Dopamine promotes head direction plasticity during orienting movements

Abstract

In neural networks that store information in their connection weights, there is a tradeoff between sensitivity and stability^1,2. Connections must be plastic to incorporate new information, but if they are too plastic, stored information can be corrupted. A potential solution is to allow plasticity only during epochs when task-specific information is rich, on the basis of a 'when-to-learn' signal³. We reasoned that dopamine provides a when-to-learn signal that allows the brain's spatial maps to update when new spatial information is available-that is, when an animal is moving. Here we show that the dopamine neurons innervating the Drosophila head direction network are specifically active when the fly turns to change its head direction. Moreover, their activity scales with moment-to-moment fluctuations in rotational speed. Pairing dopamine release with a visual cue persistently strengthens the cue's influence on head direction cells. Conversely, inhibiting these dopamine neurons decreases the influence of the cue. This mechanism should accelerate learning during moments when orienting movements are providing a rich stream of head direction information, allowing learning rates to be low at other times to protect stored information. Our results show how spatial learning in the brain can be compressed into discrete epochs in which high learning rates are matched to high rates of information intake.

Fig. 1. ExR2 dopamine neurons are correlated with rotational speed.

a, Schematic of the head direction map. b, Imaging jGCaMP7f in ExR2 neurons while measuring rotational and forward walking speed. c, Mean ExR2 ΔF/F versus rotational speed (one line per fly, n = 13 flies). Grey shading indicates transitions between resting and moving; outside this range, ΔF/F and rotational speed are linearly related. d, Mean ExR2 ΔF/F binned by rotational and forward speed, aggregated over 13 flies and averaged over time points. Grey bins are empty. e, Variance explained (adjusted R²) for linear regression models that use speed to predict ExR2 activity. Each pair of dots is one fly (n = 13). Models were fitted separately for each fly. Rotational speed alone produced a high R²; adding forward speed produced a small additional increase (***P = 5.3 × 10⁻⁵, two-sided paired t-test). f, ExR2 responses to optic flow. A stationary vertical grating begins to rotate, and the onset of optic flow drives a sustained increase in ExR2 activity (mean ± s.e.m. across flies; ΔF/F is significantly different from zero with P = 0.0012, two-sided one-sample t-test, n = 13 flies). Here we analysed only trials when the fly was standing still. g, Example data used as model input. Flies walked in a virtual environment with a visual head direction cue. h, Schematic ER-to-EPG connectivity. Adjacent ER neurons in the schematic have adjacent receptive fields in azimuthal space. Connection weights are denoted by circle sizes. Weights are initialized randomly, and then evolve through Hebbian plasticity. i, Weights from a typical model run. j, Mean circular correlation between the population vector average of ER output weights and EPG input weights; mean (n = 117 simulations trained on shuffled data) ± 95% confidence interval. At the end of the simulation, the correlation is higher with the adaptive learning rate (P = 6.2 × 10⁻²¹, two-sided Wilcoxon sign rank test).

Fig. 2. ExR2 dopamine strengthens the association between EPG neurons and a visual cue.

