
==== Front
Proc Natl Acad Sci U S A
Proc Natl Acad Sci U S A
PNAS
Proceedings of the National Academy of Sciences of the United States of America
0027-8424
1091-6490
National Academy of Sciences

38252843
202320953
10.1073/pnas.2320953121
datasetDatasetresearch-articleResearch ArticleneuroNeuroscience424
Biological Sciences
Neuroscience
Network architecture of intrinsic connectivity in a mammalian spinal cord (the central nervous system’s caudal sector)
Swanson Larry W. larryswanson10@gmail.com
a 1 https://orcid.org/0000-0002-4260-3892

Hahn Joel D. a https://orcid.org/0000-0003-4024-0247

Sporns Olaf b c
aDepartment of Biological Sciences, University of Southern California, Los Angeles, CA 90089
bIndiana University Network Science Institute, Indiana University, Bloomington, IN 47405
cDepartment of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405
1To whom correspondence may be addressed. Email: larryswanson10@gmail.com.
Contributed by Larry W. Swanson; received November 28, 2023; accepted December 21, 2023; reviewed by Allan I. Basbaum and Tomas G. Hökfelt

22 1 2024
30 1 2024
22 7 2024
121 5 e232095312128 11 2023
21 12 2023
Copyright © 2024 the Author(s). Published by PNAS.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

Significance

The spinal cord (SP) is the major central nervous system component that directly mediates sensorimotor reflex behavior for most parts of the body except the face. Here, we analyze with network neuroscience methods SP intrinsic axonal circuitry as part of a comprehensive project to clarify organizing principles of the neural network forming the mammalian nervous system and its interactions with the body. The results of cluster analysis reveal a hierarchy of structure–function subsystems with top-level components dealing most obviously with motor functions, general somatosensory functions, and the processing specifically of nociceptive information. Common general organizing features of complex networks were not detected within the SP.

The vertebrate spinal cord (SP) is the long, thin extension of the brain forming the central nervous system's caudal sector. Functionally, the SP directly mediates motor and somatic sensory interactions with most parts of the body except the face, and it is the preferred model for analyzing relatively simple reflex behaviors. Here, we analyze the organization of axonal connections between the 50 gray matter regions forming the bilaterally symmetric rat SP. The assembled dataset suggests that there are about 385 of a possible 2,450 connections between the 50 regions for a connection density of 15.7%. Multiresolution consensus cluster analysis reveals a hierarchy of structure–function subsystems in this neural network, with 4 subsystems at the top level and 12 at the bottom-level. The top-level subsystems include a) a bilateral subsystem related most clearly to somatic and autonomic motor functions and centered in the ventral horn and intermediate zone; b) a bilateral subsystem associated with general somatosensory functions and centered in the base, neck, and head of the dorsal horn; and c) a pair of unilateral, bilaterally symmetric subsystems associated with nociceptive information processing and occupying the apex of the dorsal horn. The intrinsic SP network displayed no hubs, rich club, or small-world attributes, which are common measures of global functionality. Advantages and limitations of our methodology are discussed in some detail. The present work is part of a comprehensive project to assemble and analyze the neurome of a mammalian nervous system and its interactions with the body.

cluster analysis
connectomics
hubs
subsystems
==== Body
pmcThe vertebrate central nervous system (CNS) is a longitudinal organ that lies in the midline, dorsal to the notochord, and traditionally is divided into two fundamental parts, the brain rostrally and the spinal cord (SP) caudally. As part of a comprehensive project to analyze the network architecture of a complete nervous system in a mammal (rat), we have thus far dealt with the intrinsic axonal connections of the major brain divisions (1–11), including the CNS rostral and intermediate sectors (IMS) (12), and here with the same methodology, we describe the CNS caudal sector (CDS), the SP (Fig. 1). The intended logical conclusion of this effort is next to consider the brain and SP together as the CNS, then to consider the peripheral nervous system, then to consider the CNS and peripheral nervous system together as the nervous system, and finally to consider nervous system interactions with the body—a network we refer to as the neurome (1).

Fig. 1. Conceptual framework for analyzing intrinsic SP macrocircuitry: axonal connections from one gray matter region to another gray matter region. (A) Schematic outline of the early neural tube, with its primary forebrain vesicle (PFBV), primary midbrain vesicle (PMBV), primary hindbrain vesicle (PHBV), and SP part of the neural tube (SPNT), superimposed on a model of the human embryo. The rostral sector (ROS) consists of PFBV and PMBV together, the IMS is the PHBV, and the CDS is the SPNT (green). All vertebrates display a qualitatively similar arrangement at an equivalent developmental stage (~embryonic day 10 in the rat). (B) The bilateral SP (SP2, green), and other CNS divisions (gray), shown on a flatmap (13). (C) Schematic view of the adult rat SP2 connection matrix template, which has 50 rows and 50 corresponding columns (25 for SP gray matter regions on each side, as indicated). For all connectomes, the same sequence of regions is used for both rows and columns. The dashed line from Upper Left to Lower Right is the main diagonal, indicating the connection of a region to itself (with no value in a macroconnectome where regions on the main diagonal are treated as black boxes). (D) Topographically arranged nested hierarchy of major CNS parts (with abbreviations) common to adult vertebrates; SP and CDS are synonyms. Gray matter regions are a nested level below the bottom level shown here, and neuron types are a nested level below the region level.

