nature neuroscience https://doi.org/10.1038/s41593-026-02344-7 Article Connectomic evidence that ordered activity drives neuromuscular network formation In the format provided by the authors and unedited Supplementary information 1 Supplementary Information for “Connectomic evidence that ordered activity drives neuromuscular network formation” Random synapse elimination cannot explain the adult motor-unit pattern As discussed in the section “Prenatal activity’s role” in the Discussion, random synapse elimination cannot account for the adult motor-unit pattern. Consistent with the newborn-to-adult shift in motor-unit size distributions (Fig. 6B, 1D; Extended Data Fig. 1B), our simulation of stepwise random elimination of synapses from the P0 connectome (see Methods) yielded 300 connectomes that were statistically distinct from the adult data in size distribution and range (Extended Data Fig. 10). In particular, the largest motor units in the actual adult connectomes (35 and 36 muscle fibers) were far larger than predicted by the random elimination model (mean 20.1 ± 2.05 muscle fibers, p < 0.01; 0/300 occurrences). These results support the conclusion in the Discussion that selective synapse elimination, rather than random pruning, shapes the adult motor-unit pattern. Organization of the newborn neuromuscular connectome We found that the order of the neurons in the linear order at birth was compatible with the tendency of some axons to specifically innervate, more often, fibers with larger CSA (Extended Data Fig. 1C-D). First, the 5 motor units encompassing the thinnest muscle fibers (which were among the 8 smallest motor units) did not innervate any MEF (out of the total of 6 motor units that did not innervate MEFs). Second, among the six axons that preferentially innervated small fibers (rank sum test, p < 0.05), five did not innervate any MEF and the sixth axon was located at the periphery of the linear order (Extended Data Fig. 8). The two axons that preferentially innervated the large muscle fibers were located in the center of the linear order and were the two largest motor units (Extended Data Fig. 8C). Although the neonatal neuromuscular connectivity exhibited extensive fan-in (convergence) and fan-out (divergence) (Fig. 6C, Extended Data Fig. 7), motor axons did not randomly innervate muscle fibers. Rather, both motor axons and muscle fibers showed connectional selectivity even at birth. Several aspects of this non- randomness were evident. First, motor units were more variable in size (Extended Data Fig. 1B-D) than expected from a uniform random connectivity model (see Methods). In particular, the (large) standard deviation of motor unit sizes, 32.4, is unlikely to arise from a random distribution of connectomes (p < 10-5). Such variability was manifested in the fact that 11 motor units each innervated at least 100 muscle fibers and 4 motor units each innervated only 13-53 muscle fibers, exhibiting a 9.2-fold size difference between the largest and the smallest motor units. Second, the number of axons converging onto single muscle fibers was highly variable (range: 3-16), inconsistent with a uniform random innervation model (p < 10-5 using random connectomes with motor unit sizes the same as in the data). Third, the number of inputs per muscle fiber was significantly correlated with the cross- sectional area (CSA) of the muscle fiber (Extended Data Fig. 9A; p < 0.001). Furthermore, we found that axons that preferentially innervated muscle fibers with large CSA (Extended Data Fig. 9B, Extended Data Fig. 8C-D) were located close to the middle of the linear order (i.e., where the central cluster of motor units resides). In contrast, axons with no preference for large muscle fibers were at the edges (poles) of the linear order (Extended Data Fig. 8C-D). Most axons at the periphery sampled from both small and large muscle fibers, except one axon (#6) that appeared to be specific to thin muscle fibers. Thus, motor axons that are specific to larger fibers share more targets with other axons of their kind. 2 One possible explanation for this ordering would be if motor units were topographically arranged so that the sharing was secondary to where in the muscle axons established synaptic branches. Although some small motor units were by virtue of their size unable to uniformly sample muscle fibers throughout the muscle (Supplementary Fig. 8), all of the larger motor units were widely distributed (Fig. 6A-B, Supplementary Fig. 6A-B), and, as previously described in the adult, spatial segregation of motor units is not seen in this muscle in adults or in younger muscles ([1] and see below). Hence, spatial maps do not explain this ordering. Altogether, these observations suggest that innervation is already ordered before birth and is related to structural properties of the muscle fibers. The convergence ratio from motor axons onto muscle fibers (Extended Data Fig. 1B) is greater