Fig 1.
Birth time cohort membership and neurite lengths of neurons govern their connectivity.
(A-B) Matrices representing synaptic (A) and gap-junctional (B) connections that exist between neurons, grouped into three classes [indicated by blue broken lines] according to their process lengths ℓ measured relative to the worm body length L, viz., short (ℓ ≤ L/3), medium (L/3 < ℓ ≤ 2L/3) and long (ℓ > 2L/3), and ordered within each class according to birth time. Increasing birth time is indicated by arrows, with red lines marked th (time of hatching) separating neurons which differentiate in the embryonic stage from those born later. Matrix entries correspond to the existence of a connection, with its color representing the distance (measured in mm) between cell bodies of the corresponding neurons (see legend). We observe that there is evidence of birth time assortative mixing, with neurons born early(later) having a higher probability of connecting with other early(late) born neurons, which is particularly marked in the case of neurons having short processes. The gap junction matrix shows a large number of entries adjacent to the diagonal which correspond to connections between paired neurons [see Fig 5(A)]. (C) Distribution of distances d between cell bodies of pairs of neurons distinguished in terms of their respective process lengths (S: short, M: medium, L: long), which are connected by synapses (top) and gap junctions (bottom). As synaptic connections are directed, there are nine possible combinations of pairs of the classes (S/M/L) to which the pre- and post-synaptic neurons belong (e.g., SL refers to a synapse from a neuron with a short process to a long process length neuron). On the other hand, as gap junctions are undirected, only six possible combinations need be considered. We note the bimodal distributions of d when at least one of the two neurons connected by synapse or gap junction has a long (or medium) process. (D) The mean distance 〈d〉 between cell bodies of neurons connected by synapses (left) and gap junctions (right) are grouped according to their process lengths (L/M/S) [indicated by blue broken lines] and further subdivided into those born early (i.e., embryonic stage) and those born late (i.e., L1, L2 or L3 stages) [separated by red lines]. Distances are expressed in mm (see legend for the color code). We note that pre-synaptic neurons with long processes tend to connect with post-synaptic neurons having short processes which are located far from them, corresponding to the higher peak in the bimodal distribution for LS in top panel of (C). Note that we have considered in this analysis the subset of 225 neurons for which information about process length is available.
Fig 2.
Lineage of neurons affects their synaptic connectivity and spatial localization.
(A) Schematic diagram of a lineage tree of cells resulting from consecutive mitotic divisions of the zygote. The terminal nodes of the tree correspond to terminally differentiated mature cells (shown in red) while other nodes represent progenitors (shown in blue) that appear at different rounds of cell division. Cells born at each round of cell division are indicated by the corresponding rung of the tree they belong to, the numerical value for the rung (shown at the left) being the number of divisions starting from the zygote. The lineage distance l between a pair of mature cells is measured as the total number of cell divisions leading to each from their common progenitor. An example of lineage distance measurement is shown in the figure for the pair of cells a and b which are separated by four cell divisions (the distance of a from each of the intermediate dividing progenitors is indicated in the figure). (B-C) Frequency distributions of the birth time of different neurons (B, separated into the different developmental stages) and the lineage distances for each pair of neurons (C). (D) The probability of a pair of neurons to be connected through a synapse decreases with increasing lineage distance between them, as indicated by a statistically significant linear correlation between the two (r = −0.87, p < 10−7). For gap junctional connections, the correlation is marginally weaker (r = −0.79, p < 10−5). (E-F) Joint probability distributions of lineage distance l along with distance between cell bodies D (E) and birth time difference Δtb (F) between all pairs of neurons. The marginal distributions for the corresponding quantities are also shown. We notice that the distribution of physical distances in (E) exhibit a bimodal nature. However, cells which are closely related in terms of lineage (l < 5) also has a high probability of being physically located nearby (indicated by a prominent peak at the lower end of the distribution of D) which suggests that lineage influences spatial localization of cells. In panel (F), the distribution shows peaks at odd values of the lineage distance (particularly for low Δtb) suggesting that neurons born close in time are located at the same rung on the lineage tree.
Fig 3.
Lineage distance reveals developmental patterns of ganglia.