The SP presents clear advantages and limitations for examining the intrinsic connectivity of a major CNS division. The main advantage, compared to the brain, is that SP global structure–function organization is much simpler and clearer. The SP is the least differentiated part of the embryonic neural tube (Fig. 1A); through its set of paired dorsal and ventral roots, the SP is associated specifically with motor and somatic sensory processing for most parts of the body except the face; and thus, the SP has long been regarded as the preferred model for investigating the structure–function organization of relatively simple reflex behaviors (14, 15). Considering these fundamental advantages, the limitations associated with analyzing intrinsic SP connectivity, encountered in the present study of a small mammal, may appear surprisingly extensive.

First, the SP has a long, thin shape compared to the brain (Datasets S1 and S2). In adult rats, the bilateral SP is 6 to 7 cm long and at most about 4 mm wide by 3 mm tall (16); it weighs about 500 mg (16) and reportedly contains on the order of 6 to 7 million neurons (17). As a result of this thin, elongated shape, most SP gray matter regions in the rat are too small for analysis with bulk labeling axonal pathway tracing methods, and intracellular filling methods for tracing individual axons have rarely been applied to the rat (or mouse). Second, analyses of intraspinal connections very rarely examine labeling throughout the length of the SP, which in the rat typically consists of 34 levels or “segments” corresponding to the 34 paired spinal nerves with their dorsal and ventral root SP connections. Third, the dendrites of neurons in many SP gray matter regions extend for considerable distances into other regions allowing for synapses to occur there, outside the region of interest. Fourth, in the last 50 y, there has been less interest in studying intrinsic SP connectivity than in studying brain, and especially forebrain, connectivity. And fifth, much of the earlier work on SP intrinsic connectivity was performed in the cat and to a lesser extent in the monkey. As a result of these factors, compared with our earlier brain network studies mentioned above, the present analysis has had to rely somewhat more on results with the Golgi method and with retrograde transneuronal labeling methods and to a very limited extent on results from other species (mouse).

Results

Constructing the Foundational Database.

Construction of the connectivity database will be summarized first, followed by a consideration of the basic parameters associated with this information, and then its analysis and interpretation. As already described thoroughly (7), analysis was performed on a database created primarily from the results of experimental axonal pathway tracing studies indicating the presence (and weight) or absence of from–to (directed) axonal connections between all 50 gray matter regions (nodes; referred to subsequently simply as regions) on the right (25 regions) and left (25 corresponding regions) sides of the rat SP in our reference nomenclature hierarchy and spatial atlas (see SI Appendix, Materials and Methods and Dataset S1, for the nomenclature hierarchy and abbreviations and Dataset S2 for the atlas).

The SP atlas was designed to complement our open access adult rat brain atlas (18) in traditional parceling strategy (into gray matter regions and white matter tracts) and graphical style. This 4th edition of our brain atlas (18) has a simple parceling scheme for the SP, but the collation efforts undertaken for the present connectomics analysis required a more systematic, up to date account of the SP that included maps to illustrate the parcellation scheme. The parcellation is represented on the right side of the SP atlas maps, and for direct comparison the widely used parceling scheme devised by Rexed for cat (19, 20), and adapted for rat by Molander and colleagues (21, 22), is shown on the left side. The Rexed scheme is based on a bilaterally symmetric set of nine layers and one area on each side of the SP. Both parceling schemes are useful, partly because descriptions in the literature using the Rexed scheme of 10 basic gray matter parts often fail to account for the many other differentiations that have been identified.

The data were described with a defined vocabulary for axonal connections (23, 24). In this scheme, connections are arranged in a nested hierarchy: between regions (macroconnections), then between neuron types (mesoconnections), and then between individual neurons (microconnections). Because datasets for all three levels are incomplete, they were combined to define the macroconnection matrix (macroconnectome) used here; for convenience in what follows, macroconnections between gray matter regions are referred to simply as connections.

Connection Reports (ranging from none to 6 for connections arising on one side and none to 12 for connections arising on both sides) for each possible connection (region-pair) in the connection matrix (from region A to region B; Fig. 1C) were expertly collated by L.W.S. from the primary structural neuroscience literature and recorded in a conditionally formatted Excel worksheet (Axiome M 3.20, designed by J.D.H.; Dataset S3) with ≥18 columns of metadata per report; for a comparison of collation results for the same connection matrix by two experts, see ref. 3.

Basic Features of the Database.

Basic features of the bilateral intrinsic SP2 database are summarized in Fig. 2. No statistically significant right-left, female-male, or strain differences were identified during the systematic collation performed here. Thus, a) all ipsilateral and contralateral connections were assigned to one side of the SP, and the same dataset was employed for the other side; and b) our SP analysis applies generally to the species level (adult female and male Rattus norvegicus domestica). There are SP regions that are clearly sexually dimorphic, including specifically the nucleus of bulbocavernosus (25) and nucleus of ischiocavernosus (NIV) (26), but the possible existence within the SP itself of sexually dimorphic connections involving these regions has not yet been subjected to rigorous statistical analysis.

Fig. 2. Summary of major connection data measures for the SP.

The full dataset has 3,544 Connection Reports for 2,450 possible SP2 connections. These data were collated from 40 original research publications appearing in 40 journals, books, or theses since 1966; 44.9% of the Connection Reports were from the Journal of Comparative Neurology. The collated data were generated by about 30 laboratories employing 15 different axonal pathway tracing methods.

The collation identified 352 connections as existing in the SP2 network and 1,886 connections as absent. Because no data were found in the literature for 8.7% of all possible connections (a connection matrix fill ratio of 91.3%), it may be estimated that the SP2 network contains approximately 385 connections, for an overall network connection density of approximately 15.7%. During collation, connections for which data exist were assigned a weight based on an ordinal scale (Fig. 3A) because very little relevant quantitative data exist in the literature.