than that reported by previous electrophysiological studies of newborn rodent muscles: for example, 2-4 terminals per NMJ in E21- P0 rat diaphragm [2,3], 3.1-3.5 in P4 rat lumbrical muscle [4], and 2-6 in P0 rat extensor digitorum longus (EDL) [5]. This discrepancy is consistent with the methodological limitations of measuring weak synapses by electrodes [6,7]. This motor unit size-related innervation pattern at birth resembles that in the adult muscles (see also [1]), in which the motor unit size is correlated with the caliber of each motor axon at the entrance of the muscle (Extended Data Fig. 1C-D). This correlation is part of the underlying reason for the orderly recruitment of progressively more powerful motor units. Such orderly recruitment of motor neurons, known as Henneman’s size principle, is a nearly universal property of motor action in vertebrates [8–10]. Although there are several theories, how this recruitment pattern comes into being remains unclear [11,12]. The unexpected existence of size principle-like features at birth raises the possibility that axonal activity patterns are already “heterogeneous” in the newborn (see [4] for P3-P5). However, we could not detect other ultrastructural features that correlated with muscle fiber caliber such as sarcomere spacing, z-line thickness, and nuclear domain sizes, features that do differentiate muscle fiber types in adult muscles [13,14]. Rather, these features were unimodally distributed among the muscle fibers. Nonetheless, newborn muscle is populated by a heterogeneous population of both motor axons and muscle fibers. At birth, MEF fibers were thicker (p < 0.01), but their sarcomere structures such as z-line thickness and sarcomere spacing were not distinct from those of SEFs (Supplementary Fig. 14). The myonuclear domains on MEFs and SEFs were not significantly different at birth either (Supplementary Fig. 13). With respect to early development, although direct neonatal electrophysiological data are limited, several studies support the conclusion that smaller motor neurons are already more excitable in neonates [15–17]. In particular, neonates exhibit differences in membrane resistance and rheobase current that parallel those observed in adults, suggesting that the size principle emerges very early [18]. EMG studies in human infants have similarly revealed a graded recruitment sequence [19–21]. Thus, it is reasonable to infer that a recruitment hierarchy begins to emerge either at or before birth, even though high-resolution recordings of neonatal rodent motor unit firing remain relatively sparse in the literature. The heterogeneity in the neonatal innervation pattern prompted us to assess whether certain pairs of axons are more likely to share targets. We calculated the probabilities of observing the number of co-innervated muscle fibers between each pair of motor axons, under the null hypothesis that each axon innervates each muscle fiber with equal probability independent of other axons (Extended Data Fig. 8, Supplementary Figs. 9, 10A, 17). We found 3 in the newborn connectome that many axonal pairs co-innervated significantly more muscle fibers than expected by the null model (2000 random connectomes; p < 0.001, see Methods). Interestingly, some pairs exhibited significant avoidance of innervating the same muscle fibers (p < 0.001). This organization of motor axons based on the targets they share, or avoid, indicates that the innervation pattern of axons is not random but rather reflects differences between motor neurons. However, the overall pattern could not be discovered by this pairwise analysis and required looking at the entire network. To determine whether the nonrandom innervation of muscle fibers by motor axons was part of a more global connectional scheme, we mapped the pairwise co-innervation pattern on a graph. In this graph each node represented one axon and each edge corresponded to a pair of axons co-innervating significantly more or fewer muscle fibers than expected by chance. We then weighted each edge by the degree to which the co-innervation deviated from the chance level. This approach allowed all axons to be normalized to the same scale independent of their motor unit sizes. To visualize this network, we embedded it into a plane using a force-directed graph drawing [22]. Axons that co-innervated significantly more muscle fibers than expected by chance were pulled together; conversely, axons that shared fewer muscle fibers than expected by chance were farther apart. This axonal network appeared elongated in one direction (Fig. 6D, Extended Data Fig. 8A). To determine whether this global elongation could have emerged by chance, we simulated 500 random connectomes constrained by the same fan-in and fan-out statistics of motor axons and muscle fibers found at birth (i.e., the “configuration model”; [23]), and computed a metric of network elongation for each simulated connectome (see