a, A 30-s pulse of ATP (5 mM) excites ExR2 neurons expressing P2X2 receptors (n = 5 cells). The fly is not standing on a spherical treadmill in this figure or in Fig. 3. b, An example EPG neuron responding to a rotating cue. For each cue cycle, we measured the neuron’s preferred cue position and its response amplitude (maximum − minimum membrane potential). A position of 0° means the cue is in front of the fly. Extended Data Figure 6a shows another example. c, Preferred cue position over time for six EPG neurons. Each point is one stimulus cycle. The green shading shows the pulse of ATP (5 mM) or dopamine (200 µM). In controls (cells 1 and 2), ExR2 neurons did not express P2X2 receptors. With ExR2 activation (cells 3 and 4), the cell’s preferred cue position became more consistent, and it sometimes shifted. Dopamine produced similar changes (cells 5 and 6). s.d., circular standard deviation. d, Variability of preferred cue position, before and after ExR2 activation (n = 11) or dopamine (n = 12) versus ATP treatment in controls in which ExR2 neurons do not express P2X2 (controls, n = 10). The fine lines represent individual EPG neurons; the thick lines represent means. The preferred cue position becomes less variable after ExR2 activation (**P = 0.0049). Dopamine produces a similar trend, although falling short of significance (not significant (NS), P = 0.052). ATP has no effect in controls (NS, P = 0.77, two-sided Wilcoxon sign rank tests). The values are measured over the windows shown in c. e, Amplitude of the response to the visual cue, normalized to each cell’s baseline, averaged over cells (±s.e.m.); n values as in d. f, The normalized response amplitude increases after ExR2 activation (**P = 0.0068) or dopamine treatment (**P = 0.0024) but not in controls (NS, P = 1, two-sided Wilcoxon sign rank test). The dots represent single cells; the lines represent means; n values as in d.

Fig. 3. Pairing ExR2 activation with a visual cue increases the cue’s influence on the head direction map.

a, Imaging jGCaMP7f in EPG neurons while rotating a visual cue around the fly. ATP was delivered during the activation period. In some experiments, ExR2 neurons did not express P2X2 receptors (‘no ExR2 activation’) or ATP was delivered in darkness (‘no cue’). b, Example data from two flies. The EPG bump position (pos.) is the angular phase of the bump within the ellipsoid body. In each ΔF/F heatmap, adjacent rows are adjacent wedges of the circular map in the ellipsoid body. c, Mutual information between the cue position and the EPG bump position, estimated for each cue rotation cycle; mean ± s.e.m. across flies (ExR2 activation, n = 20; no ExR2 activation, n = 18; ExR2 activation with no cue, n = 19 in this and all subsequent panels). d, Change in the mutual information between the cue position and the bump position (post − pre), measured in the windows shown in c. Dots represent flies; lines represent means (no ExR2 activation, NS, P = 0.12; ExR2 activation, ***P = 0.00036; ExR2 activation with no cue, NS, P = 0.49; two-sided one-sample t-tests with Bonferroni correction). e, Bump amplitude for each cue rotation cycle (maximum − minimum ΔF/F); mean ± s.e.m. across flies. When no cue was visible, the bump amplitude was calculated in the equivalent time windows. f, Change in bump amplitude (post − pre), measured in the windows shown in e. Dots represent flies; lines represent means (no ExR2 activation, NS, P = 0.34; ExR2 activation, **P = 0.0039; ExR2 activation with no cue, NS, P = 0.22; two-sided one-sample t-tests with Bonferroni correction). g, Change in the mean offset between the bump position and the cue position (post − pre), measured in the windows shown in c. Dots represent flies; lines represent means (NS, P = 0.70 in both cases, Kruskal–Wallis tests).

Fig. 4. Suppressing ExR2 activity reduces the influence of a visual cue on the head direction map.

a, Imaging jGCaMP7f in EPG neurons while ExR2 activity is suppressed through Kir2.1 expression. In the training period, the visual cue was controlled by the fly’s rotation on the spherical treadmill. In the test period, the cue was rotated at a constant velocity. b, Example test period data for three control flies (top) and two Kir2.1 flies (bottom). In each ΔF/F heatmap, adjacent rows are adjacent wedges of the circular map in the ellipsoid body. c, Estimate of the mutual information between the cue position and the bump position in the test period. Dots represent flies; lines represent means (n = 21 with Kir2.1 expression; n = 20 control here and in e); examples in b are labelled. Mutual information is lower in the Kir2.1 flies (*P = 0.027, two-sided two-sample t-test). d, EPG bump amplitude versus the fly’s rotational speed for both genotypes; data are binned by speed and averaged within a fly before averaging across flies (±s.e.m. across flies). Only speeds ≤100° s⁻¹ are included. Bump amplitude is z-scored within each fly. The schematic shows higher bump amplitude with higher rotational speed. e, Correlation between bump amplitude and rotational speed throughout the experiment. Dots represent flies; lines represent means. In flies in which ExR2 neurons express Kir2.1, this correlation is lower (***P = 3.5 × 10⁻⁶, two-sided two-sample t-test with Fisher transformation).

