Sequential Non-linear Filtering of Local Motion Cues By Global Motion Circuits

SUMMARY

Many animals guide their movements using optic flow, the displacement of stationary objects across the retina caused by self-motion. How do animals selectively synthesize a global motion pattern from its local motion components? To what extent does this feature selectivity rely on circuit mechanisms versus dendritic processing? Here we used in vivo calcium imaging to identify pre- and postsynaptic mechanisms for processing local motion signals in global motion detection circuits in Drosophila. Lobula plate tangential cells (LPTCs) detect global motion by pooling input from local motion detectors, T4/T5 neurons. We show that T4/T5 neurons suppress responses to adjacent local motion signals whereas LPTC dendrites selectively amplify spatiotemporal sequences of local motion signals consistent with preferred global patterns. We propose that sequential nonlinear suppression and amplification operations allow optic flow circuitry to simultaneously prevent saturating responses to local signals while creating selectivity for global motion patterns critical to behavior.

eTOC Blurb

Barnhart et al show that sequential nonlinear summation of local motion cues shapes feature selectively in the Drosophila visual system. In global motion circuits, adjacent local signals are suppressed presynaptically, whereas specific spatiotemporal sequences of local signals are amplified postsynaptically.

INTRODUCTION

Sensory perception requires the selective extraction of behaviorally relevant signals from the complex milieu of a natural environment. To this end, many sensory systems employ neural circuits that selectively respond to input signals that match specific stimuli of particular behavioral relevance (Wehner, 1987; Smith and Lewicki, 2006; Warrant, 2016). These “matched filters” allow animals to rapidly and robustly respond to salient stimuli while ignoring behaviorally-irrelevant signals in diverse contexts (von der Emde and Warrant, 2016). However, the circuit and cellular mechanisms underlying the emergence of matched filters remain incompletely understood.

Motion vision provides a paradigmatic context in which to examine neural mechanisms that underpin feature selectivity in general, and the emergence of matched filters in particular. Flies use a matched filtering strategy to selectively respond to global optic flow patterns evoked by movement of the animal, with different cells responding to different kinds of body and head movements (Krapp et al., 1998; Kim et al., 2017). Global motion detection depends on two processing steps (Reichardt, 1987; Borst and Egelhaaf, 1990). First, elementary motion detectors estimate local motion signals by comparing luminance contrast at neighboring points in time and space, and respond direction-selectively to motion in a particular direction (Yang and Clandinin, 2018). Building on a substantial body of earlier work, a number of studies have examined the mechanisms mediating elementary motion detection in both the fruit fly Drosophila and in the mammalian retina and cortex (Jagadeesh et al., 1993; Euler et al., 2002; Priebe and Ferster, 2005; Maisak et al., 2013; Takemura et al., 2013; Behnia et al., 2014; Kim et al., 2014; Fisher et al., 2015; Leong et al., 2016; Salazar-Gatzimas et al., 2016; Yang et al., 2016; Arenz et al., 2017; Koren et al., 2017; Mauss et al., 2017; Strother et al., 2017; Vlasits et al., 2017; Gruntman et al., 2018; Wienecke et al., 2018). In Drosophila, visual inputs are received by photoreceptors in the retina and relayed to the first and second optic ganglia, the lamina and the medulla (Figure 1A). In the lamina, different post-synaptic targets of photoreceptors integrate signals from small regions of visual space and provide input to two separate pathways, one selective for contrast increments, an ON pathway, and one selective for contrast decrements, an OFF pathway (Yang and Clandinin, 2018). Direction-selective local motion signals emerge at the third synaptic layer in both the ON and OFF pathways in the dendrites of the columnar neurons T4, which selectively respond to moving light (ON) edges, and T5, which selectively respond to moving dark (OFF) edges (Maisak et al., 2013; Strother et al., 2014; Fisher et al., 2015; Strother et al., 2017). T4/T5 axons are segregated into four retinotopically organized layers in the third neuropil of the visual system, the lobula plate (Maisak et al., 2013). Each layer receives inputs from T4 and T5 cells with the same direction preference, with the four layers of the lobula plate corresponding to the cardinal directions (Figure 1A).

Figure 1. Direction-selective calcium responses in HS dendrites.

A: Schematic illustration of the global motion detection circuit in Drosophila. Left panel: Local motion detection circuits in the lamina and medulla process signals from photoreceptor (PRs) in the retina. Global motion detection circuits in part of the lobula complex, the lobula plate, pool local motion signals. Right panel: Local motion detecting neurons, T4 and T5, project to the four layers of the lobula plate based on their preferred direction of motion (arrows). Lobula plate tangential cell (LPTC) dendrites sample and integrate signals from T4 and T5 neurons. The HS and VS LPTCs largely confine their dendrites to lobula plate layers 1 (front-to-back) and 4 (top-to-bottom), respectively. B: The dendrites of HS neurons labelled using MultiColor Flp-Out (MCFO) labelling. Each optic lobe has three HS neurons, HSN, HSE and HSS. C: Experimental setup. Two photon imaging of GCaMP6f signals in HS dendrites while the fly observed motion stimuli projected on a screen. D: Visual stimulus. Full contrast moving square wave gratings, λ=30°, that spanned the entire stimulus screen (~60°x60°). The diagram on the left shows the stimulus screen over time. The stimulus cycled among 12 different epochs, with gratings moving in a different direction for each epoch. On the right, a space-time plot shows the stimulus time course within an epoch. The y-axis is time, and the x-axis is the stimulus screen position sampled along an axis parallel to the direction of motion, as indicated by the dashed line on the stimulus screen on the left. For each epoch, the grating was static for 1 s, moved at 30°/sec (1Hz temporal frequency) for 2 s, and then stopped and remained static for 1 s before switching to the next epoch. E: Two photon images (maximum projections of z stacks) of GCaMP6f signals in HS dendrites with no stimulus (F₀, left image) or during presentation of a grating moving from front-to-back (F, center image). The image on the right is the difference between the left and center image (ΔF = F-F₀). F: Average projection of GCaMP6f signals in an HSN dendritic branch. G-H: Direction-selective GCaMP6f responses to moving square wave gratings. G: Left panel: GCaMP6f signals, plotted over time, in responses to square wave gratings moving in four different directions. Right panel: magnitude of GCaMP6f responses to square wave gratings moving in 12 different directions, normalized to the maximum response and plotted as a function of the direction of motion in polar coordinates. Signals were measured in the branch indicated by the dashed white line in F. H: Histograms showing the distribution of preferred directions for a population of HS (left panel, N = 34 branches from 16 flies) and VS dendrites (right panel, N = 34 branches from 11 flies). See also Figure S1.

In the second step of global motion detection, downstream circuits – the matched filters – selectively sample and pool local motion signals to extract specific global patterns relevant to behavior. The specific cells underlying spatial pooling of local motion signals are well characterized in flies (Hausen, 1984; Borst and Haag, 2002; Mauss et al., 2015), and are under active investigation in vertebrates (Hedge et al., 2011; Kubo et al., 2014). In flies, the dendrites of lobula plate tangential cells (LPTCs), such as HS (“horizontal system”) and VS (“vertical system”) cells (Borst and Haag, 2002), receive direct synaptic input from T4 and T5. There are three HS neurons and six VS neurons in Drosophila, each of which pools hundreds of T4/T5 inputs distributed across large regions of visual space (Figure 1A-B, S1A). HS and VS cells depolarize in response to motion in a preferred direction (PD) and hyperpolarize in response to motion in the opposite, or non-preferred, direction (ND) (Joesch et al., 2008; Schnell et al., 2010). Depolarization in response to PD motion is driven by direct excitatory input from T4/T5 neurons. Hyperpolarizing responses to ND motion emerge via feedforward inhibition from lobula plate intrinsic (LPi) neurons that receive excitatory input from T4 and T5 cells innervating the ND lobula plate layer (Mauss et al., 2015).