Methods). We discovered that the actual P0 connectome was more linear (elongated) than expected by chance (p < 0.04) (Supplementary Fig. 10A,D). This elongation signifies that axonal preferences are ordered in a roughly linear way: axons that are adjacent in the order have preferences to co-innervate the same muscle fibers, axons that are distant in the order share little innervation to the same muscle fibers. This order appears to be a continuous set of preferences rather than two or more strictly selective cohorts - as would occur if there was a strict specificity between motor neurons of one type for muscle fibers of a corresponding type (Extended Data Fig. 8, Supplementary Fig. 9). As discussed before (Figs. 1H-I, 5A-B, 6D), this ordering pattern becomes stronger with maturation (Supplementary Fig. 10B-D). To make this ordering more concrete, we provide this example (Extended Data Fig. 8A). Axon #8 shares a significant number of muscle fibers with axons #1 and #10, and both of them share significant numbers of muscle fibers with each other and with axon #2. In addition to these connections, axon #2 also shares a significant number of muscle fibers with 4 axons that are part of a central cluster of axons that mutually share many muscle fibers. On the north side of that cluster, axons #18 and #5 each share a significant number of muscle fibers with several axons in the central cluster as well as with each other. However, these two axons (18 and 5) do not have significant shared connectivity with any axons on the south side of the central cluster. Both of them, however, share a significant number of muscle fibers with axon #6, an axon that is not sharing a significant number of muscle fibers with any other axon, and hence is the northmost axon in this ordered array. This arrangement indicates that many motor axons have strong preferences to share muscle fibers with just a few other motor units, and those motor units in turn have strong preferences for a slightly shifted subset of motor units. We thus termed this elongation a “linear order of co-innervation.” Properties of adult multiple-endplate muscle fibers Consistent with the adult MEF connectivity pattern described in the main text, adult muscle B also exhibited a non- random pattern of MEF co-innervation (Supplementary Fig. 2). As already mentioned, the same pairs of motor 4 units shared more than one MEF. Moreover, two axons concentrated their innervation on MEFs to a greater degree than expected by chance: axon 1 innervated 9 of 13 MEFs (69.23%) and a total of 10 NMJs on MEFs (38.46% of the 26 MEF NMJs) (p < 0.05), whereas axon 2 innervated 5 of 13 MEFs (38.46%) and a total of 7 NMJs on MEFs (26.92% of the MEF NMJs) (p < 0.03). This repeated innervation of MEF NMJs by 7 axons (p < 0.005; see Methods) indicates that the adult innervation pattern remains structured despite its sparse connectivity. We found no evidence that MEFs constitute a distinct group. For example, the CSA of an adult muscle fiber is a strong indicator of its functional type [24]. However, adult MEFs exhibited a broad distribution of CSAs comparable to that of SEFs (bootstrapping test, p > 0.1 in Muscle A) (Extended Data Fig. 1B). Moreover, the motor unit sizes of axons innervating MEFs (12/18 axons in muscle A and 7/16 axons in muscle B) were what we would expect to occur by chance (mean in Muscle A 16.1 NMJs, p > 0.1; mean in Muscle B 18.3 NMJs, p > 0.1). This conclusion is further supported by myonuclear domain analysis, which showed no significant differences between MEFs and SEFs at birth (Supplementary Fig. 13), ruling out substantial differences in oxidative capacity as an explanation for the connectivity patterns. Thus, as discussed above, the non-random connectivity in adult MEFs shares features with the innervation pattern at earlier stages, providing a potential link between the developmental ordering phenomenon and the adult pattern of innervation (i.e., the size principle). The distance between NMJs on developing MEFs The distance between the closest NMJs increased significantly across maturation: between newborn (P0) and all other developmental ages P10, P12, P30, and P60 (Fig. 2A; rank sum of the mean of the left side of the distribution; largest p-value p < 0.025 between P0 and P10, and p < 0.001 between P0 and intermediate stage (P10 and P12), p < 0.02 between intermediate stage and adults, p < 10-9 between P0 and adults). The loss of the nearby NMJ pairs occurred gradually during the first weeks of postnatal life. EM correlates of neural degeneration One of the advantages of carrying out an exhaustive anatomical study with nanometer resolution is the ability to chart neural connections that might not be functionally active. Throughout our P0 EM dataset, we observed signs of neural degeneration. This is in line with findings from [25] who showed that the peak of motor unit size is just before birth (E18). These data are consistent with