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Diversity of meso-scale architecture in human and non-human connectomes

Richard F. Betzel, John D. Medaglia, Danielle S. Bassett

arXiv:1702.02807v2q-bio.NC

TL;DR

The dominant view treats connectome communities as assortative and segregated, while common detection methods may rule out other architectures. The authors apply weighted stochastic blockmodels across human and non-human connectomes; they find non-assortative structures, links to functional connectivity and gene co-expression, and cognitive-performance associations in humans.

  • Problem

    Common approaches assume assortative, segregated communities and may preclude detecting non-assortative connectome structure.

    Source: Introduction · pp. 1–2

  • Method

    The authors use weighted stochastic blockmodels to identify community structures and quantify how brain regions participate across community types in human and non-human connectomes.

    Source: Introduction · pp. 3–4, Results · p. 4

  • Results

    Connectomes contain assortative, core-periphery, and disassortative communities; WSBM communities better recapitulate human functional relationships and mouse gene co-expression, while human diversity peaks in control and subcortical systems and predicts Stroop and Navon performance.

    Source: Introduction · p. 4, Discussion · p. 12

  • Takeaways & Limitations

    Connectome meso-scale architecture is more diverse than a view of segregated communities linked by integrative hubs alone suggests.

    Source: Connectomes exhibit rich,… · p. 13

    WSBM requires a specified number of communities, and principled statistical selection of K remains an open problem; human connectome reconstructions may also be inaccurate.

    Source: Methodological Considerations and… · p. 14

Abstract

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The brain's functional diversity is reflected in the meso-scale architecture of its connectome, i.e. its division into clusters and communities of topologically-related brain regions. The dominant view, and one that is reinforced by current analysis techniques, is that communities are strictly assortative and segregated from one another, purportedly for the purpose of carrying out specialized information processing. Such a view, however, precludes the possibility of non-assortative communities that could engender a richer functional repertoire by allowing for a more complex set of inter-community interactions. Here, we use weighted stochastic blockmodels to uncover the meso-scale architecture of \emph{Drosophila}, mouse, rat, macaque, and human connectomes. We confirm that while many communities are assortative, others form core-periphery and disassortative structures, which in the human better recapitulate observed patterns of functional connectivity and in the mouse better recapitulate observed patterns of gene co-expression than other community detection techniques. We define a set of network measures for quantifying the diversity of community types in which brain regions participate. Finally, we show that diversity is peaked in control and subcortical systems in humans, and that individual differences in diversity within those systems predicts cognitive performance on Stroop and Navon tasks. In summary, our report paints a more diverse portrait of connectome meso-scale structure and demonstrates its relevance for cognitive performance.

Introduction

Cognitive processes are linked to the connectome’s meso-scale communities, which are usually treated as assortative and segregated. The authors use weighted stochastic blockmodels to examine whether connectomes also contain non-assortative structures and whether diverse community participation relates to cognitive performance.

Introduction

  • These structures can coexist with assortative organization, potentially enabling different interactions among communities and a wider functional repertoire.The authors hypothesize that diversity in meso-scale structure supports a wider functional repertoire and that individual differences predict cognitive performance on tasks requiring coordination among diverse systems.Source: Figure 1 · p. 2, Introduction · p. 3
  • Common community-detection algorithms seek internally dense, externally sparse subnetworks, so they preclude detecting non-assortative structure and leave unclear whether detected assortativity reflects brain architecture or algorithmic assumptions.Source: Introduction · p. 2
  • Disassortative communities preferentially avoid within-community connections, while core-periphery organization pairs a dense central core with sparsely interconnected peripheral communities.Source: Introduction · p. 3
  • Weighted stochastic blockmodels are used to uncover meso-scale architecture in human and non-human connectomes.The approach is intended to address hypotheses about non-assortative structure and diverse community participation.Source: Introduction · pp. 3–4
  • Human and non-human connectomes show disassortative and core-periphery structures alongside assortative communities, and diversity peaks in human control and subcortical systems and predicts Stroop and Navon performance.The authors define a node-level diversity index to quantify participation in communities of all classes.Source: Introduction · p. 4

Results

Across human and non-human connectomes, WSBM partitions reveal less-assortative and more varied community structure than modularity maximization. In humans, these partitions better match functional connectivity, while motif diversity is concentrated in control and subcortical systems and associated with cognitive-task performance.

