How much of fly walking is written in the wiring?

Isabel Guan; Yuntian Zhao; Dingyuan Zhang; Shipeng Lyu; I-Ming Chen

Figure 1: Rhythm is common to real and rewired wiring; antagonist coordination is strongest in the real wiring. a , Question and system (schematic): leg-motor subnetworks of two male fly ventral-nerve-cord connectomes (MaleCNS, 10,173 neurons, 462,650 connections; MANC, 10,440 and 634,207); dots, the four joints of a leg. b , Approach (schematic): a rate network with the signed synapse counts as fixed weights, driven through the DNg100 descending neurons; 20 extensor–flexor pool pairs are scored for rhythmicity and for antagonist coordination S (mean

-

corr(extensor, flexor)). Thirty rewired networks per connectome (six families of five, preserving progressively more of the real structure) receive the same protocol and pre-specified claim levels (Supplementary Fig. 1). c , Rhythmicity (left) and S (right) of the real networks (bars; dark teal, MaleCNS; teal, MANC) and the rewired networks (points, coloured by family), each at its own frozen setting (60-s confirmation, 15–25 s, mean of 20 noisy runs). 9 and 14 of 30 rewired networks are at least as rhythmic as the real networks, but none reaches their S (0.31 against at most 0.14; 0.17 against at most 0.08; levels strong and moderate). d , Reciprocal innervation (schematic): for example, a premotor neuron excites one pool and, through an inhibitory neuron, inhibits its antagonist, so the pools alternate. Bottom, reciprocal-innervation index (real 0.48 and 0.38; all rewired networks below 0). Right, S relative to the real network after premotor input is moved across antagonistic pools with motor neurons’ input strength nearly unchanged (median change below 4%): within-pool controls (x = 0), strength-matched and dose-matched cross-pool reassignments (points, networks; lines, medians; 15–25 s; Fig. 4). e , Joint scores of the real networks and of the best rewired network (lines), 15–25 s; only the thorax–coxa joint is ‘strong’ in both connectomes in all four windows (Supplementary Fig. 4). Source data are provided as a Source Data file.

Figure 2: Rewired networks produce rhythm but weaker antagonist coordination. a , Example activity of the six thorax–coxa pairs in the real MaleCNS network and in the rewired network with the highest confirmation score (lineage block), each at its own frozen setting (example simulation with a CPU re-implementation of the model; not a confirmation run; S = 0.32 and 0.16). Each pair is scaled by its larger pool s.d.; r, extensor–flexor correlation over 15–25 s; n.m., amplitude gate not met. b,c , Parameter scan: best S against maximum rhythmicity over the eligible settings of the 132-setting scan (one 25-s simulation per setting). Shaded, rhythmicity above the real network’s maximum. d–g , 60-s confirmation at each network’s frozen setting: rewired networks (points, mean

\pm

s.e.m. of 20 runs; hollow, secondary MaleCNS families that also preserve reciprocal connections; diamond, a network with 9 of 20 undefined runs, mean of 11), family medians (dark ticks), real network (line; band

\pm

s.e.m.) and the margin required of every family median for the pre-specified ‘strong’ level (dotted). Panel titles give the level reached. h,i , S of every confirmation run of the real networks; amber, runs that entered a fast state (

\geq

3 Hz with

\leq

3 modulated pairs; open circles) after 15–25 s; dashed, noise-free runs; thick line, mean of 20 noisy runs. The 300-s continuation is shown in Supplementary Fig. 2. Source data are provided as a Source Data file.

Figure 3: Reciprocal innervation of antagonistic pools is specific to the real wiring. a , The reciprocal-innervation index on data: each point is one neuron’s signed one- plus two-step influence on the extensor pool (x) and on the flexor pool (y) of the MaleCNS T2L thorax–coxa pair (one of the two pairs defining the real network’s median index), in the real network and in leg-block rewired network 0 (symmetric-log axes, linear within

\pm

0.01); index =

-

Pearson r across neurons (0.48 and

-

0.34). b , Network-level index (median over the 20 pairs) of every rewired network (points; dark ticks, family medians) and of the real networks (lines). c , Pair by pair: real index (circles; filled, above all 30 main rewired networks) against the range (bars) and median of the 30 rewired networks; 19 of 20 pairs in MaleCNS, 18 of 20 in MANC. d , Real per-pair index in the two connectomes; Spearman

\rho

= 0.82 (n = 20 pairs). Source data are provided as a Source Data file.

