Article Figures & Data
Figures
- Figure 1.
Rich club of the C. elegans nervous system. a, The blue curve illustrates the rich club coefficient Φ(k) for the C. elegans neuronal network and the red curve is a randomized rich club curve, Φrandom(k), generated by averaging the rich club coefficients of 1000 random graphs at each value of k. The green curve is the normalized coefficient. Error bars on the Φrandom(k) and Φnorm(k) curves are 1σ of the random graphs. Φ(k) ≥ Φrandom(k) + 1σ over the range 35 ≤ k ≤ 73, indicating that this is the rich club regime (highlighted in lightest gray). The more conservatively defined rich clubs of Φ(k) ≥ Φrandom(k) + 2σ and Φ(k) ≥ Φrandom(k) + 3σ are shaded darker grey (Table 1). b, A purely topological view of the rich club network. Nodes in yellow are located in the tail and those in red are located in the head. c, The rich club is shown in the context of the whole body of the animal. It only has components in the head and tail, which are enlarged to show the subset DVA and PVCL/R (tail, right) and the subset AVAL/R, AVBL/R, AVDL/R, and AVEL/R (head, left). Only synaptic connections between rich club neurons are shown.
- Figure 2.
Motifs of the C. elegans network. a, The frequency of motif occurrence in the nematode network, compared with frequency of the same motif occurring in random networks, was defined in terms of interquartile deviances from the median and motifs were ranked in order of decreasing values. The motif that occurred with greatest (nonrandom) significance in the nematode network linked a pair of peripheral nodes via a series of local (L), feeder (F), and club (C) edges (denoted L-F-C-F-L). This indicates that many more of the shortest paths between peripheral neurons in the C. elegans network are mediated by the rich club than would be expected in a random network. b, The histogram shows the frequency distribution of the L-F-C-F-L motif in 1000 random networks. The frequency of the L-F-C-F-L motif in the nematode network is also shown; it is greater than the maximum frequency in the random network distribution, so it has p < 1/1000 = 0.001 under the null hypothesis that the frequency distribution of this motif is random in the nematode network. The top x-axis marks quartile deviances from the median, a nonparametric measure of distance from the central location of the random distribution. c, Construction of motifs from the shortest paths between pairs of neurons. As described in the key, rich club neurons are colored red and peripheral neurons are colored blue. An example of the frequently occurring motif L-F-C-F-L is given as a series of local (L), feeder (F) and club (C) connections to show how the topologically central rich club mediates many of the connections between topologically more peripheral neurons in the nematode nervous system. It is also illustrated anatomically within the head of the C. elegans network, where large bold nodes belong to the L-F-C-F-L motif and small pale nodes are in the rest of the network.
- Figure 3.
The C. elegans rich club has higher nodal efficiency, betweenness, centrality, participation coefficient, and connection distance than the rest of the nervous system (the poor periphery). a–e, Box plots detailing the distributions of degree, betweenness centrality, average connection distance, nodal efficiency, and participation coefficient (a measure of intermodularity). For each metric, the rich club is compared with the poor periphery and with the network as a whole. f, Distribution of connection distances. Rich club connections have a bimodal distribution, including a relatively large proportion of the longest connection distances in the network and a majority of much shorter distance connections, feeder connections linking a peripheral node to a rich club node have intermediate probability of long connection distance, and local edges linking two peripheral nodes have the lowest probability of a long connection distance.
- Figure 4.
Topological and spatial properties of the C. elegans nervous system are related: rich club neurons (red triangles) are distinguished from poor periphery neurons (blue circles) on all topological metrics. Rich club neurons tend to have higher degree (by definition), higher efficiency, higher betweenness, and higher participation coefficients than peripheral neurons. The connection distance of each neuron is the average of the physical distances between it and all of the other neurons to which it is synaptically connected in the network. Most rich club neurons have greater connection distance than most peripheral neurons, but some of the neurons with greatest connection distance are in the periphery.
- Figure 5.
Neuronal birth times and key events in the development of C. elegans. Top (red bars), Number of rich club neurons born in each 5 min interval after fertilization. Bottom (dark blue bars), Birth times of the rest of the neurons in the C. elegans nervous system. The dashed vertical lines indicate when the animal begins to twitch, when it is first capable of coordinated movement, and when it hatches.
Tables
Neuron Degree Rich club Function Birth time AVAR 94 3σ Head interneuron; role in locomotor decisions 311 AVAL 93 3σ Head interneuron; role in locomotor decisions 312 AVBL 76 3σ Head interneuron; role in locomotor decisions 318 AVBR 75 3σ Head interneuron; role in locomotor decisions 314 AVER 57 3σ Head interneuron; role in locomotor decisions 329 AVDR 56 3σ Head interneuron; role in locomotor decisions 301 AVEL 56 3σ Head interneuron; role in locomotor decisions 325 PVCL 55 3σ Tail interneuron; role in locomotor decisions 449 PVCR 53 3σ Tail interneuron; role in locomotor decisions 450 DVA 51 3σ Tail sensory interneuron; regulates sensory-motor integration during locomotion; modulates locomotion 296 AVDL 45 3σ Head interneuron; role in locomotor decisions 299 AIBR 39 2σ Head interneuron 299 RIBL 38 1σ Head interneuron 299 RIAR 37 1σ Head interneuron 299 The rich club in the nematode network can be defined by comparison with random networks: the most conservatively defined rich club, denoted 3σ, has a normalized rich club coefficient Φnorm(k) > 1 + 3σ, where σ is the standard deviation of Φrandom(k); less conservatively defined rich clubs, denoted 2σ and 1σ, include a few more neurons with somewhat lower degree than the 3σ rich club neurons. Birth times are given as minutes after fertilization.
