Structure–function subsystem model and computational lesions of the central nervous system’s rostral sector (forebrain and midbrain)

Significance

The central nervous system’s rostral sector consists of forebrain and midbrain, and this sector is responsible for coordinating voluntary behavior, cognition, and affect with instinctive survival behaviors and bodily physiology. To clarify biological mechanisms underlying this coordination, we have generated a hierarchical structure–function subsystem model of intrarostral sector neuronal connectivity, and we have examined how localized changes in connectivity impact global network architecture. Three key factors are found to play a significant role: the hub score (centrality) of altered nodes, the hierarchy position of the altered nodes, and the distribution of altered node input and output connections within the subsystem network. This conceptual framework is a hypothesis-generating engine for clarifying mechanisms linking neuronal subsystems, behavior, and disease.

Abstract

The craniote central nervous system has been divided into rostral, intermediate, and caudal sectors, with the rostral sector containing the vertebrate forebrain and midbrain. Here, network science tools were used to create and analyze a rat hierarchical structure–function subsystem model of intrarostral sector neural connectivity between gray matter regions. The hierarchy has 109 bottom-level subsystems and three upper-level subsystems corresponding to voluntary behavior control, cognition, and affect; instinctive survival behaviors and homeostasis; and oculomotor control. As in previous work, subsystems identified based on their coclassification as network communities are revealed as functionally related. We carried out focal perturbations of neural structural connectivity comprehensively by computationally lesioning each region of the network, and the resulting effects on the network’s modular (subsystem) organization were systematically mapped and measured. The pattern of changes was found to be correlated with three structural attributes of the lesioned region: region centrality (degree, strength, and betweenness), region position in the hierarchy, and subsystem distribution of region neural outputs and inputs. As expected, greater region centrality results, on average, in stronger lesion impact and more distributed lesion effects. In addition, our analysis suggests that strongly functionally related regions, belonging to the same bottom-level subsystem, exhibit similar effects after lesioning. These similarities account for coherent patterns of disturbances that align with subsystem boundaries and propagate through the network. These systematic lesion effects and their similarity across functionally related regions are of potential interest for theoretical, experimental, and clinical studies.

Current developmental, morphological, and molecular evidence suggests that chordates share a unique longitudinal body plan with three defining features: segmented muscles, a notochord, and a dorsal tubular central nervous system (CNS) derived from a neural plate (1). This evidence further suggests that the chordate CNS displays three basic units or histogenetic fields, referred to as rostral, intermediate, and caudal sectors (1). In terms familiar to vertebrate neuroscience (2, 3), the rostral sector (ROS) includes the forebrain and midbrain, the intermediate sector is the rhombicbrain (cerebellum, pons, and medulla), and the caudal sector is the spinal cord. While it is uncommon today to consider the forebrain and midbrain together as a basic unit of the CNS, there is an old tradition in mammalian system physiology and topographic anatomy (3, 4) simply to divide the brain into cerebrum (the “large brain,” consisting of forebrain and midbrain) and cerebellum (the “small brain,” consisting of cerebellum, pons, and medulla), a relationship that is easy to appreciate schematically (Fig. 1D). This distinction was reinforced by histological evidence that the definitive, condensed, glycogen-rich floor plate of the vertebrate neural tube ends rostrally at the junction between pons and midbrain (5), at the border between intermediate and rostral sectors.

Fig. 1.

Conceptual framework for analysis of rostral sector intrinsic macrocircuitry. (A) Schematic outline of the early neural tube, with its primary forebrain vesicle (PFBV), primary midbrain vesicle (PMBV), primary hindbrain vesicle (PHBV), and spinal cord part of neural tube (NTSP), superimposed on a model of the human embryo. The rostral sector (ROS) consists of the PFBV and PMBV together (green), the intermediate sector (IMS) consists of the PHBV, and the caudal sector (CDS) consists of the NTSP. A qualitatively similar arrangement is a feature of all vertebrates at an equivalent stage of development. (B) Topographically arranged hierarchy of major CNS subdivisions common to adult chordates (larval tunicates, cephalochordates—amphioxus, and craniotes). Note that the PHBV (A) becomes the adult rhombicbrain, or intermediate sector, and that the adult hindbrain has a more restricted meaning than in the early neural tube; see ref. 3. (C) Schematic view of the adult rat bilateral ROS connection matrix (ROS2) with the subconnectomes associated with the forebrain (green), midbrain (green), and connections between forebrain and midbrain (yellow) on each side of the brain. The ROS2 connection matrix has 560 rows and 560 corresponding columns (233 for forebrain gray matter regions on each side and 47 for the MB regions on each side, as indicated). 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 are treated as black boxes (connections within the parts shown in B are, of course, analyzed). The two shorter diagonals (lighter dashed lines) parallel to the main diagonal represent homotopic crossed connections: from a region on one side of the brain to the corresponding region on the other side. (D) Rostral sector (ROS2, green) shown on a rat CNS flatmap (14).

The extent to which the putative three sequential sectors of the craniote CNS share a basic plan of neural connectivity or network organization remains an open question. We are approaching this problem in comparative neuroscience by assembling and analyzing with network science methods a connectome for the entire nervous system of a mammal, the rat, for which by far the most comprehensive set of connectional data has been published. Currently this dataset is only reasonably complete for the macrolevel of analysis, that is, for the directed and weighted axonal connections between the roughly 1,000 distinct gray matter regions in mammals (6). This analysis level deals with the coarse wiring diagram that is species specific and presumably genetically determined during development (7), in contrast to the refined wiring diagram that is specific to an individual and is modified dynamically from the coarse original, conferring adaptability to changing internal and external conditions (8). More formally, neural circuitry may be viewed as a nested hierarchy of analysis levels. The top, macrolevel deals with axonal connections between gray matter regions, whereas the mesolevel of analysis deals with connections between the neuron types within and between each region, the microlevel deals with connections between individual neurons of each neuron type, and the bottom, nanolevel deals with the set of synapses formed between two or more neurons (6).

Our strategy has been to start at the rostral end of the CNS and work progressively toward the spinal cord at the caudal end (Fig. 1 B and D) before adding the peripheral nervous system and its connections with the body, a grand connectome referred to as the neurome (7). Thus far, databases for the intrinsic macrocircuitry of the forebrain (9) and of the midbrain (10) have been constructed and analyzed. Here we add the set of macroconnections (hereafter referred to simply as connections) between the forebrain and midbrain (Fig. 1 C, yellow) to create the subconnectome for all known connections within the ROS. Viewed in isolation, the ROS has several features of particular interest based on current evidence. First, two cranial sensory nerves (olfactory and optic) terminate entirely within the ROS, which also generates somatomotor nuclei for most of the oculomotor muscles and all the neuroendocrine motoneurons controlling the pituitary gland. Second, the ROS contains the nigrostriatal and mesolimbic dopaminergic projections that play a critical role in motivation and reward mechanisms. Third, the ROS contains the extensive set of forebrain projections to the midbrain periaqueductal gray involved in controlling a variety of basic social behaviors critical for survival of the individual and of the species.