Figure 4: Reassigning premotor inputs across antagonistic pools abolishes coordination. a , Reassignment (schematic): edges onto motor neurons exchange targets within a pool (within-pool control) or between the extensor and flexor pools of the same leg and joint (cross-pool); strength-matched versions exchange only edges of the same sign and synapse-count decile. b , Example activity of the six thorax–coxa pairs in the real MaleCNS network and in cross-pool network 0 at the real frozen setting (example simulation as in Fig. 2a). c,d , S relative to the real network in the same window (R above each panel) for every reassigned network at the real frozen setting: original, strength-matched, and dose-matched reassignments (labels: designed net fraction of input moved across pools; MaleCNS 22% and 27%, MANC 20% and 25%). Filled circles, 15–25 s; open diamonds, 50–60 s; bars, medians of five networks; error bars, s.e.m. of 20 runs divided by R; lines at R, 0.8 R (within-pool criterion) and 0.5 R (cross-pool criterion). e , Cross-pool arms relative to the real network: S, rhythmicity and the fraction of oscillating motor neurons, for the original reassignment and the dose-matched one (medians of five networks; circles MaleCNS, squares MANC; filled 15–25 s, open 50–60 s); shaded, pre-specified criterion met. f , Extensor–flexor correlation of the pairs that contribute in the real networks (MaleCNS 9, MANC 8), real (bars) and within-pool (mint) or original cross-pool (dark red) networks (hollow, pair modulated in fewer than half the runs); 8 of 9 and 7 of 8 pairs stay modulated after cross-pool reassignment. g , S relative to the real network against the net fraction of premotor input moved across antagonistic pools, every network (15–25 s); dashed, medians of the strength-matched cross-pool series; circles MaleCNS, squares MANC. Source data are provided as a Source Data file.

Figure 5: Wiring-specific coordination is concentrated at the thorax–coxa joint. a , Score of each antagonistic pair in the real network (fill; mean of 20 runs, 15–25 s) drawn at its joint on a schematic fly, MaleCNS and MANC; ring, the real network exceeds all 30 main rewired networks for that pair (6 of 20 and 4 of 20 pairs);

\times

, joint without an antagonistic pair. b , Mean pair score per joint for the real network (bar; pale band

\pm

s.e.m.) and the 30 rewired networks (points sorted within each joint, coloured by family;

\pm

s.e.m.). c , Pre-specified readouts: S over all 20 pairs, the 16 pairs of exactly assigned motor neurons, and the 14 pairs outside the thorax–coxa joint; squares, pre-specified level at 15–25 s (left) and 50–60 s (right). The thorax–coxa joint alone is ‘strong’ in both connectomes and all four windows (Supplementary Fig. 4). Source data are provided as a Source Data file.

Figure 1: Model, rewired networks and protocol. a , Model (schematic). The leg-motor subnetwork of each connectome is simulated as a rate network with fixed connection weights (equation; W, signed synapse counts; g, gain;

\beta

, inhibition scale) driven only by a sustained input d to the left and right DNg100 descending neurons. Motor neurons are grouped by annotated target muscle into extensor (coral) and flexor (green) pools at four joints of each leg: thorax–coxa (ThC), coxa–trochanter (CTr), femur–tibia (FTi) and tibia–tarsus (TiTa). The antagonist score S averages, over the 20 antagonistic pool pairs,

-

corr(extensor, flexor) for pairs in which both pools are modulated and 0 otherwise. b , Composition of the extracted subnetworks: MaleCNS 10,173 neurons and 462,650 connections; MANC 10,440 neurons and 634,207 connections. Lower bars, motor neurons with an exact or approximate joint assignment, or unmapped. c , The six families of rewired networks and the structure each preserves (filled circles); five networks per family. d , Protocol. Every network is simulated at the same 132 settings (11 gains

\times

3 inhibition scales

\times

4 drives; 25-s runs scored at 15–25 s); shown are the scores of the real MaleCNS network at its 27 eligible settings (data; sand, not eligible; amber ring, selected setting). The best eligible setting is frozen and re-simulated for 60 s with 20 new noise realizations and 3 noise-free initial states, scored in four windows. Source data are provided as a Source Data file.