Extended Data Fig. 1. Proximity of ExR2 dopamine release sites to ER→EPG synapses.

All data in this figure originate from the ‘hemibrain’ large-scale serial section electron microscopy dataset. a) Total number of synaptic contacts from ExR2 neurons onto EPG neurons and ER neurons. b) Schematic of dopamine spillover. Work in the Drosophila mushroom body has suggested that dopamine can act on synapses up to ~3 µm away from its sites of release. This motivated us to count ER→EPG synapses <3 µm from an ExR2 release site; here we consider all ExR2 release sites, regardless of the postsynaptic cell. This analysis assumes that plasticity at ER→EPG synapses is regulated by dopamine receptors residing at or near the synapse, rather than dopamine receptors elsewhere in ER or EPG neurons. c) Skeleton of one EPG neuron and one ER neuron (ER2a subtype). Gray regions show neuropil boundaries. ER→EPG synapses between these two neurons are shown in gold. Bottom images show the ellipsoid body at an enlarged scale. Nearby ExR2 release sites are in blue (<3 µm from a gold site). Arrows denote cell body locations. d) Skeleton of one ExR2 neuron. There are four ExR2 neurons in total (two in each hemisphere), and the blue release sites come from all four of these neurons. At right is an overlay of the example cells shown in (c). Arrow denotes ExR2 cell body location. e) Cumulative probability histogram of Euclidean distances from all visual ER→EPG synapses to the closest ExR2 release site. We define “visual ER neurons” as subtypes ER2a, ER2b, ER2c, ER2d and ER4d^,,. f) Cumulative probability histogram of distances in the mushroom body γ lobe from Kenyon cell → mushroom body output neuron synapses (KC→MBON synapses) to the closest mushroom body dopamine neuron (MB-DAN) release sites. Note that the proximity of dopamine release sites to KC→MBON synapses is similar to the proximity of release sites to ER→EPG synapses. See also ref. . g) Cumulative probability histogram of the distance from each ER→EPG synapse to its closest ExR2 release site, plotted separately for each ER subtype.

Extended Data Fig. 2. Rotational speed tuning in ExR2 dopamine neurons.

a) Mean ExR2 ΔF/F versus rotational and forward speed for two example flies. Data are binned by speed and averaged over time points. Gray bins are empty. Figure 1d shows the average over all time points for all flies. b) Mean forward speed versus rotational speed for the combined behavioral data of all 13 flies in Fig. 1c–f. Data are binned by rotational speed and then averaged across time samples. Note that rotational and forward speed are positively correlated for rotational speeds <100 °/s. c) Cumulative histogram of rotational speed data from this data set. Note that rotational speed <100 °/s for the large majority of time points; thus, rotational and forward speed are generally positively correlated. d) Pearson’s correlation coefficient between ExR2 ΔF/F and rotational or forward speed. Each set of connected dots represents an individual fly (n = 13); horizontal lines are mean values. ExR2 activity is more correlated with rotational speed than with forward speed (p = 0.0002, two-sided Wilcoxon signed rank test). The positive correlation with forward speed is expectable, based on the fact that rotational and forward speed are themselves correlated. e) Comparison of the explanatory power (adjusted R² values) of linear regression models that aim to predict ExR2 ΔF/F using rotational and forward speed, rotational speed only, and forward speed only. In Wilkinson notation, the model formula is ΔF/F ~ speed_rotational + speed_forward. Each set of connected dots represents an individual fly; horizontal lines are means (n = 13 flies). Models were fit separately for each fly. Models that used only forward speed as a predictor variable performed significantly worse than those that used rotational speed (p = 3.1 × 10⁻⁵), and models that used both forward and rotational speed performed better than those using rotational speed alone (p = 0.04, one-way repeated measures ANOVA with Tukey post hoc test). However, the incremental benefit of adding forward speed was small, implying that forward speed is mainly predictive of ExR2 activity simply because it is predictive of rotational speed.