The original goal of this research was to construct hierarchical subsystem models of major nervous system divisions and to analyze and describe the topographic and topological network architecture of these models (7). However, more recently we have begun also to explore the effect on global network architecture of focal neuronal connection weight changes (9). This approach is expanded here to identify possible factors correlated with sexual dimorphisms and with the pattern of differences established by simulated structural lesions of the neural inputs and outputs associated directly with one or two regions.

Results

Creating the Foundational Database.

Our overall strategy is based on embryological (Fig. 1A) and topographic (Fig. 1 B and D) first principles. As in our preceding article (10), the database used for analysis was extracted from the results of axonal pathway tracing experiments indicating the presence (and weight) or absence of connections between all 560 gray matter regions (nodes) on the right (280 regions) and left (280 regions) sides of the ROS in our rat brain reference atlas (11) (see Dataset S1 for abbreviations), described with a defined vocabulary for axonal connections (12, 13), and displayed on the atlas (11) or on a CNS flatmap (14). Connection reports (ranging from none to multiple) for each possible connection in the connection matrix (Fig. 1C) were expertly collated from the primary structural neuroscience literature as described thoroughly elsewhere (9); for a comparison of collation results for the same connection matrix by two experts see reference (15). Our previously published subconnectomes for intraforebrain (9) and intramidbrain (10) connections were revised and updated here with new data (see SI Appendix, Materials and Methods). The remaining eight subconnectomes connecting the two divisions (Fig. 1 C and D, yellow) were collated by L.W.S. for the present analysis to complete the ROS connection matrix.

First and foremost, the number of possible intra-ROS connections on one side of the brain (ipsilateral, uncrossed, or association connections; ROS1, the ipsilateral network) is 78,120 (280² minus 280; intraregional connections are ignored), and the number of possible ROS connections to the other side (contralateral, crossed, or commissural) is 78,400 (280²), making 313,040 possible intra-ROS connections bilaterally (ipsilateral + contralateral times 2; ROS2, the bilateral network). With this level of complexity, the utility and necessity of data matrices and cluster analysis for identifying connectivity patterns and perturbations of those patterns are apparent.

Our systematic collation identified no statistically significant right–left (or strain) ROS2 connectional differences, so all ipsilateral and contralateral connections were assigned to one side, and the same dataset was used for the other side. Thus, our analysis applies generally to the species level (adult female and male rat, Rattus norvegicus domestica).

Second, a dataset of 276,772 Connection Reports (≥18 items of metadata per report) for ipsilateral and contralateral connections from the ROS on one side was collated from 898 original research articles published since 1973, for 156,520 possible connections (reports selected for network analysis were drawn from 757 of these publications). With no right–left differences, doubled values are 553,544 Connection Reports for 313,040 possible connections for both sides. The collated Connection Reports were sourced from 88 different titles, including 80 journals (51.4% from the Journal of Comparative Neurology), 3 books, and 5 theses. The collated data were generated by about 483 laboratories (22.6% from the L.W.S. laboratory) using 40 different experimental intra-axonal pathway tracing methods; these and other metadata for each Connection Report are provided in Dataset S2.

Basic Connection Numbers and Validity.

The collation identified 17,997 ipsilateral intra-ROS (ROS1) connections as existing and 56,439 as absent, a 24.2% connection density. As before (10, 16), “unclear” values are binned with “absent” values, “axons-of-passage” are binned conservatively with “weak,” and “present” values are binned with “moderate.” In contrast, 6,316 contralateral intra-ROS connections from one side were identified as existing and 66,798 as absent (8.6% connection density). Thus, for each ROS side, 24,313 ipsilateral and contralateral connections were identified as existing, and 123,237 were identified as absent (16.5% connection density). These numbers are doubled for the complete bilateral intra-ROS (ROS2) connection matrix (48,626 connections exist and 246,474 are absent; connection density is also 16.5% because no right–left differences are documented). Also, 96.4% of the Connection Reports used for the connection matrix did not report which ROS side was microinjected with pathway tracer.

Importantly, no published data were found for 17,940 (5.731%) of all 313,040 possible connections in the ROS2 connection matrix, yielding a coverage (fill ratio) of 94.3%. Based on this coverage, assuming the Connection Reports representatively sample the 560 × 560 region matrix, a complete bilateral intra-ROS connection matrix (ROS2) would contain ∼51,582 connections: (313,040/48,626 + 246,474) × 48,626.

For the next step, network analysis, reported connection-weight values of “no data” were binned with “absent” and “unclear” values (see Dataset S3), and then all values were converted from the descriptive ordinal scale to a log₁₀ scale covering five orders of magnitude (see Dataset S4, layer F) because this is the reported range of rat connectional data (9, 10) (Fig. 2, Middle Column). The resulting connection densities for ipsilateral and contralateral intra-ROS connections are ipsilateral (ROS1), 23.0%; contralateral, 8.1%; and both ipsilateral and contralateral, 15.5% (Dataset S3). For the complete set of bilateral ROS regions (ROS2), the range of ipsilateral and contralateral output connections (the output connection degree range) is 0–403, the input connection degree range is 2–293, and the total (input + output) degree range is 6–523 (see Dataset S5A).

Fig. 2.

Bilateral intrarostral sector macroconnectomes for male (ROS2f, Top Row) and female (ROS2m, Bottom Row) rat. Directed and weighted monosynaptic macroconnection matrices with gray matter region sequence in a subsystem (SS) arrangement derived from MRCC analysis. Collated data are represented by descriptive terms corresponding to ordinal weight values (Left Column) and then converted to log-weighted values (second column) for computation. MRCC analysis of the log-weighted connection data generated coclassification matrices (third column), also represented as a hierarchal dendrogram cluster tree (Right Column). Coclassification refers to how consistently a given node 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 uniformly sampled partitions. Three top-level SSs are outlined by yellow lines (the small third SS is in the lower right corner). In an MRCC hierarchy, the length of a branch 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 the branch’s 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. All solutions plotted in the tree survive statistical testing with a significance level of α = 0.05. Note that specific sexual dimorphisms are not easily discernible here; much greater magnification is needed (see SI Appendix, Fig. S2). For region (row and column) identity and additional details see Datasets S3 and S4, where the underlying connection data and subsystem organization are easy to explore.

Finally, a validity metric was applied to the pathway tracing method associated with each Connection Report (9, 10). The metric uses an ordinal 7-point scale (1–7/lowest–highest validity). In this approach, a validity score was generated for each region-pair in the connection matrix (Dataset S4, Layer V). The following average validity values were determined for the data that were used for network analysis: for connections reported to exist, ipsilateral (within one side) = 6.47, contralateral (between sides) = 6.47; for connections reported to not exist, ipsilateral = 6.15, contralateral = 6.18 (Dataset S2).