(A-B) Statistically significant features of the distribution of intra and inter-ganglionic lineage distances, quantified by deviations of the mean 〈l〉 (A) and coefficient of variation CV (B), from a surrogate ensemble of randomized lineage trees of neurons in the C. elegans somatic nervous system. These deviations (measured by z-score) show that the mean intra-ganglionic lineage distances (represented by diagonal blocks of the matrix) are significantly lower than that of the inter-ganglionic lineage distances (off-diagonal blocks), with the exception of G6 and G9. By contrast, CV for the intra-ganglionic lineage distances are significantly higher than that of the inter-ganglionic lineage distances. (C-E) Developmental chrono-dendrograms for three representative ganglia (viz., G1, G4 and G5) show that each comprises multiple localized clusters of neurons occurring at different locations on the developmental lineage tree, explaining the statistically significant deviations of the mean and CV for intra-ganglionic lineage distances. Colored nodes represent neurons belonging to the specified ganglion while gray nodes show the other neurons. Branching lines trace all cell divisions starting from the single cell zygote (located at the origin) and terminating at each differentiated neuron. The time and rung of each cell division are indicated by its position along the vertical and radial axis respectively. The entire time period is divided into four stages, viz., Embryo (indicated as E), L1, L2 and L3. A planar projection at the base of each cylinder shows the rung (concentric circles) of each progenitor cell and differentiated neuron. (F-H) The probability distribution functions for the intra-ganglionic lineage distances show bimodality (unlike that of the inter-ganglionic distances), which is consistent with the segregation of a ganglion into multiple clusters along the chrono-dendrogram. The different ganglia are indicated by symbols G1-G9 (1: Anterior, 2: Dorsal, 3: Lateral, 4: Ventral, 5: Retrovesicular, 6: Posterolateral, 7: Preanal, 8: Dorsorectal and 9: Lumbar) and the Ventral cord as G10.
Fig 4.
Birth times and lineage distances constrain connections between neurons whose cell bodies are spatially distant from each other.
(A-B) The mean birth time of synaptically connected pairs of neurons exhibit a trimodal distribution, with connections clustering into three temporal groups corresponding to those (i) between neurons that are both born early, i.e., in the embryonic stage, (ii) between one born early and the other born late (i.e., in the post-embryonic stage), and (iii) between neurons that are both born late. The hatching time ht separating the embryonic from other developmental stages is indicated by the broken line. We note from panel (A) that when both neurons are born late (corresponding to the uppermost cluster of connections), synaptic connections are more likely to occur between neurons whose cell bodies are located close to each other. (C-D) Synaptic connections between neurons that are closely related to each other in terms of lineage (l < 10) occur almost always when their cell bodies are in proximity, regardless of the time of birth of the neurons. We note that this restriction is more pronounced than observed in Fig 2(E), where P(D, l) shows a prominent peak at the lower end of D for small l suggesting that most closely related neurons (whether connected or not) typically have short distances between their cell bodies. (E-H) Neurons connected by gap junctions show patterns similar to those seen in the case of synaptic connections.
Fig 5.
Symmetrically paired neurons have a high probability of being connected and also exhibit strong association in their birth times and spatial positions.
(A) Bilaterally symmetric neurons that are positioned on the left and right of the body axis of the organism tend to have a much higher probability of synaptic, as well as, gap junctional connections between them, compared to that for all pairs of neurons. In addition, the synapses are highly likely to be reciprocal (bidirectional). (B) The distribution of lineage distances between paired neurons shows that the mean value is lower than that for all neurons. We note that almost all lineage distances between symmetric neurons are odd-valued suggesting that they occur at the same rung of the lineage tree. (C-D) Symmetrically paired neurons have cell bodies located in physical proximity of each other (C) and are born close in time as indicated by low birth-time differences Δtb (D), compared to all pairs of neurons.
Fig 6.
Developmental histories of neurons show a bifurcation into early and late branches, with a predominance of motor neurons in the latter.
(A) Bulk of the sensory and interneurons appear early, i.e., during the embryonic stage, while a large fraction of motor neurons differentiate much later (L2 or L3) during development. (B) Planar projections of a three-dimensional representation of the developmental history of the entire somatic nervous system of C. elegans. Different colors and symbols have been used to denote distinct neuron types (viz., sensory, motor and interneurons). The projection on the top surface shows the lineage tree with branching lines connecting the single cell zygote (shown at rung 0) to each of the differentiated neurons located on their corresponding rungs. At higher rungs (>11) we see that the differentiated cells are tightly clustered into two bundles of branches with a predominance of motor neurons (also seen in the chrono-dendrogram projection shown at the right face of the base). We note the absence of segregated clusters comprising exclusively the same functional type of neurons (viz., sensory, motor or inter), suggesting that the progenitor cell can give rise to neurons of different types. This in turn implies that commitment to a particular neuron function occurs quite late in the sequence of cell divisions. The projection along the base (left face) shows trajectories representing the developmental history of each final differentiated neuron, indicating the time of each cell division starting from the zygote along with the corresponding rung. For the first few rungs, cell divisions across different lineages appear to be synchronized and occur at regular time intervals, which is manifested as an almost linear relation between time of division and rung. However, between rungs 6-9, we observe a bifurcation of the trajectories into two clusters widely separated in time. One of these comprises cells which differentiate in the embryonic stage (termed as the “early branch”) while the other consists of cells that differentiate much later (“late branch”). This is manifested in a bimodal distribution of birth times for neurons occurring in rungs ≥ 10. In contrast to the regularly spaced cell divisions in the early branch, the trajectories belonging to the late branch are widely dispersed, with relatively little correlation between birth time of neurons and their rungs.