Figure 2: The coordinated state over five minutes. 300-s simulations at the frozen settings of the real MANC network, its two strongest rewired networks (lineage block 1 and 0) and the real MaleCNS network; 40 noisy trajectories per network (20 continuing the confirmation runs, 20 new) and 10 noise-free trajectories. A 10-s window counts as coordinated when S

\geq

0.10 with at least six modulated pairs (pre-registered). a , Fraction of noisy trajectories in the coordinated state. b , Mean S (undefined S counted as 0; band,

\pm

s.e.m.). Sand band, the last window (290–300 s). c , State of every trajectory in every window (filled, coordinated; below the line, noise-free trajectories). d , Switching rate: departures from the coordinated state (followed by at least three non-coordinated windows) per minute spent coordinated, with exact Poisson 95% confidence intervals; MANC real 0.24 per minute (mean dwell 4.2 min), lineage block 1 3.7 and lineage block 0 5.6; MaleCNS real, no departure. e , S of every noisy trajectory at 290–300 s; bars, means. Source data are provided as a Source Data file.

Figure 3: Dose-matched reassignment of premotor inputs. a , Design check: net fraction of premotor input moved across antagonistic pools against the change in the motor neurons’ input strength (median relative change, larger of excitatory and inhibitory), every reassigned network; hollow, strength-matched constructions (exchanges restricted to the same sign and synapse-count decile); W, dose-matched within-pool control; X lo and X hi , dose-matched cross-pool arms. Right, each dose-matched network’s median change (marker) and 95th percentile (bar top), larger of excitatory and inhibitory; across both connectomes and both input signs the medians are 1.0–2.3% (W), 1.5–2.6% (X lo ) and 2.0–3.9% (X hi ) and the 95th percentiles 9–19%, 9–20% and 11–30%, so the within-pool control, which kept coordination, changed its tail by a similar amount to X lo , which lost most of it. b , Pre-registered conditions for a selective loss (filled, met): primary test X hi against W at the real network’s frozen setting; secondary, X hi at re-optimised settings and X lo at the real setting. c , S of W and X hi at their own re-optimised frozen settings (filled, 15–25 s; open, 50–60 s; mean

\pm

s.e.m. of 20 runs; lines, real network). d , Activity maintenance relative to the real network: fraction of oscillating motor neurons (circles) and of the real network’s contributing pairs still modulated (triangles), medians of five networks; shaded, criterion (

\geq

0.8) met. Source data are provided as a Source Data file.

Figure 4: Where and when the advantage of the real wiring holds. a , Pre-specified level (dark teal strong, light teal moderate, white weak) of each readout in each confirmation window, with the real network’s value: S over all 20 pairs, over the 16 pairs of exactly assigned motor neurons, over the 14 pairs outside the thorax–coxa joint, and each joint alone. b , Score of every antagonistic pair of the real networks in the four windows (dot, modulated in at least half of the runs); in MANC the contributing pairs shift over time towards the thorax–coxa joints. Source data are provided as a Source Data file.

Connectome	Window (s)	Real $S$	Strongest rewired (family)	Smallest margin (family)	Families all below	Level
MaleCNS	15–25	$0.312$	$0.144$ (Lineage block)	$0.271$ (Lineage block)	6/6	strong
MaleCNS	25–35	$0.302$	$0.146$ (Lineage block)	$0.260$ (Lineage block)	6/6	strong
MaleCNS	35–45	$0.313$	$0.144$ (Lineage block)	$0.274$ (Lineage block)	6/6	strong
MaleCNS	50–60	$0.312$	$0.147$ (Lineage block)	$0.277$ (Lineage block)	6/6	strong
MANC	15–25	$0.173$	$0.084$ (Lineage block)	$0.134$ (Lineage block)	6/6	moderate
MANC	25–35	$0.161$	$0.080$ (Lineage block)	$0.114$ (Lineage block)	6/6	moderate

Table 1: Pre-specified claim levels in the 60-s confirmation runs. Network values are means of 20 stochastic runs at each network’s frozen setting; family values are medians over the five networks of a family. Strongest rewired network and smallest margin (real minus family median) are taken over the six main families. Strong: real above all 30 networks and every margin

\geq 0.15

; moderate: real above every network in at least five families and above every family median.