Female–Male Difference.

Of 313,040 possible ROS2 connections, 4/48,626 identified as existing are markedly sexually dimorphic based on statistical analysis. The right and left ipsilateral connections from bed nuclei of terminal stria principal nucleus (BSTpr) to anteroventral periventricular nucleus (AVPV) are reportedly six times stronger in males (very strong vs. weak; ordinal scale), and the right and left ipsilateral connections from BSTpr to ventral premammillary nucleus (PMv) are reportedly four times stronger in males (rated very strong vs. moderate) (see Datasets S2 and S3). These connections are involved in controlling the estrous cycle and other reproductive functions (17). Because of these established sexual dimorphisms, it was necessary to construct Fig. 2 and analyze separate female ROS2 (ROS2f) and male ROS2 (ROS2m) connection matrices.

Subsystem Analysis.

One approach to clarify organizing principles of nervous system circuitry is to examine its subsystem architecture with multiresolution consensus cluster (MRCC) analysis (18, 19). It is designed to detect strongly connected clusters (called communities, modules, or the synonym used here, subsystems) among the directed and weighted axonal connections between all regions (nodes) of the network represented in a connection matrix (connectome), across all levels of partitioning resolution or scale (1–47 possible levels for ROS2). The result identifies without preconceived biases (unsupervised or agnostically) clusters of various size arranged in a nested hierarchy that represents a compact description of all subsystems (SSs) and interactions between them (Fig. 2, Right Two Columns).

Because datasets for connections arising from rostral sector sides 1 and 2 are identical, MRCC analysis of ROS2f and ROS2m should generate precisely symmetric subsystems across the median plane. However, because of the MRCC algorithm mechanism, the presence of extremely strong crossed homotopic connections can prevent their symmetric division and allocation. Using an approach described previously (20), we found that symmetric MRCC solutions (Fig. 2) were obtained only after omitting the right and left nucleus of lateral olfactory tract dorsal cap, a tiny cerebral cortex region with a very strong crossed homotopic connection that should be viewed as a very small top-level subsystem (the right and left nucleus of lateral olfactory tract dorsal cap), though not considered further here. Thus, MRCC analysis proceeded on 558 × 558 ROS2 connection matrices.

Hierarchical Structure–Function Subsystem Models.

As performed for the intraforebrain (9) and intramidbrain (10) connectomes, the MRCC structural hierarchy for ROS2f (Fig. 2, Far Right Column) has been annotated with the most obvious and general functional correlates accessed through the references associated with Connection Reports in Dataset S2. The basic hypothesis here is that each subsystem may subserve a unique functional role because the regions defining a subsystem are, as revealed by multiresolution cluster analysis, more strongly clustered with each other than with other subsystems. This version 1.0 of the ROS2f structure–function subsystem model is admittedly incomplete, and as with the connection matrix substrate, future versions are expected to improve continually with additional data.

As shown in Fig. 2 (Far Right Column), the ROS2f cluster tree has three top-level or first-order subsystems, 109 bottom-level subsystems (with a mean of 5 regions and a range of 1–15), and 47 levels (parent branches). The challenge is to extract organizing principles and a conceptual framework from this complex arrangement. The annotated structure–function hierarchy and its levels cannot be illustrated legibly in standard page format but is easily examined in Dataset S4, layers B–D. The two top-level or first-order subsystems (SS1.0 and SS2.0) form a huge mirror-image pair. Each subsystem has 276 regions (nodes), all but two of which (retina and parabigeminal nucleus) are on one side of the brain. So, to a first approximation, the ROS2 is divided into right and left mirror-image subsystems whose intrinsic connections are an order of magnitude stronger than connections between them (Fig. 3 A and B). This arrangement is very similar to that for intraforebrain connections (9) but quite different from that for intramidbrain connections (10), where the cluster tree’s top level has 6 subsystems. The third top-level subsystem (SS3.0) is very small and bilaterally symmetrical, and this subsystem contains the remaining 6 ROS2 regions: right and left oculomotor nuclei, interstitial nuclei of Cajal, and nuclei of posterior commissure. Nothing more will be said about this subsystem, which is obviously associated with oculomotor function.

Fig. 3.

Different connectivity graph views of relationships between high-level ROS2 subsystems. (A) High-level topological circuit diagram of the ROS2f network created with an algorithm (SpringVisCom: https://github.com/LJeub/SpringVisCom) that produces network layouts emphasizing a prespecified community structure, here the five highest-level ROS2 subsystems. Nodes (gray matter regions) for each of these subsystems, which can be seen clearly in Fig. 4 and the hierarchy displayed in Dataset S4, are color-coded, and line thickness is proportional to the symmetrized (mean) edge (connection) weight. As labeled, mirror-image SS1 and SS2 are in the top and bottom halves of the graph, whereas the small SS3 is bilateral and in the middle on the right. SS1 then divides into SS1.1 and SS1.2, and SS2 divides into mirror-image SS1.2 and SS2.2. Vertical lines correspond to homotopic commissural connections between corresponding mirror-image node pairs. For clarity only a small percentage of the stronger connections are shown, enough to show at least one connection per node. For the purposes of this visualization, all connections are undirected (computed as the mean of the two reciprocal connection weights), and the subsystem locations are preseeded (the nodes within them are too small to label; for identification see Dataset S4, layer D). (B) The two major top-level, first-order subsystems (SS1 and SS2) are mirror images, each having all but two (retina and parabigeminal nucleus) of its 276 nodes/regions on one side of the brain. As measured by weighted connection density (aggregate connection strength/total number of regions, ×100; values in Dataset S3), the intrinsic (intrasubsystem) connections of SS1 or SS2 are 11.7× stronger than connections between them (intersubsystem connections). (C) Schematic diagram of second-order subsystem interaction strengths (line thickness approximately proportional to weighted connection density value). For simplicity, Subsystem 3 is not shown in B or C. For ordered list of subsystems see Dataset S4.

SS1.0 (and mirror-image SS2.0) in turn simply has two branches, SS1.1 and SS1.2, that interact as shown in Fig. 3C. At this point, two fundamental questions arise: What is the possible functional significance of this dichotomy in the second-order branches, and what is the spatial relationship between SS1.1 and SS1.2? To approach functional significance, our strategy has been (9, 10) to start with the bottom-level, presumably most specialized subsystems and then systematically work toward the upper, more general levels. The results for the ROS2f hierarchy (Dataset S4) suggest that SS1.1 (and mirror-image SS2.1) is concerned primarily with controlling voluntary behavior, accompanied by cognition and affect, whereas SS1.2 (and mirror-image SS2.2) is concerned primarily with coordinating innate survival behavior and bodily physiology. Again, this dichotomy closely resembles the one for intraforebrain connections (9) but sharply differs from the one for intramidbrain connections (10).