Fig 7.
Neurons functioning as connectors between different network modules lead in development.
(A) Schematic representation of the network of neurons belonging to the somatic nervous system of Caenorhabditis elegans, indicating the role of each neuron (indicated by the node size, see legend) in the mesoscopic structural organization of the network. This organization is manifest in the partitioning of the entire network into six structural modules [34] which are characterized by relatively dense connections among neurons in each module compared to the connections between neurons belonging to different modules (node color representing the identity of a module to which a neuron belongs). Within each module, neurons can be further distinguished into those which have significantly higher number of connections to neurons within their own module (hubs) and those which do not (non-hubs). According to their intra- and inter-modular connectivity, every neuron is then classified into one of seven possible categories (see Methods), viz. R1: ultra-peripheral (non-hub nodes with all their connections confined to their own module), R2: peripheral (non-hub nodes with most of their connections occurring within their module), R3: satellite connectors (non-hub nodes having with many connections to other modules), R4: kin-less (non-hub nodes with connections distributed uniformly among all modules), R5: provincial hubs (hub nodes with a large majority of connections within their module), R6: connector hubs (hub nodes with many connections to other modules) and R7: global hubs (hub nodes with connections distributed uniformly among all modules). One representative neuron from each of the categories is separately indicated with a label identifying them by name (note that there are no neurons in the C. elegans somatic nervous system which belong to categories R4 or R7). Neurons which function as connectors, e.g., RIAL (R6) and RIFL (R3), are seen to have links to neurons belonging to many different modules (as indicated by the node color of their network neighborings) while neurons belonging to other categories are connected predominantly to neurons within their own modules (indicated by their network neighborhood being almost homogeneous in terms of node color). Neighbors of labeled neurons are either shown clustered around them (for VA07, PVM, RIFL and DD02) or indicated by a lighter shade of node color (for RIAL). (B) Distributions of differentiation times of neurons belonging to the different network functional role categories indicate that the development of those functioning as connectors and/or hubs (i.e., R3, R5 and R6) lead the other classes of neurons in the embryonic, as well as, L1 stages. In particular, more than 90% of satellite connectors, provincial hubs and connector hubs have appeared before hatching, while for the peripheral categories (R1 and R2), 70% or less of their members would have differentiated by that time.
Fig 8.
The developmental duration of functional circuit neurons are strongly indicative of their process length and connectivity.
(A) Distribution of differentiation times of neurons that belong to any of nine functional circuits identified from behavioral assays. Note that the entire complement of neurons belonging to three functional circuits [shown using solid lines] have differentiated before hatching, while those for others [shown using broken lines] are completed later. (B) The distribution of neurons having short, medium and long processes [indicated at left], among the different functional circuits [right]. We note a correlation between the morphological feature of neurite length and the development time of functional circuit neurons, viz., those in the circuits completed before hatching predominantly have short processes, while those in circuits that are completed later mostly have medium to long processes (the exceptions being thermotaxis and CO2 sensation circuits that comprise a majority of short process neurons). (C) Comparison between the distributions of the number of incoming and outgoing synaptic connections (kin [top panel] and kout [middle panel], respectively), as well as, gap junctions (kgap [bottom panel]) of neurons in the entire somatic nervous system (blue) and of the subset of functional circuit neurons (red). We note that the distribution of outgoing synaptic connections for the functional circuit neurons is significantly different from that for the entire network, as indicated by the result of a two-sample Kolmogorov-Smirnov test at 1% level of significance (hKS = 1), but this is not the case for incoming synaptic connections or gap junctions (hKS = 0). (D) Dispersion of kin (top panel), kout (middle) and kgap (bottom) for the functional circuit neurons differentiating at various times is shown in terms of the adjoining box plots where neurons are clustered into four groups according to the developmental stage during which they are born, viz., Embryo, L1, L2 or L3. In general, the distributions are far more broad for the early born neurons (Embryo) compared to those born later (L1-L3). Focusing on the functional circuit neurons that develop in the embryonic stage, we note that the distribution of incoming connections is more skewed than that for outgoing connections. The distribution of gap junctions is even more skewed, with outliers lying very far from the median.