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# Motor neurons generate pose-targeted movements via proprioceptive sculpting

Benjamin Gorko, Igor Siwanowicz, Kari Close, Christina Christoforou, Karen Hibbard, Mayank Kabra, Allen Lee, Jin-Yong Park, Si Ying Li, Alex Chen, et al.

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Benjamin Gorko, Igor Siwanowicz, Kari Close, Christina Christoforou, Karen Hibbard, et al. Motor neurons generate pose-targeted movements via proprioceptive sculpting. Nature, 2024, 628 (8008), pp.596-603. 10.1038/s41586-024-07222-5. hal-04803223

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Submitted on 1 Apr 2025

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Distributed under a Creative Commons Attribution 4.0 International License
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Motor neurons generate pose-targeted movements via proprioceptive sculpting

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AUTHORS

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Benjamin Gorko¹,², Igor Siwanowicz¹, Kari Close¹, Christina Christoforou¹, Karen L. Hibbard¹,

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Mayank Kabra¹, Allen Lee¹, Jin Yong Park¹, Si Ying Li¹,⁵, Alex B. Chen¹,⁶, Shigehiro Namiki¹,³,

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Chenghao Chen¹,⁴, John C Tuthill⁴, Davi D. Bock¹,⁷, Hervé Rouault¹,⁸, Kristin Branson¹, Gudrun

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Ihrke¹, Stephen J. Huston¹,⁹*

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1. Janelia Research Campus, Howard Hughes Medical Institute, 19700 Helix Dr., Ashburn, VA 20147, USA

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2. Molecular, Cellular, and Developmental Biology, University of California, Santa Barbara, CA, USA

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3. University of Tokyo, Research Center for Advanced Science and Technology, 4-6-1 Komaba, Meguro, Tokyo 153-8904, Japan

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4. Department of Physiology and Biophysics, University of Washington, 1705 N.E. Pacific Street, Seattle, WA 98195, USA

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5. The Solomon H. Snyder Department of Neuroscience, Johns Hopkins University, Baltimore, MD 21205, USA

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6. Program in Neuroscience, Harvard Medical School, Boston, MA 02115, USA

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7. Department of Neurological Sciences, University of Vermont, Burlington, VT 05405, USA

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8. Turing Centre for Living systems, Aix-Marseille University, Université de Toulon, CNRS, CPT (UMR 7332), Marseille, France

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9. Present address: Mortimer B. Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY, USA. stephen.huston@columbia.edu

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Summary

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Motor neurons are the final common pathway¹ through which the brain controls movement of the body, forming the basic elements from which all movement is composed. Yet how a single motor neuron contributes to control of natural movement remains largely unknown. Here, we anatomically and functionally characterize the individual roles of the motor neurons that control head movement in the fly, *Drosophila melanogaster*. Counter-intuitively, we find activity in a single motor neuron rotates the head in different directions depending on the head's starting posture, such that the head converges towards a pose determined by the identity of the stimulated motor neuron. A feedback model predicts that this convergent behavior results from motor neuron drive interacting with proprioceptive feedback. We identify and genetically² suppress a single class of proprioceptive neuron³ that changes the motor-neuron-induced convergence as predicted by the feedback model. These data suggest a framework for how the brain controls movements: instead of directly generating movement in a given direction by activating a fixed set of motor neurons the brain controls movements by adding bias to an ongoing proprioceptive-motor loop.

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## Main

To understand how the nervous system controls movements, it is necessary to understand the repertoire of motor-neuron-driven movements available to the brain when choreographing the body's motion. Any given motor neuron resides deep within a nested hierarchy of neural feedback loops⁴,⁵ and can participate in many different movements where its effects will vary depending on the state of the rest of the motor system. Thus, a concise, interpretable, but still accurate description of the movement generated by any given motor neuron remains a fundamental hurdle to understanding how the brain controls movement.

*Drosophila* offers an emerging platform in which single, identified neurons can be perturbed during behavior, with the potential to create tools to do so for an entire motor subsystem⁶,⁷. Here we comprehensively analyze how the behavioral consequences of single motor neuron activation change across motor context. We perform this characterization for most of the motor neurons that control head position, revealing the contribution to behavior of a population of the nervous system's most fundamental motor elements.

## Neck MNs transform vision into movement

Many behaviors incorporate head movements, which in the fly are controlled by ~25 motor neurons (MNs) driving small muscles in the neck (figure 1a)⁸,⁹. Flies can rotate their head around all three cardinal axes (roll, pitch, and yaw) and such movements are often visually driven. In particular, to stabilize its gaze, the fly must continuously adjust its head in response to visual motion¹⁰,¹¹. To ascertain the role of an example neck motor neuron in controlling head movement in *Drosophila*, we first focused on the neck motor neuron CvN7 and investigated its potential role in gaze stabilization⁸.

In flies, gaze stabilization utilizes a class of visual projection neurons, the Lobula Plate Tangential Cells¹²,¹³ (LPTCs) that detect optic flow patterns resulting from particular axes of self-rotation¹⁴. To determine if LPTCs input directly to CvN7, we double labeled LPTCs (magenta, figure 1b) and CvN7 (green, figure 1b). This revealed that the visual neuron axons wrap around the dendrites of CvN7. Reconstruction of two motor neurons in the FAFB whole brain electron microscopy data set¹⁵ (Extended Data Fig. 1) confirmed synaptic connectivity between five specific visual neurons within the larger bilateral LPTC population¹³ and the motor neurons CvN 6 & 7⁸,¹⁶ whose dendrites branch in both sides of the brain (inset, figure 1b, Extended Data Fig. 1). To determine the particular optic flow pattern that CvN7 is most responsive to, we performed patch clamp recordings during visual stimulus presentation. This revealed that CvN7 responds to downward visual motion (figure 1c). Scanning small visual stimuli across the fly's visual field allows reconstruction of the motor neuron's visual receptive field¹⁴,¹⁷ (figure 1d), the structure of which suggests the neuron should respond most strongly during pitch up movements that result in downward visual motion across the retina¹⁴. To test this, we presented the fly with wide-field 'star field' stimuli and recorded the motor neuron's responses as the star field was rotated around different axes (figure 1e). CvN7 responds most strongly to rotation of
the visual world around the axis predicted from the piecewise receptive field mapping (figure 1e, dotted line is the axis predicted from the receptive field in 1d).

If CvN7 participates in gaze stabilization, it should, in response to the pitch up motion it detects, drive pitch down head rotations to stabilize the fly's gaze. We tested this by optogenetically stimulating CvN7 and measuring in 3D the resulting head movements (figure 1f). CvN7 activation pitches the head downward as predicted from its visual responses (figure 1g, mean axis of head rotation: 69° azimuth, 18° elevation with a spherical variance¹⁸ of 0.09 where 0 indicates that all data are perfectly aligned and 1 indicates that the data are distributed equally across the entire sphere). Like in other fly species¹⁷, Drosophila neck motor neurons are thus compactly transforming the visual consequences of the fly rotating in space into the appropriate counter-rotation of the head to stabilize the fly's gaze.

