Comprehensive analysis of the C. elegans connectome reveals novel circuits and functions of previously unstudied neurons

As a first step towards assigning functions to neurons, the neurons and muscles may be partitioned into subgroups by their connectivity. Previous and less complete descriptions of the C. elegans connectome, notably lacking the muscles, have been subjected to graph analysis [6–10]. Various graph theoretic algorithms are available for identifying subgroups (modules or communities) where the probability of an edge between members of communities is significantly greater than expected if edges are distributed randomly. In such community detection, the boundaries in optimal partitions vary by algorithm and by the value of an unavoidable arbitrary threshold parameter, as generally it is not possible to reach a unique solution. Here, as a starting point for analysis, the spectral method of Leicht and Newman [11] is used. This algorithm partitioned the connectivity graph of the adult hermaphrodite of Cook and colleagues [4] into 10 communities (Fig 1). The graph used is a weighted graph where the values of the edge weights represent the strength of connection. The strength of the connection between 2 neurons is calculated by determining the size of each synapse connecting them, then summing these sizes over all the often multiple synapses present. Synapse sizes are estimated by counting the number of EM serial sections across which they extend. This ranges from a single section to many tens of sections. Connection strength is the total number of serial sections. Chemical and gap junctional graphs, the latter treated as 2 opposing directed edges with edge weights divided by ½, were added together to create a single graph with 473 nodes and 6,951 edges (S2 File). (Communities created for the chemical and gap junction graphs separately are given in S3 and S4 Files.)

Fig 1. Assignment of the neurons and muscles of the adult hermaphrodite to 10 communities by the spectral method of Leicht and Newman [11].

The connectivity matrix used, based on the data of Cook and colleagues [4] (S1 File), was the sum of the weighted chemical matrix plus the weighted, symmetrical gap junction matrix with gap junction weights divided by 2 (since each edge is counted twice, as directed edges in each direction) (S2 File). Modularity parameter Q = 0.517. P −6.

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It is important to emphasize that description of the network in this manner is artificial in requiring nodes to be placed into one or another of a small number of groups. A 2D, spring-electric or force directed layout of the C. elegans nervous system that, like modularity analysis, arranges nodes according to the amount of connectivity between them, is given as S5 File [4]. While it groups neurons and muscles consistent with the modularity analysis, it shows no obvious boundaries or separations between many of the modules. The precise location of the boundary drawn by the modularity algorithm may be quite arbitrary and highly sensitive to particular connections. Thus, as an example, the separation of SIADL and SIADR in community 2 away from SIAVL, SIAVR, and 4 SIB neurons in community 4 is not reflected in the 2D layout and probably does not indicate a difference in function.

In the overall process of multisensory integration, information from multiple sensory streams is brought together for control of effector output. This process can be dissected stepwise in terms of convergence onto individual neurons and muscles—the number of neurons targeting each cell, its indegree. By this measure, in the C. elegans nervous system, muscle cells are important sites of convergence. C. elegans locomotion and posture are determined by the 4 rows of longitudinal body wall muscles (95 mononucleate muscle cells) (Fig 2A). Neurons of all types, sensory neurons and interneurons as well as neurons classified as motor neurons, make neuromuscular junctions. The majority of muscle input (the sum of nmj edge weights in the chemical graph) (91%) is from 3 major motor neuron classes: head motor neurons (14%), sublateral motor neurons (41%), and ventral cord motor neurons (37%).

Fig 2.

(A) The nervous system and body wall muscles of C. elegans (upper: hermaphrodite; lower: male). The major ganglia, containing the cell bodies, and the primary process tracts are shown. Neurons are largely unbranched; processes run in bundles with a small number of neighbors to which they make en passant synaptic connections. CG, cloacal ganglion; DRG, dorsorectal ganglion; LG, lumbar ganglion; PAG, preanal ganglion; RVG, retrovesicular ganglion; VG, ventral ganglion. The 95 body wall muscles are arrayed in 4 quadrants: dorsal left, dorsal right, ventral left, ventral right. (B) First neighbor connections of the longitudinal body wall muscles (brown rectangles). Throughout the paper, the symbols and colors used in the connectivity diagrams are those of Cook and colleagues [4]. Node shapes: triangles, sensory neurons; hexagons, interneurons; circles or ovals, motor neurons or glial cells; squares or rectangles, muscles. Node colors: dark red, amphid neurons; medium red, oxygen and other sensors; light red, proprioceptors; pink, cephalic sensory neurons; yellow, head motor neurons; orange, sublateral motor neurons; tan, ventral cord motor neurons; grey, glial cells; bright and dark pink nodes with turquoise borders are hermaphrodite-specific sex neurons. For the interneurons, the 4 blue colors, lightest to darkest, represent the 4 interneuron layers assigned in Cook and colleagues [4]. Edges: black lines with arrowheads: chemical connections; red lines: gap junction connections; line thickness is proportional to connection weight, based on number of synapses and synapse sizes as explained in the text. (C) Number of neurons targeting the body wall muscles. Value shown is the average of the left/right pairs at each longitudinal and dorsoventral position. Fig 2B shows how input from all the various classes of neurons making neuromuscular junctions is distributed across the dorsal and ventral longitudinal muscle chains. On average, each muscle cell receives chemical input from 10 neurons (9.5 in the dorsal set, range 5–12.5, left/right averaged, 10.5 in the ventral set, 4–18.5) (Fig 2C). Each muscle cell also has gap junctions with its neighbors. Thus, muscle cells are strongly convergent. (Data for Fig 2C is in S1 Data).