Extended Data Fig. 3. Lateralized ExR2 responses to rotational movements.

a) Left: Skeleton of one ExR2 neuron (from the hemibrain dataset) overlaid with a mirrored version of the same skeleton. Note that the LAL dendritic arbor is mainly ipsilateral (not bilateral); therefore, we analyzed ExR2 GCaMP7f fluorescence in the LAL to compare the velocity tuning of the left and right copies of ExR2. There are four ExR2 neurons in total (2 cell bodies in each hemisphere). Right: Pearson’s correlation between ExR2 ΔF/F in the LAL and the fly’s rotational velocity. Rotational velocity is defined as positive for rightward turning and negative for leftward turning (as distinct from rotational speed, i.e. the absolute value of rotational velocity, which is strictly non-negative). This analysis shows that ExR2 signals are correlated with rotational velocity in the ipsilateral direction, and the right-left difference in ExR2 activity is significantly correlated with the fly’s rotational velocity (correlation significantly different from zero, p = 1.8 × 10⁻⁷, two-sided one-sample t-test). Each fly contributes one data point per condition (n = 13 flies). b) Pearson’s correlation with rotational velocity overlaid on raw fluorescence images acquired at 5 different horizontal planes through the same brain, for two different 5-minute trials with a 5-minute period between them. Scale bar is 20 μm. Correlation coefficients are represented by a blue-to-red colormap, with R > 0 in blue and R < 0 in red, with stronger absolute correlations having more saturated color values. Correlation values are only shown for the pixels with the strongest correlations (top 15% of absolute correlation values). Note that many pixels have consistent tuning across the two trials. Pixels with positive and negative correlations are likely to arise from the right and left copies of ExR2, respectively. This analysis demonstrates that the direction-selectivity we see in the LAL arbors is preserved in the EB and BU arbors of these cells. If dopamine release from each ExR2 neuron is proportional to the fly’s ipsilateral rotational velocity, then total (summed) dopamine release in the EB should be proportional to the fly’s rotational speed.

Extended Data Fig. 4. Small ExR2 responses to the movement of a visual object.

a) We placed flies in a virtual reality environment with a visual cue which rotated around the fly in closed loop with its rotational velocity on the spherical treadmill. In an environment with this type of visual cue, EPG neurons track the fly’s head direction more accurately than they do in darkness; here we ask whether this type of cue affects ExR2 activity also. Left: mean ExR2 ΔF/F versus the fly’s rotational speed for 8 example flies. Right: slopes and y-intercept of lines fit to the data for each fly in the linear portion of each curve (rotational speeds >30°/sec), with one data point per fly. In the epochs with the visual cue, slopes were significantly smaller and intercepts were larger, compared to epochs of darkness in the same experiments (slope: p = 6.3 × 10⁻⁵, intercept: p = 0.0004, two-sided paired t-tests with Bonferroni correction, n = 29 flies). This indicates that the visual cue boosts ExR2 activity for low rotational speeds; however, the magnitude of this effect is very small. These results are consistent with the fact that ExR2 neurons respond to optic flow (Fig. 1f), and the movements of the cue produce a small amount of optic flow. b) We also tested the effect of jumping the visual cue by 90° during these closed-loop epochs; we found that this produced a very small and transient ExR2 response, which is likely due to the small transient increase in optic flow that the cue jump produces (compare with Fig. 1f). Shown here is the average response from a typical example fly (mean of 11 trials ± SEM). To assess the effect of the cue jump, we analyzed only those trials where the fly happened to be standing immobile for several seconds before and after the jump, in order to avoid confounds associated with jump-induced behaviors. c) Here we compare epochs of walking in darkness with epochs of open-loop cue rotation at constant velocity (with the same cue velocity used in Figs. 2, 3, and 4, i.e. ~18°/s). Left: mean ExR2 ΔF/F versus the fly’s rotational speed for 8 example flies. Data are binned by rotational speed and averaged across time points. Right: slope and y-intercept of lines fit to the data for each fly in the linear portion of the curves (rotational speeds >30°/s). Visual cue rotation at constant velocity had no significant effect on the relationship between ExR2 activity and the fly’s rotational speed (slope: p = 0.87, y-intercept: p = 0.15, two-sided paired t-tests with Bonferroni correction, n = 11 flies). However, this data set shows a small trend in the same direction as what we observed in the closed-loop case; because there are fewer replicates here, there is less statistical power. The main result of this experiment is simply that we find no evidence that open-loop cue movement produces any larger response than closed-loop cue movement does. The flies in this panel are the same as those shown in Fig. 1c–f.