At the third-order level of the hierarchy, the voluntary behavior subsystem, SS1.1 (and its mirror image, SS2.1), divides into four subsystems, and the innate survival subsystem, SS1.2 (and its mirror image, SS2.2), divides into three subsystems (Dataset S4). The voluntary behavior subsystem’s first branches include those associated with visual–auditory perception, somatic–visceral–gustatory sensorimotor function and “basal ganglia”, olfactory–intrahippocampal circuitry, and cortical executive function. In contrast, the innate survival subsystem’s first branches include those associated with arousal and reward; interactions between ingestive and reproductive behaviors, and visceromotor integration; and interactions between agonistic and reproductive behaviors.

Subsystem Spatial Relationships.

The gray matter regions associated with a subsystem could be distributed either in a checkerboard pattern through the ROS2 or in a spatially compact formation. When regions associated with the upper-level voluntary behavior (SS1.1 and mirror-image SS2.1) and innate survival behavior (SS1.2 and mirror-image SS2.2) subsystems are mapped onto the reference atlas, it is immediately obvious from visual inspection that they form remarkably spatially segregated components of the ROS2 (Fig. 4). In the forebrain, the voluntary behavior subsystem is larger physically and lies dorsolaterally, whereas the innate survival subsystem is smaller physically and lies ventromedially. This spatial pattern resembles that described for the isolated intraforebrain connectome (9), where the voluntary behavior subsystem is associated with the lateral forebrain system of axons, and the innate survival subsystem is associated with the medial forebrain system of axons. In contrast, the isolated intramidbrain connectome (10) has six top-level subsystems, only two of which are clearly spatially contiguous, and these subsystems are associated with sensory–motor mechanisms, motivation and reward, regulating reproductive and agonistic behaviors, and behavioral state control.

Fig. 4.

Spatial distribution of top-level, mirror-image subsystems (SS1.0 and SS2.0), and the tiny bilateral SS3.0, associated with the ROS2f connection matrix (Fig. 2, Top Row). The distribution is shown on a series of transverse atlas levels through the rat brain, arranged from rostral (A) to caudal (G). Adapted from the reference atlas used here (11), which is licensed under CC BY 4.0, and which may be consulted for complete parceling and annotation of each atlas level.

From the viewpoint of topographic divisions (Fig. 1 B and D), cerebral cortex and dorsal thalamus regions are associated primarily with the voluntary behavior subsystem, whereas hypothalamus, epithalamus, and midbrain regions are associated primarily with the innate survival subsystem. In contrast, cerebral nuclei regions are divided more evenly between the voluntary and innate survival subsystems. One might hypothesize that this basic topographic arrangement provides more physical protection from external forces for the innate survival subsystem, which lies deep to the voluntary behavior subsystem. If this physical arrangement does provide some survival benefit for the individual and species, it may have been selected for during evolution.

Global Network Features.

Three basic network attributes were examined to clarify global organizing features of the ROS2 connectome. First, network centrality suggests the relative importance of regions (nodes) in a network, with the most central referred to as hubs. Hub identification was based on aggregated rankings across four regional/nodal centrality measures (degree, strength, betweenness, and closeness; Dataset S5); after ranking regions on each metric, an aggregate “hub score” was determined for each region, expressing the number of centrality metrics for which each region appeared in the top 20% (7). Using this criterion, 36 top-ranked putative hubs (with an aggregate score of 4) were identified, consisting of 18 mirror-image region pairs. The cerebral cortex has 16 hubs (8 region pairs) that cluster in two spatially continuous patches in each hemisphere and are all part of the voluntary behavior subsystem (SS1.1). One patch is in the medial temporal region and consists of the lateral entorhinal and perirhinal areas, whereas the other patch is in the frontal region and consists of the medial and ventral orbital, infralimbic, prelimbic, dorsal anterior cingulate, and face primary motor areas. One hub lies in the cerebral nuclei: the innominate substance (ventral pallidum). The dorsal thalamus midline group has three hub pairs (paraventricular thalamic, and rostral and caudal reuniens nuclei), and the ventral thalamus has one hub pair, the zona incerta. The hypothalamus has three hub pairs (posterior nucleus and juxtaparaventricular and juxtadorsomedial regions of lateral hypothalamic area), and the midbrain has only two hub pairs, the precommissural nucleus of periaqueductal gray and superior colliculus. All noncortical hubs but one (caudal reuniens nucleus) are associated with the innate survival behavior subsystem, SS1.2 (all hubs are indicated by an “H” in parentheses following the corresponding region abbreviation in Dataset S4, layer D).

The second network attribute is the so-called rich club: a set of individually highly connected nodes that are also mutually highly interconnected (21). Rich-club membership is a graded property with no clearly defined boundaries, and the ROS2 rich club is potentially quite large, involving regions with a degree centrality >100 (Fig. 5). To narrow down membership, we identified four peaks in the plot of normalized rich-club coefficient versus node/region degree (Fig. 5). Starting with the smallest node degree, peak 1 has 45 region pairs, peak 2 has 34 region pairs, peak 3 has 16 region pairs, and peak 4 has 10 region pairs. Because peak 3 has the largest normalized rich-club coefficient—the internal density of the subnetwork at peak 3 exceeds the null model (randomized connection densities) by the greatest percentage—and is reasonably small, its components were chosen to describe here.

Fig. 5.

Detection of the most prominent rich club members of the ROS2f network. Rich club (RC) index is plotted against an ordering of all 560 nodes/regions by their degree centrality metric, and the four peaks to the right, labeled 1–4 and indicated by red “X” marks, were considered most prominent and statistically significant (with P = 0 for all four peaks). Peak 3 may be considered the “richest club” because the connection density of its members most exceeds the expected (null) mean (= 1), that is, the mean connection density of the same region subset but with connection weights randomized, hence the “normalized RC coefficient” (RCnorm on the y axis). On the x-axis, a value of degree indicates regions/nodes with that degree or higher; thus, peak 4 is a subset of peak 3.

The 16 mirror-image region pair members of the “richest club” (Fig. 5, peak 3) form the most strongly connected subnetwork in the ROS2 network, and they are distributed across both of the major second-order subsystems (voluntary and innate survival behaviors) and across 5 of the 7 third-order subsystems discussed in Hierarchical Structure-Function Subsystem Models and shown in Dataset S4, layer D (indicated by “RC” in parentheses following the region abbreviation). This distribution pattern suggests that the rich club forms a secondary network that plays a prominent role coordinating interactions between the major subsystems of the ROS2 network via intersubsystem connections. In addition, some third-order subsystems have multiple rich club members, suggesting that the rich club also generates prominent intrasubsystem connections. As shown in Dataset S4 (layer D), the voluntary behavior subsystem SS1.1 has just three rich club member pairs (the adjacent infralimbic and prelimbic areas of medial prefrontal cortex, and the thalamic nucleus reuniens caudal division). In contrast, the innate survival behavior subsystem SS1.2 has the remaining 13 rich club member pairs, with the reward and arousal subsystem SS1.2.1 having four pairs, the ingestive-reproductive behavior interactions and visceromotor integration subsystem SS1.2.2 having one pair, and the reproductive-agonistic behavior interactions subsystem SS1.2.3 having eight pairs.

