DNa01 and DNa02 predict different features of steering.

A) Schematic morphologies of these DNs (Namiki et al., 2018), which have distinct projections in the ventral nerve cord (VNC).

B) Output synapses in the VNC (Cheong et al., 2023; Marin et al., 2024; Takemura et al., 2023), categorized by postsynaptic cell type.

C) Number of VNC cells postsynaptic to each DN. Both DN types are restricted to one side of the VNC.

D) Example dual recording from DNa01 and DNa02, both on the left. Both cells are depolarized just before the fly steers in the ipsilateral direction (asterisks). Both cells are hyperpolarized when the fly briefly stops moving (arrowhead). Here and elsewhere, ipsi and contra are defined relative to the recorded DN(s).

E) Rotational velocity filters. These filters describe the average rotational velocity impulse response, given a delta function (unit impulse) in firing rate. Thin lines are filters for individual flies (n=13 single-cell recordings for DNa02, n=10 single-cell recordings for DNa01). Thick lines are averages.

F,G) Same for sideways and forward velocity.

H) Variance explained by each filter type. Data points are flies. Boxplots show interquartile range (IQR), whiskers show range of data (except for diamonds, observations >1.5×IQR).

See also Figs. S1-S3.

DNa02 and DNa01 have different firing rate dynamics and steering gain.

A) Correlation between DNa01 and DNa02 firing rates. Each line is a different paired recording (4 flies).

B) The rotational velocity filter for each cell was convolved with its firing rate to generate rotational velocity predictions. Whereas DNa02 over-predicts large rapid steering events, DNa01 under-predicts these events.

C) Binned and averaged rotational velocity as a function of DNa01 and DNa02 firing rate, for an example paired recording. Rows represent the relationship between DNa01 and turning, for each level of DNa02 activity. Columns represent the relationship between DNa02 and turning, for each level of DNa01 activity. Gray bins have too few datapoints to plot.

D) Slope m of the linear regression fitting rotational velocity vr to each cell’s firing rate f (vr=mf+b). The difference between cell types is significant (p=10-4, paired t-test, n=4 flies).

E) Same as (C) but for voltage changes rather than firing rate changes.

Bilateral differences in DN firing rate predict steering.

A) Example bilateral recording from DNa02. The neurons are anti-correlated when the fly is turning, and hyperpolarized when the fly stops moving (arrowhead).

B) Binned and averaged rotational velocity for each value of bilateral DNa02 firing rates for an example paired recording.

C) Mean rotational velocity for each value of the bilateral firing rate difference. Each line is a different fly (n=4 flies).

D) The rotational velocity filter for each cell was convolved with its firing rate to predict rotational velocity. Combining the predictions of the two cells (with equal weighting) generates a good prediction.

E) Top: predicted rotational velocity versus actual rotational velocity, for both single-cell predictions for an example experiment. Bottom: the dual-cell prediction for this experiment. Thick lines are LOWESS fits. Each axis ranges from 800 °/s rightward to 800 °/s leftward, and dashed lines denote 0 °/s.

DNa02 participates in compass-directed steering.

A) A bump of activity rotates around the ensemble of EPG neurons (compass neurons) as the fly turns. We microstimulate PEN1 neurons with ATP to evoke a bump jump. This is followed by a compensatory behavioral turn that returns the bump to its initial location.

B) Percentage of trials with a bump jump after the ATP puff. Each point is a fly (each genotype n=4). In controls lacking PEN1 Gal4, ATP only occasionally preceded bump jumps, which is likely coincidental, as the bump often moves spontaneously.

C1) Change in bump position after ATP. The bump returns to its initial position in many trials (red) but not all (gray) in this sample experiment. C2) Red trials from C1 aligned to the time of maximal bump return speed, color-coded by the fly’s steering direction during bump return.

D) The fly’s rotational velocity during the bump return, plotted against the initial bump jump. Clockwise bump jumps are generally followed by rightward turns (which drive bump return via a counterclockwise path), and vice versa. Clockwise bump jumps (18 trials) and counter-clockwise bump jumps (35 trials) are followed by significantly different mean rotational velocities (p<0.05, t-tailed t-test, pooling data from 4 flies).