Extended Data Fig. 5. Model illustrating the effect of synaptic plasticity in combating synaptic weight noise.

Here we began with weights from the end of a typical model run with an adaptive learning rate (“dopamine”). As before, the input to the model was a temporal sequence of visual cue positions and associated rotational velocities, taken from our behavior data (as shown in Fig. 1g). At each time step, we then made small random changes to individual synaptic weights. These random changes could represent (for example) fluctuations in the numbers of presynaptic calcium channels or postsynaptic neurotransmitter receptors. If the Hebbian learning rule continues to operate, with the adaptive learning rate (“dopamine”), then as the fly continues to walk and sample the visual environment, the effects of these small random changes are erased, and the synaptic weight pattern is preserved. But without dopamine, the synaptic weight pattern degrades, because the fly often orients in a fixed direction for long periods, and so over-learns the retinotopic cue location that is associated with that direction. Finally, if learning is turned off, synaptic weights degrade very rapidly, because the random synaptic weight changes accumulate without any correction. The plot shows the mean circular correlation between the population vector average of ER output weights and EPG input weights; mean (n = 16 simulations trained on shuffled data) ± 95% confidence interval. At the end of the simulation, all pairwise comparisons between conditions are significantly different (normal learning vs. fixed rate learning: p = 0.0004; normal learning vs. no learning: p = 0.0004; fixed rate learning vs. no learning: p = 0.0006; two-sided Wilcoxon sign rank tests with Bonferroni correction).

Extended Data Fig. 6. Additional examples of visual response changes and spiking in EPG neurons.

a) Example EPG neuron responding to a rotating visual cue, recorded in whole-cell mode. For each stimulus cycle, we measured the neuron’s preferred cue position and its response amplitude (max - min membrane potential). Insets show membrane potential on an expanded timescale. In this EPG neuron, ExR2 activation produced a relatively long-lasting increase in visual cue response amplitude, whereas the increase was more transient in the example EPG neuron in Fig. 2b. b) Across all recorded cells, the change in visual cue response amplitude was significantly higher after ExR2 activation, as compared to control experiments where ATP was applied but ExR2 neurons did not express P2X2 (p = 0.015, two-sample two-sided Wilcoxon rank sum test). Dots are individual cells (same cells as in Fig. 2); horizontal lines are means; n = 11 for ExR2 activation and n = 10 for control. Changes in visual cue response amplitude (post − pre) are measured in the time windows shown in Fig. 2e. c) Example EPG spike rate changes following ExR2 activation during the rotation of a visual cue. In this EPG neuron, spikes are unambiguously identifiable, but that was not true in all recordings, because ExR2 activation causes an acute depolarization and a large (and often persistent) increase in visually-evoked EPG spike rates. Under these conditions, the EPG spike amplitude decreases, making spike identification uncertain in many recordings. d) Membrane voltage response for the same cell during the epoch as shown in (c). e) Analysis of spike rates for the same example cell in (c). Preferred cue position over time (left) and amplitude of the response to the visual cue (bottom). Each point is one stimulus cycle. f) Same but for membrane potential. The response amplitude is normalized to the cell’s baseline period.