The third network attribute, “small world,” applies to networks with highly clustered nodes connected by short paths (22). The small-world organization of ROS2f and ROS2m is virtually identical, and it falls between the bilateral intraforebrain network’s small-world index, which is larger, and the bilateral intramidbrain network’s small-world index, which is smaller (SI Appendix, Fig. S1). This finding suggests that, despite significant differences in global topological features of individual rat brain topographic subdivisions, small-world organization persists in the aggregate, especially when considering bilateral connectomes. For example, while ipsilateral thalamus (TH1), hypothalamus (HY1), and cerebral nuclei (CNU1) display classic small-world connectivity, larger divisions such as ROS2 tend to maintain short path length while also exhibiting high clustering. Future work, incorporating additional information on the geometry of regions and connections, is needed to determine how much of the global topological features we observe in the rat brain is due to physical embedding.

Comparing Female and Male Subsystem Organization.

The two mirror-image pairs of sexually dimorphic connections, both arising from BSTpr (BSTpr > AVPV and BSTpr > PMv), produce widespread differences in female and male ROS2 subsystem hierarchies as measured by differences in node-pair (present or absent connection) coclassification score, a measure of subsystem (cluster) affinity, and thus perhaps reflecting overall network coherence properties. First, a difference matrix for the two coclassification matrices (Fig. 2, Third Column) shows subtle differences in the coclassification score for 8.46% of the ROS2 node pairs (Dataset S4, layer I). Second, regions with the greatest differences in coclassification index/subsystem affinity were rank ordered; the top 20th percentile comprised 42 regions (SI Appendix, Fig. S2 A and B). Third, the female and male ROS2 subsystem hierarchies were directly compared (SI Appendix, Fig. S2C). This demonstrated that 25 of the 42 regions in the top 20th percentile occur within three narrow hierarchy domains.

The top 10 most dimorphic regions all cluster in one lowest-level subsystem, associated most clearly with control of gonadotropin secretion, that has the same region composition in both sexes, including the BSTpr, AVPV, and PMv (SI Appendix, Fig. S2D). The next 5 most dimorphic regions all also cluster in one lowest-level subsystem, associated most clearly with pheromone detection and composed of the same regions in females and males (SI Appendix, Fig. S2E). The final domain has 6 adjacent lowest-level subsystems in females and males, but here the subsystem composition and hierarchical arrangement is different between the sexes (SI Appendix, Fig. S2F). This domain has 27 regions; 17 of them are not in the top 20th percentile of dimorphic regions, and 10 are among the lower-ranked dimorphic regions. This third subsystem domain is associated most clearly with interactions between reproductive and agonistic behaviors. Thus, ROS2 network subsystems with multiple highly dimorphic regions may or may not be dimorphic with respect to region composition or with neighboring hierarchy relationships (compare SI Appendix, Fig. S2F with SI Appendix, Fig. S2 D and E, respectively).

Simulated Structural Lesion Effects on Global Network Organization.

In an earlier article (9) we began to explore the impact of focal computational lesions on network organization by removing the input–output connections of an individual region, or two regions, in the intraforebrain connection matrix, followed by recomputing the coclassification matrix of the lesioned network, and then plotting differences with the intact coclassification matrix as changes in coclassification score and subsystem affinity. In this article, to examine systematically factors influencing the pattern of lesion effects on global network organization, all 279 region pairs (right and left members of the same region) in the ROS2f and ROS2m MRCC matrices were lesioned individually. Three features were examined: global magnitude of significant lesion effects, distribution of significant lesion effects throughout the coclassification matrix, and region pair vulnerability to significant lesion effects. The results are followed by instructive examples.

To begin, we confirmed the well-known correlation between global lesion impact and region centrality measures. The magnitude of lesion effects (the sum of root mean square of subsystem affinity scores for all region pairs in a lesioned MRCC matrix) is correlated with the degree (ρ = 0.513, P = 3.6 × 10⁻²⁰), strength (ρ = 0.733, P = 0), and betweenness (ρ = 0.692, P = 0) centrality of the lesioned node (Spearman rank–order correlations, ROS2f matrix). These correlation coefficients are well above chance but account for only part of the variance. The results can also be viewed by plotting the aggregated centrality score of each lesioned region (Dataset S5) against total lesion impact for that region. There is a trend for lesion magnitude (Fig. 6A) and lesion distribution (Fig. 6B) to increase with increasing centrality score, but there is also considerable overlap.

Fig. 6.

Effects of focal lesions in the ROS2f MRCC matrix. In A and B, each of the 279 mirror-image region pairs in the matrix was lesioned and global lesion effects were measured in two ways. (A) First, total impact was measured by the sum of RMS changes in coclassification/subsystem affiliation score (index) for all region pairs (connections) in the matrix, and this value was plotted against the lesioned region’s hub score. The median lesion impact (red horizontal bars) increased with each increase in hub score, although the range of effects showed considerable overlap between scores. (B) Second, total lesion impact was assessed by determining how much of the matrix was significantly affected, a measure of lesion effect distribution. Significance threshold was set to the 99.9th percentile of the differences between identical runs on the ROS2f matrix. As in (A), mean lesion impact significantly increased with each increase in hub score, with considerable overlap between hub scores. (C) Relationship between two measures of lesion impact for all region pairs: total RMS (A) and distribution (B). For the data, a second-degree polynomial fit with 95% confidence intervals is displayed. Six regions show unusually broad distribution of lesion changes (Top) and seven regions display considerable total lesion impact restricted to a small part of the matrix (Bottom). For one region (ENTl), neural inputs and outputs were lesioned separately. (D) The vulnerability of a region pair as a function of its coclassification score (index). The vulnerability score indicates how many of the 279 lesions significantly impacted the coclassification score of the region pair of interest. The results of lesioning individually each of the 279 region pairs show an inverted U-shaped distribution, with little vulnerability at the two extremes of the coclassification score; that is, region pairs with an intermediate coclassification score are most vulnerable to lesion effects. MRCC matrices were calculated with 50,000 sampled partitions; the results correlate very well with larger runs sampling 250,000 partitions (Fig. 8), with similarity (Pearson correlation) ranging between r ∼0.96 and 0.91. ACB, accumbens nucleus; AIp, posterior agranular insular area; ENTl, lateral entorhinal area; ICd; dorsal inferior colliculus; IGL, intergeniculate leaflet; ILA, infralimbic area; IPN, interpeduncular nucleus; LCd, dorsal lateral geniculate nucleus; MH, medial habenula; ORBm, medial orbital area; OV vascular organ lamina terminalis; PERI, perirhinal area.