HS and VS selectively respond to global optic flow patterns that correspond to specific movements of the animal (Krapp et al., 1998; Kim et al., 2017). HS neurons detect front-to-back global flow patterns evoked by forward translation or yaw rotation of the animal, whereas VS neurons detect rotary flow patterns evoked by roll rotation. This selectivity emerges, at least in part, from the direction-tuning of HS/VS local motion detector inputs. HS dendrites localize to lobula plate layer 1 and construct matched filters for global front-to-back flow via input from T4/T5 neurons tuned for front-to-back local motion. VS neurons, on the other hand, construct matched filters for rotary flow via input from T4/T5 neurons tuned for local motion in different directions in different parts of the visual field. The prevailing model in the field is that this selective sampling of T4/T5 inputs is sufficient for pattern selectivity, and that HS/VS simply sum inputs – excitatory inputs from T4/T5 and inhibitory signals from LPi neurons – with equal weight regardless of their location in visual space or on HS/VS dendrites (Mauss et al., 2015). However, this model is likely to be too simplistic. HS and VS are graded potential neurons with limited bandwidth, but in blowfly local stimuli can drive membrane depolarizations in VS that are nearly half the magnitude of those evoked by preferred global stimuli (Joesch et al., 2008; Schnell et al., 2010, Krapp et al., 1998). This suggests that simple linear summation of local motion signals could result in saturating responses to non-preferred stimuli, thus preventing selective responses to the preferred pattern. Moreover, recent biophysical modeling suggests that VS weights inputs differently depending on their position on the dendritic arbor (Dan et al., 2018), raising the possibility that dendritic processing may also contribute to feature selectivity in global motion detection circuits.

In this work, we sought to address two questions. First, do global motion detection circuits sum local motion signals in a non-linear fashion? Second, does nonlinear weighting occur via circuit mechanisms upstream from LPTCs, via dendritic processing within LPTCs, or both? To address these questions, we used in vivo two-photon microscopy to measure HS/VS and T4/T5 calcium responses to various combinations of local motion signals. We found, first, that T4/T5 neurons suppress responses to adjacent motion inputs. This suppression emerges from the spatial structure of individual T4/T5 receptive fields, combined with the precise spatial overlap between neighboring cells. In addition, we found that HS/VS dendrite morphology correlates with direction selectivity. Individual dendritic branches are oriented such that PD stimuli sweep across each branch from its distal tip towards more proximal regions. These oriented dendrites discriminate between local motion cues arranged in preferred versus non-preferred spatiotemporal sequences by specifically amplifying responses to PD sequences of local motion signals. Finally, global motion discrimination is also apparent in fly behavior, in a quantitative assay for visually evoked turning behavior. Altogether, our results suggest that suppression of adjacent local signals along with amplification of global, spatiotemporal sequences, at sequential layers of motion processing circuits, promotes selective coding of behaviorally relevant global motion patterns.

RESULTS

Direction-selective calcium responses to global motion in HS and VS dendrites

To determine whether LPTCs weight local stimuli in a non-linear fashion, we set out to measure HS and VS dendritic calcium responses to combinations of local motion stimuli arranged in specific spatial and spatiotemporal patterns. We expressed a genetically encoded calcium indicator (GCaMP6f (Chen et al., 2013)) in either HS or VS neurons using specific GAL4 drivers. Then, we used in vivo two-photon microscopy to measure dendritic calcium signals while presenting structured visual stimuli on a screen in front of the fly (Figure 1C). Before we could measure calcium responses to specific combinations of local motion stimuli, we had to map the preferred direction (PD) of motion and receptive field (RF) positions for HS and VS dendrites. We first measured PDs for individual HS or VS dendritic branches by measuring calcium responses to moving square wave gratings that spanned the entire stimulus screen (60°x60°; Figure 1D). The screen was positioned such that motion signals primarily stimulated the dorsal portion of the eye, and we therefore observed strongest calcium signals in the dorsal HS neuron, called HSN (Figure 1E). HSN tertiary dendrites exhibited strong calcium responses, but primary or secondary dendrites had only modest responses (Figure 1E-F). We therefore measured PDs in tertiary branches. As expected based on HS dendrite localization in lobula plate layer 1, HS tertiary dendrites responded primarily to gratings moving from front-to-back across the visual field, with little branch-to-branch variability in PD (Figure 1G-H).

All six VS neurons have dorsal dendrites (Figure S1A), and as for HS we measured calcium responses to moving gratings in tertiary dorsal dendrites. VS tertiary dorsal dendrites are more heterogeneous than HSN tertiary dendrites, with some oriented along the dorsal-ventral axis and others along the medial-lateral axis (Figure S1A, D,H). VS dendrites also exhibited more heterogeneity in direction preference: some dendrites responded most strongly to top-to-bottom motion, whereas other dendrites responded preferentially to front-to-back motion, consistent with previous measurements from blowflies (Figure 1H, S1E,I). These direction preferences are consistent with evidence in blowflies and Drosophila showing that although primary VS dendrites localize to lobula plate layer 4, some VS neurons send higher order dendrites to the other lobula plate layers (Scott et al., 2002; Hopp et al., 2014).

Local calcium responses to local motion stimuli in HS and VS dendrites

After measuring the PD for a particular HS or VS tertiary dendrite, we then mapped RF centers for dendritic segments within that branch. We presented local PD motion stimuli – square wave gratings that spanned 13.5° of visual space – at different positions on the stimulus screen (Figure 2A) and measured local calcium responses in 2 μm long dendritic segments for each grating position (Figure 2B-G, S1D,F-H,J-K). Dendritic segments exhibited large calcium increases in response to an optimal grating position, with response amplitudes decreasing as the grating position moved away from this position, allowing us to calculate a precise RF center (Figure 2C-H, S1F-G,J-K). These data revealed that RF centers map onto tertiary HS and VS dendrites in a retinotopic fashion (Figure 2G-H, S1G,K), again consistent measurements in blowfly (Hopp et al., 2014). We were also able to measure responses to local stimuli in secondary dendrites in VS, but they were much weaker than in the tertiary branches (Figure S1N). Moreover, short dendritic segments in secondary branches responded to a much broader range of stimuli positions (Figure S1O). Thus, we restricted subsequent experiments to tertiary dendrites in both HS and VS dendrites.

Figure 2. HS dendrite responses to local motion stimuli.

A: Local stimulus. Same as the stimulus in Figure 1D, except that the moving gratings were restricted to an aperture spanning only 13.5° of the stimulus screen, moving in the PD, presented at a different screen position during each epoch. B: Average projection of GCaMP6f signals in the HSN dendritic branch from Figure 1F, shown again here for ease of comparison. C-G: Local GCaMP6f responses to local gratings in HS dendrites. C-D: Response of the dendrite in B to local grating 1 (C) and local grating 2 (D), presented at different positions on the stimulus screen. E-F: GCaMP6f responses to local grating 1 (E) or local grating 2 (F), plotted over time, in the ROIs indicated by the purple (ROI i) and red (ROI ii) lines in E. G: Amplitudes of GCaMP6f responses to local gratings at each position on the stimulus screen, measured in ROI i (purple) and ROI ii (red). Circle size and color saturation indicate the amplitude of the response at each screen position, normalized to the maximum response for each ROI. The dashed boxes indicate the positions of gratings 1 and 2. H: Receptive field (RF) centers, plotted as a function of stimulus screen position, for overlapping, 2 mm segments of the dendrite in E (see Methods). The colored circles are the RF centers for ROI i (purple) and ROI ii (red). See also Figure S1.