Results

  • The study fits WSBM to human, mouse, rat, macaque, and Drosophila connectomes and compares its partitions with Qmax across K = 2, . . . , 10.The WSBM can detect assortative, disassortative, and core-periphery structures, whereas Qmax is designed to detect assortative structure.Source: Results · p. 4

Connectomes support diverse meso-scale architecture

  • Using functional data analysis to compare mean assortativity by community size, WSBM communities scored lower than Qmax communities (p < 10^-3), and this finding was consistent across connectome data from all species.Source: Connectomes support diverse meso-scale… · p. 5

Many (but not all) communities are assortative

Functional relevance of the WSBM

  • WSBM communities show greater within- than between-community functional connectivity than Qmax communities across K = 2, . . . , 10; mouse gene-expression patterns show consistent findings.The functional-connectivity difference was significant (t-tests, p < 0.01).Source: Functional relevance of the WSBM · p. 7, Figure 5 · p. 8

Community morphospace reveals rules for between-community interactions

  • Across K = 2, . . . , 10, Qmax yields almost exclusively assortative community interactions, whereas WSBM also identifies core-periphery and disassortative motifs.The motif proportions differed beyond chance (p = 0.029; 1000 permutations), with similar findings in non-human connectomes.Source: Community morphospace reveals rules… · p. 8, Figure 6 · p. 9

Community motifs identify a class of diversely connected nodes

  • Motif participation varies with node strength: low-strength regions are predominantly assortative or peripheral, high-strength regions predominantly core, and above-average but not highest-strength regions are most diverse.Control and subcortical systems have the most diverse motif participation, robust across K (permutation tests; p = 0.001).Source: Community motifs identify a class of… · pp. 9–10, Figure 7 · p. 10

Behavioral relevance of motif diversity

  • Regional diversity correlates with task accuracy: positive correlations cluster in control and subcortical systems, while visual-system correlations are more negative than expected.The pattern remained largely unchanged for K > 4; tests were FDR corrected for multiple comparisons.Source: Behavioral relevance of motif diversity · p. 11, Figure 8 · p. 11

Discussion

The discussion argues that connectome architecture includes non-assortative community structures alongside assortative ones, and that diversity in this architecture relates to cognitive performance. It situates these findings within a broader effort to identify large-scale structural motifs and computational tools.

Discussion

  • WSBM communities recapitulated human functional relationships and mouse gene co-expression better than commonly used techniques, while diversity in control and subcortical systems predicted task performance.The authors report this as evidence that structural diversity is relevant to human behavior.Source: Discussion · p. 12

Topological support for cognitive processes

  • Structural motifs at the meso-scale offer a way to study how large-scale connectome structure relates to cognitive processes, a connection that has been challenging to establish.The authors frame their work as offering concepts and computational tools for studying motifs and individual differences in cognitive control.Source: Topological support for cognitive… · p. 12

Community and meso-scale connectome analyses

  • Meso-scale analysis coarse-grains network features, and blockmodels offer a way to examine non-assortative wiring that modularity-based techniques may miss.The study tests the approach against functional dynamics in humans and gene co-expression in mice.Source: Community and meso-scale connectome… · p. 12

Connectomes exhibit rich, non-assortative structure

  • Human and animal connectomes contain assortative, core-periphery, and disassortative interactions, refining a view centered on segregated communities linked by hubs.The authors report these patterns in Drosophila, mouse, rat, macaque, and human connectomes.Source: Connectomes exhibit rich,… · p. 13

A critical role for the topological middle class

  • Brain regions with above-average, but not greatest, strength showed the most diverse motif participation, highlighting the topological middle class.The authors suggest such regions may both exert influence on and be influenced by others; they describe this as an empirical observation with initial evidence for cognitive relevance.Source: A critical role for the topological… · p. 13

Community diversity predicts cognitive performance

  • Regional diversity predicted performance on Stroop and Navon tasks, with the most predictive regions associated with control and subcortical systems.These systems also had the greatest average diversity; the authors suggest diverse motif participation may support flexible cognitive behavior.Source: Community diversity predicts cognitive… · pp. 13–14

Broad utility of novel network-based metrics

  • The work introduces network metrics including assortativity scores, community morphospace analysis, motif classification, and node-level participation and diversity indices.Apart from the diversity index, the exploration of these measures was largely theoretical; the tools are not restricted to brain networks.Source: Broad utility of novel network-based… · p. 14

Methodological Considerations and Limitations

The authors identify uncertainty in choosing the number of WSBM communities and possible inaccuracies in reconstructed human connectomes as methodological limitations. They note that findings replicated across species and data types, though this does not resolve those underlying issues.