When extent of lesion distribution throughout the matrix is plotted against absolute magnitude of impact, two small sets of regions are identified as outliers, based on their placement above and below the range of lesion impact metrics observed across the full dataset. One region set (n = 6; “Broad” in Fig. 6C) is exemplified by the lateral entorhinal area (ENTl); the network impact of lesioning its members is not only strong (high magnitude) but also exceptionally broad and far-reaching (high distribution). The other region set (n = 7; “Restricted” in Fig. 6C) is exemplified by the medial habenula and interpeduncular nucleus; the overall network impact of lesioning its members, while relatively strong (high magnitude), is highly restricted (low distribution), affecting only a very limited set of regions. None of the members of the “restricted” set are hubs (all hub scores = 0), consistent with a stronger association between hub score and lesion distribution (Fig. 6B) over lesion magnitude (Fig. 6A). Indeed, correlations between node centrality metrics and lesion distribution are greater than for lesion magnitude (ρ = 0.684, ρ = 0.917, ρ = 0.755, for degree, strength, and betweenness, respectively).

Relation Between Lesion Effect Distribution and Network Subsystem Organization.

Next, we moved from global lesion impact measures (magnitude and distribution) to the pattern of lesion effects as correlated with subsystem organization of the MRCC matrix and hierarchy (Fig. 2 and Dataset S4). For this, a “path length” connecting any two regions in a nested hierarchy was computed by counting the number of distinct branches that must be traversed to travel between the two regions in the hierarchical tree (Fig. 7, Inset). For the 279 individual region lesions, there is a steady decline in lesion impact similarity for a hierarchy path distance zero to about six, after which small, apparently irregular fluctuations occur out to the longest path length in the ROS2f matrix. Thus, for a region pair of interest, distance in the hierarchy is systematically related to how similar lesion effects turn out to be, and shorter distances (path lengths) tend to produce more similar effects. This effect is by far greatest for region pairs colocalized within a bottom-level subsystem (distance = 0; Fig. 7), indicating that lesioning them individually will have similar effects throughout the rest of the network. This finding also suggests that the effects on global network organization induced by imposing gradual modifications to connectivity will be more similar for regions that are placed within the same bottom-level subsystem. Such similarity, if reflected at a functional level, has potentially useful theoretical, experimental, and clinical implications.

Fig. 7.

The influence of structure–function subsystem hierarchy on the pattern of focal lesion effect distribution in the ROS2f MRCC matrix as described in the text. A “path length” that connects any two regions in a nested hierarchy was determined by counting the number of hierarchy branches between the two regions (Inset). Lesion impact similarity was calculated as the Pearson correlation of the two upper diagonal vectors of the coclassification. Each data point in the plot indicates the mean Pearson correlation across all region pairs separated by a given distance in the MRCC tree (x-axis).

This relationship between subsystem placement and lesion effects results in patterns of lesion impact that display characteristic and coherent features. As shown in the remaining sections of the Results, the most striking effects of focal lesions tend to present in the MRCC matrix as identical horizontal–vertical “stripes” with widths corresponding to subsystem boundaries (Figs. 8 and 9). This observation confirms the suggestion just mentioned that perturbations of regions within a subsystem tend to have similar effects on network organization, and the observation itself may be correlated with the definition of a subsystem as a region set whose members, in aggregate, are more strongly connected and clustered with each other than with other regions in the network. Another striking feature of the lesion-induced subsystem stripes is that they are discontinuous (Figs. 8 and 9) and that the stripe discontinuities also tend to follow subsystem boundaries in the matrix. This result suggests another factor influencing the pattern of lesion effects on network organization: the subsystem distribution of input–output connections associated with the lesioned nodes. This possibility is easy to confirm visually by examining the ipsilateral and contralateral connection segments of the lesion-induced stripes; in the ROS2 network, contralateral connections are almost always much weaker than ipsilateral connections, and this is reflected in the magnitude of ipsilateral and contralateral stripe discontinuities.

Fig. 8.

Effect of exemplar focal lesions on general patterns of ROS2f network organization. The results are displayed as coclassification difference matrices (intact matrix minus lesioned matrix) where positive differences (displayed in blue) indicate significantly greater coclassification/subsystem affinity in the intact over the lesioned matrix element (region pair). As a control, the original ROS2f matrix was run twice (each with 250,000 uniformly sampled partitions), and there were negligible differences between these two replicates. The 99.9th percentile of differences between these replicates was taken as a significance threshold, and this threshold was applied to all other sexes and lesions in this article (below-threshold differences were discarded). (A, B) Effects of AOB deletion compared with the effects of a combined AOB + MOB deletion. In all panels the lesioned rows and columns are replaced by black lines, and the subsystem containing the lesioned region is indicated with a green triangle. (C, D) Effects of an SNc lesion with the effects of a VTA lesion. (E). Effect of lesioning the ILA of the medial prefrontal cortex. (F, G) Effect of lesioning the ENTl compared to lesioning the ENTl and the adjacent PERI. In E, the green triangles indicate the subsystem containing MOB and ILA; arrows and asterisks in other parts of the figure are explained in the text. To allow comparisons, the same canonical ROS2f ordering scheme is used for all panels. For region and subsystem hierarchy labeling see Dataset S4, layer D; to examine details of matrices in Fig. 8 see Dataset S4, layers H–R, where clear legibility is attained at 1,600% zoom. The same yellow line pattern in all panels outlines the three upper-level subsystems, S1, S2, and S3, and connections between them (see Fig. 2).

Fig. 9.

Comparing the effects of lesioning separately all 279 regions (actually, the right and left members of each region) in the female and the male ROS2 network. For each lesion, the effect in male was subtracted from the effect in female for each region pair (present or absent connection) of the MRCC matrix. The effect was thus measured as a difference in coclassification/subsystem affinity score for each region pair (see Fig. 8). (A) Plot of how many lesions with a significant sexually dimorphic effect affected each region pair in the MRCC matrix. Note the pattern of three discontinuous subsystem crosses (e, d, f) that are aligned along the main diagonal (dashed line) and discussed in the text. The significance threshold was set as the 99.9th percentile of comparing two intact female runs. The yellow line pattern is the same as in Figs. 2 and 8. (B) Magnitude of dimorphic lesion effects on the whole network plotted against the number of lesions that produce a given effect. Magnitude was measured as the RMS sum of all region pair changes in coclassification score for the entire network. The four labeled regions to the right and left indicate outliers discussed in the text. The leftmost region (BSTpr) indicates that the dimorphic lesion effect is near zero. This is consistent with the fact that lesioning BSTpr entirely erases the connectional sex differences. The peak around 0.8 reflects the magnitude of the sexual dimorphism itself, present in all postlesion comparisons. Values to the right of the peak indicate sex-specific lesion effects above and beyond this baseline sex difference. MPNm, medial preoptic nucleus medial part.