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## MN induced movement is pose-dependent

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Unexpectedly, the head rotations resulting from neck motor neuron stimulations were highly variable. Grouping CvN7-elicited movements by the head's initial posture revealed that the induced head rotations were highly dependent on the starting posture (figure 1h-j, Supplemental Videos 1-2). For example, when the head started in a pitched up posture, stimulating the motor neuron induced pitch downward movements (figure 1h). However, when the head started in a pitched down posture, activation of the same motor neuron induced much weaker movements in the opposite direction (figure 1i). To understand this posture dependence, we grouped trials with similar starting head postures and plotted the mean trajectory of the head for each group (figure 1j, Extended Data Fig. 2). We name such a plot the 'action field' of the motor neuron. For all starting poses, stimulating a given motor neuron caused the head pose to move towards a point of convergence within the action field (figure 1j). This means that stimulating the same motor neuron can lead the head to move in different directions depending on starting posture. Which posture the head converges towards changed depending on the identity of the motor neuron stimulated (figure 1k, single DproN2 motor neuron), in such a way to span the range of possible head movements (Supplemental Figs 1-16).

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Convergent movements resulting from microstimulation¹⁹ have previously been attributed by some²⁰ to long and intense stimulation leading antagonistic muscles to be artificially co-activated. To test whether the convergent movements we observe are an artifact of our stimulus parameters, we tested the effect length and intensity of stimulation had upon the observed movement. We performed patch clamp recordings from the CvN7 motor neuron and identified stimulus intensities that spanned the neuron's range of action potential frequencies (Extended Data Fig. 3). When using identical stimuli to activate CvN7 neurons in our behavioral experiments we observed convergent head movements regardless of stimulus intensity (Extended Data Fig. 3). Increasing stimulus intensity does however increase the rotational velocity with which the head moves towards the convergence point (Extended Data Fig. 3). The convergence is not due to the head reaching the limit of its range of motion; CvN7's point of convergence is positioned 10-15° pitched down, whereas the head can pitch downward unimpeded as far as 35°. Restricting our analysis to only the first 80 milliseconds of the

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133 stimulus period still shows convergent head movements (Extended Data Fig. 4). Similarly,
134 excluding fast, saccadic movements of the head from our analysis or using a different head-
135 fixed reference frame to measure rotations²¹ still results in convergent head movements
136 (Extended Data Fig. 4).

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139 **Feedback model captures pose-dependence**
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142 One potential explanation for the convergence behavior is that the motor neuron
143 stimulus is adding an offset to the control signal in an ongoing feedback loop responsible for
144 centering the head. To test for this, we computationally extracted an estimate of the stimulus-
145 induced control signal from the recorded head movements. The plot in figure 2a shows the
146 action field for CvN7. We generate an equivalent plot for control data, in which no stimulus was
147 present and the head displayed a tendency to return to its central position (figure 2b). For each
148 time point of each trajectory in these plots, we compute the rotation required to transform the
149 posture recorded in the control trajectory to the posture recorded at the same time in the
150 matching stimulus trajectory. The resulting trajectories are plotted in figure 2c. These
151 trajectories are approximately straight, reflecting a reduction in the correlation between head
152 posture and stimulus-induced rotation (R² reduced from 0.45 to 0.22, Extended Data Fig. 2g).
153 This analysis reveals an approximately constant stimulus-induced offset that our optogenetic
154 stimulus added to the head control feedback loop. The ability to extract this constant control
155 signal from the curved and convergent head movements suggests that, while the head
156 movement system is likely nonlinear, a linear feedback model may still be able to approximate a
157 significant portion of the stimulus-induced behavior.

157 Based on these results, we developed a linear feedback model in which motor neuron
158 drive interacts with feedback carrying information about head-position and velocity (figure 2d).
159 The modeled head movement generated at any given time is proportional to the weighted sum
160 of the external motor neuron stimulus and the head's current pose (figure 2e). Thus, the
161 convergent movements observed during motor neuron stimulation are modeled by the stimulus
162 adding bias to a feedback loop that centers the head. The model was fit to half of our data set
163 and then used to simulate the other half without access to the data. The resulting simulated
164 movements are qualitatively similar to the data, displaying the same convergent behavior
165 (compare figures 2f and 1j). The feedback model's performance on simulating single trials was
166 compared to that of a model without the feedback component which reflects the more classical
167 view that motor neurons generate the same movement independent of the animal's initial
168 posture (figure 2g). The feedback model performs better at simulating individual trials, with a
169 normalized root mean squared error (NRMSE) of 0.4 compared to the feedforward model's 0.6
170 (figure 2i). A NRMSE value of zero means the model predicted the trajectory of all individual
171 trials perfectly and a NRMSE of one means that a model where the head doesn't move from its
172 initial position would have performed better. Similarly, the proportion of trials where the error in
173 the simulated head pose was below 5 degrees is 71% compared to the feedforward model's
174 45% (figure 2h)
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177 Proprioception sculpts pose-dependence

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179 The source of postural feedback predicted by our model could be of neural or biomechanical
180 origin. To distinguish the relative contributions of these mechanisms we performed
181 proprioceptive manipulations, which are unlikely to affect the biomechanics, but will alter any
182 neural mechanisms reliant on proprioceptive feedback.

183 To perturb specific subsets of proprioceptors and change the proprioceptive feedback in
184 a targeted manner we generated two split-GAL4 lines. Each line expresses in a different
185 subpopulation of proprioceptive sensory neurons that innervate the neck chordotonal organ.
186 The neck chordotonal organ is a stretch sensitive internal mechanoreceptor<sup>8,22,23</sup> strung parallel
187 to the neck muscles by connective tissue (figure 3a-c, Extended Data Fig. 5). One sensory
188 neuron type, which we call the Lateral Neck Chordotonal neurons (LNCs), innervates the lateral
189 side of the chordotonal organ (figure 3a-c). Another anatomically distinct sensory neuron type,
190 which we call the Medial Neck Chordotonal neurons (MNCs), innervates the far medial side of
191 the organ (figure 3e-f). Both sensory neuron types project to the Ventral Nerve Cord via the
192 Prothoracic nerve, where they travel through the dorsal medial tract and send process towards
193 the midline (figure 3a,d, Extended Data Fig. 5).

