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Fragility and volatility of structural hubs in the human connectome

Abstract

Brain structure reflects the influence of evolutionary processes that pit the costs of its anatomical wiring against the computational advantages conferred by its complexity. We show that cost-neutral ‘mutations’ of the human connectome almost inevitably degrade its complexity and disconnect high-strength connections to prefrontal network hubs. Conversely, restoring the peripheral location and strong connectivity of empirically observed hubs confers a wiring cost that the brain appears to minimize. Progressive cost-neutral randomization yields daughter networks that differ substantially from one another and results in a topologically unstable phenomenon consistent with a phase transition in complex systems. The fragility of hubs to disconnection shows a significant association with the acceleration of gray matter loss in schizophrenia. Together with effects on wiring cost, we suggest that fragile prefrontal hub connections and topological volatility act as evolutionary influences on brain networks whose optimal set point may be perturbed in neuropsychiatric disorders.

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Fig. 1: Schematic of surrogate network methods.
Fig. 2: Wiring costs as a function of the fraction of randomized edges.
Fig. 3: Fundamental structural features of the connectome.
Fig. 4: Hub variability and evolution of interhub connectivity.
Fig. 5: Fragility of hubs.
Fig. 6: Fragility as a predictor for gray matter changes in schizophrenia.

References

  1. 1.

    Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012).

    Article  PubMed  CAS  Google Scholar 

  2. 2.

    Honey, C. J., Kötter, R., Breakspear, M. & Sporns, O. Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl Acad. Sci. USA 104, 10240–10245 (2007).

    Article  PubMed  CAS  Google Scholar 

  3. 3.

    Bassett, D. S. et al. Hierarchical organization of human cortical networks in health and schizophrenia. J. Neurosci. 28, 9239–9248 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  4. 4.

    van den Heuvel, M. P. & Sporns, O. Rich-club organization of the human connectome. J. Neurosci. 31, 15775–15786 (2011).

    Article  PubMed  CAS  Google Scholar 

  5. 5.

    Sporns, O. & Betzel, R. F. Modular brain networks. Annu. Rev. Psychol. 67, 613–640 (2016).

    Article  PubMed  Google Scholar 

  6. 6.

    Roberts, J. A. et al. The contribution of geometry to the human connectome. Neuroimage 124, 379–393 (2016). Pt A.

    Article  PubMed  Google Scholar 

  7. 7.

    van den Heuvel, M. P., Kahn, R. S., Goñi, J. & Sporns, O. High-cost, high-capacity backbone for global brain communication. Proc. Natl Acad. Sci. USA 109, 11372–11377 (2012).

    Article  PubMed  Google Scholar 

  8. 8.

    Rilling, J. K. Human and nonhuman primate brains: are they allometrically scaled versions of the same design? Evol. Anthropol. 15, 65–77 (2006).

    Article  Google Scholar 

  9. 9.

    van den Heuvel, M. P., Bullmore, E. T. & Sporns, O. Comparative connectomics. Trends Cogn. Sci. 20, 345–361 (2016).

    Article  PubMed  Google Scholar 

  10. 10.

    Herculano-Houzel, S. The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost. Proc. Natl Acad. Sci. USA 109 Suppl 1, 10661–10668 (2012).

    Article  PubMed  Google Scholar 

  11. 11.

    Frankel, N. W. et al. Adaptability of non-genetic diversity in bacterial chemotaxis. eLife 3, e03526 (2014).

    Article  PubMed Central  CAS  Google Scholar 

  12. 12.

    Schindler, D. E. et al. Population diversity and the portfolio effect in an exploited species. Nature 465, 609–612 (2010).

    Article  PubMed  CAS  Google Scholar 

  13. 13.

    Friston, K. Life as we know it. J. R. Soc. Interface 10, 20130475 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Zalesky, A. et al. Disrupted axonal fiber connectivity in schizophrenia. Biol. Psychiatry 69, 80–89 (2011).