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This input to the muscles comes from all the communities. Each community contains a different subset of the 3 major motor neuron classes—most ventral cord motor neurons in community 1, sublateral motor neurons in community 3, head motor neurons and sublateral motor neurons in community 4, additional ventral cord motor neurons in community 9. In addition, IL1 sensory motor neurons, in community 2, and VC hermaphrodite-specific motor neurons, in community 10, provide additional significant input (Fig 3).

Fig 3. Hierarchical arrangement of the hermaphrodite connectome with neurons clustered by community (not illustrated: community 1, containing many motor neurons and body wall muscles; community 5, the pharyngeal neurons and muscles, connected via RIP).

This is an adaptation of Fig 2 of Cook and colleagues [4]. In that figure, nodes were algorithmically arranged along the vertical axis to reflect hierarchical position in the network and along the horizontal axis roughly anterior to posterior in the body. Here, to visualize edges between nodes within single communities versus edges between nodes in different communities, the members of the separate communities were shifted slightly by hand to bring them closer together. The neurons and muscles are grouped by class, for instance, left/right homologs are shown as a single node; node sizes roughly represent the number of cells in each class (see S9 File for the list of classes). Classes with members in different communities are positioned outside the groupings: SMBDL and SMBDR are in community 2, SMBVL and SMBVR are in community 3; AIML is in community 3, AIMR is in community 10; ventral cord motor neurons (MNVC) are in community 1 and community 9, body wall muscles (MUHEAD, MUBODY) are in community 1, community 2, community 4, and community 9. hyp is the hypodermis.

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The motor neurons themselves are strongly convergent; input comes from both sensory neurons and interneurons, as well as from other motor neurons (Fig 4). The average indegree for the 3 major motor neuron classes in the combined chemical plus gap junction graph (S2 File) are 19.4 for the head motor neurons, 20.1 for the sublateral motor neurons, and 13.7 for the ventral cord motor neurons. Much of the input to the ventral cord motor neurons (62% of the weighted chemical input and 55% of the weighted electrical input) comes through the so-called command interneurons, interneurons running through the ventral chord that have inputs across the entire chain of ventral cord motor neurons (AVA, AVB, AVD, and PVC). The average indegree of the command interneurons as a group in the combined chemical and gap junction graph is 48.5 (excluding the gap junction connections to the ventral cord motor neurons, which are most likely best considered output). Command interneurons are members of a so-called rich club of high degree, interconnected neurons [8,12]. However, calcium imaging of brainwide activity patterns confirms that the command interneurons are only one element of a motor command network dispersed widely through the nervous system [12,13].

Each of the 4 large sensory modules appears to bring together a spectrum of similar or related sensory inputs that have a common implication for behavioral output. Groupings corresponding roughly to communities 2, 3, and 4 were pointed out by White and colleagues [1] (Fig 2A–2C). The sensory neurons in community 2 are a subset of those neurons having sensory endings in the inner labial sensilla, IL1 and IL2, and also include the SDQ neurons, which lie along the body and apart from participation in oxygen sensation are of no known function. IL1 and IL2 assess chemical and tactile information near or at the nose for positioning the nose in foraging [14]; both target the body wall muscles in the head via head motor neurons RME and URA, while IL1 targets these muscles directly as well. SDQR targets the RMH head motor neurons.