Fig. 3. Bilateral macroconnectomes (connection matrices) for the SP. Directed and weighted monosynaptic connection matrices with gray matter region sequence in a multiresolution consensus cluster (MRCC) analysis-derived subsystem arrangement. Region (row and column) identity and additional details are provided in Fig. 4A and Datasets S3–S5, where the underlying connection data and subsystem organization are easy to explore. In the Left column, collated data are represented by descriptive terms corresponding to ordinal weight values, and the second column shows this data modified so that “No data” and “Unclear” values are binned with “Absent” values. The binned data are then converted to log-weighted values (third column) for computation. MRCC analysis of the log-weighted connection data generated coclassification matrices (fourth column), also represented as a scale-defined, nested hierarchical dendrogram/cluster tree (Right column). In an MRCC hierarchy, branch length represents a distance between two points, one where it was first created and the other where it splits or reaches the end of the hierarchy. This length may be interpreted as branch stability (or persistence) across the entire hierarchy such that dominant solutions (branches more resistant to splitting) have longer branches and fleeting or unstable solutions have shorter branches. For uniformity, all four matrices are based on the 40 regions used for network analysis, as explained in the text. All solutions plotted in the tree survive statistical testing with a significance level of α = 0.05.

For individual gray matter regions, the range of SP2 output connections (the output connection degree range) is 0 to 19, and the range of SP2 input connections (the input connection degree range) is 0 to 24. For individual gray matter regions, the range of total inputs + outputs is 0 to 40 (Dataset S4).

For network analysis, values of connection weight reported as “no data” were binned with “absent” and “unclear” values (Fig. 3, second column; Dataset S4), and the descriptive ordinal scale was then converted to a log10 scale covering the five orders of magnitude reported for rat connectional data (7, 8) (Fig. 3, third column; Dataset S5, layer G). In this network analysis dataset, five right-left region pairs (10 of the 50 total regions) were found to have no reported input or output connections intrinsic to the SP, and they were by necessity eliminated from further network analysis (10). These region-pairs included the spinal accessory nucleus (XI), central cervical nucleus, dorsal spinal nucleus thoracolumbar part (DSNtl) and sacral part (DSNtl), and internal basilar nucleus. They may have intraspinal connections and/or connections with the brain, peripheral nervous system, or body that are not yet identified or reported (for example, a projection to muscles in the case of somatomotor nucleus, XI).

Finally, a validity metric based on a 7-point ordinal scale (1 to 7/lowest-highest validity) was applied to the axonal pathway tracing method associated with the Connection Report for each region-pair in the connection matrix (7, 8) (Dataset S5, layer I). This was based on three criteria: the axonal tracing method’s reach (monosynaptic preferred over polyneuronal), sensitivity, and possible axons-of-passage involvement. The following average validity values were determined for the data used for SP2 network analysis: for connections reported to exist, ipsilateral (within one side) = 4.72, contralateral (between sides) = 4.78, both sides = 4.74 (for the 15.7% of connections indicated to exist); for connections reported to not exist, ipsilateral = 4.78, contralateral = 4.80, both sides = 4.79 (for the 84.3% of connections indicated to not exist) (Dataset S3). By comparison, the average validity values for ipsilateral connections reported to exist within the rostral segment was 6.47 (9), and within the intermediate segment/rhombicbrain it was 5.58 (10). Detailed consideration of the methodological validity of axonal (pathway) tracing methods as we have applied them here, was given previously (see supporting information [appendix] in ref. 7). Notably relevant to the present study is that for negative data (84.3% of SP2 connections indicated to not exist), a lower methodological validity score (for example, for an axonal tracer known to be taken up and transported by axons-of-passage) does not necessarily decrease the validity of the data.

Hierarchical Structure–Function Subsystem Analysis.

The complexity of nervous system network organization can be simplified by examining its subsystem architecture with multiresolution consensus cluster (MRCC) analysis (4, 27). The algorithm detects strongly connected clusters (communities, modules, or our synonym, subsystems) among the directed (from–to) and weighted axonal connections (projections) between all regions of the network represented in a connection matrix or connectome—across all levels of partitioning resolution/scale. The unsupervised results distinguish clusters of various sizes that are arranged in a matrix and accompanying scale-defined, nested hierarchy that together represent a compact description of all subsystems and all interactions between them (Fig. 3, Right two columns).

For interpretation of the results, a fundamental hypothesis is that each subsystem may subserve a unique functional role because MRCC analysis identifies the regions defining a subsystem as more strongly clustered or interconnected with each other than with any other subsystem. Based on this testable hypothesis, the MRCC structural hierarchy for SP2 (Fig. 3, Right column) has been annotated with the most general and obvious functional correlates documented in the references for Connection Reports in Dataset S3, as done previously for cluster trees associated with intrinsic connections of the forebrain (7), midbrain (8), rostral sector (ROS) (9), and rhombicbrain/CDS (10). This version 1.0 of the SP2 subsystem model is based on a connection dataset that includes data for 91.3% of possible SP2 connections. A more complete dataset may improve future versions.