194 If neural integration of proprioceptive feedback contributes to the convergence behavior
195 during motor neuron stimulation, then changing the proprioceptive feedback should change the
196 motor neuron's action field. We tested this hypothesis by perturbing the LNC proprioceptive
197 neurons with Kir2.1-induced hyperpolarization during CvN7 stimulation (figure 3l). Our
198 hypothesis predicts this should change proprioceptive feedback to the entire neck motor
199 system, making the system more permissive around the axis the LNCs monitor, and hence
200 making any CvN7-induced head movement stronger around this axis. As predicted, changing
201 the proprioceptive feedback changes the motor neuron action field (compare figure 3g & 3k or
202 Extended Data Fig. 5p&r). Specifically, the resulting head movements are, on average, faster
203 around the pitch axis than for proprioceptor-intact flies (figure 3g,k, Extended Data Fig. 5u-v,
204 median pitch velocity at peak: 34°/s ±43 median ± IQR for control flies, 60°/s ±66 for LNC
205 hyperpolarized flies, p=5x10<sup>-4</sup>, N=43, two-sample Kolmogorov-Smirnov test that the per-fly
206 peak pitch velocities for the two genotypes are from the same continuous distribution, median
207 difference effect size: 21 ±13 °/s). As a result, the head overshoots CvN7's normal
208 convergence point (12° pitch, measured by the starting posture that results in the smallest
209 average head movement) and converges instead towards a more pitched pose (19° pitch). This
210 suggests that the LNC proprioceptor neurons and their downstream circuit function to damp the
211 pitch velocity of the head. Indeed, freeing different parameters of the previously fit feedback
212 model one-by-one (figure 3n, see Supplemental Methods) reveals that the best fit to the LNC
213 hyperpolarized data is obtained by allowing the model parameter responsible for pitch velocity
214 feedback to be reduced by 53% (figure 3m-o). In contrast to the strong effect observed during
215 motor neuron stimulation, expressing Kir2.1 in the LNCs did not measurably affect the resting
216 posture of the head, likely because the velocity damping performed by the LNCs falls outside
217 the velocity range of normal head movements at rest (Extended Data Fig. 5t, two-sample
218 Kolmogorov-Smirnov test that the data are from the same continuous distribution: p-values 0.3,
219 0.9 and 0.2 for roll, pitch and yaw respectively, median difference effect sizes: 0.12°, 0.09°, -
220 0.09°, N=43 flies). Expressing Kir2.1 in either the MNCs or another neck proprioceptor, the
221 Prosternal Organ²⁴, also changed CvN7's action field (Extended Data Fig. 5) but the effect
222 couldn't be captured by changing a single parameter in our model.
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225 A library of neck motor neuron types
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227 We have found that stimulating a single motor neuron elicits convergent movements of the head
228 which can be concisely described by its action field. To more fully characterize the motor
229 system and determine if this convergent behavior was a general property of motor neurons, we
230 measured action fields for the majority of the motor neurons innervating the neck motor system.

231 We constructed a library of genetic drivers (Extended Data Fig. 6, Supplemental Table
232 1) that between them expressed in at least 16 of the ~25 pairs of motor neurons that drive fly
233 head movements⁹. This is likely an undercount of the unique neuron types we performed
234 experiments on, as some neurons could not be uniquely identified by their anatomy. For
235 example, we could not separate the three VCVN motor neurons and treat them as one class.
236 We stochastically drove the optogenetic protein CsChrimson in single neurons from within the
237 expression patterns of our genetic drivers and measured the head movements resulting from
238 stimulating each neuron type. After the behavioral experiment we used confocal imaging of the
239 same individual flies to identify the neurons that had been stimulated. Figure 4a-b shows the
240 individually identified neurons we discovered. In addition, we obtained confocal images of the
241 same neuron types in-situ with the muscles still present to determine the structure of the neck
242 motor system and identify which muscles each motor neuron innervates (figure 4c-f, j).

243 Anatomically, the motor neuron population falls into two groups, those whose cell bodies
244 are in the brain and those in the ventral nerve cord. Neck motor neurons in the brain send
245 axons posteriorly down the neck connective where they branch off to innervate muscles. Those
246 neck motor neurons in the ventral nerve cord send axons anteriorly to the muscles either
247 through nerves that leave the ventral nerve cord directly or by sending axons half way up the
248 neck connective to then branch off (figure 4a-b, Extended Data Fig. 7). Most neck muscles do
249 not directly enter the neck and are contained within the fly's thorax. These muscles control
250 head movements either via long tendons that travel through the neck to attach to the head
251 directly or indirectly by moving the cervical sclerite: a triangular shaped, hardened cuticle
252 segment within the thorax that comes to a point in the neck where it contacts the head⁸ (figure
253 4g-i, Extended Data Fig. 7). The exceptions to this organization are three small OH muscles
254 whose tendons, unusually, do not attach directly to cuticle structures but instead fuse at a
255 roughly 45° angle with the thick tendon of the much larger TH muscle (Extended Data Fig. 8).
256 The majority of muscles are innervated by a single motor neuron⁸ (figure 4h) but many muscles
257 have similar attachment points and therefore likely similar pulling planes. Figure 4h gives a
258 summary of the motor neuron to muscle connectivity.

259 To generate a compact characterization of the function of each motor neuron and thus
260 the whole neck motor system, we stimulated each neuron one-by-one and fit the feedback
261 model to each set of generated movements (Supplemental Figs 1-16). As with the CvN7 data,
262 convergent movements were observed in the majority of motor neurons and a feedback model
263 fit the data from all neuron types better than a feedforward one (mean NMSE 0.5 for the
264 feedback model, 0.8 for the feedforward model) indicating convergent movements are a general
property of this motor neuron population. The axis each motor neuron rotates the head around is summarized in figure 4i and the speed of the induced head movement in figure 4j. The convergent action field of each motor neuron is shown in Supplemental Figs 1-16.

# Discussion

## Related work

Our data implies that motor commands from the brain cannot generate a fixed movement by always activating the same set of motor neurons. This is because the movement produced by motor neurons changes with posture. Instead, our data suggests that motor neuron inputs can control movement by adding bias to an ongoing proprioceptive control loop. Similar, but distinct, ideas have been proposed previously as part of the 'Equilibrium Point Hypothesis'²⁵,²⁶, but have been contentious²⁷. The Equilibrium Point Hypothesis has two discrete components: (1) That the combination of multi-muscle biomechanics and spinal proprioceptive loops lead a limb to converge to a given posture and that this equilibrium posture can be changed by descending inputs altering the spinal circuitry's threshold to proprioceptive inputs. (2) That the brain takes advantage of this convergence behavior to specify desired movements as a sequence of such equilibrium points. Our data are consistent with the first part of the hypothesis. Indeed, previous work²⁸ on some fly neck motor neurons has found that descending input from the visual system doesn't lead to action potentials but instead changes the action potential threshold for mechanosensory inputs²⁸. However, our data provide no evidence either way for the second part of the equilibrium point hypothesis. Rather than critically supporting the equilibrium point hypothesis, our data argue for the more general conclusion that the nervous system generates movement by changing ongoing control laws that govern the relationship between estimates of the body's state and movement of the body²⁹,³⁰. This is likely a multi-level process consisting of multiple nested feedback loops⁴,⁵ using different levels of abstraction in the estimate of the body's state of which our direct proprioceptive-motor neuron loop is a low-level example.

## Limitations

Our approach of stimulating individual motor neurons one-by-one relied on an assumption of pseudo-linearity; that stimulating an individual motor neuron is informative about its role when acting in concert with others. This approach succeeded because we stimulated the same motor neuron many times during free behavior, capturing and analyzing its effects during many different movements and thus many different motor neuron population states. However, by definition, this approach will not capture nonlinear interactions between motor neurons. For example, we found that the tendons of the small OH muscles fuse at an approximately 45°
309 angle with the much larger TH muscle tendon, possibly enabling the OH muscles to adjust the
310 line of action of the TH muscle (Extended Data Fig. 8). This tendon fusion likely results in a
311 non-linear inter-reliance of the muscles that our analysis will not have captured³¹,³².