Connectome	Reassignment	Rule	Window (s)	$R$	$W$	$X$	$X/R$	(1)	(2)	(3)	(4)	(5)	(6)	All six
MaleCNS	Original	real	15–25	$0.312$	$0.298$	$-0.071$	$-0.23$	✓	✓	✓	✓	✓	✓	✓
MaleCNS	Original	real	25–35	$0.302$	$0.294$	$-0.071$	$-0.24$	✓	✓	✓	✓	✓	✓	✓
MaleCNS	Original	real	35–45	$0.313$	$0.295$	$-0.070$	$-0.22$	✓	✓	✓	✓	✓	✓	✓
MaleCNS	Original	real	50–60	$0.312$	$0.297$	$-0.070$	$-0.23$	✓	✓	✓	✓	✓	✓	✓
MaleCNS	Original	own	15–25	$0.312$	$0.283$	$-0.029$	$-0.09$	✓	✓	✓	✓	✗	✓	✗
MaleCNS	Original	own	25–35	$0.302$	$0.294$	$-0.028$	$-0.09$	✓	✓	✓	✓	✗	✓	✗

Table 2: Pre-specified conditions for a selective loss after motor-input reassignment.

R

, real network;

W

and

X

, medians over the five within-pool and five cross-pool networks (each a mean of 20 runs). Parameter rule: real, every network at the real network’s frozen setting; own, every network at its own selected setting. Conditions: (1)

W\geq 0.8R

; (2)

X\leq 0.5R

and

R-X\geq 0.10

; (3)

X\leq 0.5W

and

W-X\geq 0.10

; (4) every cross-pool network below the real network and below every within-pool network; (5) cross-pool rhythmicity at least 80% of both references; (6) at least 80% retention of modulated antagonistic pairs and of oscillating motor neurons, here assessed from the number of modulated pairs (the 60-s runs did not store pair identities; see Supplementary Table 4 for the pair-identity assessment).

Connectome	Readout	Window (s)	Real	Strongest rewired (family)	Smallest margin	Families all below	Level
MaleCNS	All pairs (20) †	15–25	$0.312$	$0.144$ (Lineage block)	$0.271$	6/6	strong
MaleCNS	All pairs (20) †	25–35	$0.302$	$0.146$ (Lineage block)	$0.260$	6/6	strong
MaleCNS	All pairs (20) †	35–45	$0.313$	$0.144$ (Lineage block)	$0.274$	6/6	strong
MaleCNS	All pairs (20) †	50–60	$0.312$	$0.147$ (Lineage block)	$0.277$	6/6	strong
MaleCNS	Exact map (16)	15–25	$0.200$	$0.126$ (Degree)	$0.178$	6/6	strong
MaleCNS	Exact map (16)	25–35	$0.190$	$0.126$ (Degree)	$0.174$	6/6	strong

Table 3: Pair-level readouts of the confirmation runs (second-round pre-registration). Same trajectories as the 60-s confirmation (reproduced to within rounding error), every network at its own frozen setting; pairs failing the amplitude gate count as zero. Readouts without a dagger were pre-specified decision readouts; † , descriptive. Level: the rule of Supplementary Table 1 applied to each readout.

Connectome	Reassignment	Window (s)	Contributing pairs	Pair retention	Oscillation retention	Met
MaleCNS	Original cross-pool	15–25	9	0.89	0.97	✓
MaleCNS	Original cross-pool	25–35	9	0.89	1.04	✓
MaleCNS	Original cross-pool	35–45	9	1.00	1.00	✓
MaleCNS	Original cross-pool	50–60	9	0.89	1.02	✓
MaleCNS	Original within-pool	15–25	9	1.00	0.99	✓
MaleCNS	Original within-pool	25–35	9	0.89	1.05	✓

Table 4: Condition 6 assessed by pair identity (reassigned networks at the real frozen setting). Contributing pairs: pairs that pass the amplitude gate in at least half of the real network’s 20 runs. Pair retention: fraction of these pairs that still pass the gate in at least half of a reassigned network’s runs (median over five networks). Oscillation retention: fraction of oscillating motor neurons relative to the real network (median over five networks). Condition met: both medians

\geq 0.8

.