Extended Data Fig. 7. Preferred visual cue positions of individual EPG neurons.

a) Preferred visual cue position over time, for all EPG neurons single-cell recordings (Fig. 2b–f). Each color denotes a different cell (n = 11 for ExR2 activation, n = 10 for controls, n = 12 for dopamine). Preferred cue position was measured once per cue rotation cycle. To assess the significance of baseline tuning, we applied the Rayleigh test for non-uniformity to the entire baseline period, using the circ_rtest() function in Matlab; two cells in the ExR2 activation dataset and one cell in the dopamine dataset were not significantly tuned to visual cue position during the baseline period. These cells and the corresponding p-values are annotated above the plot (with p values from Rayleigh tests indicating the probability that the cell is untuned). Note that preferred cue positions tend to be biased toward +90° and −90°, and this bias becomes more prominent following ExR2 activation or dopamine treatment. This bias is probably inherited from visual ER neurons, which overrepresent these lateral positions; as a result, many EPG neurons tend to receive disproportionate inhibition at these locations, and thus they might be expected to receive disproportionate disinhibition at the opposite location (−90° and +90°, respectively). This bias should be less notable when the visual stimulus is reinforcing the internal self-motion inputs to the head direction system (i.e., motor efference and/or proprioceptive inputs^,), because these self-motion inputs presumably do not exhibit any retinotopic bias. Accordingly, a recent study found a strong egocentric bias in butterfly head direction cells during passive viewing of a visual cue, but not when the butterfly’s steering movements were controlling the position of that same visual cue. If the bias arises from the properties of visual ER neurons, then we might expect the bias to increase when the influence of the visual cue increases, and indeed this is what we observe when we pair the visual cue with ExR2 activation or dopamine treatment. b) Same as (a) but expressed as a change from the cell’s baseline average preferred cue position. c) Absolute value of the change in preferred cue position. Dots are single cells, line is mean. Cells without significant baseline tuning are included in this plot but excluded from all statistical analysis of single cell remapping. N values are the same as in (a).

Extended Data Fig. 8. Effects of optogenetic ExR2 activation.

a) Schematic of the experimental design. The voltage response of an EPG neuron to a rotating visual cue was obtained in whole cell recording mode, and visual tuning was measured in the pre- and post-activation periods by rotating a visual cue around the fly. During the activation period, orange light was pulsed to activate Chrimson-expressing ExR2 neurons while we continued to rotate the visual cue around the fly. We performed the same protocol in genetic controls where ExR2 neurons did not express Chrimson. In a separate set of controls, we used Chrimson-expressing ExR2 neurons but we turned off the visual cue during ExR2 activation. b) Preferred cue position and response amplitude (max - min membrane potential) for 3 example EPG neurons, pre and post ExR2 activation with Chrimson; all these flies had the visual cue paired with ExR2 activation. Each point is one stimulus cycle. c) Mean response amplitude, pre and post activation. P-values show results of Wilcoxon paired, two-sided rank tests. Results are similar to Fig. 2f (chemogenetic activation of ExR2). (n = 10 for no Chrimson, n = 18 ExR2 activation, n = 10 ExR2 activation with no cue). d) Changes in visual cue response amplitude. Horizontal lines are means. P-values show results of a two-sample two-sided Wilcoxon rank sum tests (n = 10 for no Chrimson, n = 18 ExR2 activation, n = 10 ExR2 activation with no cue). Results are similar to Extended Data Fig. 6b (chemogenetic activation of ExR2), although the absolute change in response amplitude is smaller than with chemogenetic activation. e) Standard deviation of prefered cue position, pre and post activation. P-values show results of Wilcoxon paired, two-sided rank tests (n = 10 for no Chrimson, n = 18 ExR2 activation, n = 10 ExR2 activation with no cue). Compared with Fig. 2d (chemogenetic activation of ExR2), the same trends are visible, although the effect of ExR2 activation falls short of statistical significance. This may be related to the fact that the absolute change in response amplitude was smaller with optogenetic activation than with chemogenetic activation. Overall, for ExR2 activation with Chrimson, 16 of 18 cells were significantly tuned to cue position during the baseline (“pre”) period; of those, 3 changed their preferred cue position after we delivered orange light to activate ExR2 neurons. For the no Chrimson condition, 9 of 10 cells were significantly tuned during the baseline period and 0 of those cells changed tuning after we delivered orange light. For the ExR2 activation with no cue condition, 10 of 10 cells were tuned during the baseline period and 2 showed changes in tuning after we delivered orange light. Tuning during the baseline period was assessed with a Rayleigh test for non-uniformity (at the p > 0.05 criterion for significance). Changes in preferred cue position tuning were assessed using parametric Watson-Williams multi-sample tests with Bonferroni correction.

