Network-control predictions of C. elegans locomotion neurons are a tail motor-neuron-to-muscle matching; they repeat in Cook 2019 data but need extrapolated tail synapses and no node self-dynamics

Yan et al. (2017) used structural control theory on the C. elegans connectome. They predicted the neurons that are necessary to control the 95 body wall muscles from the touch neurons: 12 classes, PDB, and DD04-DD06 but not DD01-DD03. We ran their code and network again and got the same numbers. Then we repeated the analysis on the Cook et al. (2019) hermaphrodite connectome. We show that the computed bound can never be larger than the maximum matching of motor neurons to muscles. In the published network, the two numbers are equal (89 of 95 muscles). The matching alone gives 18 of the 20 single-neuron calls. These 18 neurons are the motor neurons of a tail block of muscles that has no spare innervating neurons. In Cook 2019, all 95 muscles are controllable. 17 of the 18 tail motor neurons are again necessary and PDA is new, so the DD and PDB calls stay. AVA, AVB, AVD and PVC are not necessary. The Cook tail block is exactly tight (18 muscles, 18 neurons). One added link from another neuron into this block removes all 18 calls (2,160 of 14,434 possible links). Ten random added links remove the DD04-06 versus DD01-03 split in 80% of runs. Most of these tail links are not observed: the Cook scored-only synapse table has no neuromuscular synapses from DD04-DD06, and the adjacency tables fill them by extrapolation. With node self-dynamics, which the model equation states, or with the annotated muscle-to-muscle gap junctions, all 95 muscles are controllable and no ablation lowers the bound. We also re-analysed the 299 public ablation recordings (PDB, DD02-DD05). The published effects repeat: smaller |EP4| bends after DD04 (Hedges g = -1.00) and DD05 (g = -0.44) ablation, and fewer ventral omega turns after PDB ablation (63.8% vs 81.9%). But DD03 ablation, which no connectome version predicts to matter, gives the same omega-turn change (61.8% vs 79.5%, p = 0.0007 in the published pooled test). No test in a 160-test feature screen passes a 5% false-discovery rate. Thus, in this framework the locomotion predictions are a tail innervation count, and the ablation data do not support network control theory more than this simpler rule. Main limitation: only five single-neuron ablations have public recordings.

C. elegans · connectome · network control theory · structural controllability · target control · neuromuscular junction · bipartite matching · reproduction · laser ablation · locomotion · Cook 2019 · Varshney 2011 · eigenworms · motor neurons · robustness