E) Example trial. Top: DNa02 activity. Middle: fly’s rotational velocity toward the left side, i.e., the side of the recorded DNa02 neuron). Bottom: grayscale EPG ΔF/F over time, where each row is a 45°-sector of the compass, and red is bump position. ATP causes a bump jump (arrowhead). Then, the left copy of DNa02 bursts, the fly turns left, and the bump returns via a clockwise path (arrowhead).

F) Trials where the bump returned to its initial location via a clockwise path were aligned to the time of peak bump speed. Trials were averaged within a fly, and then across flies (mean ± SEM across flies, n=4 flies).

G) In an example experiment., rotational velocity correlates with DNa02 firing rate on a trial-to-trial basis (R2=0.51, p=3×10-3, two-tailed t-test). Trials are color-coded as in (D). In all other experiments, p was also <0.05.

H) Data sorted by the direction of the bump’s return (mean±SEM across flies, n=4 flies). Whereas clockwise (blue) bump returns were typically preceded by leftward turning, counter-clockwise (green) bump returns were preceded by rightward turning, as expected. On average, the left copy of DNa02 was only excited on trials where the bump moved clockwise, meaning the fly was turning left.

DNa02 participates in stimulus-directed steering.

A) CsChrimson was expressed in most olfactory receptor neurons. As a fly walked on a spherical treadmill, a fiber-optic filament illuminated either the right or left antennae alternately. Ipsi- and contralateral stimuli are defined relative to the recorded neuron. Top: two example trials, one ipsi and one contra, showing the fly’s rotational velocity and DNa02 activity on each trial. Bottom: mean ± SEM across flies, n=4 flies. Gray shading shows the 500-ms period of fictive odor.

B) Same as (A) but for fictive heat. CsChrimson was expressed in heat-activated neurons of the antenna. Fictive heat drives behavioral turning away from the stimulus, rather than toward it.

C) Mean data on an expanded timescale to show that DNa02 firing rate increases precede turning toward ipsilateral fictive odor (mean ± SEM across flies, n=4 flies).

D) Trial-to-trial variability in an example experiment. Each datapoint is a trial where fictive odor was presented on the ipsilateral side; gray line is linear fit (R2=0.33, p=10-5, two-tailed t-test). In other experiments, R2 ranged from 0.16 to 0.40, with p always <0.005.

Latent steering drives during immobility.

A) Example showing how DNa02 hyperpolarizes during immobility. Total speed is defined as rotational speed + sideways speed + forward speed.

B) Mean total speed and DNa02 firing rate during (left) the transition to immobility and (right) the transition to activity (± s.e.m. across flies, n=7 flies). Transitions were detected by setting a threshold for total speed (dashed line). The firing rate increase precedes the onset of movement by ∼250 ms.

C) Examples of DNa02 activity during fictive odor presentation when the fly was active versus immobile. Note that, when the fly is immobile, ipsilateral odor still evokes depolarization and spiking. Note also that contralateral odor can still evoke hyperpolarization during immobility.

D) Summary data (mean ± s.e.m. across flies, n=4 flies) for active versus immobile trials. Odor produces a similar change in neural activity for trials where the fly is behaviorally active versus immobile. However, the entire dynamic range of neural activity is shifted downward during immobility, so that the peak firing rate (and peak depolarization) is reduced.

Converging brain pathways onto DNa02.

A) Number of cells in the brain connectome presynaptic to each DN (Dorkenwald et al., 2023, 2022; Lin et al., 2024; Zheng et al., 2018).

B) Input synapses in the brain, categorized by presynaptic cell type.

C) Major pathways from PFL3 cells to DNa02. Glutamatergic connections are likely inhibitory (Liu and Wilson, 2013).

D) Schematic: how PFL3 cells might perform see-saw steering control. When the fly deviates to the left of its goal direction, PFL3 cells are positioned to excite DNa02 on the right, while also inhibiting DNa02 on the left. When the fly deviates to the right of its goal direction, this should occur in reverse.

E) Left: Major pathways from PFL2 cells onto DNa02. Right: major pathways from VES041 onto DNa02.

F) Major pathways from MBON32 onto DNa02.

