There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N ϭ 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.

Recent studies on the controllability of complex systems offer a powerful mathematical framework to systematically explore the structure-function relationship in biological, social and technological networks1–3. Despite theoretical advances, we lack direct experimental proof of the validity of these widely used control principles. Here we fill this gap by applying a control framework to the connectome of the nematode C. elegans4–6, allowing us to predict the involvement of each C. elegans neuron in locomotor behaviours. We predict that control of the muscles or motor neurons requires twelve neuronal classes, which include neuronal groups previously implicated in locomotion by laser ablation7–13, as well as one previously uncharacterised neuron, PDB. We validate this prediction experimentally, finding that the ablation of PDB leads to a significant loss of dorsoventral polarity in large body bends. Importantly, control principles also allow us to investigate the involvement of individual neurons within each neuronal class. For example, we predict that, within the class of DD motor neurons, only three (DD04, DD05, or DD06) should affect locomotion when ablated individually. This prediction is also confirmed, with single-cell ablations of DD04 or DD05, but not DD02 or DD03, specifically affecting posterior body movements. Our predictions are robust to deletions of weak connections, missing connections, and rewired connections in the current connectome, indicating the potential applicability of this analytical framework to larger and less well-characterised connectomes.

Lesioning studies have provided important insight into the functions of brain regions in humans and other animals. In the nematode Caenorhabditis elegans, with a small nervous system of 302 identified neurons, it is possible to generate lesions with single cell resolution and infer the roles of individual neurons in behaviour. Here we present a dataset of ~300 video recordings representing the locomotor behaviour of animals carrying single-cell ablations of 5 different motorneurons. Each file includes a raw video of approximately 27,000 frames; each frame has also been segmented to yield the position, contour, and body curvature of the tracked animal. These recordings can be further analysed using publicly-available software to extract features relevant to behavioural phenotypes. This dataset therefore represents a useful resource for probing the neural basis of behaviour in C. elegans, a resource we hope to augment in the future with ablation recordings for additional neurons.

Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesize that the brain's wiring is predetermined by the need to maintain control across multiple scales, maintaining the stability of key internal variables, and producing behaviour in response to environmental cues. Recent advances in network control have offered a powerful mathematical framework to explore the structure-function relationship in complex biological, social and technological networks, and are beginning to yield important and precise insights on neuronal systems. The network control paradigm promises a predictive, quantitative framework to unite the distinct datasets necessary to fully describe a nervous system, and provide mechanistic explanations for the observed structure and function relationships. Here, we provide a thorough review of the network control framework as applied to (Yan 2017 , 519-523. (doi:10.1038/nature24056)), in the style of Frequently Asked Questions. We present the theoretical, computational and experimental aspects of network control, and discuss its current capabilities and limitations, together with the next likely advances and improvements. We further present the Python code to enable exploration of control principles in a manner specific to this prototypical organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling at cellular resolution'.