312 For all single neuron studies, the isolation of a single neuron's influence is only an
313 approximation; stimulating one neuron will in turn activate connected neurons. Studies in other
314 species¹⁶ have shown electrical synapses between synergistic motor neurons. Additionally, our
315 analysis doesn't consider the temporal patterning of motor neuron activity³³.
316

317 *Mechanism of convergence*

318
319 In vertebrates, convergent force fields resulting from spinal stimulation are robust to
320 proprioceptive deafferentation³⁴ and are thought to be constructed by spinal interneurons
321 indirectly engaging muscles with opposing viscoelastic properties²⁶. Indeed, gross stimulation
322 of vertebrate motor neuron pools did not result in convergent forces (after correction for forces
323 at rest) as frequently as interneuron stimulation³⁵. We have found that motor neurons produce
324 convergent movements which change when a single subclass of proprioceptive neuron is
325 perturbed. This suggests that one of the mechanisms underlying the convergence in our data is
326 proprioceptive feedback. Proprioceptive feedback is, however, unlikely to be the only
327 mechanism underlying the effects we observe; passive properties of the fly neck are likely to
328 also contribute³⁶,³⁷.

329

330 *Functional role of convergence*

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332 In robotics, flexible movements have been achieved through dynamic movement primitives³⁸,
333 where time-varying inputs modulate the behavior of lower-level dynamical systems which
334 behave similarly to the motor neuron elicited movements reported here. These low-level
335 dynamical systems ensure the trajectory specified by their inputs reaches the desired target.
336 Analogously, neuron-proprioceptor loops may transform descending motor commands into
337 control laws useful for generating complex movements that are robust to perturbations.
338

338 Motor neurons driving convergent movements may be useful for behaviors where a
339 stimulus triggers the adoption of a particular posture such as in grooming³⁹ or escape
340 preparation⁴⁰. However, many other behaviors require the generation of movements in a fixed
341 direction, such as the control of head movements by the superior colliculus in mammals⁴¹ or fly
342 optomotor head movements (Figure 1). In such systems, descending control from the brain
343 must dynamically adjust with posture to account for the posture-dependence of the downstream
344 motor neurons⁴²⁻⁴⁴. In some cases, generating fixed motion in the relevant sensory reference
345 frame may actually require convergent movements²¹.
346

346

347 The motor system is able to produce flexible and diverse outputs thanks to the ability of the
348 same motor neurons to contribute in different ways to many different movements. Because of
349 this multifunctionality it has been challenging to obtain a condensed, interpretable description of
350 a motor neuron's output that also captures its changing roles across different movements. Here
351 we obtain such a condensed description of motor neuron output for a population of motor
352 neurons. This description paves the way for understanding how the descending control of
353 movement interfaces with a dynamic motor system.

354
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356
357
358 *Data availability*
359
360 Data to reproduce the figures in this paper are available at
361 bitbucket.org/stephenhuston/code_data_gorko_et_al. The expression patterns and flies for
362 split-gal4 lines generated in this study are available online at splitgal4.janelia.org (release:
363 "Gorko et al 2024"), except for JR153 and JR161 whose expression patterns can be
364 downloaded at bitbucket.org/stephenhuston/code_data_gorko_et_al, flies available upon
365 request. Electron Microscopy data is available at fafb.catmaid.virtualflybrain.org (SKIDs:
366 1167858 (CvN6), 1337777 (CvN7)).
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368 Code availability
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370 Code to reproduce the figures in this paper is available at
371 bitbucket.org/stephenhuston/code_data_gorko_et_al.
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375 Author contribution statement
376
377 B.G, S.J.H, S.Y.L & A.B.C carried out behavioral experiments. I.S, K.C, C.Christoforou & G.I
378 carried out all anatomical imaging. J.Y.P & S.J.H performed electrophysiology. S.N, C.Chen,
379 K.L.H, J.C.T generated and characterized the fly lines. D.D.B generated EM data set. M.K, A.L
380 & K.B wrote the behavioral tracking software. H.R & S.J.H modelled the data. B.G. & S.J.H
381 analyzed the data and wrote the paper.
382
383
384
385 Acknowledgments
386
387 The Janelia Project Technical Resources team (including: K. Close, C. Christoforou, G. Ihrke, C.
388 Managan, Y. He) performed CNS dissections, histological preparations, and confocal imaging.
389 Members of the Janelia Fly Facility (including: T. Laverty, A. Cavallaro, G. Zheng, J. Kao, S.
390 Pitts, M. Mercer, J. McMahon, B. Sharp & G. Gonzalez) constructed the stocks used. The

391 Janelia Media Facility (B. Rebhorn, R. Simmons, H. Naz) provided fly food. S. Imtiaz

392 contributed to the EM tracing. H. Dionne provided the PJFRC315-10XUAS-IVS-tdtomato::Kir2.1

393 construct. The LED arena display and cameras used were a gift from the Reiser Lab and W.

394 Korff respectively. We thank S. Laughlin, L. Abbott & V. Jayaraman for feedback on the

395 manuscript

396

397

398 Competing interests

399

400 The authors declare no competing interests.
**Figure 1:** Motor neuron stimulation generates convergent movements.

(a) Schematic and (b) confocal image showing neck motor neuron dendrites (green) overlapping with LPTCs (magenta, scale bar: 50µm). Subpanel: synapse counts between LPTCs and two neck motor neurons¹³,¹⁵. HSS is ipsilateral to the motor neuron axons, VS1-3 and H2 are contralateral. (c) CvN7 responses to downward (red) or upward (blue) local visual motion. The upward response (blue) is time-reversed so each x-axis location corresponds to the same portion of visual space for both traces. (d) The visual receptive field of CvN7 (see methods). Black arrows indicate the preferred visual motion direction and response magnitude. Shaded region: data from (c). (e) The response of CvN7 to full-field visual rotation. Thin lines: individual trials (n=5), thick line: mean. Dotted blue line: axis of rotation predicted from d to give the strongest response. (f) Behavioral setup (see methods). Images are video frames taken simultaneously from two angles; colored dots are 3D tracked points. (g) Red arrow: grand mean axis of head rotation following unilateral CvN7 stimulation, thin red lines: individual fly means. Blue arrow: axis of wide-field visual rotation that elicited the maximum response in e. (h-i) Pitch movements induced by bilateral CvN7 stimulation with (h) pitched up (21 trials) or (i) pitched down (11 trials) starting postures. Grey lines: individual trials from multiple flies; black lines: mean, red region: stimulus. Positive angular velocity indicates downward head movement. (j-k) The "action fields" of two neurons (see methods), showing the average head rotation elicited during motor neuron activation at different starting postures. Data is plotted in 'quaternion space'⁴⁵, not Euler angles, see methods. Color: time during stimulus. Inset: example image of neurons. (l) Bilateral CvN7 (2442 trials, 32 flies). Solid and dotted circles: starting postures of h and i respectively. (m) DproN2 (3912 trials, 21 flies).

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**Figure 2:** A feedback model explains the convergent movements elicited by motor neuron stimulation.

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(a) The action field of the bilateral pair of CvN7 neurons (3912 trials, 32 flies), (b) the equivalent plot for a period of no stimulus (3260 trials, 32 flies). (c) The rotations required to transform each data point in (b) into its equivalent data point in (a). (d) The feedback model. The step-like optogenetic stimulus is bandpass filtered and drives a rotation of the head around a 3D axis (blue arrow). This drive is summed (⊗) with the weighted 3D pose and velocity of the head.