G-H) Schematic: how MBON32 might drive steering toward an attractive stimulus (like an attractive odor), as well as steering away from an aversive stimulus (like aversive heat).

Behavioral results of directly activating and silencing DNs.

A) As flies walked on a spherical treadmill, they were illuminated repeatedly for 500-ms epochs. ReaChR was expressed uni- or bilaterally in DNa02.

B) Ipsilateral rotational velocity, mean of 16/17 flies (uni/bilateral ReaChR). The mean of the unilateral data (thick gold line) lies outside the 95% confidence interval (thin blue lines) of the distribution of outcomes we obtain when we randomly assign bilateral (control) flies to the “right” or “left” expression group.

C) Ipsilateral rotational velocity. Each data point is one fly (or simulated fly), averaged across the illumination epoch.

D) GtACR1 was expressed bilaterally in DNa01 or DNa02. Flies were illuminated repeatedly for 2-min epochs as they walked in an arena.

E) Sideways and rotational speed distributions for light on/off in each genotype. The p-values in black denote ANOVA genotype×light interactions after Bonferroni-Holm correction; the p-values in gray denote post hoc Tukey tests comparing light on/off within a genotype; n.s. = not significant, n.t. = not tested (because genotype×light interaction was not significant). The number of points (500-ms time windows) in each distribution is shown in italics; see Methods for fly numbers.

F) Stance duration of inner back (iB) leg, normalized to other legs (oF, oM, oB, iF) was measured in 500-ms time windows (n=755 windows) and plotted versus rotational speed. For some windows where rotational speed is high, iB stance duration is prolonged i.e., the fly pivots on its iB leg.

G) Distribution of normalized iB stance durations, for 500-ms time windows where rotational speed exceeded a threshold of 20 °/s for ≥100 ms.

H) Step frequency, step length, and forward velocity distributions.

Discriminating DNa01 from DNa02 in dual recordings

We combined the split-Ga4 line that targets DNa01 (SS00731) with a Gal4 line that targets DNa02 (R75C10-GAL4). With a 10XUAS-IVS-mCD8::GFP(attP40), this combination of driver lines labeled only two somata in the vicinity of DNa01 and DNa02. Here we show that we can discriminate DNa01 from DNa02 in dual recordings from this genotype.

A) Top: spike waveforms from a known DNa02 cell, recorded in the specific split-Gal4 line (SS00730). Bottom: spike waveforms from a known DNa01 cell, recorded in a different specific split-Gal4 line (SS00731). Individual spikes are gray, averages in black.

B) Spike waveforms from dual DNa01/DNa02 recordings in 4 flies.

C) Magenta and green lines show overlaid averages from (A). Red and blue show overlaid averages from (B). Dashed lines show the part of the waveform used in classification analysis. Values in parentheses show the number of spikes in each average.

D) A linear classifier was trained to separate cells from known DNa01 and DNa02 recordings, using the data shown in (A). In essence, the classifier separates spike waveforms based on their shapes and amplitudes. This classifier was then tested using another pair of known DNa01 and DNa02 recordings.

Values shown are the percentage of spikes assigned to each cell type. Because most of the DNa01 spikes were assigned to the DNa01 category, and most of the DNa02 spikes were assigned to the DNa02 category, we can conclude that this classifier produces the correct identification of the two cells.

E) The same classifier was then applied to dual DNa01/DNa02 recordings from all 4 flies, in order to determine which cell was which. In every case, the classification was essentially unambiguous. Moreover, in every case, the classifier assigned the DNa01 label to the cell with the smaller and deeper soma, consistent with our observation that the soma of DNa01 is somewhat smaller and deeper than the soma of DNa02.

Forward and reverse linear filters for DNa01 and DNa02 neurons

A) Firing rate autocorrelation for DNa01 and DNa02.

B) Firing-rate-to-rotational-velocity filters for DNa01 and DNa02.

C) Firing-rate-to-sideways-velocity filters for DNa01 and DNa02.

D) Firing-rate-to-forward-velocity filters for DNa01 and DNa02.