The sensory neurons in community 3 have endings in the amphid sensilla. All the amphid neurons are in this module except for pheromone sensors ASJ and ASK, which are in community 10. Amphid neurons detect soluble and volatile chemicals in the environment, as well as temperature, factors that may exist in long-range gradients. Such gradients provide a global coordinate system for the worm to use for navigational guidance, for example, to navigate to a point where it last obtained food. Here, the relevant behavioral output is the durations of the bouts of forward and backwards locomotion and the deep bends and turns that punctuate them, known as pirouettes. The major interneuron targets of amphid sensory neurons, AIA, AIY, and AIZ, are in layer 3 of the hierarchical network layout (Fig 3). From these, pathways of connectivity lead to the head motor neurons and to the ventral cord motor neurons via the command interneurons [15].

The sensory neurons of community 4, like those of community 2, have both chemical and mechanosensory endings in the sensilla of the nose and also include several with processes lying along the body or facing the coelomic cavity. The major interneuron targets in this module, RIB, RIC, RIG, and RMG, are in layer 2 (Fig 3). This module includes the so-called “neck” muscles, ventral body wall muscles 5 to 9, as well as the head motor neurons RMD, RMH, and RIV, which target this muscle group and receive inputs from RIC, RIG, and RMG. The AVE interneuron controls both dorsal and ventral ventral chord motor neurons 1 to 4. Modalities of the sensors of community 4 are not well characterized but include oxygen sensation. The selective innervation of muscles in the head and neck region suggests control of searching activity that involves movement of the head.

A possible generalization emerges from this partitioning of the network. Each sensory module may control a separate searching strategy: community 2 for targets right at the nose (foraging), community 4 for targets or goals nearby (possibly behavior known as steering), and community 3 for locating targets or goals farther away (runs punctuated by pirouettes). Such strategies might respectively involve regulating movement of the nose, the head, and the entire body. This viewpoint helps to explain the many pathways to the motor system with independent contributions from each of the sensory modules (Fig 3).

In contrast to communities 2, 3, and 4, which include sensation of signals in the external environment, community 9 appears to assess information on the condition of the body itself. It includes the various types of mechanoreceptors (touch neurons, deirids, PVD, and FLP) as well as neurons with sensory endings facing into the body cavity (AQR and PQR). Finally, module 10 brings in information relevant to reproductive behavior. The sex-specific circuits involving AVF and PVQ are shown in Cook and colleagues [4], Fig 6G and 6H.

It might be expected that sensory information with a common implication for behavior would first be compared and conflicts over priority resolved within each module, and then this unified modular output would be brought together with that of the other modules for prioritization and regulation of the motor neurons and muscles. Such integration would be a major function of the interneurons. Some would be involved in processing inputs within modules, while others would be nodes for comparing modular outputs. In this scheme, interneurons would in general have an overall convergent function, that is, they would have higher indegrees than outdegrees, reducing a larger number of incoming information streams to a smaller number of outputs. Interneuron connectivity indicates the above scheme is too simplistic. For most interneurons, the ratio of indegree to outdegree is close to 1 (Fig 5). That is, they do not have an overall convergent function. In each module there are some interneurons that in fact disperse information more than they aggregate it. Notably, as an example, the 2 interneurons in community 10, AVF and PVQ, which receive sexually relevant inputs, disperse this information widely across the nervous system. The most strongly convergent interneurons are premotor interneurons, that is, neurons with a preponderance of output onto motor neurons. In addition to the command interneurons discussed above, these include RIA and AVE. (AVE has been considered a command interneuron heretofore, even though it only synapses onto the anterior subset of ventral cord motor neurons).

Fig 5.

Out (blue) and indegrees (orange) for classes of interneurons. These are the degrees of classes onto other classes, taken from the cell class adjacency matrix of S9 File; ventral cord motor neurons, muscles in the head, and remaining muscles through the body, are counted as one node. (DVA has been classified as a sensory neuron previously because it is stretch sensitive [16]). (Data is given in S1 Data).

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The high level of connectivity of the interneurons, particularly their generally high chemical outdegrees and large amount of electrical connectivity, which is of uncertain directionality, is the reason interneuron functions have been difficult to parse out from connectivity (Fig 6). The interneurons with the highest degrees, particularly gap junction degrees, include interneurons that run across the body in the ventral cord between the nerve ring and the tail ganglia, termed here ventral cord interneurons. (A few additional interneurons, such as LUA and DVB, run partway through the ventral cord). All the ventral cord interneurons are in community 9 except AVF and PVQ, which are in community 10. This group includes the well-known command interneurons AVA, AVB, AVD, and PVC, but the remainder are little studied. Collectively, the 13 classes of non-command, ventral cord interneurons synapse onto a large fraction of all the neurons in the nervous system—by chemical connections, 59% in 1 step, 98% in 2 steps; by gap junctions, 41% in 1 step, 85% in 2 steps. Moreover, they are heavily connected to each other (Fig 7).