Connectome	Arm, rule	Window (s)	$R$	$W$	$X$	$X/R$	Rhythm ratio	Pairs kept	Osc. kept	(1)	(2)	(3)	(4)	(5)	(6)	All six
MaleCNS	X hi , real ∗	15–25	$0.312$	$0.277$	$-0.076$	$-0.24$	$0.97$	0.89	0.85	✓	✓	✓	✓	✓	✓	✓
MaleCNS	X hi , real ∗	25–35	$0.302$	$0.272$	$-0.075$	$-0.25$	$1.09$	0.89	0.87	✓	✓	✓	✓	✓	✓	✓
MaleCNS	X hi , real ∗	35–45	$0.313$	$0.270$	$-0.079$	$-0.25$	$0.78$	0.89	0.85	✓	✓	✓	✓	✗	✓	✗
MaleCNS	X hi , real ∗	50–60	$0.312$	$0.275$	$-0.082$	$-0.26$	$0.92$	0.89	0.86	✓	✓	✓	✓	✓	✓	✓
MaleCNS	X hi , own	15–25	$0.312$	$0.229$	$-0.000$	$-0.00$	$0.42$	0.78	2.03	✗	✓	✓	✓	✗	✗	✗
MaleCNS	X hi , own	25–35	$0.302$	$0.239$	$0.009$	$0.03$	$0.44$	0.78	2.10	✗	✓	✓	✓	✗	✗	✗

Table 5: Dose-matched reassignment: pre-specified conditions (second-round pre-registration). Cross-pool arms X hi (dose-matched) and X lo (lower dose, matched to the within-pool control W in the fraction of new edges), five networks each, exchanges restricted to edges of the same sign and synapse-count decile. Rule: real, every network at the real network’s frozen setting; own, every network at its own re-optimised setting; ∗ , primary test.

R

, real network;

W

and

X

, medians of five network means (20 runs each). Rhythm ratio, cross-pool rhythmicity relative to the real network. Pairs kept and oscillation kept: condition 6 by pair identity (medians of five networks, relative to the real network). Conditions (1)–(6) as in Supplementary Table 2 .

Network	Runs	Mean $S$ 290–300 s	Coordinated at 290–300 s	Switches	Minutes coordinated	Switches per minute coordinated (95% CI)
MaleCNS real	40	$0.312$	100%	0	193.3	0.00 (0.00–0.02)
MANC real	40	$0.088$	45%	26	109.5	0.24 (0.16–0.35)
MANC lineage block 1	40	$0.076$	10%	96	26.2	3.67 (2.97–4.48)
MANC lineage block 0	40	$0.072$	0%	26	4.7	5.57 (3.64–8.16)

Table 6: 300-s simulations (second-round pre-registration). Noisy trajectories (20 continuing the confirmation runs, 20 new) at each network’s frozen setting. Coordinated: a 10-s window with

S\geq 0.10

and at least six modulated pairs. Switch: a coordinated window followed by at least three non-coordinated windows. Rate: switches per minute spent coordinated, exact Poisson 95% interval. Post hoc (not pre-registered): the difference in mean

S

at 290–300 s between the real MANC network and lineage-block network 1 was 0.011 (bootstrap 95% interval -0.013 to 0.036).