HS and VS dendrites exhibit sublinear summation of adjacent local motion signals

Global optic flow patterns are composed of populations of local motion signals that, at any point in time, cover a large swath of visual space. If global motion circuits simply add up these local motion signals in a linear fashion, then HS or VS responses to the simultaneous presentation of pairs of local motion stimuli should be the sum of the responses to each individual stimulus, regardless of their relative positions in space. To test this, we presented combinations of local stimuli. Each local cue was a single 13.5° tall dark edge that expanded 13.5° in the PD over 0.5 s (speed = 27°/s). We presented moving dark edges alone or in pairs, with pairs of edges offset in space along the PD axis (Figure 3A). As for local moving gratings, individual moving edges drove strong local responses in HS and VS dendrites (Figure 3C-K, S2A-C). Simultaneous presentation of pairs of moving edges offset by 13.5° in the PD drove calcium responses that were significantly smaller than the linear sum of the responses to individual edges (Figure 3L-N,R; S2B-C, F). Sublinear summation was apparent only for adjacent edges; moving edges offset by 27° summed in an approximately linear fashion (Figure 3O-R; S3F). Suppression of adjacent local motion signals in LPTC dendrites was also spatially asymmetric. Within a particular dendritic segment, local motion signals offset by 13.5° in the PD reduced calcium responses to a greater extent than signals offset in the ND (Figure 3L-N,R; S2B-C,F). We measured the same spatially asymmetric suppression of responses to adjacent edges at a faster stimulus speed (speed = 54°/s, Figure 3S). GCaMP6f signals saturate at high calcium concentrations (Chen et al., 2013), but saturation of the indicator cannot explain these results, as local calcium responses to moving edges did not simply plateau as would be expected if the indicator was saturated. Instead, adjacent moving edges suppressed responses so that the response to two moving edges at once was weaker than the response to one edge (Figure 3L-N). Thus, these data demonstrate that local motion signals are not weighted equally: responses to signals that appear in closely abutting regions of visual space are specifically suppressed.

Figure 3. HS dendrites exhibit sublinear summation of local motion signals.

A: Stimulus screen, over time (left) and space-time plots (right) depicting the local visual stimulus. A single moving dark edge expanded in the PD, covering 13.5° of visual space over either 0.5 or 0.25 seconds (stimulus speed = 27°/sec or 54°/sec) before disappearing. We presented dark edges alone (“single edge”) or in pairs (“edge pair”) offset by either 13.5° or 27°. B: Average projection of GCaMP6f signals in an HSN dendritic branch. C-Q: GCaMP6f responses to moving dark edges in the HS dendrite shown in part B. C: XT plot showing the timing and position of a single moving dark edge, edge 1. D: GCaMP6f signals, plotted over time, in either the whole dendritic branch (yellow line in B) or smaller regions of interest (ROI i-iii, white dashed lines in B). E: Response of the dendritic branch to a single moving edge at position 1, with the baseline fluorescence subtracted. F-Q are the same as C-E, except with different stimuli: a single moving edge at position 2 (F-H), a single moving edge at position 3 (I-K), edges 1 and 2 at the same time (L-N), and edges 1 and 3 at the same time (O-Q). In M and P, the dashed lines are the expected responses, based on the sum of the responses to single edges, whereas the solid lines are the measured responses. Arrowheads in E, N and Q point to the distal portion of the dendrite stimulated by edge 1 (E). The response to edge 1 is strongly suppressed by the addition of edge 2 (N), but not edge 3 (Q). R-U: Sublinear responses to pairs of moving edges in HS dendrites. A metric capturing the nonlinearity of the response ((M-E)/E; zero indicates linear summation and negative and positive values indicate sublinear and supralinear summation, respectively) is plotted as a function of distance between the edges. Positive distances indicate offset in the preferred direction, whereas negative distances indicate offset in the opposite, non-preferred direction, as shown in A. Responses are shown for dark (R-S) and light edges (T-U) moving at either 27°/s (R,T) or 54°/s (S,U). Box and whisker plots show the median (black line), interquartile range (boxes), 1.5 times the interquartile range (whiskers). Dot plots showing each data point are overlaid on the box plots. N indicates the number of ROIs; the total number of flies for R, S, T, and U was 13, 5, 7, and 3, respectively. Asterisks indicate p < 0.01 (*), p < 10⁻⁵ (**), and p < 10⁻¹⁰ (**), Independent Sample T-tests. See also Figures S2–4.

Local motion detection circuits are split between ON (T4) and OFF (T5) pathways. We performed the bulk of our experiments using moving dark edges (OFF pathway), but we also measured responses to moving light edges (ON pathway) in HS dendrites. We were only able to measure responses in a handful of dendrites, since responses to moving light edges were significantly weaker than responses to moving dark edges (Figure S3). This was particularly true for the distal portions of HS tertiary dendrites (Figure S3F), suggesting that input from ON and OFF pathways onto HS dendrites may not be spatially uniform. However, for the small number of dendrites for which we could measure moving light edges responses, we observed spatially delimited, asymmetric suppression of calcium responses to pairs of moving light edges, as for moving dark edges (Figure 3T-U).

We reasoned that this local suppression could contribute to the spatial frequency tuning of HS. In particular, one prediction of this suppression is that HS cells should respond more strongly to global patterns with lower spatial frequencies (i.e., with edges that are farther apart). To test this, we presented widefield square wave gratings moving in the PD with different grating wavelengths, ranging from 10° to 100°, holding either velocity or contrast frequency constant (Figure S4). In both cases, we found that HS dendrites responded strongly to gratings with spatial periods of 20° or greater, and only weakly to gratings with 10° spatial periods. This is consistent with previously published behavioral experiments, in which 10° gratings drove much weaker optomotor responses than 20° and 30° gratings (Gotz and Wenking, 1973). Moving gratings have alternating light and dark edges; as light edges drive very weak HS calcium responses, the spacing between dark edges is the relevant consideration. We infer that for 10° gratings, dark edges separated by 10° suppressed each other, whereas for 20° (or larger) gratings, dark edges were too far apart for suppression to occur. These results suggest that local suppression of adjacent local motion signals shapes HS spatial frequency tuning.

Suppression of adjacent local motion cues in T4/T5 axons

The suppression we measured in HS dendrites could emerge in the dendrites themselves, or it could reflect suppression at the level of the T4/T5 inputs. Consistent with the later, the spatial asymmetry we measure in HS dendrites is reminiscent of the receptive field (RF) structure of T4 and T5 neurons, as these cells have inhibitory surrounds that extend in the PD but not the ND (Haag et al., 2016; Leong et al., 2016; Salazar-Gatzimas et al., 2016; Haag et al., 2017, Gruntman et al, 2018; Wienecke et al., 2018). We therefore hypothesized that suppression of responses to adjacent stimuli in HS and VS dendrites might emerge from the antagonistic center-surround structure of their presynaptic inputs. If this hypothesis is correct, T4 and T5 axon terminals should also exhibit reduced calcium signals in response to adjacent, but not distant, local motion signals. To test this, we first measured T4/T5 responses to widefield square wave gratings moving in different directions, and we found, as previously observed, that T4/T5 axons were segregated within the lobula plate based on their direction preference (Figure S5A-D). We then mapped T4/T5 RF centers, using the procedure described above, and measured calcium responses in axon terminals to simultaneous presentations of pairs of moving dark or light edges (Figure 4A). Adjacent moving edges did indeed suppress calcium response amplitudes, compared to responses to single moving edges, with the same spatial asymmetry observed in HS and VS dendrites (Figure 4C-N,R-U). More distant edges did not suppress each other (Figure 4O-U). All together, these results demonstrate that the global motion circuit uses T4/T5 center-surround antagonism to selectively suppress responses to adjacent local motion inputs.