Methodological Considerations and Limitations

  • The WSBM requires a user-specified number of communities, and principled statistical selection of that number remains an open problem.The authors therefore show results robust across a reasonable choice of K rather than focusing on one value.Source: Methodological Considerations and… · p. 14
  • Human connectome reconstruction is limited by diffusion imaging and tractography algorithms that can produce inaccurate networks.The authors note that tractography may be accurate for particular white-matter pathways and that newer reconstruction approaches may improve estimates.Source: Methodological Considerations and… · p. 14
  • Findings replicated across Drosophila, mouse, rat, macaque, and human connectomes, which the authors argue cannot be explained by deficiencies in any one data modality.The data modalities differ between the human and non-human connectomes.Source: Methodological Considerations and… · p. 14

Conclusion

The paper applies weighted stochastic blockmodels to connectomes from five species and reports that the resulting communities better explain selected functional and gene-expression relationships. A diversity measure derived from these communities predicts behavioral outcomes in cognitive control tasks.

Conclusion

  • The authors applied a weighted stochastic blockmodel to connectome data from Drosophila, mouse, rat, macaque, and human.Source: Conclusion · p. 14
  • The detected communities provided statistically better explanations of human resting-state functional connectivity and mouse gene co-expression than those commonly discussed in the literature.Source: Conclusion · pp. 14–15
  • A diversity metric derived from the communities predicted behavioral outcomes in cognitive control tasks.Source: Conclusion · p. 15

Materials and Methods

The methods assemble human and animal connectomes with behavioral and auxiliary data, then compare weighted blockmodels with modularity maximization. Model fitting and partition comparisons provide the basis for assessing community structure across datasets.

Connectome datasets

  • The study used five previously published connectomes: Drosophila, mouse, rat, macaque, and human.The connectome is defined as the set of neural elements and their physical connections.Source: Connectome datasets · p. 15

Human

  • Five species’ connectomes were analyzed, with human networks reconstructed from 30 adults and represented as individual and group-level weighted connectivity matrices.The human network covered 128 brain regions; the group network was formed by aggregating individual networks.Source: Human · p. 15, Connectome datasets · p. 15
  • Human networks comprised individual and group-representative undirected, weighted matrices based on streamline counts normalized by the geometric mean of regional volumes.The 30 participants’ data were reconstructed from diffusion spectrum images and tractography, and the group network used distance-dependent consistency thresholding.Source: Human · p. 15

Behavioral tasks

  • Participants completed modified Navon local-global perception and Stroop tasks, while resting-state functional connectivity and functional-system labels supplied additional data.The Stroop task included trials eligible and ineligible to elicit interference effects.Source: Behavioral tasks · pp. 15–16, Additional data · p. 16

Stochastic blockmodel

  • A standard stochastic blockmodel assigns each node to one of K communities and makes connection probabilities depend on the two nodes’ community labels.Fitting estimates community labels and block parameters to maximize the likelihood under an edge-independence assumption.Source: Stochastic blockmodel · p. 16

Weighted stochastic blockmodel

  • The weighted stochastic blockmodel extends the model to weighted edges, and the sparse version models edge presence separately from edge weights.The weight model uses a normal distribution; α = 0.5 balances edge presence and weight in inference, and fits used variational Bayes across K = 2–10 with 250 initializations per K.Source: Weighted stochastic blockmodel · pp. 16–17

Modularity maximization

  • Modularity maximization selects community assignments that maximize internal density above a null model, with γ controlling structural resolution.The study used the configuration model and a greedy procedure to obtain exactly K communities, with γ = 1.Source: Modularity maximization · p. 17

Statistics for comparing the WSBM with Qmax

The study compares community structure across techniques at whole-network, community, and regional scales. It also classifies community-pair interaction motifs and summarizes how individual nodes participate in them.