    Article  PubMed  Google Scholar 

  15. 15.

    Watts, D. J. & Strogatz, S. H. Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998).

    Article  PubMed  CAS  Google Scholar 

  16. 16.

    Fornito, A., Zalesky, A. & Breakspear, M. Graph analysis of the human connectome: promise, progress, and pitfalls. Neuroimage 80, 426–444 (2013).

    Article  PubMed  Google Scholar 

  17. 17.

    Sporns, O. & Zwi, J. D. The small world of the cerebral cortex. Neuroinformatics 2, 145–162 (2004).

    Article  PubMed  Google Scholar 

  18. 18.

    Harris, J. J. & Attwell, D. The energetics of CNS white matter. J. Neurosci. 32, 356–371 (2012).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  19. 19.

    Horvát, S. et al. Spatial embedding and wiring cost constrain the functional layout of the cortical network of rodents and primates. PLoS Biol. 14, e1002512 (2016).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  20. 20.

    Samu, D., Seth, A. K. & Nowotny, T. Influence of wiring cost on the large-scale architecture of human cortical connectivity. PLOS Comput. Biol. 10, e1003557 (2014).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  21. 21.

    Henderson, J. A. & Robinson, P. A. Using geometry to uncover relationships between isotropy, homogeneity, and modularity in cortical connectivity. Brain Connect. 3, 423–437 (2013).

    Article  PubMed  Google Scholar 

  22. 22.

    Cropley, V. L. et al. Accelerated gray and white matter deterioration with age in schizophrenia. Am. J. Psychiatry 174, 286–295 (2017).

    Article  PubMed  Google Scholar 

  23. 23.

    Salvador, R. et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15, 1332–1342 (2005).

    Article  PubMed  Google Scholar 

  24. 24.

    Zamora-López, G., Chen, Y., Deco, G., Kringelbach, M. L. & Zhou, C. Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs. Sci. Rep. 6, 38424 (2016).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  25. 25.

    Mišić, B. et al. Cooperative and competitive spreading dynamics on the human connectome. Neuron 86, 1518–1529 (2015).

    Article  PubMed  CAS  Google Scholar 

  26. 26.

    Fulcher, B. D. & Fornito, A. A transcriptional signature of hub connectivity in the mouse connectome. Proc. Natl Acad. Sci. USA 113, 1435–1440 (2016).

    Article  PubMed  CAS  Google Scholar 

  27. 27.

    Crossley, N. A. et al. The hubs of the human connectome are generally implicated in the anatomy of brain disorders. Brain 137, 2382–2395 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Fornito, A., Zalesky, A. & Breakspear, M. The connectomics of brain disorders. Nat. Rev. Neurosci. 16, 159–172 (2015).

    Article  PubMed  CAS  Google Scholar 

  29. 29.

    Colomer-de-Simón, P. & Boguñá, M. Double percolation phase transition in clustered complex networks. Phys. Rev. X 4, 041020 (2014).

    Google Scholar 

  30. 30.

    Gollo, L. L., Copelli, M. & Roberts, J. A. Diversity improves performance in excitable networks. PeerJ 4, e1912 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Mesulam, M.-M. From sensation to cognition. Brain 121, 1013–1052 (1998).

    Article  PubMed  Google Scholar 

  32. 32.

    Margulies, D. S. et al. Situating the default-mode network along a principal gradient of macroscale cortical organization. Proc. Natl Acad. Sci. USA 113, 12574–12579 (2016).

    Article  PubMed  CAS  Google Scholar 

  33. 33.

    Huntenburg, J. M., Bazin, P.-L. & Margulies, D. S. Large-scale gradients in human cortical organization. Trends Cogn. Sci. 22, 21–31 (2018).

    Article  PubMed  Google Scholar 

  34. 34.