MRCC analysis of the SP2 network yields 17 subsystems arranged in a nested hierarchy with 6 levels (branch points), as well as 4 subsystems at the top level and 12 at the bottom level (Fig. 4A and Datasets S4 and S5). From a global, top–down perspective, the four most general, first-order subsystems fall into three readily identifiable structure–function categories. The first category is a large bilateral subsystem (subsystem 1) whose best-known members are associated with somatic and autonomic motor functions. This subsystem is further divided into four second-order subsystems, two of which are associated with autonomic and pelvic motor functions, and the other two form a bilaterally symmetric pair associated with somatic motor functions. The second category (subsystem 2) is associated with the processing of somatosensory information generally; it is centered in the head, neck, and base of the dorsal horn (for this topographic description in relation to our regional parcellation, see ref. 28). Subsystem 2 branches once, forming a bilaterally symmetric pair of unilateral second-order subsystems. The third and final category of first-order subsystems (subsystems 3 and 4) consists of two small unilateral subsystems that are bilaterally symmetrical. The components are the gelatinous substance and marginal zone of the SP’s dorsal horn (apex) that together play a critical role in nociception and pruriception (29). These last two top-level subsystems are the smallest and most stable: unlike top-level subsystems 1 and 2, subsystems 3 and 4 are unbranched across all MRCC partitioning resolutions (branch length being indicative of subsystem stability), and they have the most unambiguous functional associations.

Fig. 4. Subsystem identification, distribution, and interactions for intraspinal connections. (A) The SP2 MRCC matrix and subsystem hierarchy annotated with the most obvious functional attributes associated with the region sets indicated. Note that the hierarchy has four top-level subsystems, as described in the text and color coded here. In a cluster hierarchy and associated matrix, the order of child branches from a parent branch, and the order of regions within a bottom-level subsystem, is random within a given branch level; branches have been manually rearranged here for clarity. The yellow lines (squares) partition the matrix according to the four top-level subsystems (numbered) arranged along the main diagonal and shown with yellow lines also in Fig. 3. For a more detailed view of this matrix and hierarchy, see Datasets S4 and S5. For an explanation of the hierarchy index, see Fig. 3; for abbreviations, see Dataset S1. (B) Topographic or spatial distribution of gray matter regions associated with each of the four top-level subsystems, mapped for the cervical enlargement (cervical level 5). The four top-level subsystems are color coded as in A (key at bottom, with predominant functional associations given in parentheses). Note that the subsystem gray matter region sets tend to be spatially compact. For all abbreviations and a complete account of SP parts, see Dataset S1; for a completely labeled map of cervical level 5 (and other levels), see Dataset S2. Note our traditional nomenclature scheme on the Right side, compared with the Rexed (see text) nomenclature scheme on the Left side. (C) Quantitative topological relationships between the four top-level intrinsic SP subsystems, color coded as in A and B. Numbers refer to the weighted connection density (aggregate connection strength/total number of regions, ×100; individual values in Dataset S4) for intrinsic subsystem connections and for connections between subsystems. According to the MRCC algorithm, weighted connection density values are always greater within as compared to between subsystems.

In principle, the spatial distribution of region sets associated with the top-level subsystems could tend toward either a checkerboard arrangement or spatial compactness. The description in the preceding paragraph suggests that the latter arrangement is more likely, and this assumption is verified by displaying the subsystem-related region sets on atlas maps of the SP, as illustrated for the cervical enlargement in Fig. 4B and confirmed at all the other spinal levels mapped in Dataset S2.

The most granular view of network subsystem organization is provided by a bottom–up approach. This is useful in generating strong hypotheses for experimental testing because bottom-level subsystems consist of experimentally tractable region sets, ranging from 2 to 8 for SP2, that are assumed to be functionally related. The following implications have been discussed elsewhere (7) and are illustrated for SP2 in Fig. 4A. First, it may be hypothesized that subsystem members with poorly understood functional attributes share overall functional attributes of the subsystem as a whole. Second, it may be hypothesized that if a parent subsystem has two or more descendants with apparently distinct functional properties, then the parent subsystem combines those two or more functional properties. And third, it may be hypothesized that if a parent subsystem has two children, one with clear functional properties and the other without, then the parent SS displays the known and unknown function of its children. These principles are easy to apply fruitfully to the bottom-level subsystems displayed in Fig. 4A, some of which contain regions with relatively poorly understood functional attributes.

Connections between Subsystems.

Each cluster/subsystem identified by MRCC analysis is a set of gray matter regions that are more highly interconnected with each other than with any other cluster/subsystem (across the range of partitioning resolutions at which the subsystem persists). The MRCC analysis just considered displays all these subsystems in a hierarchical arrangement (Fig. 4A). However, this hierarchy does not display the organization of weaker connections between subsystems, which are clear in the MRCC matrix itself (Fig. 4A and Datasets S4 and S5) and are quantified in Fig. 5. For SP2 connections it is most instructive to examine the weight of interactions between the four top-level subsystems, compared to the weight of interactions within the subsystems themselves (Fig. 4C). The results suggest that these top-level intraspinal subsystems interact weakly at most with each other. From a functional perspective, the motor-related subsystem 1, centered in the ventral horn and intermediate zone, receives almost no inputs from the somatosensory-related subsystems 2-4, centered in the dorsal horn, and subsystems 3 and 4 share no connections at all. Overall, most of these weak connections are from subsystems 1, 3, and 4 to subsystem 2 (Fig. 4C). How this intraspinal network interacts with the peripheral nervous system and body on the one hand, and with the brain on the other, remains for future connectomics work to clarify.

Fig. 5. A matrix to show interactions between all structure–function subsystems defined in the hierarchy derived from MRCC analysis (Fig. 4A). Interactions between the four top-level subsystems (outlined in the Upper Left by thicker white lines) are further detailed in Fig. 4C. Matrix entries record each subsystem pair's weighted connection density (as a mean across all its constituent region pairs), while entries along the main diagonal (from Upper Left to Lower Right) record the mean connection density within individual subsystems. Subsystem pairs with regions in common are marked with a yellow dot. The unlabeled row (Top) and column (Far Left) represent the full network. The mean connection density is color-coded according to the log10 scale indicated at the bottom with 0 equaling a weight of 1, −1 equaling a weight of 0.1, −2 equaling a weight of 0.01, and so on.