Extended Data Fig. 9. Effects of hyperpolarizing ExR2 dopamine neurons.

a) Mean rotational speed (left), forward speed (center), and percentage of time spent locomoting (right) throughout the experiment, for both the control genotype and the genotype where ExR2 neurons express Kir2.1 (n = 20 control and 21 Kir2.1 flies throughout this figure). Dots are individual flies; horizontal lines are means. There was no significant difference between the two genotypes for any of these locomotor parameters (p = 0.81, p = 0.97, and p = 0.79, two-sided Wilcoxon rank sum test). In short, we find no evidence that ExR2 neuron hyperpolarization causes locomotor defects. b) EPG bump amplitude was not significantly different in the genotype where ExR2 neurons express Kir2.1 versus the control genotype (p = 0.76, two-sided two-sample t-test). c) Left: Data from two example flies from each genotype, showing a similar correlation between the bump rotational velocity and the fly rotational velocity. This result implies that hyperpolarizing ExR2 neurons does not impair the tendency of the bump to track the fly’s internal self-motion signals. Each data point is a time point. Right: Pearson’s correlation coefficient between bump rotational velocity and fly rotational velocity, for all flies. Note that these correlations are all relatively low, because they were all measured as the visual cue was rotating in open loop around the fly, and so internal self-motion signals were competing with visual cues for control of the bump. The visual cue has less influence when ExR2 neurons express Kir2.1 (Fig. 4c), and so it not surprising that there is a trend toward a larger relative influence of self-motion signals in the Kir2.1 flies (i.e., a slightly stronger correlation with the fly’s rotational velocity), although this trend was not significant (p = 0.28, two-sided two-sample t-test, n = 20 Kir2.1 flies and 20 control flies). The two example flies from each genotype both have relatively high correlations, but they are typical in having a fitted slope less than unity; this has been observed previously in flies walking in darkness, and it suggests that the native gain of the EPG network is <1, i.e. the brain tends to underestimate the fly’s rotation on the spherical treadmill. d) EPG bump amplitude versus the fly’s rotational speed for both genotypes; data are binned by speed and averaged within a fly. Bump amplitudes are z-scored. Each line is an individual fly. Fig. 4D shows the mean±SEM within each genotype. e) Left: Pearson’s correlation coefficient between bump amplitude and forward speed throughout the experiment. Dots are flies; lines are means. In flies where ExR2 neurons express Kir2.1, this correlation is lower (p = 0.029, two sample t-test with Fisher transformation). Right: same but for rotational speed (p = 3.5 × 10⁻⁶, two-sided two sample t-test with Fisher transformation). This plot is reproduced from Fig. 4e for comparison. Note that the magnitude of correlation coefficient is stronger for rotational speed than for forward speed. Because forward speed and rotational speed are themselves correlated (Extended Data Fig. 2b), it is expected that bump amplitude would be at least weakly correlated with forward speed.