This results in the modelled net rotational *change* (Δ) in head position which is integrated (∫) to give the modelled head position (red arrow). (e) An illustration of the effect on the model of the same motor neuron stimulus delivered at different starting head postures. Gray arrows plot the acceleration vector that the feedback loop alone applies to the head (see Extended Data Fig.

5w for plot of velocity dependence). Blue arrows plot the acceleration component purely due to the drive from the optogenetic stimulus. Red arrows plot the net head movement that occurs as

a result of the interaction of the optogenetically driven activity (blue) and pose dependent feedback (gray). (f) The feedback model (FB) simulating held-out validation data. (g) A

feedforward (FF) model applied to the same data as in f. Any variance in trajectory length in g is due to variance in the data being simulated, not due to any postural dependence of the model. (h) Percentage of simulated trials that predicted head poses within 5° of the actual head

pose in the corresponding validation data. (i) The Normalized Root Mean Square Error (NRMSE) of each model's performance (0 = perfect match, 1 = no better than model where head doesn't move).
<figure><img src="image_3.png" /></figure>
476 **Figure 4:** An anatomical and functional library of neck motor neurons

477
478
479 (a-b) Confocal images of neck motor neurons surveyed in this study whose cell bodies are in the brain (a), and ventral nerve cord (b). Gray = standard brain/VNC template (male
480
481 JRC2018⁴⁶) which each image is aligned to⁴⁷. Black = CsChrimson-mVenus expression in the
482 neuron of interest. (c-d) side (sagittal plane) view confocal image (c) and diagram (d) of the
483 CvN7 neck motor neuron in-situ within the head (left), neck, and thorax (right) of the body. The
484 motor neuron's cell body (green, anti-GFP) can be seen at the left of the image in the back of
485 the fly's brain, its axon passes through the neck towards the thorax on the right of the image
486 where it innervates the VL1 muscle (magenta, Phalloidin), which moves the head via cuticular
487 structures (blue, Calcofluor White). (e-f) The same as in (c-d) from an above (horizontal plane)
488 view. All scale bars are 50 µm, color channel separated images available in Supplemental Fig.
489 17. (g) Diagram of all identified neck muscles, key muscle types labeled. View from inside the
50 prothorax facing towards the neck. Red = muscle; orange = tendon; gray = cuticle; green =
491 chordotonal organ. See Extended Data Fig. 7 for the complete set of muscle and cuticle
492 structure labels. (h) Motor neuron to muscle connectivity table (note that OH indicates a group
493 of 3 muscles). See Extended Data Fig. 7 for muscle name abbreviations. (i) The mean axis of
494 induced head rotation for each motor neuron. (j) The speed of rotation around each motor
495 neuron's mean axis of rotation (those shown in i). See Supplemental Figures 1-16 for number of
496 trials and flies contributing to each trace in i-j.
497
498
499
500
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603

604

605 Methods

606

607 Generation of genetic lines

608

609 Genetic lines were generated that expressed in sparse subsets of 1-10 neck motor neurons by using the split-GAL4 technique⁴⁸,⁴⁹ to generate novel intersections from published hemidrivers²,⁵⁰.

612 For the majority of motor neurons, it is necessary to activate only a single neuron out of each bilateral pair expressed by the split-GAL4 line to ensure the innervated muscles of the two neurons don't oppose each other. For example, in the case of a yaw-inducing motor neuron the left and right neurons of the bilateral pair will drive the head to move in opposite directions making interpretation of the movement induced by bilateral stimulation challenging. In the special case of pitch-inducing motor neurons, for example CvN7, unilateral stimulation isn't necessary as both motor neurons in the bilateral pair drive the same pitch movements.
613
614
615
616
617
618
619 Accordingly, for CvN7 we used genotypes that only expressed in one unilateral neuron or both
620 bilateral neurons as the experimental constraints demanded. For all other motor neurons, we
621 only performed unilateral simulation. To achieve expression of the optogenetic protein
622 CsChrimson⁵¹ in single motor neurons we stochastically expressed it within each of the split-
623 GAL4 lines (see Supplemental Methods). Flies were dissected after the behavioral experiments
624 to identify the motor neuron expressing CsChrimson. Flies that did not express CsChrimson in
625 any neurons served as genetically identical controls. To determine the effect of silencing
626 proprioceptors on motor neuron elicited movements we used similar fly lines but with the
627 CsChrimson driven by a sparse LexA driver that expressed in CvN7 and proprioceptor specific
628 split-GAL4 lines expressing Kir2.1 in specific subsets of neck proprioceptive neurons. See
629 Supplemental Methods, Extended Data Table 1 and Supplemental Table 1 for details of
630 genotypes and protocols. See Supplemental Table 2 for details of neurons identified in Electron
631 Microscopy connectome data sets.

632

633

634 Behavioral experiment pipeline

635

636 Tethered, flying flies were videoed from two orthogonal angles at 125 frames per second while
637 presenting 300 millisecond flashes of red light (625nm, 0.37 mW/mm²) spaced 1.5 seconds
638 apart for a total of 120 flashes. Due to the presence of a loss of function allele of *norpA*⁵², flies
639 were blind and did not show any behavioral reaction to the red light stimulus. The resulting
640 videos were then tracked in 3D⁵³. Flies were individually dissected, subject to direct-label
641 immunohistochemistry and imaged using confocal microscopy while keeping track of fly identity.
642 This enabled us to determine which neurons were optogenetically activated in each fly. See
643 Supplemental Methods for details of histology and imaging.

644

645 Head tracking
To track head movements we used the Animal Part Tracker⁵³ to track five points on the fly head. We tracked these landmarks in 2D using a custom deep-learning based network (see Supplemental Methods), and then combining these estimates to generate a 3D estimate of their position. The resulting set of 3D points are rotated so that the hand-annotated 3D body axis is aligned across all flies and the origin sits in the neck at the computationally estimated pivot point. The data are presented rotated so that the body axis is pitched upwards 40 degrees relative to the horizon in approximately the posture seen during Drosophila flight. The 3D rotations between frames are then calculated from the tracked points using Horn's method⁵⁴. The global, lab frame coordinate conventions used are described in Extended Data Fig. 2c.

To visualize how the movements induced by single neuron activation change with time and posture we plot 'action fields' for each neuron e.g., figure 1j. The head rotations from individual motor neuron stimulation trials were grouped into bins⁵⁵ according to the starting posture of the head in the frame before the stimulus started. We plot the average⁵⁶ rotation trajectory of each group, color coded by time or rotational velocity. The position within the three axes describes the 3D rotational pose of the head at any given time. The three axes of the plot are labeled roll, pitch and yaw but are not Euler angles; instead, they plot the 3D axis of rotation scaled by the magnitude of the same rotation⁴⁵. Thus, the data are plotted in what has previously been termed 'quaternion space'¹⁴⁵: the axis the head is rotated about relative to its normal resting position determines in which 3D direction the point is plotted, the magnitude of the rotation determines how far from the origin the point is plotted along that direction. No interpolation is performed on these data.

To both measure the visual responses of a motor neuron (figure 1d-f) and also to calibrate the optogenetic stimulus (Extended Data Fig. 3) we performed patch clamp recordings from the CvN7 motor neuron using previously described methods (Supplemental Methods)⁵⁷. The optic fiber was placed in the similar location and distance relative to the neck as in the behavioral experiments and the same stimulus sequence delivered as in the behavioral experiments while monitoring CvN7's spike rate.