Global Network Features.

Possible global organizing features of the SP2 connectome were approached by examining three basic network attributes. The first attribute is network centrality, which suggests the relative importance of regions in a network, with hubs being defined as the most central because they are typically more highly connected to the rest of the network, and may facilitate global integrative processes, and/or play critical compensatory roles when the network is damaged (30). Hub identification was based on aggregated rankings across four region centrality measures (degree, strength, betweenness, and closeness; Fig. 6 and SI Appendix, Fig. S1); after ranking regions on each metric, an aggregate “hub score” was determined for each region by summing the number of centrality metrics for which each region appeared in the top 20% (1). A hub region is presumed to rank within the top 20% for each of the four centrality metrics. Using this criterion, no region achieved a hub score of 4, and hence, no hubs were identified in the SP2 network. The lack of hub regions is consonant with the preponderance of weak connectional interactions among SP2 subsystems.

Fig. 6. Ranking of SP regions according to two centrality measures: degree centrality and strength centrality. Total degree centrality (A) is the number of connections associated with a region, and strength centrality (B) represents the total weight of connections associated with a region. Degree centrality (A) has been separated (C) into in-degree (input connections) and out-degree (output connections). Strength centrality (B) has been separated (D) into in-strength (for input connections) and out-strength (for output connections). The region-order on the vertical axis established for degree (A) is used for the other three panels (B−D). Because the right and left member of each region pair has the same value, only the value for one side is shown. Histograms for betweenness centrality and closenesss centrality are presented in SI Appendix, Fig. S1. For abbreviations, see Dataset S1.

Nevertheless, it is interesting to examine the distribution of degree and strength measures among the 40 regions used for network analysis (Fig. 6). For example, the spinal reticular nucleus has the most intraspinal connections of any gray matter region (highest degree centrality; Fig. 6A) and the greatest strength of connections (greatest strength centrality; Fig. 6B), and these measures are relatively evenly distributed between input connections and output connections (Fig. 6 C and D). In contrast, the NIV is dominated by strong input connections (Fig. 6 C and D)—it may thus be considered a “receiver” region in terms of intrinsic SP connectivity, whereas the intermediomedial nucleus is dominated by output connections (Fig. 6 C and D) and may thus be considered a “sender” region.

The so-called “rich club” is a second global network attribute; it is defined as a core set of individually highly connected regions that are also mutually highly interconnected (31). Although rich-club membership is a graded property without clearly defined boundaries, no set of rich-club members, for which the density of mutual connections was significantly larger than that of a null model distribution, was identified in the SP2 network. Rich-club organization is most commonly associated with functional attributes such as centralized processing and integration, which are not apparent within the SP2 network.

“Small world” is the third common global network attribute, and it applies to networks with highly clustered regions connected by short paths (32)—the “six degrees of separation” phenomenon. The SP2 network does not display small-world features when either unilateral connections or bilateral connections are considered (Fig. 7, SP1 and SP2, respectively). This result occurs despite a large decrease in path length when bilateral intrinsic SP connections are considered, whereas clustering, at the same time, remains virtually unchanged (Fig. 7). Fig. 7 also shows that the bilateral rhombicbrain/IMS displays essentially no small-world attributes, like the SP/CDS, whereas the ROS, and especially its forebrain component, displays the strongest small-world attributes detected thus far (the bilateral cerebral cortex occupies an intermediate position).

Fig. 7. Small-world analyses for the SP (red circles) compared with analyses for major divisions of the brain (pink circles), with values for unilateral networks (Left) and bilateral networks (Right) compared. The SP1 and SP2 do not show small-world properties. Small-world networks have two main properties: highly clustered (densely interconnected) regions and relatively short paths between two regions. Clustering is computed as the nodal mean of all weighted-directed clustering coefficients, and path length is computed as the global mean of the weighted path lengths between all region pairs. Both metrics are scaled by the corresponding measures’ medians from 1,000 degree-preserving randomized networks. The ratio between scaled clustering and scaled path length is the small-world index (SWI) (32). For a network to display small-world attributes, its SWI should be >1, with a high (scaling >> 1) clustering index and a short (scaling near 1) path length. In the plot, networks with strong small-world characteristics would be found close to the x axis (near a path length value of 1) and far to the right (with high clustering). For comparison, values are also plotted for previously reported subconnectomes: endbrain (EB1 and EB2) (4) and its component parts, cerebral nuclei (CNU1 and CNU2) (2) and cerebral cortex (CTX1 and CTX2) (3); interbrain (IB1 and IB2) (6) and its component parts, hypothalamus (HY1 and HY2) (11) and thalamus (TH1 and TH2) (5); forebrain (FB2: female, f; and male, f) (7), which have the highest SWI of all items plotted; midbrain (MB2) (8); rostral sector (ROS2: female, f; and male, m) (9), and IMS/rhombic brain (RB1 and RB2) (10).

Discussion

The network analysis results described here for intrinsic SP connectivity suggest four main conclusions. First, the structure–function organization of the subsystem hierarchy derived from MRCC analysis is relatively simple and conforms to generally recognized SP properties; three top-level subsystem categories are associated with motor, general somatosensory, and specifically nociceptive functions. Second, top-level motor and somatosensory subsystems tend to be spatially segregated and only weakly interconnected. Third, common global network features including hubs, a rich club, and small-world attributes were not detected in the SP2 network; this negative evidence contrasts with results we have obtained with the same methodology for other major divisions of the brain, especially the forebrain. And fourth, for the rat, less research has been done on connectivity between SP regions than has been done on connectivity between regions of the major brain divisions, especially the forebrain.