Figure 4. Sublinear summation of local motion signals by T4/T5 neurons.

A: Stimulus screen, over time (left) and space-time plots (right) depicting the local visual stimulus (as in Figure 3A). B: Average projection of GCaMP6f signals in T4 and T5 axons. Three ROIs are demarked by yellow circles. C-Q: GCaMP6f responses to dark edges moving 27°/s in the T4/T5 axon terminals shown in B. C,F,I,L,O: Space-time plots of the stimulus. D,G,J,M,P: GCaMP6F signals, plotted over time, in each of the three ROIs in B. E,H,K,N,Q: Responses of T4/T5 axon terminals to moving dark edges, with baseline fluorescence subtracted. The dashed lines in M and P are the expected responses, based on the sum of the responses to single edges, whereas the solid lines are the measured responses. The arrowheads in E, N and Q point to the T4/T5 axon terminals stimulated by edge 1 (E) and suppressed by edge 2 (N) but not edge 3 (Q). R-U: Sublinear responses to pairs of moving edges in T4/T5 axons. Responses are shown for dark (R-S) and light edges (T-U) moving at either 27°/s (Q,S) or 54°/s (R,T). The nonlinearity of the responses is captured using the same metric as in Figure 3. N indicates the number of ROIs; the total number of flies for R, S, T, and U was 12, 5, 5, and 5, respectively. Asterisks indicate p < 0.01 (*), p < 10⁻⁵ (**), and p < 10⁻¹⁰ (**), Independent Sample T-tests. See also Figure S5.

LPTC orientation correlates with direction selectivity

Our results thus far suggest that mechanisms presynaptic to LPTCs facilitate selective responses to preferred global motion patterns. We next wanted to know whether LPTC dendritic processing also plays a role in LPTC feature selectivity. Over the course of our experiments, we observed that HS/VS dendrite morphology appeared to correlate with direction selectivity. Specifically, HS and VS dendrites that preferentially responded to front-to-back motion tended to extend along the medial-lateral axis of the fly, whereas VS dendrites that responded to top-to-bottom motion tended to extend along the dorsal-ventral axis (Figure 1E-G, Figure S1D-E,H-I). For front-to-back sensitive HS and VS dendrites, local motion stimuli presented in the frontal part of the visual field stimulated distal portions of the dendrite, and stimuli presented more laterally stimulated more proximal portions of the dendrite (Figure 2G-H, 3C-K, S1H,K). For top-to-bottom sensitive VS dendrites, more dorsal local motion cues stimulated distal portions of the dendrite whereas more ventral cues stimulated proximal dendritic segments (Figure S1D,G). In VS branches with orthogonal orientations and direction preferences, single dark edges moving in the PD evoked a wave of increasing calcium along the length of the dendrite, starting at the distal dendritic tip and then sweeping towards the proximal portion of the branch (Figure 5A-F).

Figure 5: LPTC dendrite orientation correlates with preferred direction of motion.

A-F: GCaMP6f responses to dark edges moving in the preferred direction in two VS dendrites. The two dendrites have orthogonal orientations in the brain (A,D) and orthogonal preferred directions (B,E). A,D: Average projections of GCaMP6f signals. B,E: Polar plot depicting the directional tuning for the branches in A and D. Arrows indicate the PD for each branch. C,F: Spatiotemporal profiles of GCaMP6f responses to PD moving dark edges, measured at one micron increments along the length of the dendrites and plotted over time. The slope (dashed line) reflects a sequential increase in the GCaMP6f signal as the edge sweeps from distal-to-proximal along the length of the dendrite. The yellow ROIs shown on the images in A and D indicate the regions in which GCaMP6f signals were measured. G: Branch orientation plotted as a function of preferred direction of motion for populations of HS (open circles, N = 29 branches from 16 flies) and VS (black circles, N = 24 branches from 14 flies) dendrites. Pearson’s correlation coefficient = 0.87, p < 10^-16.

To systematically examine whether dendrite orientation correlates with direction preference, we measured direction selectivity and dendrite orientation for many individual HS and VS tertiary dendrites. We measured dendrite orientation by mapping RF centers for short dendritic segments, and then measuring the angle of dendrite orientation, from distal to proximal, based on these RF center positions (as in Figure 2G-H). We found that dendrite orientation and direction preference are indeed correlated across HS and VS dendrites, such that PD motion signals stimulate the distal dendrites first and then move proximally towards the axon (Figure 5G). More specifically, HS cells prefer front to back motion and have homogenous direction preferences and dendrite orientations across their visual field; conversely, VS cells prefer patterns of motion corresponding to roll, and have heterogeneous local direction preferences (Krapp et al., 1998; Hopp et al., 2014). Nonetheless, the correlation between orientation of each individual dendrite and its particular local direction preference is robust across a wide range of angles, including the dorsal dendrites in VS neurons, which have dramatically divergent orientations (Figure 5A-F, Figure S1).

LPTC dendrites selectively amplify responses to PD spatiotemporal sequences of local motion signals

T4/T5 RF structure likely accounts for nonlinear summation of simultaneous, adjacent local motion signals. In addition, the correlation between dendrite orientation and direction selectivity suggests that dendritic mechanisms could contribute to processing of global motion signals. In particular, HS/VS dendrites could process motion signals over longer temporal and spatial scales, compared to T4/T5, as long-range motion signals sweep from distal-to-proximal across tertiary dendrites. HS/VS dendrites could suppress responses to spatiotemporal sequences. For example, as local motion signals move along the length of a dendrite, membrane depolarization could reduce the driving force for further depolarization (London and Hausser, 2005). Such synaptic saturation would result in sublinear responses to sequences of local motion signals. In this case, local motion signals combined in a global spatiotemporal sequence that stimulates an individual dendritic branch should drive smaller responses than individual local motion signals. Alternatively, HS/VS dendrites could amplify responses to spatiotemporal sequences. Cortical pyramidal dendrites with active conductances exhibit supralinear summation of spatiotemporal sequences that process from distal to proximal along the length of the dendrite (Branco et al., 2010). HS/VS dendrites could similarly boost responses to spatiotemporal sequences of local motion signals that stimulate the dendrite from distal-to-proximal.