the signs of structured innervation seen at P0 (Fig. 6B,D, Extended Data Fig. 8, Extended Data Fig. 1). We observed different levels of degeneration: on one hand, we saw retraction of single branches of specific motor neurons (Supplementary Fig. 15), while on the other hand, we saw retraction of entire sub-bundles of the neural circuit (Supplementary Fig. 16). In the first case, specific anatomical features typically associated with retraction were circumscribed to local branches of specific axons. In particular, there were many axonal bulbs throughout the dataset, which were either found at the synapse or branched off the main axonal path (Supplementary Fig. 15A). It is worth noting that these bulbs were devoid of synaptic vesicles; however, they likely harbored axoplasm, traces of membrane recycling, or a higher concentration of lesser identified black dashes, which we hypothesized could have been either endoplasmic reticulum, or signs of cytoskeleton dismantling (see [26]). Another axon-specific sign of retraction was axonal local portions filled with vesicles (Supplementary Fig. 15C), in alignment with previous studies [27,28]. Importantly, all axons surrounding the vesicle-bearing axon did not present vesicles in the same proportion (or at all). As reported above, one interesting phenomenon observed in our P0 dataset was signs of retraction – and perhaps neural degeneration – encompassing entire neural sub-bundles. From a morphological perspective these sub- bundles presented swellings in all the axons. It was not uncommon to see these axonal swellings filled with the 5 aforementioned black dashes, or with signs of membrane recycling (Supplementary Fig. 16B-D). The reason why we believe that these branches were retracting is that no axon of these sub-bundles was forming a synapse with muscle fibers. Furthermore, there was no evidence of synaptic vesicles within the motor neurons, suggesting that these terminals were no longer active, and hence a likely hypothesis is that they were retracting. These sub- bundles did not form synaptic contact with muscle fibers, but rather they terminated their journey in what we named “graveyards,” i.e. debris made up of Schwann cell and axonal material (Supplementary Fig. 16A-B). Taking a closer look at samples of graveyards, we observed just how many of these shreds of axons contained a relatively high concentration of organelles, such as mitochondria and even vesicles. Moreover, the black dashes became prominent and more concentrated (Supplementary Fig. 16B). While locating these graveyards, it was worth noticing that many were positioned in proximity to muscle fibers. Some of these fibers presented a higher concentration of mitochondria and lipid droplets, perhaps the heritage of a recently active postsynaptic site (Supplementary Fig. 16B), while other fibers did not show any correlates of active zones (Supplementary Fig. 16A). Lastly, an intriguing anatomical correlate of our hypothesized retraction both at the axonal and at the sub-bundle level was the presence of putative degenerating synapses, devoid of synaptic vesicles. In some cases, these were present at the NMJ site (axon-specific) (Supplementary Fig. 15B), while in other cases they were seen interfacing with non-active areas of muscle fibers (Supplementary Fig. 16E-F). 6 SUPPLEMENTARY FIGURES AND TABLES Day Fibers NMJs % P0-1 (EM) 0.5 188 262 39.4 P1yfp1 1 245 341 39.2 P1yfp3 1 222 309 39.2 P1yfp4 1 234 307 31.2 P1yfp2 1 248 344 38.7 P1yfp5 1 270 368 36.3 P3-1 3 250 356 42.4 P3-2 3 230 315 37.0 P5-1 5 262 328 25.2 P5-2 5 254 334 31.5 P5-3 5 268 357 33.2 P5-4 5 254 309 21.7 P10-1 10 312 370 18.6 P10-2 10 252 287 13.9 P10-3 10 253 300 18.6 P10-4 10 252 282 11.9 P12-1 12 264 303 14.8 P12-2 12 244 283 16.0 P30-1 30 254 300 18.1 P30-2 30 205 216 5.4 P30-3 30 220 223 1.4 YFP1 60 219 233 6.4 YFP2 60 231 248 7.4 Table S1. Muscle samples studied. Inventory of all muscle samples examined. The age (postnatal days after birth), total number of muscle fibers, NMJs, and percentage of MEFs per sample are listed. EM= sample used for electron microscopy; YFP= XFP sample used for confocal microscopy. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7 Table S2. Prediction of collision of postsynaptic AP in developmental multiple-endplate muscle fibers with pairs of nearby endplates. The distance between an axon terminal and its nearest branching point (L1 and L2) and the distance between NMJs (L) along the muscle fiber (MF) were estimated by reconstructing and skeletonizing axons and muscle fibers. The axon conduction velocities (CV-Axons) near terminals were obtained from [33], and see also [34], using properties of axons of similar diameter. Due to possible differences in the cable properties between the studies, the maximal experimentally observed axon terminal CV was used (in favor of collision). We assume that the standard deviation in the synaptic delay time is 0.25 ms, in line with Katz & Miledi [33]. The model predicts that postsynaptic AP collision may occur only with very low probability at P10, which may suffice to induce interjunctional elimination. