How much of fly walking is written in the wiring?

Introduction

• The real wiring coordinated antagonistic motor pools more strongly than every rewired network and carries Sherrington’s reciprocal innervation.Reciprocal innervation means pathways that excite one muscle inhibit its antagonist.Source: Introduction · p. 1
• Because producing behavior does not establish that specific wiring matters, the study tests antagonist coordination beyond what generic network structure provides.Earlier connectome simulations used learned interfaces or showed that coarse degree and weight statistics can reproduce gross dynamics.Source: Introduction · pp. 1, 3
• 9 and 14 of 30 rewired networks were at least as rhythmic as the real networks, but none matched real-network S (0.31 against at most 0.14; 0.17 against at most 0.08).These comparisons use frozen settings and the figure reports strong and moderate coordination levels, respectively.Source: Figure 1 · p. 2
• Reallocating premotor input between antagonistic pools abolished coordination despite only a 2–4% median change in motor-neuron input strength.The reallocation result met every pre-registered criterion in MaleCNS and had the same direction in MANC.Source: Introduction · p. 3
• The study compares fixed-weight leg motor models of two independent connectomes with nested rewiring controls and pre-registered criteria.Walking separates rhythm generation from pattern formation, including antagonist alternation.Source: Introduction · p. 3

Results

• The models used signed synapse counts as fixed weights, with glutamatergic synapses inhibitory, and compared each connectome against six rewiring families.The models included motor, proprioceptive, descending and intrinsic neurons, with motor outputs grouped into antagonist pools at four leg joints.Source: Fixed-weight models of the leg motor… · pp. 3–4

Rhythm is everywhere; antagonist coordination is strongest in the real wiring

• 19 of 40 rewired MaleCNS networks and 8 of 30 rewired MANC networks reached higher maximum rhythmicity than their real networks.In MaleCNS, the maximum rhythmicity was 0.96 for rewired networks versus 0.70 for the real network.Source: Rhythm is everywhere; antagonist… · p. 4

The real wiring carries Sherrington’s reciprocal innervation

• The real networks had positive reciprocal-innervation indices—0.48 in MaleCNS and 0.38 in MANC—while every rewired network had a negative index.The index reflects opposite-signed influence on antagonistic pools, largely from shared inputs; it was high even for pairs not active in simulation.Source: The real wiring carries Sherrington’s… · pp. 4, 6

Rhythm is everywhere; antagonist coordination is strongest in the real wiring

• In confirmation runs, real MaleCNS scored 0.312 in both main windows versus rewired maxima 0.144 and 0.147; real MANC scored 0.173 and 0.128 versus 0.084 and 0.080.The real network exceeded every rewired network in every confirmation window in both connectomes.Source: Rhythm is everywhere; antagonist… · p. 4, Figure 2 · p. 5

Reallocating premotor input between antagonistic pools abolishes coordination, even with input strength nearly unchanged

• Dose-matched cross-pool reassignment drove MaleCNS coordination below zero while retaining rhythmicity and activity; MANC showed the same direction, but its pre-registered test was not met.In MaleCNS, S fell to −0.076 and −0.082 in the two main windows; MANC’s activity retention and within-pool control narrowly missed pre-set criteria.Source: Reallocating premotor input between… · pp. 7–8

Coordination is concentrated at the thorax–coxa joint and persists for minutes

• Coordination was strongest at the thorax–coxa joint and persisted for minutes in MaleCNS, whereas MANC sometimes switched to a fast, uncoordinated rhythm.Low distal-joint scores reflected few recruited pairs rather than active antagonists being in phase; MANC’s coordinated episodes averaged about 4.2 min over 5-min trajectories.Source: Coordination is concentrated at the… · pp. 8, 10, 11, Figure 5 · p. 10

Discussion

• The connectome’s wiring specifies antagonist coordination beyond generic rhythm generation, with coordination concentrated at the thorax–coxa joint.The thorax–coxa pair at which earlier work observed a phase offset is also where this study finds wiring-specific coordination concentrated.Source: Discussion · p. 11
• Reciprocal innervation is a network-wide input pattern, implemented through excitatory-to-inhibitory paths and inhibitory disinhibition of antagonists.Earlier simulations found that cutting the 13A/13B motif did not reduce coordination beyond weight-matched control cuts, and no single cell type stood out in a knockout screen.Source: Discussion · pp. 11–12
• The results concern models, not flies, and assume inhibitory glutamatergic transmission, synapse-count weights, predicted transmitter signs, and no body or sensory feedback.About a quarter of motor-neuron joint assignments are approximate; MANC’s thorax–coxa advantage mainly comes from hind-leg pairs with approximately assigned rotators.Source: Discussion · p. 12
• Further tests should compare predicted antagonist phase relationships with recordings from walking flies and examine additional connectomes.MANC reproduced the main findings in direction but with smaller margins; its dose-matched test missed activity-retention and, in the primary window, control criteria.Source: Discussion · p. 12