Region pair (presence or absence of a connection) vulnerability to lesions elsewhere in the network was assessed by counting how many of the 279 lesions significantly impacted the region pair of interest’s coclassification score. The resulting vulnerability scores ranged from 0 to just over 200, and when these scores are plotted against region pair coclassification (subsystem affinity) scores, an inverted U-shaped distribution emerges (Fig. 6D). Lesion vulnerability is very low near the two extremes of possible coclassification scores, where 1 indicates perfect coclassification and 0 indicates no coclassification. Region pairs with an intermediate coclassification score are most vulnerable to lesion effects, although variance is obviously considerable.

Focal Lesion Examples.

The first region set broaches comparative connectomics by comparing the effects of two deletion types, either the accessory olfactory bulb (AOB), which is absent in adult humans, or the main and accessory olfactory bulbs (MOB + AOB) together as the olfactory bulb, which is typically absent in adult toothed whales. The pattern of lesion effects for the AOB deletion appears simple, and for clarity only changes in SS1 are described in this section because changes in mirror-image SS2 are identical (Fig. 8). Differences are quite restricted compared to the whole matrix (see Fig. 6C) and most clearly restricted to region pairs associated with the bottom-level subsystem containing the AOB (the broad horizontal and vertical discontinuous stripes in Fig. 8A indicated by green triangles, the bottom-level subsystem containing AOB; see Fig. 7, branch distance 0). The combined MOB + AOB deletion (Fig. 8B) prominently displays the AOB lesion effect, a horizontal–vertical cross associated with the MOB-containing subsystem, and subsystem crosses between the first two (see green arrows in Fig. 8B). This set of three adjacent subsystem crosses is associated with branches of the same hierarchy parent branch (SS1.1.3; Dataset S4, layers C and D). In addition, both matrices show a second prominent but thin subsystem cross farther down the main diagonal (Fig. 8 A and B; asterisks); it corresponds to SS1.2.3.2.2.1.2, which contains the anteroventral and posteroventral medial nuclei of amygdala, recipients of strong inputs from the AOB. Relations to specific regions and subsystems can be explored in Dataset S4.

The second example set displays the impact of lesioning two topographically adjacent midbrain regions with different ascending dopaminergic projections: either the substantia nigra compact part (SNc, Fig. 8C), which degenerates in human Parkinsonism, or the ventral tegmental area (VTA, Fig. 8D), which is implicated in expectation, reward, and substance abuse. Again, both lesions display restricted distribution patterns that are dominated by two discontinuous subsystem crosses. One subsystem cross is associated with the hierarchy branch (SS1.2.1; Dataset S4, layers C and D) that includes the two bottom-level subsystems for SNc and VTA (compare Fig. 8 C and D; green arrows). The other subsystem cross (Fig. 8 C and D; asterisks) is associated with the hierarchy branch (SS1.1.2; Dataset S4, layers C and D) that includes the caudoputamen and accumbens nucleus, the most prominent terminal fields of the SNc and VTA, respectively.

The last region set concerns three cerebral cortical hubs (highest centrality scores): the infralimbic area (ILA) of medial prefrontal cortex and the lateral entorhinal area (ENTl) and adjacent perirhinal area (PERI) of medial temporal cortex. In humans, bilateral deep brain stimulation in the presumed homolog of the rat ILA may relieve symptoms of treatment-resistant depression (23), whereas the ENTl and PERI are known as the transentorhinal cortex or entorhinal–perirhinal border zone and display the earliest signs of tauopathy in Alzheimer’s disease (24). Lesions of ILA (Fig. 8E) and ENTl (Fig. 8F) produce very broad changes in the network, and combined ENTl + PERI lesions (Fig. 8G) intensify the pattern further.

The ILA lesion generates a horizontal–vertical cross associated with the bottom-level subsystem that includes it (and the MOB), and a second horizontal–vertical cross (Fig. 8 E, asterisk) associated with the subsystem (SS1.2.3.1.1) that enigmatically contains the retina and suprachiasmatic nucleus—the hypothalamic circadian rhythm generator. The ENTl lesion produces even broader and stronger changes in subsystem affiliation, affecting significantly 91.5% of all possible region pairs in the network. The most obvious horizontal–vertical cross in the matrix is associated, unexpectedly, with the bottom-level subsystem that includes the ILA and AOB (yellow triangles in Fig. 8F); the subsystems containing ENTl, and ILA and AOB, have a very close branch distance of 2 in the subsystem hierarchy (see Fig. 7 and Dataset S4). This result suggests a very close network relationship between the ILA and ENTl. Finally, the ENTl + PERI lesion generates dramatic changes throughout virtually the entire (96.1%) ROS2 network, with generally positive effects for region pairs within SS1 and generally negative effects for region pairs between SS1 and SS2. The horizontal–vertical cross associated with the bottom-level subsystem containing the ILA and AOB remains perhaps the most prominent (Fig. 8 G, yellow triangles).

More detailed information about the pattern of lesion effects on network organization may be obtained by examining at useful magnifications the matrices for individual lesion experiments, with the accompanying structure–function hierarchy, in Dataset S4.

Separate Lesions of Neural Inputs or Outputs.

So far, we have considered the influence of focal computational lesions involving both neural inputs and outputs of a region of interest. However, just the outputs (the region’s matrix row) or just the inputs (the region’s matrix column) of a region can be lesioned, and the ENTl was used as an exemplar for this procedure. As mentioned in the preceding section, in Alzheimer’s disease tauopathy tends first to appear in the ENTl, and it has been suggested based on cortical network organization that tau then spreads predominantly in the retrograde direction, after release from dendrites, through axonal inputs to the ENTl, rather than in the anterograde direction through axonal outputs of the ENTl (24). Not surprisingly, lesioning ENTl outputs produces different effects on ROS2 network organization than lesioning ENTl inputs (SI Appendix, Fig. S3), with the ENTl output lesion being somewhat more disruptive (Fig. 6C). Furthermore, the most obvious differences between the ENTl output and ENTl input lesions occur in the dentate gyrus and hippocampal fields CA3 and CA2 (SI Appendix, Fig. S3D) as predicted (24).

Influence of Genetic Sex on Lesion Effects.

To examine the effects of sex on how focal lesions influence the global organization of the ROS2 network, all 279 regions in the male ROS2 MRCC network were lesioned individually, as just described for the female. A plot of how many lesions produced a significant change in each region pair of the MRCC matrix reveals a pattern that is virtually identical to the direct plot of differences between the ROS2f and ROS2m networks (Dataset S4, layer I): three subsystem crosses (Fig. 9 A, d–f) that also correspond to the three sexually dimorphic hierarchy domains shown in SI Appendix, Fig. S2 C–F. Thus, the pattern displayed in Fig. 9A and SI Appendix, Fig. S3C and Dataset S4 (layer I) reveals a secondary, sexually dimorphic network embedded within the remaining parts of the ROS2f and ROS2m networks that are marginally dimorphic at best. For individual regions, a plot of the magnitude of lesion effect on the entire network versus the number of lesions producing that effect displays an essentially normal distribution with four clear outliers (Fig. 9 B, labeled regions). The two outliers closer to zero are the BSTpr and AVPV, the origin and termination, respectively, of the most dimorphic connection in the network, which is thought to control the ovulatory cycle (17); removing these two regions from the network by computational lesion should produce the smallest dimorphic difference between matrices. The two outliers with the maximal effect are the PMv and medial preoptic nucleus medial part; all four outliers are in the same large, bottom-level subsystem (Fig. 9 A, d and SI Appendix, Fig. S3 C and D).

