reality system for olfactory navigation

(a) Left: Schematic of the closed loop virtual reality system for plume navigation in which a tethered, walking fly’s heading on an air-supported ball is used to control the angular position of a nozzle delivering a constant airstream, with or without odor. Right, above: The fly’s fictive position is used to control the odor concentration delivered through the airstream. Right, below: Schematic depicting how the position of the airstream and odor concentration change as a head-fixed fly navigates across the fictive plume boundary (dashed line). Trajectory is red when the fly is in the odor and blue outside the odor corridor. (b) Left: an example trajectory of a fly tracking a 50 mm wide odor corridor with an ascending gradient (10-100% apple cider vinegar over 1 m). Trajectory is red when the fly is in the odor and blue outside the odor corridor, with enlarged view of the highlighted segment delineated by dashed box. Right: x-position (crosswind axis), y-position (upwind axis), and upwind speed for the inside/outside bouts shown in the highlighted segment. (c) Distribution of crosswind distances (left) and durations (right) for the inside and outside bouts of 40 flies. Each dot represents a single bout inside the odor corridor (red) or outside the odor in clean air (blue). (d) Comparison of average behavioral metrics for all bouts inside the odor (red) or outside the odor in clean air (blue). Plume distance refers to distance traveled along the longitudinal plume axis while orthogonal distance refers to distance traveled orthogonal to the plume. Each line represents the average for all inside or outside bouts for an individual fly, with the average across flies ±S.E.M. shown in red or blue. n=40 flies. (e) Aligned trajectories inside (red) and outside (blue) the plume. Left: all trajectories (thin lines) for the fly shown in (b) and the scaled average for that individual (thick line). Right: Aligned scaled average trajectories for 40 flies (thin lines) and average across all animals (thick line). (f) Comparison of the inbound and outbound segments of outside trajectories, defined as leading away from (outbound, black) or returning to (inbound, red) the point farthest from the plume in the crosswind direction (see Methods). Top right: Angles between outbound and inbound segments and plume as depicted in schematic at left. Bottom: Pathlength of outbound and inbound segments, plotted on logarithmic scale. Each thin line represents the average for all trajectories of an individual fly, with the inter-individual average ±S.E.M. shown. n=40 flies. (g) The total pathlength of an outside bout as a function of crosswind distance away from the plume for fly data (black stars) or a random-walk model (see Methods and Extended Data Fig. 5) with (dark blue) and without an upwind bias (light blue). Dashed line represents maximal possible efficiency (e.g. when the pathlength is twice the crosswind distance indicating a straight path away from the plume and back through the shortest pathlength). Right top: the distribution of path lengths from real flies (black) and random models, without an upwind bias (dark blue) and with upwind bias (light blue). Right bottom: the probability of returning for $n$ consecutive returns with data from real flies (black) and random models, without an upwind bias (dark blue) and with upwind bias (light blue). n=755 outside trajectories from 40 flies and 755 simulated trajectories. n.s. not significant; ***p < 0.001; ****p < 0.0001. Details of statistical analyses and sample sizes are given in Table S1.

Figure 2:. Flies track plumes that are not aligned with the wind.

(a-c) Flies track plumes with different orientations relative to the wind. For each plume type, we show a single representative trajectory (red, with starting position denoted by black circle); heatmap in greyscale depicting occupancy, and occupancy as a function of distance perpendicular to the plume. (a) n=40 flies; (b) n=21 flies; (c) n=20 flies. (d) Representative trajectory of a fly navigating a ‘jumping’ plume where the plume shifts 20 mm to the right, each time the fly exits the plume. Trajectory is shown in red with starting position denoted by black circle. (e)-(h) Left: aligned and averaged inside and outside trajectories for each plume orientation. Each thin line represents the scaled average for a single individual and the thick line represents the average across all individuals. Right: distribution of entry and exit angles for each plume type. Each thin line represents the average for all exits and entries from a single fly and the thick line represents average across all individuals. (e) n=40 flies; (f) n=21 flies; (g) n=20 flies; (h) n=24 flies. Entry and exit angles were determined by calculating the mean heading in the 0.5 sec prior to and 0.5 sec after crossing the plume’s boundary as shown in (e). (i) Trajectories of flies after the plume vanishes while the fly is on outside bout the plume for 0-degree (vertical), 45-degree and 90-degree plume. For each plume orientation, a representative example is shown with the plume’s boundary indicated by black line, and inside bouts shown in red and outside bouts in grey. The point at which the plume disappears is indicated by the black arrowhead, with the fly’s trajectory over the next two minutes shown in blue. For each, top polar plot shows the distributions of average heading direction while animals walked in closed loop wind in the absence of odor during the two minutes prior to plume tracking (pre, black) and average entry angle during plume tracking (blue). Bottom polar plot shows the average heading direction at indicated times after the plume’s disappearance. Each dot represents an individual fly with vertical n=12 flies; 45-degree n=11 flies; 90-degree n=6 flies. (j) Comparison of the average entry angle during plume tracking (innermost circle) and traveling direction for the indicated times after the plume’s disappearance for all flies in (i). Each circle reflects the indicated time bin, with mean and SEM shown. Details of statistical analyses and sample sizes are given in Table S1. n.s., not significant, ***p < 0.001. Details of statistical analyses and sample sizes are given in Table S1.