It is reasonable to question the value of analyzing just the intrinsic connectivity of the SP (or any other major nervous system division). The most general rationale is that analysis of any complex system requires a knowledge of how each part works (that is, its intrinsic organization), combined with a knowledge of how those parts interconnect to generate the function of that system (33). Regarding the nervous system specifically, it is worth noting that the history of connectomics has focused largely on one major brain division, the cerebral cortex, and moreover on just one half (left or right side) of the cerebral cortex (1, 30). This “corticocentric” perspective on brain networks does not imply that network attributes such as modules, hubs, rich clubs, and small-world organization are ubiquitous across all major brain divisions. Indeed, only modularity (that is, the existence of subsystems for which there is some level of statistical evidence) appears universal, while other attributes, often associated with cost-effective and efficient integration, are not encountered in all major divisions and are conspicuously absent in parts such as the SP. Our rat connectome project has provided insight into commonalities and differences in connectional organization by advancing systematically through the major nervous system divisions (Fig. 1). This stepwise approach simplifies acquiring, managing, and analyzing vast amounts of connectional data, and it is well suited to reveal nested layers of complexity within the overall architecture. As noted in the Introduction and Results, our next steps in this project are to analyze connections between the brain and SP, then between the peripheral nervous system and SP, and finally between the nervous system and body.

The main limitations of our current approach are important to consider, and although they have been mentioned previously (2, 9), it is useful here to elaborate on them in view of our data on intrinsic SP axonal connectivity. To begin, it is assumed that a long-term goal from the experimental perspective is to correlate the synaptic organization and function of the entire nervous system with the expression of behavior and control of bodily physiology, and from the theoretical perspective, a long-term goal is to use the experimentally acquired data to model computationally this biological reality. Providing solutions to these immensely complex goals is far beyond what can be accomplished with current resources (30). However, an empirically validated, general approach to complex systems analysis is to work progressively from global to local solutions. This strategy was nicely illustrated for the human genome project, which progressed from linkage maps at the beginning, to physical maps, and finally to the sequencing of popular model organisms—an approach also advocated for the human connectome project (34).

Our strategy for solving connectome problems is to view neural circuitry within the framework of a nested hierarchy (23, 24, 35). In this scheme, nervous system gray matter is divided completely into discrete, nonoverlapping regions (the macrolevel); each region is divided into a unique set of neuron types (the mesolevel); and each neuron type contains a set of individual neurons (the microlevel). At the top, most general, level, a macroconnection is defined as a weighted axonal connection from one gray matter region to another gray matter region (Region 1 > 2), for example, from the retina to the superior colliculus. At the second, nested, level, a mesoconnection is defined as a weighted axonal connection from a neuron type in a region of interest to a neuron type in that region or another region (Type 1 > 2), for example from rod photoreceptors to rod bipolar neurons. And at the third, nested, level, a microconnection is defined as a weighted axonal connection from one neuron in a neuron type of interest to another neuron (Neuron 1 > 2), for example from one rod photoreceptor to one rod bipolar neuron.

In connectomics, valid statistical analysis requires that the data in a connection matrix are reduced to the same level of granularity. For the mammalian nervous system that granularity currently is most complete at the macroconnectivity level. And while a complete macroconnectivity dataset is not available for any mammalian species, the dataset is complete enough in the rat for a reasonable analysis of top-level, global network organization (36). Furthermore, this rat dataset is enriched with information from the mesolevel and microlevel, binned to the macrolevel. However, datasets specifically for mammalian mesoconnectomes and microconnectomes are currently very sparsely populated, even for the mouse and rat.

In view of these considerations, our necessary reliance on the macroconnectome has inevitable limitations that mostly revolve around incomplete data and thus require strict versioning of datasets and analyses with future enhancements in mind (3). The incomplete data problem is complex and associated with two main factors. The first factor relates to the specific granularity level under consideration, here the macroconnectome. Our current dataset for the rat is comprehensive and mainly complete (there is no available evidence for the presence or absence of around 10% of all possible connections), and it is based on a variety of axonal tracing methods, some providing more valid data than others (3). The fundamental consideration here is that when data about a node (region) or set of nodes in a network changes, then the network parameters of that node and other nodes in the network may also change, thus possibly changing the network’s subsystem organization, along with global network features such as hubs, rich club members, and small-world organization. As an extreme example, when subconnectomes are added, the network properties of the combined connectome are different. For example, the network properties of rat cerebral cortical areas are quite different when a comparison is made between the ipsilateral association connection matrix alone and the combined bilateral association and commissural connection matrix (3). Less extreme, but in some cases rather extensive, network changes may also result from focal computational “lesions” of one or more regions in a connectome, and there are subtle differences between the male and female connectomes of the rat (7, 9). And finally, as a counterexample, in one instance it was shown that converting all data points for absent connections to very weak connections had very little effect on network properties (4).

The second main factor associated with the incomplete data problem relates to the fact that lower granularity levels contain less information than higher granularity levels. For example, our current macroconnecomic models do not represent important features associated with the neuron types that characterize mesoconnectomics, such as the pattern of axon branching of one neuron type to multiple regions, other neuron types, and individual neurons. The widespread phenomenon of axon collateralization is not commonly dealt with in contemporary connectomics, and it might require the inclusion of branched edges in graph-theoretical algorithms. Another limitation of macroconnectome modeling is that biophysical mechanisms of impulse conduction and synaptic transmission, which are critical for understanding neural network functionality at the cellular level, currently are not incorporated (30) but will be especially important additions to mesoconnectome and microconnectome analyses and modeling. Furthermore, macroconnectome models do not represent local circuitry within individual regions (information that is embedded in mesoconnectomes and microconnectomes).