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ P10 MEF CV-MFs CV-Axon Axonal branch length diff (L2-L1) MF length (L) AP propagation time (NMJ1 to NMJ2) Activity onset NMJ2 Collision prob. margin - time diff (m/s) (m/s) ( m) μ ( m) μ (ms) (ms) (ms) 1 1.5 0.62 19 41.3 0.028 0.031 0.062 0.003 2 1.5 0.62 40 59.3 0.040 0.065 0.088 0.025 3 1.5 0.62 73 72.3 0.048 0.118 0.103 0.070 4 1.5 0.62 13 65.6 0.044 0.021 0.098 -0.023 8 Motor Unit Size and MI Charts per Muscle Om1 P8 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Orange 76 66 10 0 0 10 Magenta 74 54 20 0 0 20 Blue 66 53 13 0 0 13 Green 68 46 22 0 0 22 Pink 39 32 7 0 0 7 Total Muscle 287 251 36 0 0 36 Om2 P7 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Orange 43 21 18 4 0 22 Purple 30 8 20 2 0 22 Red 34 9 20 5 0 25 Blue 40 9 28 3 0 31 Green 47 10 32 5 0 37 Rasp 19 3 14 2 0 16 Total Muscle 133 60 66 7 0 73 Om3 P7 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Green 27 7 18 2 0 20 Magenta 61 16 37 8 0 45 Peach 61 13 38 9 1 48 Blue 55 11 32 11 1 44 Purple 39 9 23 6 1 30 Cyan 53 9 31 12 1 44 9 Lavender 47 7 31 9 0 40 Orange 55 27 22 6 0 28 Speariment 13 3 10 0 0 10 Total Muscle 245 102 121 21 1 143 Om4 P6 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Green 125 2 94 27 2 123 Blue 144 24 99 18 3 120 Red 127 38 65 21 3 89 Purple 88 19 54 13 2 69 Pink 145 24 86 30 5 121 Lavender 137 8 92 32 5 129 Total Muscle 412 115 245 47 5 297 Lum1 P9 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Prune 57 30 19 6 2 27 Red 57 19 29 7 2 38 Green 53 16 27 8 2 37 Crimson 60 20 32 7 1 40 Purple 61 33 23 4 1 28 Blue 39 32 6 1 0 7 Total Muscle 231 150 68 11 2 81 Lum2 P8 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI 10 Jade† 10 1 8 1 0 9 Cyan 54 44 10 0 0 10 Pink 71 40 27 4 0 31 Blue 64 32 29 3 0 32 Pear 59 26 29 4 0 33 Crimson 81 51 27 3 0 30 Total Muscle 264 194 65 5 0 70 † This neuron made additional sensory connections to the muscle. Lum3 P8 Axon Color Total MU size # Singles # Doubles # Triples # Quads # MI Orange 56 33 19 4 0 23 Blue 67 38 25 4 0 29 Yellow 77 11 55 11 0 66 Green 75 13 53 9 0 62 Cyan 64 25 34 5 0 39 Red 47 16 28 3 0 31 Total Muscle 255 136 107 12 0 119 Table S3. Developmental motor units and convergence rates at P6-P9. The motor units of four omohyoid (Om 1-4) and three lumbrical (Lum 1-3) muscles. For each unit we calculated from the Brainbow stack the number of NMJs with single (1 input), double (2 inputs), triple (3 inputs), Quadruple (4 inputs) and MI (polyneuronal) innervations. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 11 Supplementary Fig. 1. Motor-unit size and summed fiber CSA yield a highly consistent recruitment order in adult muscle. Each point represents one motor unit from a P60 interscutularis muscle (N = 16 motor units), ranked by summed muscle-fiber cross-sectional area (x-axis) and by number of innervated muscle fibers (y-axis). The two rankings were highly correlated (Spearman r = 0.95, p < 0.001), indicating that the inferred recruitment order is robust to the choice of ranking metric. As a closer proxy for contractile force, the CSA-based rank may also be a better predictor of precise recruitment timing. 12 Supplementary Fig. 2. Clustered innervation on multiple-endplate muscle fibers (MEFs) in the connectome of adult muscle. Seven motor units innervated 26 neuromuscular junctions (NMJs) on 13 MEFs; too few motor units to have occurred by chance (p < 0.0045). The weights on the edges represent the number of distinct MEFs shared by the pair of motor units. A pair of motor units co-innervated three MEFs, and two other pairs of motor units each innervated a pair of multiple-endplate muscle fibers. One motor unit (leftmost) innervated two MEFs (4 NMJs). The sum of all weights corresponds to the number of NMJs on MEFs. This patterned co-innervation contributed to the finding that pairs of motor units co-innervating the same MEFs were responsible for contractile forces that were more similar to each other than expected by chance (as shown in muscle A; Fig. 1H-I). 13 Supplementary Fig. 3. Probability of action potential (AP) collision in multiple-endplate fibers (MEFs) depends on the interjunctional distance and the relative latency of axonal APs. Assuming an AP conduction velocity in the muscle fiber of 1.5 m/s, when the interjunctional distance is short (< 100 μm), the probability of AP collision is low (~15%) even if axonal APs arrive at the terminals without any relative latency. Therefore, one neuromuscular junction (NMJ) can eliminate the other despite the short distance between them. On the other hand, the probability of muscular AP collision approaches 1 when the interjunctional distance is large and the relative latency of axonal APs is not too large. 