To discriminate between these possibilities, we presented sequences of local motion stimuli precisely positioned to stimulate individual dendritic branches of HS or VS cells. We presented two to four light or dark edges moving locally in the PD either alone or sequentially. We offset the local motion signals in space and time such that they created a PD spatiotemporal sequence that swept along the dendrite from distal-to-proximal (Figure 6A, “PD sequence”). We found that responses to these PD sequences were amplified relative to responses to individual moving edges in HS (Figure 6C-D,F, S2D-E,G). VS branches with a wide range of PDs (and thus dendrite orientations) also exhibited amplified responses to PD sequences (Figure S2H). Strikingly, we only observed supralinear summation of local motion signals in response to PD spatiotemporal sequences. We also presented sequences of local motion signals arranged such that they, in aggregate, formed an ND spatiotemporal sequence that stepped backwards along the dendrite, from proximal-to-distal (Figure 6A, “ND sequence”). These ND sequences contained PD local motion signals identical to those in PD sequences, but in this case the local motion signals summed in a linear fashion (Figure 6C, E-F). Sequences of PD local motion signals that stimulated adjacent HS branches from dorsal-to-ventral or ventral-to-dorsal also summed in a linear fashion (Figure S6A-D). Thus, HS and VS tertiary dendrites exhibit global motion discrimination: rather than simply adding up sequences of local motion signals in a linear fashion, they selectively amplify responses to spatiotemporal sequences consistent with their preferred global motion patterns.

Figure 6: HS dendrites amplify responses to PD spatiotemporal sequences.

A: Space-time plots of compound global motion stimuli. Local moving dark edges were offset in time and space such that they moved coherently in the preferred direction (“PD sequence”) or stepped backwards along the dendrite in the opposite direction (“ND sequence”). B: Average projection of GCaMP6f signals in an HSN dendrite. C: Spatiotemporal profiles of GCaMP6f signals, measured at one micron intervals within the ROI shown by the white dotted line in B, plotted over time for the single moving edges (edge1, edge2, and edge3 alone) as well as the PD and ND sequences. D,E: GCaMP6f responses, integrated over the entire dendrite and plotted over time for three local moving edges (gray lines), the expected response to sequential presentation of the edges, based on the arithmetic sum of the responses to each individual edge (dashed lines) and the measured responses to the PD sequence (D, green line) and ND sequence (E, magenta line). F: Supralinear summation of responses to PD spatiotemporal sequences of dark and light edges moving at either 27°/s or 54°/s in HS dendrites. G: Linear summation of responses to spatiotemporal sequences in T4/T5 axons terminals. The nonlinearity of the responses is captured using the same metric as in Figure 3. See also Figures S2, S6–8.

Previous work has shown that optogenetic silencing T4/T5 prevents LPTC responses to motion stimuli (Mauss et al 2017), so amplification of PD sequences likely depends on excitatory input from T4/T5. Moreover, supralinear summation of responses to PD sequences in HS/VS dendrites could, in principle, reflect amplification that occurs in T4/T5. To test this, we measured T4/T5 responses to spatiotemporal sequences. We measured GCaMP6f responses in a group of T4/T5 axons whose receptive fields spanned the region of space covered by the motion of three adjacent edges (Figure S5F). We found that selective amplification of PD sequences is absent from T4/T5 axon terminals. Responses to either PD or ND sequences were indistinguishable, and well predicted by the sum of the responses to individual edges (Figure 6G, S5G-H). In addition, we measured calcium signals in tertiary branches stimulated by PD sequences and in adjacent, unstimulated branches (Figure S6G). We measured no calcium signals in HS dendritic branches adjacent to those stimulated by PD sequences (Figure S6H-I), demonstrating that tertiary branches do not interact with each other, and that amplification emerges within the stimulated branches themselves, and does not reflect back-propagation of voltage signals from the soma. Finally, tertiary HS and VS dendrites bear small spine-like structures, “branchlets” (Figure S7A), that are enriched for acetylcholine receptors (Leiss et al., 2009). If amplification occurred at the level of the inputs to HS and VS, then these branchlets should also invariably reflect that amplification. However, although we invariably measured amplification in the dendritic shafts adjacent to the branchlets (12/12), less than half (5/12) of the branchlets we measured exhibited amplification (Figure S7B-G). Taken together, these results demonstrate that amplification of PD sequences occurs via a dendritic mechanism arising predominantly in the tertiary dendrite.

Next, we systematically determined the time interval over which supralinear summation occurs by presenting pairs of moving dark edges that stimulated distal and proximal portions of tertiary HS dendrites (Figure S8A). We varied the timing of motion onset for the two edges, with temporal offsets ranging from −1 s (proximal dendritic segment stimulated first, “ND sequences”) to +1 s (distal dendritic segment stimulated first, “PD sequences”), in 250ms increments (Figure S8B). We then measured calcium signals within the short distal and proximal segments directly stimulated by the pair of moving edges (Figure S8A, S8C-I). For temporal offsets of 0s, the edges appeared simultaneously and, as we observed above (Figure 3), calcium responses were specifically suppressed in the distal portion of the dendrite (Figure S8F, S8H, I). The edges expanded across 13.5° over 0.5 s (corresponding to edge motion of 27°/sec), so for temporal offsets of +/− 0.5 s, the second edge appeared as soon as the first edge disappeared (as in Figure 6), whereas for temporal offsets of +/− 1 s, there was a 0.5s lag between the time the first edge disappeared and the second appeared. As expected from our previous measurements, amplification occurred in response to PD sequences, only in the more proximal region of the dendrites. We also observed amplification at time intervals ranging from 0.5 sec to 1 second, thereby revealing a persistent biophysical mechanism that was slow to emerge (as it was not detected at a temporal offset of 250ms; Figure S8G-I).

Global motion discrimination in optomotor turning behavior

To determine whether global motion discrimination is apparent at the level of fly behavior, we performed a series of behavioral experiments using a fly-on-ball experimental setup (Clark et al., 2011)(Figure 7A). In this setup, Drosophila exhibit strong optomotor responses, turning in response to global motion stimuli. We tested whether flies could discriminate between stimuli with equivalent local motion signals arranged in sequences that either matched (“Matched Sequence”) or opposed (“Opposed Sequence”) the direction of local motion (Figure 7B, see Methods). In this behavioral assay, the sudden appearance of a visual feature, like a moving edge or bar, triggers a startle response (Silies et al, 2013). In order to disentangle this startle response from true motion responses, we presented 2° static bars for 0.5s before presenting sequences of moving edges. As expected, we observed a startle turning response to the static bars, with the flies turning in opposite directions for the Matched and Opposed stimuli because the static bars were on opposite sides of the screens (Figure 7C, light gray shading). Then we observed turning response to the Matched and Opposed sequences of four local edges (Figure 7C, dark gray shading). When comparing turning response to these sequences for a population of flies, we excluded the startle response to the static edges (Figure 7D, see Methods). We found that flies exhibit global motion discrimination for sequences of moving light edges: Matched Sequences drove significantly larger turning responses than Opposed Sequences (Figure 7C-D). Since the local motion signals for both the Matched and Opposed sequences were identical, this result argues strongly that local signals are summed in a nonlinear fashion at the level of fly behavior, just as they are within HS dendrites, since linear summation should, by definition, result in equivalent behavioral responses to the two sequences. However, consistent with previous studies (Fujiwara et al., 2017; Kim et al., 2017), we cannot attribute global motion discrimination in fly behavior to HS alone, since the flies exhibited significant turning responses to light edges (7C-D) but not dark edges (7E) whereas HS exhibited larger calcium responses to dark edges (Figure S3, see Discussion).

Figure 7. Global motion discrimination in optomotor behavioral responses.