Limitations aside, the main advantages of the macroconnectome strategy we have adopted are also important to appreciate, and they emerge from a different perspective on nervous system organization provided by network neuroscience. First, complete connectomes provide a global view of nervous system organizing principles based on algorithmic analysis. Second, the generation of connection matrices requires systematic data acquisition, and the results clearly demonstrate the location of knowledge gaps and/or the assignment of validity metrics for data points. Third, connection matrices can be used to construct searchable databases and may provide the conceptual framework for knowledge bases incorporating the many data types associated with nervous system circuitry (1). Fourth, macroconnectome analysis can be used to model neural networks and to model perturbations to those models (7, 9). Fifth, the subsystem hierarchy generated from cluster analysis can be used as a powerful hypothesis-generating engine (11). Sixth, a complete macroconnectome should in principle contain all connections between regions at the mesoconnectome and microconnectome granularity levels (36). And seventh, as is common for nested hierarchies, the network model derived from macroconnectome data may exhibit emergent properties derived from the meso- and microlevels (30, 37). For example, visual perception does not depend on the connections of an individual neuron in the retina (microlevel), or on the connections of an individual retinal neuron type (mesolevel), but rather on the connections of the entire retinal network.

Taking these limitations and advantages into account, the next step in our rat nervous system connectome project is to analyze connections between the SP and brain, along with intrinsic SP and brain connections, to produce a global account of intrinsic CNS organizing principles in a mammal. Adding the peripheral nervous system and body will provide the complete macroconnectome or neurome (1).

Materials and Methods

The connectome database was expertly collated from the neuroanatomical literature (7). Cluster analysis was performed using the MRCC (4, 27). Coclassification associated with this method refers to how consistently a given region-pair (present or absent connection) affiliates with the same network subsystem across all partitions captured by MRCC analysis. The linearly scaled coclassification index gives a range between 0 (no coclassification at any partitioning resolution) and 1 (perfect coclassification across all partitioning resolutions). Individual MRCC runs consisted of 250,000 partitions, sampled across a range of the resolution parameter that yields between 2 and 50 modules (the minimal and maximal possible values). Subsystem analysis and display was performed as described in the text.

Supplementary Material

Appendix 01 (PDF)

Click here for additional data file.

Dataset S01 (PDF)

Click here for additional data file.

Dataset S02 (PDF)

Click here for additional data file.

Dataset S03 (XLSX)

Click here for additional data file.

Dataset S04 (XLSX)

Click here for additional data file.

Dataset S05 (PDF)

Click here for additional data file.

Author contributions

L.W.S. and J.D.H. designed research; L.W.S. and J.D.H. performed research; L.W.S., J.D.H., and O.S. analyzed data; J.D.H. and O.S. helped to revise the manuscript; and L.W.S. wrote the paper.

Competing interests

The authors declare no competing interest.

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information. Connection Report metadata are in a Microsoft Excel spreadsheet (Dataset S3), as are data from the reports used for connection matrices (Dataset S4). Searchable Connection Report data are freely available at The Neurome Project (https://sites.google.com/view/the-neurome-project/home). Network analyses were done on the SP2 connection matrix (Dataset S4, worksheet “SP2topo”, see first worksheet “Key” for a description of the workbook contents), with tools collected in the Brain Connectivity Toolbox (https://sites.google.com/site/bctnet/).