The fly head was placed in between 3 orthogonal projector screens that formed the corner of a cube. Stimuli were corrected in Opengl for perspective and individually measured head angle to appear as if stimuli were on the sphere surrounding the fly. Data are presented
690 for motor neurons whose axon exits the nervous system on the fly's right hand side. Data from 691 motor neurons with axons that exited through a nerve on the left side of the fly are flipped to 692 appear as if they came from the equivalent neuron on the right side of the fly.

693 Visual receptive fields were mapped by scanning a 5° circular black target at 50°/s in the 694 four cardinal directions across a grid that covered the virtual sphere surrounding the fly⁵⁸. The 695 responses of the neuron to wide field rotation were measured by rotating a panoramic 'star field' 696 stimulus around different axes relative to the fly.

697
698
699 Modeling Head movements
700

701 The head movements induced by single motor neuron stimulation were modeled with a Linear 702 Time Invariant model. In this model the head acceleration at any given time is proportional to 703 the weighted sum of a motor-neuron specific 3D vector and feedback that is dependent on the 704 current head position and velocity (figure 2d-e). The band pass filtered LED stimulus r (see 705 Supplemental Methods) is multiplied by the stimulated motor neuron's direction of pull 706 [mₓ, mᵧ, m_z] within the quaternion space representation⁴⁵ and linearly combined with a weighted 707 sum of the current head posture and velocity to model any pose-dependent feedback. This sum 708 determines the acceleration of the modeled head in the x,y and z dimensions of the modeled 709 action field according to: 710

710
711 $\ddot{x} = rm_x + xp_{11} + \dot{x}p_{14}$
712 $\ddot{y} = rm_y + yp_{22} + \dot{y}p_{25} + zp_{23}$
713 $\ddot{z} = rm_z + zp_{33} + \dot{z}p_{36}$

714
715 $p_{23} = \begin{cases} -p_{23}, & z_0 < 0 \\ p_{23}, & z_0 \ge 0 \end{cases}$

716
717 Where x, y, z, $\dot{x}$, $\dot{y}$, $\dot{z}$ are the heads current position and velocity in the action field 3D
718 representation of rotational pose and $p_{i,j}$ are the weights applied to the head's current position
719 and velocity. The feedforward model was the same as the above except the feedback
720 parameters $p_{i,j}$ were all set to zero. See Supplemental Methods for details of the model, fitting
721 and simulation. Model performance was measured in two different ways. The Normalized root
722 mean squared error (NRMSE) was computed between the simulated and real individual trials
723 over the entire 300 millisecond simulated period. The NRMSE was computed as:
724

724
725 NRMSE = $\frac{\|data - model\|}{\|data - mean(data)\|}$

726
727 A NRMSE value of zero means the simulation was a perfect match to the validation data, a
728 NRMSE value of one means the simulation performed no better than one in which the head
729 doesn't move from its starting posture. The angular error was also computed for each frame of
730 the validation data. The rotation required to align the simulated head pose with the actual head
pose was calculated for each frame and averaged across the entire trial. We report the fraction of trials where this average angular error was <5°.

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Bloomquist, B. T. et al. Isolation of a putative phospholipase C gene of Drosophila, norpA, and its role in phototransduction. *Cell* **54**, 723–733 (1988).

Lee, A., Kabra, M., Branson, K., Robie, A. A. & Roian, E. APT: Animal Part Tracker. (https://github.com/kristinbranson/APT).

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760 Sexual Dimorphism in the Hoverfly Motion Vision Pathway. *Current Biology* vol. 18 661–

761 667 (2008).

762
763 Extended Data Figure Legends

764
765 Extended Data Figure 1: Comparison of light and electron microscopy images of two neck motor neurons

767
768 (a-b) Comparison of light microscopy data (a) and electron microscopy (b) data for the CvN6 neck motor neuron. (a) Confocal image of CvN6. Gray = JRC2018 male standard brain template which the confocal image of the BRP neuropil stain was aligned to⁴⁶,⁴⁷. Black = CsChrimson-mVenus expression in CvN6. Scale bar = 50 µm. (b) Skeleton of the manually traced and proofread same CvN6 neuron in the FAFB whole brain Electron Microscopy volume¹⁵ (catmaid-fafb.virtualflybrain.org, SKID: 1167858). (c) Confocal image of CvN7, colors as for (a). (d) Skeleton of the manually traced and proofread same CvN7 neuron in the FAFB whole brain Electron Microscopy volume (SKID: 1337777). Posterior and lateral views are shown for each data set.

771
772
773
774
775
776
777
778
779
780 Extended Data Figure 2: Individual trial data used to generate the CvN7 action fields shown in
781 figure 1j and 2a&c.

782
783 (a) Video frames of nine flies receiving a CvN7 stimulus when their head is initially pitched
784 upward. The grayscale video frame is taken at the end of the 300 millisecond stimulus period,
785 while the underlaid green image is from one frame before the stimulus started. The difference
786 between the two frames illustrates the pitch downward head movement elicited by the CvN7
787 stimulus when the head starts in an upward posture. (b) Similar to panel a, this panel displays
788 video frames of nine flies of the same genotype, but with the stimulus occurring when their
789 heads were initially pitched downward. The difference between the overlaid gray (end of
790 stimulus period) and green (before stimulus) frames illustrates the small pitch upward
791 movement of the head elicited by the same CvN7 stimulus as in panel a. Symbols in the lower
792 left hand corners of a & b correspond to the same symbols in panel e and indicate which data
793 bins the videos frames were drawn from. See Supplemental Videos 1-2 for the source videos.

794 (c) Coordinate system used in this paper. All head movement data (except Extended Data Fig.
795 4e-f) in this paper are presented in the global, lab-fixed frame coordinate system convention
796 shown here. The X, Y and Z axis show the axes roll, pitch and yaw occur about respectively
797 according to the right hand rule. The origin is in the fly's neck, located at the computationally
798 estimated pivot point of the head. The X axis is defined as tilted downward 40° from the
799 tethered fly's long body axis, reflecting the resting head posture of a typical fly during flight. For
800 plots of the visual responses of motor neurons we define positive elevation as moving upward
801 from the X to the Z axis and positive azimuth as moving from the fly's front to its left, i.e. from
802 the X axis to the Y axis. This azimuth/elevation convention is chosen to be consistent with our
803 right-hand coordinate system for describing rotations of the head, but it does not match that
804 previously used in the literature for describing visual receptive fields¹⁴. (d) The rotational
805 trajectories of the head for all 2442 trials (32 flies) that were used to generate the CvN7 action
806 field shown in figure 1j. Each line represents the trajectory of rotational postures occurring
807 during one stimulation trial, with black dots indicating the head's starting posture. The color of
808 the lines corresponds to the starting posture, and the axes are as in Figure 1j. (e) The same
809 data as in panel d, but with the trajectories grouped by the starting posture bin they were
810 assigned to when generating the average trajectories plotted in Figure 1j. The locations of the
811 starting posture bins have been expanded by a factor of x3.5, moving them apart to prevent the
812 data groups from obscuring each other. Black arrows indicate the quaternion averages of each
813 bin. (f) The same plot as panel e but with the individual trajectories color-coded by time since
814 the stimulus was turned on. (g) depicts the relationship between the initial head posture and the
815 CvN7 stimulus-induced change in head posture, utilizing the individual trials underlying the
816 means shown in figure 2a&c. The first column represents data from 3912 individual trials,
817 illustrating the association between the head posture recorded just before stimulus onset and
818 the subsequent change in head posture between the first and last frame of the stimulus. In the
819 second column, we employ the additional processing step depicted in figure 2c. This involves
820 calculating the 'rotational difference' between the no-stimulus and stimulus conditions.
821 Specifically, we plot the rotations required to align each frame's head posture with the
822 corresponding frame of the mean no-stimulus trajectory from the closest bin (depicted in figure
823 2b). In agreement with the mean data displayed in figure 2a-c, individual trials exhibit a
824 correlation between initial head posture and stimulus-induced movement (first column,

825 R²=0.45). However, when plotting the 'rotational difference' between stimulus and no-stimulus

826 conditions (second column), this correlation is reduced (R²=0.22).