    Steen, R. G., Mull, C., McClure, R., Hamer, R. M. & Lieberman, J. A. Brain volume in first-episode schizophrenia. Br. J. Psychiatry 188, 510–518 (2006).

    Article  PubMed  Google Scholar 

  35. 35.

    Kuperberg, G. R. et al. Regionally localized thinning of the cerebral cortex in schizophrenia. Arch. Gen. Psychiatry 60, 878–888 (2003).

    Article  PubMed  Google Scholar 

  36. 36.

    Takahashi, T. et al. Progressive gray matter reduction of the superior temporal gyrus during transition to psychosis. Arch. Gen. Psychiatry 66, 366–376 (2009).

    Article  PubMed  Google Scholar 

  37. 37.

    Gollo, L. L., Zalesky, A., Hutchison, R. M., van den Heuvel, M. & Breakspear, M. Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations. Phil. Trans. R. Soc. Lond. B 370, 20140165 (2015).

    Article  Google Scholar 

  38. 38.

    Rubinov, M. & Bullmore, E. Schizophrenia and abnormal brain network hubs. Dialog. Clin. Neurosci. 15, 339–349 (2013).

    Google Scholar 

  39. 39.

    Gogtay, N., Vyas, N. S., Testa, R., Wood, S. J. & Pantelis, C. Age of onset of schizophrenia: perspectives from structural neuroimaging studies. Schizophr. Bull. 37, 504–513 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  40. 40.

    Cocchi, L., Gollo, L. L., Zalesky, A. & Breakspear, M. Criticality in the brain: a synthesis of neurobiology, models and cognition. Prog. Neurobiol. 158, 132–152 (2017).

    Article  PubMed  Google Scholar 

  41. 41.

    Moretti, P. & Muñoz, M. A. Griffiths phases and the stretching of criticality in brain networks. Nat. Commun. 4, 2521 (2013).

    Article  PubMed  CAS  Google Scholar 

  42. 42.

    Sporns, O., Tononi, G. & Edelman, G. M. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10, 127–141 (2000).

    Article  PubMed  CAS  Google Scholar 

  43. 43.

    Goñi, J. et al. Exploring the morphospace of communication efficiency in complex networks. PLoS One 8, e58070 (2013).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  44. 44.

    Friston, K. J. The disconnection hypothesis. Schizophr. Res. 30, 115–125 (1998).

    Article  PubMed  CAS  Google Scholar 

  45. 45.

    Pantelis, C. et al. Structural brain imaging evidence for multiple pathological processes at different stages of brain development in schizophrenia. Schizophr. Bull. 31, 672–696 (2005).

    Article  PubMed  Google Scholar 

  46. 46.

    Collin, G., Kahn, R. S., de Reus, M. A., Cahn, W. & van den Heuvel, M. P. Impaired rich club connectivity in unaffected siblings of schizophrenia patients. Schizophr. Bull. 40, 438–448 (2014).

    Article  PubMed  Google Scholar 

  47. 47.

    Douaud, G. et al. A common brain network links development, aging, and vulnerability to disease. Proc. Natl Acad. Sci. USA 111, 17648–17653 (2014).

    Article  PubMed  CAS  Google Scholar 

  48. 48.

    Perry, A. et al. The organisation of the elderly connectome. Neuroimage 114, 414–426 (2015).

    Article  PubMed  CAS  Google Scholar 

  49. 49.

    Stephan, K. E., Friston, K. J. & Frith, C. D. Dysconnection in schizophrenia: from abnormal synaptic plasticity to failures of self-monitoring. Schizophr. Bull. 35, 509–527 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Breakspear, M. Dynamic models of large-scale brain activity. Nat. Neurosci. 20, 340–352 (2017).

    Article  PubMed  CAS  Google Scholar 

  51. 51.

    Zalesky, A. et al. Whole-brain anatomical networks: does the choice of nodes matter? Neuroimage 50, 970–983 (2010).

    Article  PubMed  Google Scholar 

  52. 52.