Figure 3:. EPG neurons represent a fly’s heading and are required for edge tracking.

(a) Schematic of the central complex neuropils innervated by EPG neurons. Adjacent EPG neurons in the ellipsoid body project to glomeruli in the left and right protocerebral bridge. (b) Representative recording of EPG activity as a fly edge tracks a 10 mm wide vertical plume. Left: trajectory of an individual fly, with inside bouts shown in red and outside bouts in blue. Middle: Heatmap of EPG activity ($\Delta \mathsf{F}∕{\mathsf{F}}_0$) during edge tracking. Each column in the heatmap represents EPG activity in 16 glomeruli in the protocerebral bridge as indicated at top. Right: alignment of the EPG phase estimate (grey) with the animal’s heading (black) during this same edge-tracking trial. Timing of in odor bouts are depicted in red at far right. (c) Heat-map representing the correspondence between an animal’s heading and the estimated phase of the EPG bump during edge tracking. N=16 trials from 9 animals. (d) The amplitude of phase-offset activity bumps in the left and right protocerebral bridge during edge tracking when the animal is walking in the odor (red) or in air (blue). N=16 trials from 9 animals. (e) Representative experiment showing the trajectory of an EPG>GtACR fly navigating a jumping plume in the absence (left) and presence (right) of optogenetic inhibition via LED illumination throughout the edge-tracking trial. (f) Comparison of distance traveled upwind upon re-encountering the plume (top) and number of successful return trajectories (bottom) for EPG>GtACR and UAS-GtACR control flies in the absence and presence of optogenetic inhibition. Each thin line represents an individual fly, with thick line showing mean across flies and SEM. n.s., not significant, **p < 0.01. Details of statistical analyses and sample sizes are given in Table S1.

Figure 4:. Fly trajectories depend on the spatial structure of their olfactory experience.

(a) Left: Representative ‘replay’ experiment in which a fly was allowed to edge track along a 90° plume for 10 minutes, after which the same temporal sequence of odors was presented back to the same fly. Schematic on top depicts the sequence of odor encounters during edge tracking that was replayed to the fly during the replay epoch. Representative trajectory during edge tracking shown as red in odor and dark blue when outside the odor, while trajectory during replay epoch is red inside the odor and cyan when outside the odor. Right: Trajectory of a naïve animal when presented with the same odor sequence. (b) Polar plots showing the net displacement direction when flies are outside the odor (top,) and entry direction when they encounter the odor (bottom) during edge tracking (left, dark blue), replay to the same fly (middle, cyan), or replay in naïve animals (right, black). Each point represents a single bout for an individual fly, with average vector for all flies shown as a line. n=8 flies. (c) The displacement direction and entry direction of flies over sequential outside bouts of edge tracking trials (left, dark blue), replay of the odor sequence to the same flies (middle, cyan), and replay of the odor sequence to a naïve flies (right, black). n=8 flies. The alongwind projection is shown, with 1 denoting straight upwind and −1 denoting straight downwind, to emphasize the change in the direction of outside bouts depending on the conditions in which the fly encounters the odor.

Figure 5:. A behavioral model of edge tracking suggests flies rapidly update their entry angle memories with experience.