827

828
830
831 (a) Example trace of the membrane potential (vertical scale bar = 10 mV) of the CvN7 motor
832 neuron in response to a 300ms flash of 625 nm, 0.04 mW/mm² light. Underneath the voltage
833 trace is a raster indicating the timing of action potentials from multiple trials. (b) An action field
834 plotting the head movements resulting from stimulating CvN7 with the same 0.04 mW/mm² light
835 pulse. (c) A plot of the 'rotational difference' between the action field in b and the equivalent
836 data that occurs during the no-stimulus control condition – see figure 2a-c for more detail. (d)
837 The neural response of CvN7 to a 0.09 mW/mm² stimulus. (e) The CvN7 action field resulting
838 from a 0.09 mW/mm² stimulus. (f) A plot of the 'rotational difference' between the action field in
e and the equivalent data that occurs during the no-stimulus control condition. (g) The neural
839 response of CvN7 to a 0.37 mW/mm² stimulus. (h) The CvN7 action field resulting from a 0.37
840 mW/mm² stimulus. (i) A plot of the 'rotational difference' between the action field in h and the
841 equivalent data that occurs during the no-stimulus control condition. (j) The neural response of
842 CvN7 to a 1.43 mW/mm² stimulus. (k) The CvN7 action field resulting from a 1.43 mW/mm²
843 stimulus. (l) A plot of the 'rotational difference' between the action field in k and the equivalent
844 data that occurs during the no-stimulus control condition. Genotype for all panels: SS00754 x
845 w+, norpA, 20XUAS-CsChrimson-mVenus (attP18).
846
847
848 Extended Data Figure 4: Action fields are robust to stimulation length, saccade removal and reference frame
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851 (a-b) To confirm that the motor neuron elicited convergence of head pose we observed is not an artifact of our 300 millisecond stimulation times, we plot just the first 80 milliseconds of the head trajectory when the angular velocity of the head is still increasing (figure 1h-i). (a) shows the head movements resulting from the first 80 milliseconds of CvN7 stimulation. (b) Shows the first 80 milliseconds of DProN2 stimulation. While there is, by definition, less time for the head to converge, the early head movements are still highly posture dependent and moving towards a point of convergence. Compare the different movements in the green and magenta circled trajectories in b, which are dominated by roll and pitch respectively. (c-d) To confirm that the mean head trajectories plotted in our action fields are representative of the underlying data and not biased by outlier events such as fast head saccades, we removed trials containing head saccades from the data. (c) is the action field of the CvN7 neuron replotted from figure 1j. (d) shows the same data but excluding any trial containing head saccades: defined as any trial containing yaw movements faster than 200 °/second. (e) All rotations in this study were measured in the lab reference frame. To confirm that the choice of reference frame did not substantially alter the results²¹ we plot here the head rotations resulting from CvN7 stimulation measured in the reference frame of the head at the time of stimulus onset. By definition all head rotations start at the origin. (f) To allow comparison of the head reference frame data in e with that measured in the lab reference frame in c we moved the start points of all trajectories in e from the origin to their respective start locations in the lab frame.
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Extended Data Figure 5: Proprioceptive manipulations alter the action field of a motor neuron

(a-d) central anatomy of the neck chordotonal organ afferents. (a) The central projection pattern of the Lateral Neck Chordotonal neurons (LNCs) within the ventral nerve cord. Purple: anti-BRP neuropil stain, green: anti-GFP. Genotype: JR153 x pJFRC2-10XUAS-IVS-mCD8::GFP (attP2). (b) Example of a single neuron from within the LNC population, genotype: JR153 x Multicolor flip out reporter (MCFO-1⁵⁹). (c) The central projection pattern of the Medial Neck Chordotonal neurons (MNCs) within the ventral nerve cord. Purple: anti-BRP neuropil stain, green: anti-GFP. Genotype: JR161 x pJFRC2-10XUAS-IVS-mCD8::GFP (attP2). (d) Example of a single neuron from within the MNC population, genotype: JR161 x Multicolor flip out reporter (MCFO-1⁵⁹). (e-k) Peripheral anatomy of the neck chordotonal afferents. (e) Peripheral expression of the same LNCs shown in (a-b). Large magenta structure: neck muscles, small magenta structure: actin rich scolopale cells of the chordotonal organ (F-actin binding Phalloidin), green: LNCs (anti-GFP). (f) Peripheral expression of the same MNCs as shown in c-d. Large magenta structure: neck muscles, small magenta structure: actin rich scolopale cells of the chordotonal organ (F-actin binding Phalloidin), green: MNCs (anti-GFP). (g) Magnification of the dendrites of the LNCs shown in f. LNC dendrites (green) can be seen to invade the magenta cylindrical scolopale cells at the lateral edge of the chordotonal organ. (i) Diagram of the chordotonal organ and the LNC neuron innervation. (j) Magnification of the dendrites of the MNCs shown in g. MNC dendrites (green) can be seen to invade the magenta cylindrical scolopale cells at the medial edge of the chordotonal organ. Scale bars in a-j are 50 µm. (k) Diagram of the chordotonal organ and the MNC neuron innervation. (l) Action field resulting from activation of the CvN7 motor neuron replotted from figure 3. Color indicates the head's angular velocity. (m) Action field of the same CvN7 motor neuron when the LNCs are hyperpolarized due to expression of Kir2.1, replotted from figure 3. (n) Action field of the same CvN7, with the MNCs hyperpolarized due to expression of Kir2.1 (43 flies, 5160 trials, JR161 x w+ norpA, 13XLexAop2>dsFRT>CsChrimson-mVenus (attP18), BPhsFlpPest-OPt (attP3); 81B12LexAp65 (VK00022), PJFRC315-10XUAS-IVS-tdtomato::Kir2.1 (su(Hw)attp5)). (o) Action field of the same CvN7 again, with the sensory neurons of the Prosternal Organ²⁴ head proprioceptor hyperpolarized due to expression of Kir2.1 (12 flies, 1632 trials, SS47486 x w+ norpA, 13XLexAop2>dsFRT>CsChrimson-mVenus (attP18), BPhsFlpPest-OPt (attP3); 81B12LexAp65 (VK00022), PJFRC315-10XUAS-IVS-tdtomato::Kir2.1 (su(Hw)attp5)). (p-o) 2D plots of the same data plotted in 3D in figure 3g-m. (p) The CvN7 action field. Equivalent to figure 3g. (q) 2D plot of the results of using a feedback model to simulate the CvN7 action field. Equivalent to figure 3i. (r) 2D plot of the CvN7 action field when the LNC proprioceptive neurons are expressing the Kir2.1 potassium channel and thus hyperpolarized. Equivalent plot to figure 3k. (s) 2D plot of the CvN7 action field simulated by the same model shown in q but with the pitch velocity feedback parameter reduced to match the data in r. Equivalent plot to figure 3m. (t) Distributions of head rotations recorded when no stimulus was present for flies where the LNC neurons were either unperturbed (blue, empty split-Gal4 x w+ norpA, 13XLexAop2>dsFRT>CsChrimson-mVenus (attP18), BPhsFlpPest-OPt (attP3); 81B12LexAp65 (VK00022), PJFRC315-10XUAS-IVS-tdtomato::Kir2.1 (su(Hw)attp5))) or where the LNC neurons were hyperpolarized due to expression of Kir2.1 (red, JR153 x w+ norpA, 13XLexAop2>dsFRT>CsChrimson-mVenus (attP18), BPhsFlpPest-OPt (attP3); 81B12LexAp65
(VK00022), PJFRC315-10XUAS-IVS-tdtomato::Kir2.1 (su(Hw)attp5))). The mean roll, pitch and yaw head angles for control flies were 0, 8, -1° respectively with standard deviations of 8, 12, 4° (N=36 flies). The equivalent mean values for the LNC hyperpolarized flies were 1,5 and 0°, with standard deviations of 9,15 and 5 (N=43 flies). A Two-sample Kolmogorov-Smirnov test could not reject the null hypothesis that the data from the two genotypes came from the same distribution (p-values 0.3, 0.9 and 0.2 for roll, pitch and yaw respectively, corresponding effect sizes: 0.12°, 0.09°, -0.09°). (u) Time series of the head pitch velocity during CvN7 stimulation for flies where LNC neurons were hyperpolarized due to expression of Kir2.1 (red, genotypes same as panel t) or unperturbed (blue). Shaded error bars are standard deviations, thick lines are means. Black bar indicates stimulus time course. (v) Pitch velocity distributions for LNC hyperpolarized (red) and unperturbed (blue) flies (genotypes same as t-u). Only the velocities at the average time of peak velocity (135 ms) are plotted. (w) illustrates the velocity dependence of the model described in figure 2. The position dependence of the same model is shown in figure 2e. Arrows plot the acceleration vector that, in the absence of any stimulus, the feedback loop alone applies to the head at each velocity. (x) illustrates the same velocity dependence of the model but now for the model fit to the proprioceptor perturbed (JR153 Kir2.1) flies with reduced pitch velocity damping.
939 Extended Data Figure 6: Expression patterns of split-Gal4 stocks generated as part of this study