A: Experimental setup. B: Compound global motion stimuli. Local moving light edges spanning the entire vertical extent of the stimulus screen were offset in time and space such that they formed global patterns that either matched (“Matched Sequence”) or opposed (“Opposed Sequence”) the direction of local motion. The same stimuli were presented on each of the three screens surrounding the fly. Static 2° light bars were presented for 0.5 s prior to the onset of motion, in order to avoid startle responses to the sudden appearance of moving edges. C: Fly turning responses to light edges moving 27°/sec (left panel) or 54°/sec (right panel) that formed either matched (green lines) or opposed (magenta lines) sequences, plotted over time. The light and dark gray boxes indicate presentation of static 2° light bars (light gray) followed by the sequential presentation of four moving light edges (dark gray). D-E: Integrated turning responses to light (D, N=19 flies) and dark (E, N=23 flies) edges in local-global matched or opposing patterns.

DISCUSSION

Nonlinear summation of local motion signals provides a mechanism for constructing reliable matched filters

Global motion circuits in the fly sum local motion signals differently, depending on their relative spacing and timing (Figure 8). For local signals that occur simultaneously, adjacent signals sum in a sublinear fashion while more distant signals sum linearly (Figure 3). Our results indicate that this suppression of simultaneous, adjacent signals emerges in the inputs to HS and VS cells, T4/T5 cells, and is caused by overlap between their center-surround receptive fields (Figure 4). In addition, PD spatiotemporal sequences of local signals that stimulate HS and VS dendrites from distal to proximal sum in a supralinear fashion (Figure 6). Our results indicate that this amplification of PD spatiotemporal sequences occurs within HS/VS dendrites (Figure 6, S6). We propose that this two-stage, nonlinear summation of local motion enhances the ability of HS and VS cells to function as matched filters for specific global motion patterns.

Figure 8. Sequential nonlinear summations of local motion signals enable selective encoding of global motion patterns.

Global motion detection circuits suppress responses to adjacent location motion signals at the level of T4/T5 axons and amplify responses to coherent PD spatiotemporal sequences at the level of LPTC dendrites.

Matched filters must reliably respond to preferred stimuli while ignoring non-preferred stimuli in many different contexts. In different environments, the number of local motion signals that comprise global motion patterns varies depending on the number of features in the visual scene. For example, self-motion evokes more local motion cues in a dense forest with many trees than in a sparse forest with fewer trees. Also, the strength of these local signals depends on image contrast, which can vary substantially. Thus, qualitatively similar global flow patterns evoked by a particular type of self-motion, for example, turning of the animal, can have quantitative differences in the number and strength of local motion signals. Nonlinear summations, both suppressive and enhancing, of these local signals may allow circuits to selectively respond to preferred global patterns across a broad range of visual scenes. Specifically, amplification of specific spatiotemporal sequences may allow LPTCs to robustly respond to their preferred global stimuli even when local motion signals are sparse or weak. Suppression of simultaneous, adjacent local signals, on the other hand, could allow the circuit to ignore non-preferred stimuli, like small object motion, even when local signals are strong. In this framework, nonlinear summations of local motion signals complement additional, previously described mechanisms for LPTC response selectivity, including feedforward inhibition from null direction stimuli (Mauss et al., 2015), gap junction dependent smoothing of responses among multiple VS cells (Elyada et al., 2009), pooling from multiple HS and VS cells in subsequent processing steps (Suver et al., 2016), and synergy between global optic flow and body motion in HS (Fujiwara et al., 2017).

The center-surround structure of T4/T5 neurons tunes downstream circuits

Direction-selective local motion signals first emerge on the dendrites of T4 and T5 neurons. To define the algorithms underlying the emergence of these local motion signals, several labs have recently measured T4/T5 receptive fields (Haag et al., 2016; Leong et al., 2016; Salazar-Gatzimas et al., 2016; Haag et al., 2017, Gruntman et al, 2018; Wienecke et al., 2018). T4/T5 RFs have asymmetric center-surround structures, in which an inhibitory lobe is offset from an excitatory center only in the preferred direction of motion, contributing to the emergence of direction selectivity. Our experiments suggest that T4/T5 RF structure also results in the suppression of adjacent local motion signals, thereby tuning the responses of downstream circuits to more complex motion stimuli, suppressing high spatial frequency inputs. This suppression occurs because neighboring T4/T5 RFs overlap. Specifically, T4/T5 RFs are approximately 20–30° wide (Leong et al., 2016; Gruntman et al, 2018; Wienecke et al., 2018), but RF centers for neighboring T4/T5 neurons are offset by 5°, corresponding to the angular resolution of the visual system. Both the excitatory center and the inhibitory lobe span ~10–15°, with the inhibitory lobe offset ~10–15° in the PD relative to the RF center. Thus, the inhibitory lobe of a T4/T5 cell overlaps with the excitatory lobes of neighboring T4/T5 cells offset in the PD (but not the ND), resulting in suppression of responses to adjacent local motion signals. In addition to shaping the estimation of local motion signals, the structure and spacing of T4/T5 center-surround receptive fields has functional implications for downstream circuits, including shaping spatial frequency tuning in HS.

Dendrite orientation as a cellular mechanism for feature selectivity

Our results demonstrate that properly oriented dendrites allow HS and VS neurons to implement global motion discrimination by selectively amplifying responses to specific spatiotemporal sequences of local motion inputs. This selective amplification of preferred direction, long-range motion within HS and VS offers an interesting parallel to local motion detection by circuits upstream from T4/T5. T4/T5 cells compare luminance levels between points in space over short spatial and temporal scales, causing spatiotemporal changes in luminance corresponding to PD motion to be enhanced, and causing those corresponding to ND motion to be suppressed. HS and VS also exhibit PD motion enhancement, but over larger spatial and temporal scales than T4/T5, and instead of converting non-directional inputs into direction-selective signals, instead act on inputs that are themselves direction selective to further enhance their selectivity. In this view, tertiary branches of HS/VS dendrites serve as “delay arms”, creating the differential temporal filtering required for PD enhancement. Thus, HS and VS dendrite morphologies, rather than simply reflecting metabolic and developmental constraints on wiring (Cuntz et al., 2010), also inform function.

Several other cell types have been shown to orient their dendrites in a functionally relevant manner, including starburst amacrine cells in the mammalian retina (Hausselt et al., 2007), octopus cells in the mammalian cochlear nucleus (McGinley et al., 2012), and loom-detecting neurons in the Drosophila lobula plate (Klapoetke et al., 2017). Single dendrites from cortical pyramidal neurons have also been shown to discriminate among temporal sequences of inputs, with inputs that move sequentially along the dendrite from distal to proximal driving larger somatic depolarizations (Branco et al., 2010). Biophysical modeling suggests that an impedance gradient along the length of the dendrite and nonlinear voltage-dependent conductances are sufficient for spatiotemporal sequence discrimination (Branco et al., 2010). However, a simple voltage-dependent model is unlikely to account for global motion discrimination in HS/VS dendrites. The supralinear summation of global PD sequences took more than 250ms to emerge, and persisted even for 1s offsets between pairs of moving edges. These timescales are inconsistent with the rise and decay of voltage signals. Instead, global motion discrimination may be mediated by asymmetric localization of neurotransmitter receptors or second messenger signals, as proposed for T4 dendrites (Strother et al., 2017). Regardless of the cellular mechanism, our results, along with evidence from mammalian sensory systems (Hausselt et al., 2007; McGinley et al., 2012), suggests that the specific spatial orientations of dendrites contribute to neural processing.

