A perimotor framework reveals functional segmentation in the motoneuronal network controlling locomotion in Caenorhabditis elegans

Abstract

The neuronal connectivity dataset of the nematode Caenorhabditis elegans attracts wide attention from computational neuroscientists and experimentalists. However, the dataset is incomplete. The ventral and dorsal nerve cords of a single nematode were reconstructed halfway along the body and the posterior data are missing, leaving 21 of 75 motoneurons of the locomotor network with partial or no connectivity data. Using a new framework for network analysis, the perimotor space, we identified rules of connectivity that allowed us to approximate the missing data by extrapolation. Motoneurons were mapped into perimotor space in which each motoneuron is located according to the muscle cells it innervates. In this framework, a pattern of iterative connections emerges which includes most (0.90) of the connections. We identified a repeating unit consisting of 12 motoneurons and 12 muscle cells. The cell bodies of the motoneurons of such a unit are not necessarily anatomical neighbors and there is no obvious anatomical segmentation. A connectivity model, composed of six repeating units, is a description of the network that is both simplified (modular and without noniterative connections) and more complete (includes the posterior part) than the original dataset. The perimotor framework of observed connectivity and the segmented connectivity model give insights and advance the study of the neuronal infrastructure underlying locomotion in C. elegans. Furthermore, we suggest that the tools used herein may be useful to interpret, simplify, and represent connectivity data of other motor systems.

Figure 1.

Remapping the locomotion motoneurons and muscle cells in perimotor space. a, Each dorsal (top) or ventral (bottom) muscle cell is mapped in perimotor space at its anatomical AP location. Right and left paired muscle cells are presented for each location. Each motoneuron is mapped in perimotor space at the weighted average of AP locations of the muscle cells it innervates. The location of motoneuron classes along the dorsoventral axis is arbitrary and meant to facilitate visualization of connections and their relationships. b, The perimotor location (empty circles) might not correspond to the anatomical location (tip of branches) of the cell body of each motoneuron. Notice that some motoneurons (e.g., DA06) move almost one-fifth of the length of the nematode anteriorly, while others move less, posteriorly, or not at all.

Figure 2.

Remapping connections among motoneurons in perimotor space. All electrical (round ends) (a) and chemical (arrows) (b) synapses among motoneurons in the dataset are depicted in perimotor space. As in Figure 1, the motoneuron position along the AP axis is determined by the innervated muscle cells and the dorsoventral axis is arbitrary to facilitate visualization. More specifically, iterating connections are parallel to each other in this diagram. Motoneuron classes and their outgoing chemical synapses are color-coded (AS, yellow/black; DA and VA, red, DB and VB, green; DD and VD, blue), while those with partial or no connectivity information are left colorless.

Figure 3.

Distribution of perimotor distances. The PD for each chemical synapse (blue bars) and gap junction (red bars) in the dataset was calculated as the difference between the position in perimotor space (PM_MN) of the partners. The bins of the histogram are 0.04, which correlate to the mean estimated length of a muscle cell (see Materials and Methods). Most (98%) connections are local (PD < 0.25). More specifically, 84% of chemical synapses (blue bars) are to motoneurons that innervate the same muscle cell or an adjacent neighbor, and 82% of gap junction (red bars) are to motoneurons that innervate the same muscle cell or up to three muscle cell lengths in either direction.

Figure 4.

Analysis of iterative connections. Iterativity analysis of the synaptic connections of each class of motoneuron (named at top left corner of each panel) is represented as a color map and a bar graph. Color maps (black, 0 connections; red, lowest value, to white, highest value) are arranged such that individual numbered motoneurons within the class are columns, while rows represent types of iterative connections. The numbers in each box represent the number of anatomical connections made by the source motoneuron represented by the column (e.g., VA1) to the iterative connection represented by the row. The iterativity threshold is set to two. That is, a connection is iterative if two or more members of the source class make synaptic connections to neurons of the same perimotor distance and class. The structure of connection names (e.g., “VD_S-1”; a chemical synapse to a VD motoneuron anterior to the source motoneuron) are described in the main text. The bars to the right of each panel represent the average number of synapses made by each cell in the source class onto the target motoneuron (below blue horizontal line) or input from another neuron (above line). Connection descriptions to the right of the bar graphs are simplified and motoneuron names are color-coded (e.g., “AVA” means chemical synapse from the interneuron AVA; “AVA′” means gap junctions from same). Iterativity index for each class is indicated next to class name (e.g., 0.93 for VA). Numbers with asterisks represent subclasses within VA and VB as described in the main text and Figure 6.

Figure 5.

Distribution of iterativity along AP axis and statistical validation. The iterativity index (I_it) of each individual motoneuron in the dataset (solid blue dots) is plotted along the AP axis (0.0–1.0) together with the distribution of the same quantity in 500 generated networks (open red circles) in which the target neurons were randomly shuffled. The dataset values are higher and significantly different from the generated population (*p < 0.05; **p < 0.01). We decided to use 500 scrambled networks by plotting (inset) the value of p for each VD motoneuron (VD01 to VD07) against the number of generated networks (Nr) from 50 to 1000. The value of p varies at low Nr but converges to the limit of the statistical test [1/(Nr + 1); thick gray line] by Nr = 500.

Figure 6.

Stereotypic motoneurons. a, The iterating connections for each class of motoneurons are shown as black arrows (chemical, directional, synapses) or purple double lines (bidirectional gap junctions). b, Cluster analysis was used to investigate whether the five more numerous classes (AS, DA, VA, VB, and VD) could be subdivided further. Of those, VB and VA (presented) could be further divided: VB01, VB04, and VB07 (VB*) and similarly VA01, VA03, and VA05 (VA*) have slightly different connectivity than their counterparts. These motoneurons are indicated by asterisk here and in Figures 3 and 6.

Figure 7.

A segment composed of stereotypic motoneurons. Twelve stereotypic motoneurons [iterativity threshold of 2 (a) or 3 (b)] and six muscle cells compose a segment. Each segment contains all iterating neuromuscular junctions (arrows to muscle cells), chemical synapses (arrows, colored as source and thickness proportionate to number of synapses in the data set), and gap junctions (purple double lines, size proportionate to number of gap junctions in the data set). Inputs from sensory and interneurons are included in the model but not presented. To facilitate visualization, some motoneurons are not at their perimotor location within the segment.

Figure 8.

Perimotor segments in dataset and connectivity model. a, Six segments can be interconnected along an AP axis to produce a complete connectivity model of the locomotion network (threshold of two is presented). b, c, When motoneurons, muscle cells, neuromuscular junctions (b), and interneuronal connections (c) are presented in perimotor framework, three segments emerge from the partial dataset. Small gaps were inserted between the segments to facilitate visualization of the segments (compare with Figs. 1 and 2). The complete motoneuronal system is expected to span six segments (empty frames).

Figure 9.

The noniterating connections among motoneurons. Seven electrical (round ends) and 11 chemical (arrows) synapses among motoneurons in the dataset are not iterating (compare with Fig. 2 and Table 2). Connections among and with the motoneurons with partial or no connectivity data were omitted as they were not included in the analysis.