(a) Components of the switching space model mapped onto a schematized trajectory of a fly tracking the edge (gray) of a 45-degree plume. When the fly is in the leaving state (orange), it relies on its exit angle memory (${\mathsf{m}}_{\text{exit}}$) which it updates each time it exits the plume (black arrow). When the fly is in the returning state (blue), it relies on its entry angle memory (${\mathsf{m}}_{\text{entry}}$) which it updates each time it enters the plume (red arrow). (b) Representative individual trajectories simulated from the model shown for plumes with different geometries relative to the wind. For each plume, two trajectories are shown individually (dark lines) or an overlay of 25 trajectories (semi-transparent lines). (c) Comparable efficiency of simulated and real fly trajectories revealed by plotting total path length versus total distance in the direction perpendicular to the plume’s boundary for 72 animals and 75 simulations tracking 0-,45-, and 90-degree plumes. Each dot represents a single outside bout. (d) Histograms comparing metrics across population of 72 flies tracking 0-,45-, and 90-degree plumes (gray) or across 75 simulated trajectories (blue). (e) Left: Representative trajectory of a naïve fly provided with two 45-degree plume segments demonstrating that in the absence of training (left), flies continue to progress in the direction required to re-enter the first plume segment. Right: A single operant training session (see Methods), in which a fly was exposed to odor when it spontaneously walked in the direction required to enter the second plume segment (−90° to −135°), was sufficient to enable the fly to subsequently track a 45-degree plume segment oriented in the opposite direction. Note that to enter the second plume segment flies must travel in the same direction as used for operant conditioning (−90° to −135°) and so effectively have a second operant training epoch. (f) Model simulations of the same experiment shown in (e). (g) Top left: Simulation showing how the entry angle memory gradually shifts over multiple odor encounters during operant training paradigm shown in (e), transitioning from pointing to the lower right after tracking the first 45-degree segment to pointing to the lower left. Top right: a plot of the crosswind component of entry angle memory as a function of number of odor encounters during operant training, n=29 simulations, mean +/− std deviation. Bottom: entry angle memory vectors as a function of odor encounters during operant training for same 29 simulations, with individual simulations (thin lines) and average vector (thick line). (h) A single operant training trial enhances the ability to track a 45-degree plume segment oriented in the other direction. Shown is the number of plume re-encounters on the second segment 45-degree plume of both real (left) and model (right) flies. **p < 0.01, ***p < 0.001. Details of statistical analyses and sample sizes are given in Table S1.

Figure 6:. FC2 neurons signal the direction of the plume’s boundary prior to returns.

(a) Left: Schematic of circuitry in the fan-shaped body hypothesized to store entry and exit angle memories. Memories are stored in synapses between state-activated tangential neurons and columnar neurons encoding traveling direction. Right: Schematic of the full model. Crossing the plume’s boundary drives the storage of an entry or exit angle memory that is alternately read out in the returning or leaving states. Memory is conveyed to FC2 neurons representing the fly’s goal direction, and this direction is compared to the fly’s current heading by the PFL neurons that drive corrective steering to align the fly’s current heading with its goal. (b) Representative experiment in which the activity of FC2 neurons in the fans-shaped body and EPG neurons in the ellipsoid body are synchronously recorded as a fly walks in clean air and then tracks the edge of a 10 mm wide jumping plume. After the first 20 entries to the plume, the plume is periodically jumped 3 mm away from the fly during returns (as indicated by blue arrows) to minimize the chance of incidental returns back to the plume’s boundary. (c) Epoch of edge tracking corresponding to the highlighted region in (b). Left: Trajectory of the fly as it exits and re-enters the plume. Middle: EPG and FC2 activity ($\Delta \mathsf{F}∕{\mathsf{F}}_0$) for that edge-tracking epoch plotted by wedge in the ellipsoid body for EPG neurons (greyscale) and by column in the fan-shaped body for FC2 neurons (bluescale). Right: Estimated EPG (black) and FC2 (blue) phases for that epoch with an indication of when the fly is in the odor (red) and when the plume is jumped (blue arrows). (d) Same as for (c) but for the epoch when the same fly was walking upwind prior to encountering the odor plume corresponding to the lower boxed region in (b). (e) Distributions of EPG phases (black) and FC2 phases (blue) during upwind walking (anemotaxis). Thin lines represent individual flies and thick lines represent mean across flies. n=6 flies. Distributions are centered around the upwind direction. (f) Distributions of EPG and FC2 phases in the 1 sec prior to returns to the jumped plume. Distributions are skewed toward the plume boundary (crosswind direction to the boundary indicated by vertical dashed line). (g) Distributions of EPG and FC2 phases in the 0.5 sec prior to exiting of the plume, corresponding to the epochs immediately prior to the returns shown in (f). Direction to the boundary indicated by vertical dashed line. (h) Distribution of the difference between EPG and FC2 phases during jumped returns (as in panel (f), orange) and exits (as in panel (g, blue). Crosswind direction towards the plume boundary indicated by the left dashed line and crosswind direction away from plume indicated by right dashed line. Note FC2 phase leads EPG phase in the direction of the odor boundary during returns. n =6 flies. (i) Representative mean EPG phase (black arrows) and FC2 phase (blue arrows) plotted as direction vectors onto the averaged exit and return trajectories for two flies that were tracking different sides of the plume. Transparent lines correspond to individual trajectories. Phase is plotted at 12 evenly spaced points on an interpolated time base (6 points inside the plume, 6 points outside the plume). (j) Mean progression of EPG phases (black) and FC2 phases (blue) in the 15 sec prior to when flies returned to the plume after a jump. Thin lines represent individual flies, n=6 flies. Bold lines represent mean across flies. n=6 flies. Crosswind direction towards plume boundary indicated by dashed line.