14 Supplementary Fig. 4. Linear order of connectivity in four omohyoid (Om) and three lumbrical (Lum) muscles at P6- 9. Motor units in each muscle were ordered so that units placed closer together had a greater tendency to share neuromuscular junctions (NMJs), whereas units placed farther apart had a greater tendency to avoid sharing NMJs. This arrangement was obtained by selecting the permutation of motor units that maximized the correlation between inter-unit distance and NMJ sharing. To test whether such an arrangement could arise by chance, we analyzed random graphs with the same configuration, that is, the same numbers of motor units, NMJs, inputs, and outputs. In each of the seven muscles, the observed correlation was unlikely to arise from random graphs (p < 0.05; N = 500 random connectomes). The corresponding inter-axonal connectivity graphs are shown in Extended Data Fig. 6. 15 Supplementary Fig. 5. Co-innervation of motor units in a P8 lumbrical muscle. The co-innervation of pairs of motor units in a P8 lumbrical muscle (Lum3) is shown. Nodes represent motor units, edges represent pairs of motor units sharing neuromuscular junction (NMJ) targets, the number of shared NMJ targets is indicated on the edges, and the number of innervated NMJs is shown inside the circles. As with all seven muscles at this age, this muscle shows a linear arrangement of motor units as shown in Supplementary Fig. 4. Pairs of motor units that co-innervate more NMJs than expected by a random innervation model are placed close to each other. The motor units on the left and right sides co-innervate 1 NMJ, which is significantly less than expected by chance (p < 0.01; N = 300 degree-matched random connectomes). 16 Supplementary Fig. 6. Postsynaptic sites in the neuromuscular connectome of the newborn mouse (P0) interscutularis muscle. (A) A serial-section EM reconstruction of all 20 motor units. The colors of the axons represent the size of the motor units with warm colors representing larger motor units than cool colors as in Fig. 6 and the postsynaptic sites in gray. (B) The motor units are ranked by the percentage of innervated muscle fibers as in Fig. 6. 17 Supplementary Fig. 7. Large and small neuromuscular junctions (NMJs) in the newborn dataset. NMJs are marked with an annotation of the muscle fiber’s postsynaptic regions (white), along their axonal inputs. Top: 11-input NMJ and bottom: 3-inputs NMJ. 18 Supplementary Fig. 8. Varying sizes of axonal arbors in the newborn. The middle motor unit contacts half as many fibers as the motor unit on the right, although both axons extend broadly across the innervation band. The middle axon branches less extensively from its main axonal trunks. Scale bar, 100 μm. 19 Supplementary Fig. 9. Linear order in the newborn dataset projected on a circle. A unique ranking was computed from the linear order of the newborn axons (Fig. 6D, Extended Data Fig. 8) using the coordinates of the axons along the large axis of the covariance matrix of the nodes’ positions. The ranking of the axons in this axis determined the location on the circle. Both edge brightness and thickness signify the probability to observe as many or more shared muscle fibers between pairs of axons as in the data compared to a random and uniform innervation model. The tendency of the thick edges to be located near the circle’s perimeter reflects the linearity of the co-innervation map. 20 Supplementary Fig. 10. Linear order of axonal networks during development. (A to C) The nodes in the graph representation correspond to axons, whereas edges represent the number of shared targets between pairs of motor units. For the adult muscle, results are obtained by analyzing MEFs connectivity. A pair of axons is connected by an edge if they co-innervate significantly more targets than expected by chance. The edge length represents the likelihood to observe the actual number of shared targets under the assumption of independent, uniform random innervation (short edges for excessive shared innervation). Nodes are positioned by an optimized 2-dimensional embedding using a spring-force algorithm [29]. The linearity within these axonal graphs (λ) was measured at P0 (interscutularis muscle at birth, N = 1 connectome), P6-P9 (developmental omohyoid and lumbrical muscles, N = 7 connectomes), and P60 (adult interscutularis, N = 2 connectomes) by comparing its elongation (eccentricity of the scattered nodes) to that of random connectomes with the same number of axons, fibers and motor unit sizes. The ability to embed the networks in 2D and obtain a large elongation index indicates that axons are rankable such that an axon’s innervation proclivities were most similar to the axons on either side of it in the linear ranking. (D) All three connectomes show elongation of the axonal network significantly beyond that of a random connectome (p < 0.05). The red vertical lines indicate the elongation of the biological connectomes, compared with random size-matched connectomes (cyan). 