Connectome data and subnetwork extraction

• MaleCNS and MANC subnetworks included leg motor and proprioceptive sensory neurons plus descending and intrinsic neurons meeting leg-neuropil inclusion criteria.Connections were retained at five or more synapses, self-connections removed, and presynaptic transmitter signs assigned; glutamate was treated as inhibitory.Source: Connectome data and subnetwork… · p. 12

Motor-neuron pools

• Motor neurons were assigned to joint and direction pools; each pool comprises one leg, joint, and direction, with an antagonistic pair when both directions are represented.Approximate assignments included sternal rotators at the thorax–coxa joint and long-tendon-muscle motor neurons at tarsal depression; exact-only assignments leave 16 pairs.Source: Motor-neuron pools · pp. 12–13

Rate model

• The simplified rate model used identical units, fixed synapse-count weights with a five-synapse floor, and three global parameters searched identically across networks.The model used a 20 ms mean time constant, inhibitory GABAergic and glutamatergic synapses, tonic DNg100 drive, and a parameter grid of 132 settings.Source: Rate model · p. 13

Readouts

• A motor-neuron trace counted as oscillating when its demeaned standard deviation exceeded 0.01, and antagonist pairs were gated using extensor and flexor trace amplitudes.The antagonist score was calculated over all 20 pairs, with additional readouts over specified subsets and individual joints.Source: Readouts · p. 13
• The antagonist score was also read out over exactly assigned motor neurons, pairs outside the thorax–coxa joint, and pairs within each individual joint.The full score covered all 20 pairs; the two second-round readouts covered 16 and 14 pairs, respectively.Source: Readouts · p. 13
• Rhythmicity uses each oscillating motor neuron's power spectrum and peak frequency in the 0.5–50-Hz band; a setting was eligible above 20% oscillating neurons and a 1–50-Hz dominant frequency.The dominant frequency is the median peak frequency across oscillating neurons.Source: Readouts · p. 14

Rewired networks

• The six families preserve density, cell-role edge counts, within-role in- and out-degree, leg-block counts, lineage-block counts, or both leg and lineage blocks.Density and cell-role edges were randomized; the other four families used degree-preserving target exchanges within blocks.Source: Rewired networks · p. 14
• Synapse counts were randomly reassigned in the density and cell-role families but traveled with edges in the other four families, preserving each neuron's output strength.In every family, each neuron retained its transmitter sign; five networks were generated per family.Source: Rewired networks · p. 14
• MaleCNS also had degree and leg × lineage secondary families that preserved reciprocal neuron-pair counts.These were generated by separately exchanging unidirectional edges and reciprocal pairs.Source: Rewired networks · p. 14

Selection and confirmation

• The real network's confirmation setting was selected from 132 simulated settings as its eligible setting with the highest antagonist score.Each network was simulated for 25 s and scored over 15–25 s; confirmation used the frozen setting for 60 s, with 20 independent noise realizations and three noise-free initial states.Source: Selection and confirmation · p. 14
• The primary confirmation window was 15–25 s and the secondary window was 50–60 s, with additional scoring windows at 25–35 s and 35–45 s.Network values averaged stochastic runs, while family values were medians across five networks; runs were not treated as independent networks.Source: Selection and confirmation · p. 14

Pre-specified criteria

• Strong evidence required the real network to exceed every network in all six families and every family median by at least 0.15; moderate evidence required exceedance in at least five families and every family median.Replication required the second connectome to reach at least the moderate level.Source: Pre-specified criteria · pp. 14–15
• Criteria were recorded before results for four rewiring families were seen, but the real MaleCNS network, density family, and three cell-role networks had already been scanned.Analysis windows, gates, and eligibility were not changed after results were seen.Source: Pre-specified criteria · p. 15

Motor-input reassignment

• Cross-pool and within-pool target exchanges preserved each motor neuron's input count and each presynaptic neuron's outputs, with exchange blocks defined by neuronal and motor-pool attributes.Strength-matched versions additionally restricted exchanges by presynaptic sign and synapse-count decile; networks were evaluated at the real network's frozen setting and their own selected settings.Source: Motor-input reassignment · p. 15
• The redistribution measure is the normalized half-sum of absolute changes in each presynaptic neuron's synapse allocation across leg–joint–direction pools.It uses synapse counts before and after reassignment for presynaptic neurons of non-zero sign and assigned motor neurons.Source: Motor-input reassignment · p. 15
• Selective loss required cross-pool coordination to fall to at most half of the real and within-pool control scores, while retaining at least 80% of reference rhythmicity and specified contributing pairs and oscillating neurons.The criteria also required the within-pool control to retain at least 80% of the real score and every cross-pool network to score below the real and within-pool networks.Source: Motor-input reassignment · p. 15
• The dose-matched cross-pool test limited median input-strength changes to 3.5% by design, but the restriction on presynaptic groups was removed.Consequently, the test cannot separate neuron-level from lineage-level allocation; the preregistered interpretation linked meeting all six conditions to allocation rather than input strength.Source: Motor-input reassignment · p. 16