Connectome	Pools	Window (s)	Pair	Real	Rewired maximum	Rewired $\geq$ real
MaleCNS	All assigned	15–25	T1L ThC	$0.567$	$0.662$	2/30
MaleCNS	All assigned	15–25	T1R ThC	$0.527$	$0.494$	0/30
MaleCNS	All assigned	15–25	T2L ThC	$0.630$	$0.413$	0/30
MaleCNS	All assigned	15–25	T2R ThC	$0.865$	$0.874$	1/30
MaleCNS	All assigned	15–25	T3L ThC	$0.759$	$0.664$	0/30
MaleCNS	All assigned	15–25	T3R ThC	$0.883$	$0.597$	0/30

Table 7: Thorax–coxa pairs with all assigned motor neurons or with exactly assigned motor neurons only (post hoc). Pair score of the real network (mean of 20 runs) and of the 30 main rewired networks (each at its own frozen setting). In both connectomes the promotor-side pool of the front legs contains pleural promotor (exact) and sternal anterior rotator (approximate) motor neurons, and that of the middle and hind legs only sternal anterior rotator motor neurons; exact-only pairs therefore exist only in the front legs.

Connectome	Window (s)	Active pairs	Antiphasic	Active pairs	Antiphasic	Fraction
		Real network		Rewired networks (30)
MaleCNS	15–25	9	9	428	207	48%
MaleCNS	50–60	9	9	425	219	52%
MANC	15–25	8	7	458	232	51%
MANC	50–60	6	6	455	219	48%

Table 8: Antagonistic pairs that are active are antiphasic in the real networks (post hoc). Active pair: both pools pass the amplitude gate in at least half of a network’s 20 runs (the contributing pairs of condition 6). Antiphasic: mean extensor–flexor correlation over the gated runs below zero. Rewired: pairs pooled over the 30 main rewired networks, each at its own frozen setting. Mean correlation of each active pair of the real networks at 15–25 s: MaleCNS: T1L CTr

-0.92

; T2L CTr

-0.57

; T3L FTi

-0.51

; T1L ThC

-0.57

; T1R ThC

-0.53

; T2L ThC

-0.66

; T2R ThC

-0.86

; T3L ThC

-0.76

; T3R ThC

-0.88

; MANC: T1L CTr

-0.35

; T1R CTr

-0.49

; T2R CTr

-0.46

; T2R FTi

-0.39

; T3L ThC

-0.51

; T3R ThC

-0.72

; T1L TiTa

-0.21

; T1R TiTa

0.04

.

	MaleCNS			MANC
Pair	$f^{\mathrm{both}}$	$f^{\mathrm{opp}}$	Rewired max. $f^{\mathrm{opp}}$	$f^{\mathrm{both}}$	$f^{\mathrm{opp}}$	Rewired max. $f^{\mathrm{opp}}$
T1L ThC	$0.97$	$0.85$ ∗	$0.52$	$0.96$	$0.87$ ∗	$0.53$
T1R ThC	$0.96$	$0.88$ ∗	$0.53$	$0.96$	$0.88$ ∗	$0.55$
T2L ThC	$0.98$	$0.90$ ∗	$0.59$	$0.97$	$0.83$ ∗	$0.71$
T2R ThC	$0.98$	$0.87$ ∗	$0.55$	$0.96$	$0.81$ ∗	$0.78$
T3L ThC	$0.98$	$0.93$ ∗	$0.51$	$0.94$	$0.91$ ∗	$0.58$

Table 9: Opposite-signed influence behind the reciprocal-innervation index (post hoc). For each antagonistic pair of the real networks:

f^{\mathrm{both}}

, the share of the influence on the two pools carried by neurons that influence both (Eq. ( 14 ));

f^{\mathrm{opp}}

, the opposite-signed share of their influence (Eq. ( 15 )); and the largest

f^{\mathrm{opp}}

among the 30 main rewired networks. ∗ , real value above all 30 rewired networks. Influence as in the reciprocal-innervation index (one- plus two-step, signed synapse counts). Network-level values (medians over pairs): MaleCNS, real network 0.96 and 0.88, rewired networks

f^{\mathrm{opp}}

0.16–0.49 (30 networks);

f^{\mathrm{opp}}>0.5

at 19 of 20 pairs and above all rewired networks at 18 of 20; MANC, real network 0.97 and 0.83, rewired networks

f^{\mathrm{opp}}

0.16–0.49 (30 networks);

f^{\mathrm{opp}}>0.5

at 19 of 20 pairs and above all rewired networks at 18 of 20.

How much of fly walking is written in the wiring?

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