Supporting Information

Reviewers: A.I.B., University of California San Francisco; and T.G.H., Karolinska Institutet.
==== Refs
1 M. Bota, O. Sporns, L. W. Swanson, Architecture of the cerebral cortical association connectome underlying cognition. Proc. Natl. Acad. Sci. U.S.A. 112 , E2093–E2101 (2015).25848037
2 L. W. Swanson, O. Sporns, J. D. Hahn, Network architecture of the cerebral nuclei (basal ganglia) association and commissural connectome. Proc. Natl. Acad. Sci. U.S.A. 113 , E5972–E5981 (2016).27647882
3 L. W. Swanson, J. D. Hahn, O. Sporns, Organizing principles for the cerebral cortex network of commissural and association connections. Proc. Natl. Acad. Sci. U.S.A. 114 , E9692–E9701 (2017).29078382
4 L. W. Swanson, J. D. Hahn, L. G. S. Jeub, S. Fortunato, O. Sporns, Subsystem organization of axonal connections within and between the right and left cerebral cortex and cerebral nuclei (endbrain). Proc. Natl. Acad. Sci. U.S.A. 115 , E6910–E6919 (2018).29967160
5 L. W. Swanson, O. Sporns, J. D. Hahn, The network organization of rat intrathalamic macroconnections and a comparison with other forebrain divisions. Proc. Natl. Acad. Sci. U.S.A. 116 , 13661–13669 (2019).31213544
6 L. W. Swanson, O. Sporns, J. D. Hahn, The network architecture of rat intrinsic interbrain (diencephalic) macroconnections. Proc. Natl. Acad. Sci. U.S.A. 116 , 26991–27000 (2019).31806763
7 L. W. Swanson, J. D. Hahn, O. Sporns, Structure-function subsystem models of female and male forebrain networks integrating cognition, affect, behavior, and bodily functions. Proc. Natl. Acad. Sci. U.S.A. 117 , 31470–31481 (2020).33229546
8 L. W. Swanson, J. D. Hahn, O. Sporns, Subsystem macroarchitecture of the intrinsic midbrain neural network and its tectal and tegmental subnetworks. Proc. Natl. Acad. Sci. U.S.A. 118 , e2101869118 (2021).33980715
9 L. W. Swanson, J. D. Hahn, O. Sporns, Structure-function subsystem model and computational lesions of the central nervous system’s rostral sector (forebrain and midbrain). Proc. Natl. Acad. Sci. U.S.A. 119 , e2210931119 (2022).36322764
10 L. W. Swanson, J. D. Hahn, O. Sporns, Intrinsic circuitry of the rhombicbrain (central nervous system’s intermediate sector) in a mammal. Proc. Natl. Acad. Sci. U.S.A. 120 , e2313997120 (2023).38109532
11 J. D. Hahn, O. Sporns, A. G. Watts, L. W. Swanson, Macroscale network architecture of the hypothalamus. Proc. Natl. Acad. Sci. U.S.A. 116 , E8018–E8027 (2019).
12 R. Nieuwenhuys, Deuterostome brains: Synopsis and commentary. Brain Res. Bull. 57 , 257–270 (2002).11922969
13 J. D. Hahn , An open access mouse brain flatmap and upgraded rat and human brain flatmaps based on current reference atlases. J. Comp. Neurol. 529 , 576–594 (2021).32511750
14 R. Nieuwenhuys, J. Voogd, C. van Huijzen, The Human Central Nervous System (Springer, Berlin, ed. 4, 2008).
15 S. Tan, R. L. M. Faull, M. A. Curtis, The tracts, cytoarchitecture, and neurochemistry of the spinal cord. Anat. Rec. 306 , 777–819 (2023).
16 B. N. de Sousa, L. A. Horrocks, Development of rat spinal cord. I. Weight and length with a method for rapid removal. Dev. Neurosci. 2 , 115–121 (2010).
17 R. Bjugn, H. J. G. Gundersen, Estimate of the total number of neurons and glial and endothelial cells in the rat spinal cord by means of the optical disector. J. Comp. Neurol. 328 , 406–414 (1993).8440788
18 L. W. Swanson, Brain maps 4.0—Structure of the rat brain: An open access atlas with global nervous system nomenclature ontology and flatmaps. J. Comp. Neurol. 526 , 935–943 (2018).29277900
19 B. Rexed, The cytoarchitectonic organization of the spinal cord in the cat. J. Comp. Neurol. 96 , 415–496 (1952).
20 B. Rexed, A cytoarchitectonic atlas of the spinal cord in the cat. J. Comp. Neurol. 100 , 297–380 (1954).13163236
21 C. Molander, Q. Xu, G. Grant, The cytoarchitectonic organization of the spinal cord in the rat. I. The lower thoracic and lumbosacral cord. J. Comp. Neurol. 230 , 133–141 (1984).6512014
22 C. Molander, Q. Xu, C. Rivero-Melian, G. Grant, Cytoarchitectonic organization of the spinal cord in the rat. II. The cervical and upper thoracic cord. J. Comp. Neurol. 289 , 375–385 (1989).2808773
23 L. W. Swanson, M. Bota, Foundational model of structural connectivity in the nervous system with a schema for wiring diagrams, connectome, and basic plan architecture. Proc. Natl. Acad. Sci. U.S.A. 107 , 20610–20617 (2010).21078980
24 R. A. Brown, L. W. Swanson, Neural systems language: A formal modeling language for the systematic description, unambiguous communication, and automated digital curation of neural connectivity. J. Comp. Neurol. 521 , 2889–2906 (2013).23787962
25 M. Sasaki, A. P. Arnold, Androgenic regulation of dendritic trees of motoneurons in the spinal nucleus of the bulbocavernosus: Reconstruction after intracellular iontophoresis of horseradish peroxidase. J. Comp. Neurol. 308 , 11–27 (1991).1874978
26 H. D. Schrøder, Organization of the motoneurons innervating the pelvic muscles of the male rat. J. Comp. Neurol. 192 , 567–587 (1980).7419745
27 L. G. S. Jeub, O. Sporns, S. Fortunato, Multiresolution consensus clustering in networks. Sci. Rep. 8 , 3259 (2018).29459635
28 A. G. Brown, The dorsal horn of the spinal cord. Q. J. Exp. Physiol. 67 , 193–212 (1982).6281848
29 J. Braz, C. Solorzno, X. Wang, A. I. Basbaum, Transmitting pain and itch messages: A contemporary view of the spinal cord circuits that generate gate control. Neuron 82 , 522–536 (2014).24811377
30 O. Sporns, Networks of the Brain (MIT Press, 2011).
31 V. Colizza, A. Flammini, M. A. Serrano, A. Vespignani, Detecting rich-club ordering in complex networks. Nat. Phys. 2 , 110–115 (2006).
32 M. D. Humphries, K. Gurney, Network “small-world-ness”: A quantitative method for determining canonical network equivalence. PloS One 3 , e0002051 (2008).18446219
33 D. H. Meadows, Thinking in Systems: A Primer (Chelsea Green, VT, 2008).
34 J. W. Lichtman, J. R. Sanes, Ome sweet ome: What can the genome tell us about the connectome? Curr. Opin. Neurobiol. 18 , 346–353 (2008).18801435
35 L. W. Swanson, J. W. Lichtman, From Cajal to connectome and beyond. Annu. Rev. Neurosci. 39 , 197–216 (2016).27442070
36 M. Bota, L. W. Swanson, The neuron classification problem. Brain Res. Rev. 56 , 79–88 (2007).17582506
37 M. Breakspear, C. J. Stam, Dynamics of a neural system with a multiscale architecture. Phil. Trans. R. Soc. B. 360 , 1051–1074 (2005).16087448