E) Firing-rate-to-total-speed filters for DNa01 and DNa02, where total speed is the sum of the fly’s speed in all three axes of movement. As DNa02 predicts large changes in rotational and sideways movement,, it is not surprising that it is also predicts large changes in total speed. Filters in (C-F) can be convolved with neural firing rates to predict behavior, where b(t) = H(t) * f(t). Filters in (C-E) are reproduced from Fig. 1.

F) Variance explained by each forward filter, for DNa01 and DNa02 neurons. Colors denote variables in (C-F).

G) Behavior autocorrelation for each kinematic variable.

H-K) Same as in (B-E), but in the reverse direction.. These filters can be convolved with a behavioral variable to predict neural firing rates, where f(t) = H(t) * b(t). Whereas the forward filters in (C-F are normalized for the neuron’s autocorrelation function, these reverse filters are normalized for behavior autocorrelation.

L) Variance explained by each reverse filter, for each kinematic variable, for DNa01 and DNa02 neurons.

M) Rotational velocity and sideways velocity are strongly correlated (left), whereas forward velocity is not strongly correlated with steering speed (defined as the absolute value of rotational velocity plus sideways velocity, both in units of °/s). Black lines are LOWESS fits; margins show kernel density estimates (n=20 flies)

Forward velocity and neural activity in paired recordings.

A) From an example DNa01/DNa02 paired recording, colormaps show binned and averaged forward velocity for each paired value of Δvoltage (left) or firing rate (right). Both DNa01 and DNa02 were recorded in the left hemisphere. When (ΔvoltageDNa02>>ΔvoltageDNa01), the fly is typically moving backward. When (firing rateDNa02>>firing rateDNa01), the fly is also often moving backward, but forward movement is still more common overall, and so the net effect is that forward velocity is small but still positive when (firing rateDNa02>>firing rateDNa01). Note that when we condition our analysis on behavior rather than neural activity, we do see that backward walking is associated with a large firing rate differential (Fig. S4).

B) From an example DNa02/DNa02 paired recording, colormaps show binned and averaged forward velocity for each paired value of Δvoltage (left) or firing rate (right). When both left and right DNa02 cells are firing zero spikes, the fly is typically stopped (see also Fig. 2). When either copy of DNa02 is firing at a high rate, the fly is often moving backward; this is likely because extremely fast turns are often associated with backward movement.

C) Mean forward velocity for each left-right DNa02 firing rate difference. Each line is a different fly (n=4). Large left-right differences are associated with backward movement; again, this is likely because extremely fast turns are often associated with backward movement.

Backward walking

A) Three examples of dual recordings from DNa01 and DNa02. When DNa02 is much less hyperpolarized than DNa01 (or much more depolarized), the fly is generally moving backward. Flies typically moved backward ∼15% of the time.

B) Colormap shows binned and averaged forward velocity for each value of DNa01 and DNa02 membrane voltage, for three example paired recordings. Voltages are expressed as changes from each cell’s mean.

C) Mean difference in firing rates (DNa02-DNa01), ± SEM across flies (n=4 flies), aligned to the onset of backward walking. Overlaid is mean forward velocity ± SEM across flies; horizontal

ine represents the threshold used to trigger onset of backward walking.

D) Binned and averaged rotational velocity versus bilateral firing rate difference for epochs of forward walking and backward walking. Each line is a different paired recording (n=4 flies).

Dual recordings from the right and left copies of DNa01.

A) An example dual recording from DNa01 on both sides of the brain. Colormap shows binned and averaged rotational velocity for each value of bilateral DNa01 Δvoltage (left) and bilateral DNa01 firing rates (right). Note that rotational velocity is related to the right-left firing rate difference in this DNa01 paired recording. This is similar to our results in DNa02 paired recordings (Fig. 3).

B) Same but for another example dual DNa01/DNa01 recording.

Genetic controls for fictive sensory stimuli and behavioral responses in intact flies

A) Rotational velocity (left) and DNa02 firing rate (right) in genetic control flies where no LexA transgene was present (mean ± SEM across flies, n=4 flies). These flies were treated just like those in Fig. 5, meaning that each antenna was illuminated in the same way. There is essentially no steering behavior or DNa02 response. This result confirms that the steering behavior and DNa02 responses we describe in Fig. 1 are not due to the visual or thermal effects of the fiber optic illumination per se. The lack of visual responses is likely related to the fact that the fiber optic filament is very small (50 μm diameter), and the illumination from the fiber is partially blocked by the antenna, which is positioned very close to the fiber.