• All 4,692 archived run-window records were reproduced to within rounding error, with the largest difference in S equal to 1.1 × 10−16.Source: Pair-level re-analysis · p. 16
• Decision readouts measured S across 16 exactly assigned pairs and 14 pairs outside the thorax–coxa joint, counting pairs that failed the amplitude gate as zero.Source: Pair-level re-analysis · p. 16
• The pre-registered rule would restrict the claim to the thorax–coxa joint if the non-thorax–coxa readout was weak, or make exact assignments a stated premise if that readout was weak.Source: Pair-level re-analysis · p. 16

Long simulations

• Networks were simulated for 300 s, with noisy trajectories continuing confirmation noise or using new realizations, plus noise-free initial states.The continued realizations reproduced the first 60 s of confirmation runs to within rounding error.Source: Long simulations · p. 16
• Coordination required at least six modulated pairs; the planned readouts were late-run mean S, the fraction still coordinated, and switch rate per coordinated minute.A switch required departure from coordination followed by at least three non-coordinated windows; the interpretation distinguished metastability, persistence with occasional switches, and intermediate outcomes.Source: Long simulations · p. 17

Reciprocal-innervation index

• The reciprocal-innervation index combines signed one- and two-step paths from each neuron to each antagonist pool, then uses the negative correlation of those influences across neurons.The network-level index is the median across pairs.Source: Reciprocal-innervation index · p. 17
• The post hoc decomposition separates shared-neuron influence from the share of shared influence with opposite signs on the two pools.The opposite-signed share is high when neurons driving both pools push them in opposite directions; it is zero for one-step influence alone because a neuron's outputs share its sign.Source: Reciprocal-innervation index · p. 17

• Post hoc analyses included a structural audit, a 20,000-resample trajectory bootstrap, decomposition of the reciprocal-innervation index, and two pair-level analyses.Source: Post hoc analyses · p. 17
• Pair-level analyses classified activity and antiphasis across runs, then compared thorax–coxa scores in the real network with rewired networks, using exact assignments where possible.A pair counted as active when both pools passed the amplitude gate in at least half of 20 runs, and as antiphasic when mean extensor–flexor correlation was negative.Source: Post hoc analyses · p. 18

Example simulations

• Example traces came from a CPU reimplementation with independent NumPy noise, and the six displayed thorax–coxa pairs were chosen before traces were viewed.Each example run's S fell within or next to the same network's 20 confirmation runs.Source: Example simulations · p. 18

Software

• Simulations used JAX on a single NVIDIA GeForce RTX 5090 GPU, with analyses in Python and figures drawn using Matplotlib.Source: Software · p. 18

Use of large language models

• Claude, ChatGPT, and Codex assisted with code, simulations under I.G.'s direction, and text; authors reviewed the content and took responsibility.All figures came from plotting code applied to simulation outputs, and reported numbers were recomputed from raw outputs by scripts intended for release.Source: Use of large language models · p. 18

Supplementary Note 1: Earlier analyses under a superseded short-window protocol

• MaleCNS’s score fell from 0.263 in the early window to 0.051 in the late window, revealing a transient that prompted the stationary 25-s protocol and 60-s confirmation.The transient lasted about 12 s at high gain; the earlier analyses were not repeated under the main-text protocol and do not support its main conclusions.Source: Supplementary Note 1: Earlier analyses… · p. 20
• With glutamatergic synapses treated as excitatory, MaleCNS’s antiphase index fell from 0.65 to 0.14 and no longer exceeded the lineage-block and leg × lineage networks.The authors state that the main-text conclusions are conditional on inhibitory transmission onto motor neurons.Source: Supplementary Note 1: Earlier analyses… · p. 20
• The hemilineage-activation benchmark did not test wiring specificity: transmitter identity alone predicted 9 of 12 labels, and sign-preserving rewired networks inherit that identity.The real MaleCNS network predicted 7 of 12 phenotypes; rewired networks predicted 4–10.Source: Supplementary Note 1: Earlier analyses… · p. 20
• Across 2,138-unit knockout screens, no single cell type stood out from matched random deletions; 13A/13B cuts left the antiphase index and gated score within five controls matched on inhibitory-edge and synapse counts.Hemilineage 01A lowered the antiphase index more than each of 1,000 size- and composition-matched random deletions (p = 0.001), but its amplitude-gated-score effect was not exceptional (p = 0.17); it was considered an exploratory candidate only.Source: Supplementary Note 1: Earlier analyses… · pp. 20–21

Supplementary Note 2: Timeline of pre-specification and deviations

• The planned expansion to 25 networks per family was not run, and a planned main figure on motor-neuron-layer inhibition was omitted because that analysis was not repeated under the stationary protocol.The dose-matched reassignment amendment relaxed the median input-change limit from 3% to 3.5%.Source: Supplementary Note 2: Timeline of… · p. 21

Supplementary Note 3: Active antagonistic pairs alternate in the real networks (post hoc)

• In the primary window, 16 of 17 active real-network pairs were antiphasic, whereas only 48% of MaleCNS and 51% of MANC active pairs were antiphasic across rewired networks.The secondary window also showed antiphasic activity in all nine active MaleCNS pairs and all six active MANC pairs; the analysis was post hoc and did not enter pre-registered decisions.Source: Supplementary Note 3: Active… · p. 22