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941 The full expression patterns of the split-Gal4 stocks generated and used in this study. Full stacks are available at splitgal4.janelia.org (stock names beginning "SS") and bitbucket.org/stephenhuston/code_data_gorko_et_al (stock names beginning "JR"). A neuropil stain (anti-BRP nc82 stain) is shown in magenta. The expression of each stock when crossed to UAS- CsChrimson-mVenus (20XUAS-CsChrimson-mVenus(attP18)) is shown in green (anti-GFP stain). Scale bars = 50 µm.

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949 Extended Data Figure 7: Neck musculature and nerves of *Drosophila melanogaster*

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951 (a-c) Diagrams of the fly's neck muscles. Gray = cuticle, red = muscle, orange = tendon, green = neck chordotonal organ. (a) A ventral slice through the fly's neck, horizontal plane viewed from above. (b) Dorsal slice through the fly's neck. (c) View of the same muscles in a-b from inside the fly's thorax, facing towards the neck. SC-CO DV - dorsoventral muscles linking the cervical sclerite and the condyle. VL - ventral longitudinal muscles, DE - depressor muscles, SC-RO - sclerite rotator muscle, SC-RE - sclerite retractor muscle, LEV - levator muscle, TH - transverse horizontal muscles, OH - oblique horizontal muscles, AD - adductor muscle, ABD - abductor muscle. (d-f) Diagrams of the major cuticular structures within the fly's neck. Gray= cuticle, transparent red = muscles, transparent green = chordotonal organ. (g) Ventral slice through the fly's neck, (h) Dorsal slice through the fly's neck, (i) view from inside the fly's prothorax, facing towards the neck. T - tentorium, CO - condyle, SC - cervical sclerite, PO - prosternal organ, SA - sternal apodeme, PNA - pronotal apodeme, PA - pleuron apodem. Muscle and cuticle structure are named in a way that attempts to match, where possible, the terminology of Strausfeld⁸. (j) Diagram of the four neck motor outputs of the fly central nervous system after which we have named the motor neurons. CNS outline adapted from¹⁰. VCVN motor neurons exit through the Ventral Cervical Nerve (green) that branches from the subesophageal zone where it meets the cervical connective (called the VCN in Strausfeld⁸). (k) DProN motor neurons exit the ventral nerve cord through the Dorsal Prothoracic nerve (purple, called frontal nerve/FN in Strausfeld⁸). CvN motor neurons exit through Cervical Nerve (blue, called CN in Strausfeld⁸), which branches from the cervical connective half way down its length. (l) The CvN A1 and CvN A2 motor neurons (red) have the letter A before the neuron number to indicate that they ascend from the ventral nerve cord to reach the Cervical nerve, in contrast to the majority of CvN neurons which descend from the subesophageal zone. CvN A1-2 are likely homologous to ADN1-2 in the blowfly⁸ which, in the blowfly, exit from their own thin nerve that originates in the ventral nerve cord. In *Drosophila melanogaster* this nerve is missing and appears to be fused with the cervical connective and the Cervical Nerve to allow CvN A1-2 to exit the central nervous system via the Cervical Nerve.
979 Extended Data Figure 8: The tendons of yaw muscles are coupled.

980 (a) Confocal image of the dorsal neck musculature showing the OH muscles and the large, curved tendon of the TH muscles. Red = muscles (F-actin stained with Phalloidin), blue = tendons and cuticle (chitin binding Calcofluor White). Yellow arrows indicate points of coupling between the OH and TH tendons. The three small OH muscles originate from the midline and travel anterolaterally to where they connect to the large, curved TH tendon via small tendon tendrils. (b) shows a higher magnification of the coupling between the OH 3 muscle's tendon and that of the TH muscle. (c) Diagram of the image in a. Muscles are shown in red, the TH muscle tendon is shown in orange and the OH muscle tendons are shown in blue. Such an arrangement is likely to allow the OH muscles to change the line of action of the TH muscle by altering its tendon's geometry. Such inter-muscle interactions will not be captured by our linear model.

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Extended Data Figure References

999 59. Nern, A., Pfeiffer, B. D. & Rubin, G. M. Optimized tools for multicolor stochastic labeling
1000 reveal diverse stereotyped cell arrangements in the fly visual system. Proc. Natl. Acad. Sci.
1001 U. S. A. **112**, E2967-76 (2015).
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