This would appear to be an important central network for integrating and dispersing information across the nervous system. In the whole-animal somatic nervous system connectivity graphs of Cook and colleagues [4], there are a total of 4,167 chemical plus gap junction synapses in the nerve ring, usually considered the central locus of nervous system integration, and 4,897 (54% of the total) outside the nerve ring in the ventral cord and tail (S6 File, updated from SI3, Synapse Lists of Cook and colleagues [4]). Fig 8 shows how the inputs and outputs of the non-command, ventral cord interneurons are distributed across the body. While some, like DVA, PVR, and PVT, appear to bring inputs from outside the nerve ring into it, others have inputs and outputs more uniformly distributed. There are a remarkable number of gap junctions in the tail. (The possibility that this previously unnoted imbalance is a reconstruction artifact is reviewed in the Discussion).

Fig 8. Distribution of synapses by body region along ventral cord interneurons.

From S6 File. The body region here includes the ventral ganglion, the retrovesicular ganglion, and the ventral cord. The tail region includes the preanal ganglion, the dorsorectal ganglion, and the lumbar ganglia (see Fig 2A). (Data given in S1 Data).

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Two measures of network topology are betweenness centrality, a node property that reflects the number of shortest paths between pairs of nodes that pass through it, and rich-club coefficient, a measure that identifies high degree neurons that are strongly connected to each other. Nine of the top 20 interneurons by betweenness centrality in the combined hermaphrodite chemical plus gap junction graph are members of community 9 (5 are command interneurons, 4 are non-command ventral cord interneurons), 6 are in community 3, and 5 are in community 4 (S7 File; data given in S1 Data). In the analysis of Uzel and colleagues [12], among 21 neurons identified as rich clubs in the combined chemical plus gap junction graph, 11 are in community 9 (8 command interneurons, 3 non-command ventral cord interneurons), 3 are in community 3, 6 are in community 4, and 1 is in community 10).

Further emphasizing their important role in nervous system integration, not only are the non-command ventral cord interneurons in community 9 heavily connected by synapses, several are also the highest degree neurons in the extrasynaptic peptidergic communication network: AVK, PVT, PVQ, DVA, and PVR—all are higher than the next highest neurons, which are the command interneurons AVA and PVC [3].

Whereas the many sensory neurons for assessing external environmental conditions are grouped in communities 2, 3, and 4 and largely have sensory dendrites in the head and outputs focused on interneurons in the nerve ring, the various types of mechanosensory neurons with dendrites distributed across the body are in community 9 and have important interneuron targets in this community. Two of these interneurons, DVA and PVR, receive inputs from the entire spectrum of mechanosensors (Fig 9). In the hermaphrodite reconstruction (but not the male), PVR and DVA are joined by 8 gap junctions and additional reciprocal chemical connections. They share output to command interneurons AVB and PVC, but otherwise their output connections are distinctive. DVA has output onto AVA and ring interneurons involved in the navigation circuitry, while PVR apparently regulates pharyngeal function through output onto RIP, the interneuron that connects to the pharyngeal nervous system, and IL1, which also targets RIP. As noted above, not only are DVA and PVR high degree neurons in the synaptic network (Fig 6), they are among the highest degree neurons in the peptidergic, extrasynaptic communication network. DVA and PVR themselves appear to have sensory function. DVA is stretch sensitive and PVR has a process extending into the tail whip that sometimes contains a cilium [16,17]. Nevertheless, these neurons are perhaps best viewed as interneurons receiving input from a somatosensory receptive field that consists of the entire body—surface, cuticle, and coelomic cavity. In addition to output onto navigational interneurons, DVA has output onto sublateral motor neurons whose activity may be relevant to bodywide muscle tone. Such tone, as well as pharyngeal pumping, must impact pressure in the body, which needs to be kept sufficiently high for function of the cuticular exoskeleton but not so high as would cause the cuticle to burst. It has been reported that touch can stop pharyngeal pumping [18].

The touch neuron classes ALM, AVM, PLM, and PVM have been long known to target the command interneurons and stimulate a rapid locomotory response [18]. However, only a minority of their output connectivity is to these neurons: 11% (33/294 EM serial sections) of the gap junction connectivity and 32% (117/364 EM serial sections) of the chemical output. Along with PVR and DVA, among their additional targets are the BDU neurons, a pair of previously unstudied neurons with lateral cell bodies that send lateral processes into the nerve ring, to which ALM and PLM are strongly connected by gap junctions [19] (Fig 10). BDU processes run adjacent to the excretory canal, suggesting a possible sensory function. As is the case for DVA and PVR, both anterior and posterior touch receptors target BDU, indicating this is unlikely to be a signal for locomotory direction. In both sexes, among the nerve ring targets of BDU are sex-specific cells, HSN in the hermaphrodite and MCM in the male. There are also reciprocal connections to the ventral cord interneurons PVN (in the hermaphrodite reconstruction but not the male reconstruction). PVN also has chemical and gap junction connections to HSN, creating a triangular circuit with BDU (see PVN below). In the male, PVN has interactions with many components of the male mating circuitry in the preanal ganglion. BDU and PVN are thus apparently involved in circuitry for input from multiple sensory neurons to sexual circuits.