21 Supplementary Fig. 11. Uniform scaling of the newborn connectome. Top. The newborn motor-unit size distribution was linearly rescaled across a range of scaling factors and compared with the adult connectome (adult muscle A; Fig. 1; Extended Data Fig. 1B) using three summary criteria: the absolute difference in median motor-unit size, the absolute difference in the 95th percentile, and their combined discrepancy (RMSE). Black points indicate the scaling factors that minimize each criterion. Bottom. The adult motor-unit histogram (gray) is overlaid with the best scaled newborn histograms for matching the median motor-unit size (blue), the 95th percentile (orange), or the combined discrepancy (yellow). In all cases, the scaled newborn distributions remain qualitatively different from the adult distribution. 22 Supplementary Fig. 12. Primary and secondary fibers. Out of 240 muscle fiber targets in the newborn muscle, 26 were secondary fibers (green) with immature contractile properties that were attached to other more mature primary fibers (yellow). In all cases the secondary fiber possessed NMJs near the location of NMJs on the primary fibers, as reported by [30]. 23 Supplementary Fig. 13. Saturation of all myonuclei in a subset of fibers. Top. All the synaptic and nonsynaptic myonuclei of 52 randomly selected muscle fibers in the newborn sample (N = 25 MEFs and N = 27 SEFs), rendered with the axonal arbor, NMJs and muscle fibers. Bottom. For each muscle fiber the synaptic nuclei (red) were identified in the vicinity of the NMJs (yellow). The myonuclear domain of the MEFs and SEFs, which is indicative of oxidative capacity of fibers, and the number of synaptic nuclei, [31,32], were not significantly different between MEFs and SEFs (two-sided Wilcoxon rank-sum test). Scale bar is 100 μm. 24 Supplementary Fig. 14. Sarcomere spacing in the newborn sample. The distribution of sarcomere spacing is unimodal and not distinctly distributed for the multiple-endplate (MEFs) and single-endplate (SEFs) fibers. 25 Supplementary Fig. 15. Signs of synapse removal before birth. (A) EM example of one axonal bulb found off of the axonal pathway in the newborn dataset. The ovoidal inflation is connected to the axon via a narrow neck (red arrowhead) where the axonal microtubules are visible. (B) Example of putative degenerating synapse marked by the red arrow. The inflation presents signs of membrane recycling and is devoid of synaptic vesicles (present in neighboring terminals). (C) Example of an axon bulb filled with vesicles, surrounded by axons devoid of synaptic vesicles. The existence of a synapse reorganization process before birth is consistent with the connectome patterning seen at birth. 26 Supplementary Fig. 16. Anatomical correlates of entire sub-bundle retraction. (A) The “graveyard” (debris made up of Schwann cell and axonal material) is adjacent to non-active muscle fibers. (B) The graveyard is near a fiber with high content of mitochondria. (C to D) Examples of sub-bundles that dead-end in graveyards. Of interest are the highly concentrated black dashes in the axoplasm. (E to F) Examples of putative degenerating synapses. Note that these structures are devoid of synaptic vesicles. 27 Supplementary Fig. 17. Co-innervation diagram of three motor units in the newborn dataset. Each node represents one motor unit and directed edges between two motor units (source unit and target unit) represent the proportion of muscle fibers in the target motor unit that are also included in the source motor unit. For example, unit 19 included 75% of the muscle fibers of motor unit 17. For each motor unit its size relative to the total number of fibers in the muscle (N = 240) is given in parenthesis. For example, unit 17 contained 39% of the fibers in the dataset. Assuming 240 possible targets, we calculate the probability to observe the number of shared targets under the assumption that targets are picked independently and uniformly at random. 28 Supplementary Fig. 18. Quantifying the single-section CSA error used in the perturbation analysis. (A) 213 interscutularis fibers reconstructed over ~35 µm; each fiber is pseudo-colored for clarity. (B) Scatter of true fiber volume (from full stack) versus the CSA measured in a single cross-section; the red line is the least-squares linear fit (R² = 0.979). (C) Histogram of the resulting percentage error with a normal overlay (μ = 0.92 %, σ = 8.39 %, skew = ~0.10), which defines the N(0, σ²) kernel used to perturb CSAs in both empirical and random connectomes. (D) Residuals versus fitted volumes show no systematic bias or heteroscedasticity (green trend close to constant zero), supporting the homoscedastic noise model adopted in the p-value derivation based on a Monte Carlo method (see Methods). 29 REFERENCES FOR SUPPLEMENTARY INFORMATION 1. Lu J, Tapia JC, White OL, Lichtman JW. The Interscutularis Muscle Connectome. PLoS Biology. 