B) Behavioral responses in flies where no dissection was performed, i.e. we did not open the head capsule. Left: genetic controls lacking a LexA driver (n=6 flies). Middle: fictive odor (Orco-LexA, n=9). Right: fictive heat (Gr28b.d-LexA, n=9 flies). Plots show mean ±SEM across flies. Note that behavioral responses are larger and less variable in these intact flies. The reduced behavioral performance of the flies in Fig. 5 is likely due to local removal of the peri-neural sheath and/or local disruption of the neuropil surrounding DNa02 somata during the patching procedure. Nonetheless, the qualitative features of behavior in Fig. 1 are comparable to intact flies.

Lateralized fictive odor stimuli produce asymmetric responses in DNa01.

Top: Rotational velocity during fictive odor presentations.

Bottom: DNa01 activity in the same experiments.

Each plot shows mean ± SEM across flies (n=4 genetic controls with no LexA driver, n=3 flies harboring Orco-LexA). On average, DNa01 activity is weaker than DNa02 activity during odor-evoked turning behavior (compare to Fig. 5), but qualitatively DNa01 and DNa02 have similar relationships to odor-evoked turning.

Leg movements associated with body rotation

A) We selected 5 leg-kinematic variables likely to be associated with body rotation. In control flies, we computed the mean value of each variable, for each leg, binned by rotational velocity (for directional variables) or rotational speed (for nondirectional variables).

B) We defined 5 multi-leg metrics, each based on one leg-kinematic variable. For each metric, the relevant legs are labeled and color-coded. Gray legs were not used because, for these legs, the variable in question did not show a reliable correlation with the fly’s rotational movement (A). Gray legs in (B) are shown faded in (A).

C) We plotted each metric versus rotational velocity or rotational speed, to verify that the expected relationship was observed. We refined our definitions in order to optimize the signal-to-noise ratio of this relationship. Each datapoint is a time window (with n values in italics near the origin of each plot). Thick lines show LOWESS fits; thin lines show 95% confidence intervals; only a small number of datapoints have rotational speeds >120°/s, so fits are not shown above this ceiling. Importantly, we fixed the number of metrics we tested, and also the definitions of those metrics, based purely on data from control flies, before we examined any of these metrics in our experimental genotypes.

D) Finally, we asked how these metrics change when DNa01 or DNa02 neurons are silenced. We identified all body rotation events in every experiment by searching forward in time for moments when rotational speed crosses a threshold of 20 °/s. We extracted a 500-ms time window around each threshold-crossing. Events were constrained to be non-overlapping. Body rotation events were tabulated separately for light-on and light-off. The number of time windows in each distribution is shown in italics. To determine if any metric was changed when DNa01 neurons were silenced, we performed 5 two-factor ANOVAs and looked for a significant interaction between genotype (control/DNa01) and light (on/off); these p-values were Bonferroni-Holm corrected to avoid type 1 errors (m=5 tests). Then, to determine if any metric was changed when DNa02 neurons were silenced, we performed 5 two-factor ANOVAs and looked for a significant interaction between genotype (control/DNa02) and light (on/off); these p-values were again Bonferroni-Holm corrected (m=5 tests); nonsignificant p-values are not shown. In cases where these p-values were significant (D4, p=0.02, DNa01 vs control) or nearly significant (D4, p=0.505, DNa02 vs control), we followed up by performing a post hoc Tukey test to determine if there was a significant difference between light on/off in each genotype. Interestingly, the only metric to show an effect was the stance duration metric (D4). In control flies, a prolonged stance duration is observed in some but not all body rotation events (C4). This implies that body rotation can be driven by an inner-back-leg pivoting maneuver, but body rotation does not absolutely require this maneuver. This idea is consistent with our finding that rotational speeds are overall unchanged when DNa01 or DNa02 is silenced (Fig. 8E).

Note that the data for the stance duration metric (A4-D4) are reproduced in Fig. 8F,G, where this metric is called “inner back leg stance duration (normalized)”, i.e. iB pivoting.