We anticipate that future work will uncover links between branch orientation-dependent dendritic processing of sensory circuits and behavioral outputs. By using a quantitative assay for visually induced optomotor response in walking flies, we found that the global motion discrimination we observed in HS and VS dendrites is also apparent in fly behavior. Specifically, we demonstrated that spatiotemporal sequences of local motion stimuli drive larger turning responses when local motion matches the long-range motion of the sequence (Figure 7). However, we found that HS dendrites and fly optomotor responses have different contrast tuning. Although HS dendrites do amplify responses to sequences of moving light edges, moving dark edges drive much stronger responses. In our behavioral assay, on the other hand, we only observed responses to moving light edges. The relationships between HS/VS activity and specific optomotor behaviors are complex. Unilateral activation of HS is sufficient to drive turning in walking flies (Fujiwara et al., 2017), but inactivation of HS has only been shown to affect head movements, and not body optomotor responses (Kim et al., 2017). VS detects roll rotation and thus is likely to be primarily relevant in flight, rather than in walking flies (Kim et al., 2017). HS and VS are the most well characterized LPTCs in Drosophila, but many other LPTCs have been identified in other fly species (Hausen 1984). Thus, other LPTCs, in addition to or instead of HS and VS, likely contribute to global motion discrimination in fly behavior. Ongoing efforts to identify and characterize other LPTCs in Drosophila will enable future efforts toward understanding the cellular basis for global motion discrimination, as well as other complex motion vision computations such as figure-ground discrimination (Fox et al., 2013; Fox and Frye 2014; Aptekar et al., 2015). Given the broad utility of the dendritic mechanism we have described in HS and VS cells for increasing feature selectivity, we anticipate this mechanism will likely generalize to other LPTCs.

The role of redundancy in the emergence of visual feature selectivity

Our results extend current ideas about how neurons and circuits encode behaviorally relevant information in an efficient fashion. Classic theoretical studies suggest that efficient coding requires suppression of responses to redundant input signals, allowing as much information as possible to be encoded by limited capacity output channels (Attneave, 1954; Barlow, 1961). In this framework, individual neurons within a population should encode information independently, such that activity patterns are uncorrelated. However, activity patterns in the vertebrate retina exhibit significant correlations (Puchalla et al., 2005). In general, redundant signals may be beneficial for two reasons. First, the original formulation of the efficient coding hypothesis assumes a deterministic relationship between input signals and neural responses (Barlow, 1961). In fact, neuronal signaling is corrupted by noise, and averaging multiple redundant signals may serve to increase signal-to-noise ratios. A large body of work addresses the relationship between correlated activity patterns, noise, and efficient coding (Averbeck et al., 2006; Shamir, 2014). Second, and more directly relevant to the work described here, the function of the visual system is not to reconstruct the visual scene with the highest possible fidelity, but rather to extract behaviorally relevant visual cues. In this context, redundancy may facilitate efficient coding of salient signals by allowing them to carry more weight than irrelevant signals (Puchalla et al., 2005). Consistent with this, our results suggest that redundant visual input can be either detrimental – in the case of spatially adjacent local motion cues– or beneficial – in the case of spatiotemporal sequences of local signals – for the selective, efficient coding of complex visual features. More generally, this work suggests that the role of redundancy in efficient coding depends on how the encoded information is used to guide animal behavior.

STAR METHODS

Key Resources Table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Mouse monoclonal anti-nc82	DSHB	Cat# nc82; RRID: AB_2314866
Rat monoclonal DYKDDDDK Epitope Tag Antibody (L5) (bind to Flag)	Novus Biologicals	Cat# NBP1–06712; RRID: AB_1625981
Rabbit monoclonal anti-HA-Tag	Cell Signal Technologies	Cat#3724S; RRID: AB_1549585
Donkey Anti-Mouse IgG H&L (Alexa Fluor® 405)	Abcam	Cat#ab175658
Donkey Anti-Rat IgG H&L (Alexa Fluor® 647)	Abcam	Cat#ab150155
Donkey Anti-Rabbit IgG H&L (Alexa Fluor® 488)	Abcam	Cat#ab150073
Mouse anti V5-Tag:DyLight®550	Bio-Rad (Formerly AbD Serotec)	Cat#MCA1360D5 50GA
Experimental Models: Organisms/Strains
P{20XUAS-IVS-GCaMP6f}attP40	Bloomington Drosophila Stock Center	BDSC: 42747
HS-GAL4: P{GMR27B03-GAL4}attP2	Bloomington Drosophila Stock Center	BDSC: 49211
VS-GAL4: P{GMRR78F01-GAL4}attP2	Bloomington Drosophila Stock Center	BDSC: 49620
T4/T5-GAL4: P{GMR42F06-GAL4}attP2	Bloomington Drosophila Stock Center	BDSC: 41253
MCFO1: P{hs-FLPG5.PEST}attP3;PBac{10xUAS(FRT.stop)m yr::smGdP-HA}VK00005 P{10xUAS(FRT.stop)myr::smGdP-V5-THS-10xUAS(FRT.stop)myr::smGdPFLAG}su(Hw)attP1	Bloomington Drosophila Stock Center	BDSC:64085
Software and Algorithms
Python 2.7	Python	https://www.python.org
PsychoPy v1.82	PsychoPy	http://www.psychopy.org/
Fiji	Fiji	https://fiji.sc/
custom Python code	This study	This study

Contact for Reagent and Resource Sharing

Further information and requests should be directed to and will be fulfilled by the Lead Contact Dr. Thomas R. Clandinin (trc@stanford.edu).

Experimental Model and Subject Details

Fly stocks and husbandry

The Drosophila strains used in this study are listed in the Key Resources Table. Flies were raised on standard molasses medium at 25C. Crosses were flipped into fresh vials every 2–3 days. Progeny were imaged 2–4 days after eclosion.

Method Details

Visual stimulus presentation

Visual stimuli were generated using PsychoPy and presented using a digital light projector (DLP LightCrafter, Texas Instruments). The stimuli were presented on a rear projection screen positioned 6 cm away from the fly head; the screen spanned 60° of the fly’s visual field horizontally and 70° vertically. The stimulus was updated at 60 Hz. Before being projected on the screen, the stimulus was filtered using a 472/30nm bandpass filter (Semrock) in order to avoid detection of light from the stimulus by the microscope. Voltage signals from the imaging software were relayed to PsychoPy via a LabJack device, in order to synchronize the stimulus and the imaging frames.

We used the following stimuli:

Moving widefield square wave gratings:

Full contrast square wave gratings (λ = 30°) that spanned the entire stimulus screen and moved at 30°/s were presented for 2s. Static gratings were presented for 1s before and after movement. The gratings were moved in one of twelve directions, presented in a randomized order. This stimulus was used to measure the preferred direction of motion for HS and VS dendrites and T4/T5 axon terminals (Figure 1, Figures S1, S4, and S5A-D).

Moving local square wave gratings:

Full contrast square wave gratings (λ = 30°) that spanned 13.5° and moved at 30°/s were presented for 2s. Static gratings were presented for 1s before and after movement. The gratings were moved in the PD measured for each HS or VS dendrite or field of T4/T5 terminals, measured using widefield gratings. These local gratings selected from a regular array that tiled the stimulus screen and presented in a randomized order on a gray background. This stimulus was used to measure receptive field centers for HS and VS dendrites and T4/T5 axon terminals (Figure 2, Figure 5G, and Figure S1).