2009;7(2):e1000032. doi:10.1371/journal.pbio.1000032 2. Redfern PA. Neuromuscular transmission in new-born rats. J Physiol. 1970;209(3):701-709. 3. Harris AJ, McCaig CD. Embryonic proliferation of autonomic axons following muscle denervation. Neurosci Lett. 1983;11:S47. 4. Jones SP, Ridge RM, Rowlerson A. The non-selective innervation of muscle fibres and mixed composition of motor units in a muscle of neonatal rat. J Physiol. 1987;386:377-394. 5. Balice-Gordon RJ, Thompson WJ. Synaptic rearrangements and alterations in motor unit properties in neonatal rat extensor digitorum longus muscle. J Physiol. 1988;398:191-210. 6. Brown MC, Jansen JK, Van Essen D. Polyneuronal innervation of skeletal muscle in new-born rats and its elimination during maturation. J Physiol. 1976;261(2):387-422. 7. Bennett MR, Pettigrew AG. The formation of synapses in striated muscle during development. The Journal of Physiology. 1974;241(2):515-545. doi:10.1113/jphysiol.1974.sp010670 8. Henneman E. Relation between size of neurons and their susceptibility to discharge. Science. 1957;126(3287):1345-1347. 9. Henneman E, Olson CB. RELATIONS BETWEEN STRUCTURE AND FUNCTION IN THE DESIGN OF SKELETAL MUSCLES. J Neurophysiol. 1965;28:581-598. 10. Zajac FE, Faden JS. Relationship among recruitment order, axonal conduction velocity, and muscle-unit properties of type-identified motor units in cat plantaris muscle. J Neurophysiol. 1985;53(5):1303-1322. 11. Zucker RS. Theoretical implications of the size principle of motoneurone recruitment. J Theor Biol. 1973;38(3):587-596. 12. Freund HJ. Motor unit and muscle activity in voluntary motor control. Physiol Rev. 1983;63(2):387-436. 13. Tseng BS, Kasper CE, Edgerton VR. Cytoplasm-to-myonucleus ratios and succinate dehydrogenase activities in adult rat slow and fast muscle fibers. Cell Tissue Res. 1994;275(1):39-49. 14. Granzier HL, Akster HA, Ter Keurs HE. Effect of thin filament length on the force-sarcomere length relation of skeletal muscle. Am J Physiol. 1991;260(5 Pt 1):C1060-C1070. 15. Navarrete R, Vrbóva G. Changes of activity patterns in slow and fast muscles during postnatal development. Developmental Brain Research. 1983;8:11-19. 16. Keller-Peck CR, Walsh MK, Gan WB, Feng G, Sanes JR, Lichtman JW. Asynchronous synapse elimination in neonatal motor units: studies using GFP transgenic mice. Neuron. 2001;31(3):381-394. 17. Personius KE, Balice-Gordon RJ. Loss of correlated motor neuron activity during synaptic competition at developing neuromuscular synapses. Neuron. 2001;31(3):395-408. 30 18. Fulton BP, Walton K. Electrophysiological properties of neonatal rat motoneurones studied in vitro. J Physiol. 1986;370(1):651-678. 19. Forssberg H. Ontogeny of human locomotor control. I. Infant stepping, supported locomotion and transition to independent locomotion. Exp Brain Res. 1985;57(3):480-493. 20. Myklebust BM, Gottlieb GL, Agarwal GC. Stretch reflexes of the normal infant. Dev Med Child Neurol. 1986;28(4):440-449. 21. Hadders-Algra M. Development of postural control during the first 18 months of life. Neural Plast. 2005;12(2-3):99-108; discussion 263-272. 22. Morgan JL, Berger DR, Wetzel AW, Lichtman JW. The Fuzzy Logic of Network Connectivity in Mouse Visual Thalamus. Cell. 2016;165(1):192-206. 23. Newman M. Networks. Oxford University Press; 2018. 24. Frontera WR, Ochala J. Skeletal muscle: a brief review of structure and function. Calcif Tissue Int. 2015;96(3):183-195. 25. Tapia JC, Wylie JD, Kasthuri N, et al. Pervasive synaptic branch removal in the mammalian neuromuscular system at birth. Neuron. 2012;74(5):816-829. 26. Brill MS, Kleele T, Ruschkies L, et al. Branch-Specific Microtubule Destabilization Mediates Axon Branch Loss during Neuromuscular Synapse Elimination. Neuron. 2016;92(4):845-856. 27. Riley DA. Ultrastructural evidence for axon retraction during the spontaneous elimination of polyneuronal innervation of the rat soleus muscle. J Neurocytol. 1981;10(3):425-440. 28. Bishop DL, Misgeld T, Walsh MK, Gan WB, Lichtman JW. Axon branch removal at developing synapses by axosome shedding. Neuron. 2004;44(4):651-661. 29. Fruchterman TMJ, Reingold EM. Graph drawing by force-directed placement. Softw Pract Exp. 1991;21(11):1129-1164. 30. Duxson MJ, Usson Y, Harris AJ. The origin of secondary myotubes in mammalian skeletal muscles: ultrastructural studies. Development. 1989;107(4):743-750. 31. Qaisar R, Larsson L. What determines myonuclear domain size? Indian J Physiol Pharmacol. 2014;58(1):1-12. 32. Van der Meer SFT, Jaspers RT, Degens H. Is the myonuclear domain size fixed? J Musculoskelet Neuronal Interact. 2011;11(4):286-297. 33. Katz B, Miledi R. Propagation of electric activity in motor nerve terminals. Proc R Soc Lond B Biol Sci. 1965;161:453-482. 34. Katz B, Miledi R. The measurement of synaptic delay, and the time course of acetylcholine release at the neuromuscular junction. Proc R Soc Lond B Biol Sci. 1965;161:483-495.