Two other neuron classes may have an important role in bodywide regulation. Like PVR, ALNL/R and PLNL/R have endings in the tailspike. Rather than sending processes through the ventral cord like PVR, they have processes running to the head in lateral tracts adjacent to the touch cells—ALN in the anterior body region adjacent to ALM, PLN in the posterior body region adjacent to PLM. Like DVA, they have major output onto the sublateral motor neurons (Fig 11). They have been reported to have a role in oxygen sensation, but otherwise are unstudied, in spite of their association with the well-studied microtubule touch cells, to which they do not have synaptic connections (except for a gap junction between PLMR and PLNR scored in a single EM section in the hermaphrodite reconstruction) [20]. Apart from input from the phasmid neurons, ADE, and PLM, they receive no other sensory inputs and in view of their extensive output onto the sublateral motor neurons, it seems likely that they have an unknown sensory function of their own in addition to oxygen sensation. Notably, in the hermaphrodite reconstruction, there is a significant gap junction connection between ALNR and PVR, thus connecting the DVA/PVR and ALN/PLN networks. This connection is absent in the male reconstruction, which needs to be checked but could be related to the significant reorganization of the adult male tail, which lacks a tailspike.

Fig 11. First neighbors of ALN and PLN.

SAA neurons have been classified as interneurons and are a major source of input to AVA, but they have lateral processes running into the nose that express genes for stretch receptors and that also make neuromuscular junctions and so in these respects are similar to sublateral motor neurons.

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Comparison of their connectivity shows that while they share many connections, each class of non-command interneurons in the ventral cord also has distinct connections (S8 File). Most have some amount of sexually dimorphic connectivity. The differences between them may reflect distinct roles in bringing information from a particular sensory stream into the central network (Fig 7), and/or to dispersing information from the central network to a particular point of output. Two aspects of their connectivity, in addition to their module assignment, can be used to gain some information about these separate functions. One is to examine the set of first neighbors in the connectivity diagram. The second is to determine the shortest path between sensory input and motor output on which they lie. However, it should be kept in mind that, as noted, along with distinctive features, each of these neurons also has connections to the other ventral cord neurons including the command interneurons and usually to ventral cord motor neurons and even body wall muscles, emphasizing their importantly distributive nature (Fig 2B). It is also important to keep in mind that generalizations drawn from connections or absence of connections, especially weak connections, documented in single reconstructions need to be verified, as they may represent interindividual variation or even reconstruction errors. Missing connections, for instance, particularly in the male data in the head, need to be verified (Fig 4).

AVF and PVQ are 2 pairs of interneurons involved in sexual circuits. Each has significant sexual dimorphism. Their function in conveying sexual signals to central circuits has been pointed out previously (see Fig 6 in Cook and colleagues [4]).

A number of neurons have been classified as ring interneurons because their processes are contained entirely within the nerve ring [1]. Some of these have properties similar to the ventral cord neurons discussed above—they have high degrees, a large number of gap junction connections, and are understudied. Like the ventral cord neurons, several target muscles and so have been classified previously as motor neurons. As noted above, several are distinguishing targets of the non-command ventral cord interneurons. Below are deductions regarding functions of a subset of these neurons.

RIG(L/R) (community 4).

RIG and RMG are 2 high-degree neurons in community 4 that have an overall similar pattern of connections. They receive inputs from a large number of sensory neurons, often by gap junctions, and have output onto a spectrum of downstream targets (Fig 13). Unlike RMG (see below), RIG has not been studied and has no documented function presently, but the similarity to RMG suggests this may be considered a hub-and-spoke neuron. RIG and RMG are connected to each other and have multiple connections to non-command ventral cord interneurons, implicating them in a widespread role. Notably, RIG makes both chemical connections to and has gap junction connections with AVK.

Fig 13.

Hub-and-spoke neurons RIG (upper) and RMG (lower). The pattern of a large number of gap junction connections to sensory neurons and a spectrum of output targets is similar for these 2 high degree neurons, but the sets of cells involved are largely non-overlapping.

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