Moving local light or dark edges:

White edges were presented on a black background; black edges on a white background. Each individual edge was 13.5° tall (orthogonal to the PD) and moved 13.5° in the PD at either 27 or 54°/s before disappearing. Edges were presented alone, in pairs offset by 13.5° or 27° and presented simultaneously (Figures 3–4, Figure S2B-C,F) or in spatiotemporal sequences offset in space by 13.5° and time by either 500ms (for edges moving 27°/s), 250ms (for edges moving 54°/s) (Figure 6, Figure S2D-E,G, Figure S5E-H, Figure S6D-J, and Figure S7B-G), or for a range of temporal offsets (Figure S8). The spatiotemporal sequences were arranged such that the local edges moving in the PD formed larger patterns moving in either the PD or ND.

In vivo imaging

Female flies were cold anaesthetized and positioned in a fly-shaped hole cut into a thin metal shim. Each fly was positioned such that the back of the head was exposed above the shim and the retina was below the shim, and then fixed in place using a fast-curing glue (Bondic). The brain was exposed using fine forceps to dissect a small hole in the cuticle and remove overlying fat and trachea. The fly was perfused with an oxygenated saline sugar solution with the following composition: 103 mM NaCl, 3 mM KCl, 5 mM TES, 1 mM NaH₂PO₄, 26 mM NaHCO₂, 4 mM MgCl2, 1.5 mM CaCl₂, 10mM trehalose, 10 mM glucose, and 7 mM sucrose. Neurons were imaged with an Olympus FV1000 microscope equipped with a 25× 1.05 NA water immersion objective (Olympus). For two-photon imaging, a Spectra-Physics Mai Tai Ti:Sapphire laser tuned to 920nm was used to excite GCaMP6f. Emitted photons were collected using a 520/40nm emission filter. 256×256 images were collected using a frame rate of 10Hz, 12x digital zoom, and bidirectional scanning. Imaging time per fly never exceeded 2 hours.

Behavioral assay

Mated female flies used in behavior experiments were collected one day post-eclosion and raised for four additional days with circadian entrainment at 25°C on cornmeal food supplemented with yeast paste. Experiments were conducted within two hours of light period onset. Walking behavior in response to motion stimuli was measured as previously described (Silies et al., 2013). Briefly, flies were tethered to a needle with UV-curing glue and held atop an air-suspended, 6.13mm polypropylene ball. Stimuli were projected onto three screens (one in front and two to the sides of the fly) spanning −135° to 135° around the fly. Rotation of the ball about three axes resulting from fly walking behavior was captured with two optical pen mice. Experiments were performed at 34°C to encourage the flies to move.

Stimuli were presented for a total of 20 minutes, with each stimulus presented multiple times in randomized order, interleaved with 1.0 seconds of background contrast. Stimuli used in behavior experiments were as described for imaging experiments with minor modifications. Prior to the onset of edge motion, 2° vertical bars of 100% contrast were rendered offset from the center of each screen where the first edge will appear (27° for global preferred direction, 13.5° for global null direction). These bars remained in place from 0.5s before the appearance of the first moving edge to when the first moving edge disappears. The inclusion of static bars circumvents the startle response evoked by the sudden appearance of moving edges. Four moving edges were presented sequentially in either preferred (PD) or null (ND) direction relative to the direction of edge motion. The stimulus was replicated on each screen for a total of three sets of moving edges. Light edge experiments and dark edge experiments were performed on different groups of flies.

MultiColor FlpOut Labeling

R27B03-Gal4 and R78F01-Gal4 were crossed with MCFO1 virgins. Female offspring (one or two days old) were heat-shocked at 38°C for 40 minutes and dissected five days later. Fly brains were dissected in cold PBS solution and fixed in 4% PFA for 25 minutes at room temperature. The PFA was then washed off (three rinses followed by four 30 minute washes) with 0.1% PBT (0.1% Triton in PBS). The tissues were incubated in PBTDS (0.1% PBT plus 5% donkey serum) for 1.5 hours at room temperature. This was followed by incubation with primary antibodies in PBTDS for two nights, then secondary antibodies in PBTDS for two nights, then tertiary antibodies for one night, and finally SlowFade overnight, all at 4°C. Between each step, tissues were rinsed and washed as described above. Before mounting, the brains were incubated in fresh SlowFade for another two hours at room temperature. Mounted brains were imaged with a confocal microscope (Leica SP5). Primary antibodies: mouse α-nc82 (1:25; DSHB), rat α-FLAG Tag (1:200; Novus) and rabbit α-HA Tag (1:200; CST). Secondary antibodies: AF405 donkey α-mouse (1:50), ATTO647 donkey α-rat (1:200), AF488 donkey α-rabbit (1:200). Tertiary antibodies: DL550 mouse α-V5 (1:400).

Quantification and Statistical Analysis

In vivo imaging data analysis

A macro based on the ImageJ Turboreg plugin was used to align image time series in X and Y. Subsequent processing was carried out using custom written Python code. Images were first binned by stimulus type (i.e. stimulus direction, for widefield moving square wave gratings, or grating position, for local moving gratings) and then binned by time and averaged to generate average responses to each stimulus type. ROIs around HS/VS dendrites or T4/T5 axon terminals were defined using Fiji to manually select ~2μm swaths of pixels that increased their intensity in response to visual stimulus. Pixel intensities within the ROI were averaged and background subtracted. ΔF/F was calculated as (F(t)-F°)/F°, where F° was the average intensity in the 250ms prior to the onset of grating or edge movement. To calculate the PD, RF center, and response nonlinearity for each ROI, responses were first integrated over entire time window in which the stimulus was moving. Then, the PD was calculated by finding the weighted average of the responses in a 60° window around the peak response. For example, if the peak response was to stimulus direction = 30°, we calculated a more precise PD from the weighted average of the responses to directions 0°, 30°, and 60°. Similarly, the RF center was calculated by finding the weighted average in a 30°x30° window around the peak response. A metric calculating the nonlinearity of the integrated responses was calculated as (M-E)/E, where M is the measured response to moving edge pairs or sequences and E is the expected response based on the sum of the responses to individual edges.

Quantification of behavioral responses

Fly optomotor responses were analyzed using custom-written Python code. For each stimulus type, edge motion was presented in both leftward and rightward directions. Fly turning velocities evoked by equivalent stimuli moving in opposite directions were inverted and combined to correct for leftward or rightward preference. The mean translation speed for the 100ms of interleave period immediately preceding the onset of every epoch was calculated for each fly. Flies with less than 5mm/s mean translation speed during this period were omitted from further analysis. Turning velocity for each stimulus type was averaged across all epochs per fly, and then averaged across all flies passing the translation speed filter. For baseline correction per fly, the mean turning velocity during the 1.0s interleave period preceding stimulus onset for each stimulus type was subtracted from the mean turning velocity during the stimulus period. Overall turning response was determined by integrating the mean turning velocity from 100ms after the appearance of the second moving edge to 100ms after the disappearance of the fourth moving edge. Turning response during the presentation of the first edge can not include global signals, produced expected, stereotypical optomotor responses, and therefore was omitted.

Sample sizes

We report sample sizes, including the number of ROIs and the number of flies, for Figures 1, 5, 7, and S2–8 in the figure legends. For Figures 3 and 4, we report the number of ROIs on the figures themselves and the number of flies in the figure legends. For Figure 6, we report the number of ROIs and the number of flies on the figure.

Data and Software Availability

Raw data and custom Python code used to analyze the data are available from the corresponding author upon request.

Highlights.

• Global motion circuits in Drosophila exhibit nonlinear summation of local signals.

• Neurons that detect local motion suppress spatially adjacent signals.

• Dendrites that pool local motion inputs align with a preferred direction of motion.

• Oriented dendrites amplify responses to specific spatiotemporal input sequences.