Discussion

Three main results for the rostral sector of the CNS emerge from the present work. First, a benchmark neural connectivity dataset is provided for developmental, comparative, and evolutionary research in craniotes as systematic datasets for the various taxa become available for comparison. Currently, the two taxa with the most complete connectional datasets and compatible neuroanatomical nomenclature hierarchies include the mouse and rat (14). Second, a hierarchical structure–function model of nervous system subsystem organization was generated for a mammal via cluster analysis. The model predicts that for the ROS there are two top-level, mirror-image subsystems, each divided into two mirror-image subsystems. One second-level subsystem is concerned primarily with voluntary behavior control, cognition, and affect, whereas the second is concerned primarily with instinctive survival behaviors and homeostasis. This dichotomy is similar to that associated with intraforebrain circuitry alone (9) but quite distinct from that associated with intramidbrain circuitry alone (10). The advantages of this system neuroscience approach as a powerful hypothesis-generating engine for experimental, theoretical, and clinical neuroscience have been discussed elsewhere (9). Third, a systematic approach was developed to identify factors influencing the distribution of effects within the hierarchical structure–function subsystem model resulting from connectivity alterations or differences.

“Function” when referring to neural connectivity has two distinct meanings. Traditionally, in neurobiology, physiological and behavioral functions are associated mechanistically with from–to structural/axonal connections—as parts of neural circuits or of neural subsystems identified by cluster analysis, as here. In human imaging and connectomics, however, “functional connectivity” refers to temporal patterns of correlated activity that emerge dynamically from the underlying structural connectivity and neural mechanisms (25). Similarly, in experimental neurobiology, lesions and other perturbations are imposed physically on neural tissue, whereas in theoretical studies lesions or other perturbations are applied computationally to network models (26, 27), although physiological manipulation of the C. elegans connectome is beginning to yield important insights (28, 29).

Altered connectivity patterns have been examined here in two ways. First, the effect of two right–left pairs of sexually dimorphic connections (17) on ROS2 network organization was computed and a female minus male difference matrix showed that this extremely localized effect produces a significant change in the subsystem affiliation of 8.46% of the 155,403 region pairs in the matrix, providing an alternative approach to identifying a secondary, sexually dimorphic subsystem (30) embedded in identical parts of the female and male network. This result demonstrates how sensitive this approach may be for detecting network differences, and it cautions about the interpretation of results based on incomplete or unreliable connectomic data (for our data see Dataset S4, layer V).

Second, we examined the effects of simulated focal structural lesions on our structural model of the ROS2 network. These computational lesions eliminated all input or output connections of a region or of two regions. Because this approach is based on a structural model, it does not involve functional connectivity in the computational sense just described. However, recent computational work suggests that the MRCC coclassification matrix, as used here, provides a good approximation of the covariance structure of neuronal activity (31), supporting the premise that our lesion analysis may provide a reasonable way to identify hypothetical functional subsystems. Thus, the coclassification hierarchy may be viewed as a summary of how a network divides into numerous structure–function subsystems and how profoundly that organization is disturbed in response to changes in structural connectivity.

All 279 regions of the female and male ROS2 network were lesioned individually (right and left sides of a region, both inputs and outputs) to identify three potential factors correlated with patterns of effect distribution throughout the network after focal perturbations: region centrality, region position in the structure–function subsystem hierarchy, and distribution of region inputs and outputs relative to network subsystem organization. As expected (26, 32), part of lesion impact is accounted for by region centrality (Fig. 6 A and B). Region position in the subsystem hierarchy also plays a role (Fig. 7), and this finding is particularly interesting because it may partly explain the obviously coherent “striped cross” pattern of changes observed in the exemplar lesions (Figs. 8 and 9). Stripes and crosses refer to changes in network architecture that are consistent within and across subsystems. The widths of these stripes correspond to subsystem boundaries (Dataset S4), and the evidence suggests that perturbation of any region in a bottom-level subsystem tends to have a similar effect on network-wide organization. Furthermore, in each exemplar lesion or sexually dimorphic network examined thus far, there is a primary subsystem cross associated with the subsystems containing the affected lesions or dimorphic connections, and secondary subsystem crosses also aligned along the MRCC matrix’s main diagonal. The subsystem crosses in this set all display discontinuous stripes. The width of these discontinuities also correlates with subsystem boundary widths, and the distribution of stripe discontinuities appears to correlate with the distribution of input–output connections associated with the region set forming the relevant subsystem, which is obvious for the contralateral connections of every stripe examined thus far.

The network model presented here may be useful for generating testable hypotheses about mechanistic relationships between subsystems and behavior; for exploring comparative, evolutionary, and developmental aspects of network organization; and for approaching nervous system complexity in a systematic, hierarchical way. It is important to emphasize that our model deals with only part of the nervous system and that it is based on an incomplete dataset. These are critical points because network properties change as subnetworks are added or taken away, and a fully realistic model can be formulated only when the entire nervous system and its interactions with the rest of the body are taken into account (9). Yet, the method applied in this study, combining rigorous mapping of neuroanatomy with quantitative network analysis, can yield generalizable neurobiological insights into brain architecture that can be extended readily as data on brain connectivity grow in scope and sharpen in detail. Thus, this work may help lay the foundation for identifying systematically how certain connections differ between species, for determining mechanisms underlying how those differences arise during development, and ultimately for elucidating how entire connectomes might have evolved.

Materials and Methods

The connectome database was expertly collated from the neuroanatomical literature (9). Cluster analysis was performed via the multiresolution coclassification method (18). Focal computational lesion analysis was carried out as described in the text. Subsystem analysis and display were also performed as described in the text.

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 S2), as are data from the reports used for connection matrices (Dataset S3). Searchable Connection Report data are freely available at The Neurome Project (https://sites.google.com/view/the-neurome-project/home) (33). Network analyses were done on the ROS2 connection matrices (Dataset S3, worksheets “ROS2f topo” and “ROS2m topo”, see worksheet “Key” for a description of the workbook contents) with tools collected in the Brain Connectivity Toolbox (https://sites.google.com/site/bctnet/) (34).

Previously published data were used for this work (some connection reports from previous publications of ours in PNAS are part of the total dataset analyzed [Dataset S2]). These data are specifically identified with citations in the text.