Variation of information

  • Variation of information measures partition dissimilarity, with zero indicating identical partitions; comparisons were restricted to partitions with the same number of communities.The study uses this measure for whole-brain comparisons between techniques.Source: Variation of information · p. 18

Community and regional assortativity

  • Community and regional assortativity scores compare within-community connection density with the strongest density to another community.For regions, the score is the minimum difference between own-community and any other-community density; singleton communities were excluded.Source: Community and regional assortativity · p. 18

Maximally assortative set

  • The maximally assortative set is the largest set of WSBM communities exhibiting assortative structure, chosen to maximize their total number of nodes.The set can contain up to K communities.Source: Maximally assortative set · p. 18

Community interaction motifs and morphospace analysis

  • Community morphospace places each community pair by its within- and between-community connection densities and classifies interactions as assortative, core-periphery, or disassortative.Node motif participation counts how often its assigned community participates in each motif type; diversity is the entropy of normalized participation across motif types.Source: Community interaction motifs and… · p. 19

Supplementary materials

The supplement applies the main analyses to four non-human connectomes reconstructed using varied procedures. It also describes the datasets’ system labels and mouse gene-expression data.

Supplementary materials

  • Non-human connectome analyses used the same methods as the human analyses, and their results generally corroborated the main-text analyses.The varied reconstruction procedures allowed assessment of whether technique differences depended on how connectomes were reconstructed.Source: Supplementary materials · p. 30

Mouse

  • The mouse analysis used one complete cerebral hemisphere with 56 regions from a tract-tracing dataset, producing an asymmetric network.The reprocessed source parcellation had 112 regions across both hemispheres.Source: Mouse · p. 30

Drosophila

  • The Drosophila network aggregated 12,995 projection neurons into 49 local processing units and was directed and weighted.The dataset represents the female brain.Source: Drosophila · p. 30

Rat

  • The rat dataset is a directed network of 73 cortical regions from one hemisphere, with weights assigned to reported connections based on consistency and quality.The network collated rat tract-tracing reports and included more than 16,000 connections.Source: Rat · p. 30

Supplementary materials

  • Figure S2 plots within-technique and between-technique variation of information against community count for mouse, Drosophila, rat, and macaque.The figure distinguishes Qmax and WSBM within-technique scores from between-technique dissimilarity.Source: Figure S2 · p. 31

Macaque

  • The macaque dataset is an incomplete, weighted, directed connectome covering 29 cortical regions.Connection weights are fractions of labeled neurons from retrograde tract-tracing experiments.Source: Macaque · p. 31

Additional data

  • System labels accompanied each non-human connectome, and the mouse dataset also included regional expression profiles for 3,380 genes.The mouse gene set was selected from more than 20,000 assayed genes after quality control; pairwise correlations of regional profiles formed a square matrix.Source: Additional data · p. 31

Comparing the WSBM with Qmax

WSBM and Qmax yield distinct partitions and community assortativity, while non-human connectomes also show non-assortative motifs. WSBM communities align more closely with mouse gene-expression correlations than Qmax communities do.

Comparing the WSBM with Qmax

  • Qmax communities were more assortative than WSBM communities, while most regions had lower regional assortativity under WSBM.The partition comparison found each method’s partitions more internally consistent than similar to one another across K = 2–10 (p < 10^-15); community assortativity differed controlling for size (p < 10^-3).Source: Comparing the WSBM with Qmax · p. 31, Figure S3 · p. 32

Maximally assortative set

  • The maximally assortative set ranged from 0.37 ± 0.11 of nodes in Drosophila to 0.58 ± 0.09 in mouse, and was never empty.Participation was generally negatively correlated with node strength, with the opposite trend in Drosophila; rich-club nodes were generally less likely to belong, except in macaque.Source: Maximally assortative set · p. 32, Figure S4 · p. 33

Community morphospace analysis

  • Across non-human connectomes and K = 2–10, Qmax found almost exclusively assortative motifs, whereas WSBM found disproportionately more disassortative and core-periphery motifs.Differences in motif proportions were unexpected under permutation-based nulls: mouse p = 0.003; Drosophila, rat, and macaque p < 10^-3.Source: Community morphospace analysis · pp. 32–33, Figure S6 · p. 35
  • Motif-class entropy peaked for middle-strength nodes; low-strength bins were dominated by assortative and periphery motifs, and high-strength bins by core motifs.Lowest- and highest-strength nodes were associated with low entropy, suggesting participation in a narrower range of classes.Source: Community morphospace analysis · p. 33, Figure S7 · p. 36

Functional relevance of WSBM communities for mouse connectome

  • For K = 2–8, WSBM partitions produced larger within- versus between-community gene-expression correlation differences than Qmax partitions (p < 10^-5).This indicates communities with correlated expression profiles within communities and, in general, anticorrelated profiles between communities.Source: Functional relevance of WSBM… · p. 34, Figure S8 · p. 36

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