Sensory recurrence and convergent integration in the C. elegans connectome

The synaptic wiring of Caenorhabditis elegans has a global feed-forward architecture, from sensory to motor neurons. Yet, whole-brain optogenetic mapping shows that signals do not flow predominantly forward, and sensory neurons respond to more neurons than they drive. Where the wiring contains pathways leading back to their starting point is unclear. Here, we locate this recurrence using the feedback coefficient, derived from the Kubo–Martin–Schwinger framework for directed networks, which quantifies the proportion of walks reaching a neuron that originate from itself. The connectome has about three times more recurrence than strength-matched random networks, with the largest excess in sensory neurons, whereas random wiring places it on highly connected neurons. Along the thermotaxis pathway, this produces a recurrence gradient from thermosensory neurons to integrating interneurons. The ordering replicates in five reconstructions, including two independent adults, persists when reciprocal contacts are preserved or gap junctions removed, but vanishes with only short paths or loop counts. Convergence shows the reverse pattern, with every neuron receiving walks from fewer sources than in random wiring, especially sensory neurons. The wiring extends from a sensory periphery folding back on itself to interneurons and motor neurons integrating many sources, a candidate structural substrate for non-feed-forward signalling.