    Tzourio-Mazoyer, N. et al. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15, 273–289 (2002).

    Article  PubMed  CAS  Google Scholar 

  53. 53.

    Tournier, J., Calamante, F. & Connelly, A. MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22, 53–66 (2012).

    Article  Google Scholar 

  54. 54.

    Hagmann, P. et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 6, e159 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  55. 55.

    Roberts, J. A., Perry, A., Roberts, G., Mitchell, P. B. & Breakspear, M. Consistency-based thresholding of the human connectome. Neuroimage 145, 118–129 (2017). Pt A.

    Article  PubMed  Google Scholar 

  56. 56.

    Alstott, J., Klymko, C., Pyzza, P.B. & Radcliffe, M. Local rewiring algorithms to increase clustering and grow a small world. Preprint at arXiv https://arxiv.org/abs/1608.02883 (2016).

  57. 57.

    Humphries, M. D. & Gurney, K. Network ‘small-world-ness’: a quantitative method for determining canonical network equivalence. PLoS One 3, e0002051 (2008).

    Article  PubMed  CAS  Google Scholar 

  58. 58.

    Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. J. Stat. Mech. 2008, P10008 (2008).

    Article  Google Scholar 

  59. 59.

    Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).

    Article  PubMed  Google Scholar 

  60. 60.

    Ashburner, J. & Friston, K. J. Voxel-based morphometry–the methods. Neuroimage 11, 805–821 (2000).

    Article  PubMed  CAS  Google Scholar 

  61. 61.

    Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995).

    Google Scholar 

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Acknowledgements

The authors thank the chief investigators and manager of the ASRB: V. Carr, U. Schall, R. Scott, A. Jablensky, B. Mowry, P. Michie, S. Catts, F. Henskens, and C. Loughland. The authors acknowledge the support of the National Health and Medical Research Council of Australia (APP1110975 to L.L.G.; APP1145168 and APP1144936 to J.R.; APP1037196, APP1118153, and APP1095227 to M.B.; APP1047648 to A.Z.; and ID1105825 to C.P.) and the Australian Research Council (CE140100007). The Australian Schizophrenia Research Bank (ASRB) is supported by the NHMRC (enabling grant 386500), the Pratt Foundation, Ramsay Health Care, the Viertel Charitable Foundation, and the Schizophrenia Research Institute.

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L.L.G., J.A.R., A.Z., and M.B. designed the research and wrote the manuscript. L.L.G., J.A.R., and M.B. analyzed the data. L.L.G. prepared the figures. J.A.R. and A.Z. contributed new analytic tools. V.L.C., M.A.D.B., C.P., and A.Z. contributed the schizophrenia neuroimaging data. All authors contributed to editing and revising the manuscript.

Corresponding author

Correspondence to Michael Breakspear.

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The authors declare no competing interests.

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Integrated supplementary information

Supplementary Figure 1 Schematic representation of the connectivity matrices for the different surrogate networks.

Matrices show the logarithm of the edge weights for these fully connected (unthresholded) networks.

Supplementary Figure 2 Wiring length as a function of the fraction of randomized edges for the different algorithms.

Same as Figure 2 but for fiber length instead of wiring cost. Mean fiber length as a function of the fraction of randomized edges. A: Weight-preserving geometric surrogate Gw (blue). B: Strength-preserving geometric surrogate Gs (black). C: Strength-sequence-preserving geometric surrogate Gss (red). D: Geometry-ignoring random surrogates Rw (blue), Rs (black), and Rss (red). Connectomes at the top of each panel illustrate one case in which all edges have been randomized. Shaded areas indicate the standard deviation over n=100 trials.

Supplementary Figure 3 Probabilities of obtaining connectomes with reduced wiring costs and fiber lengths.

A, Probability of obtaining surrogate networks with reduced wiring cost (Pwc) as a function of the fraction of randomized edges (frac). B, Same as (A) but for a zoom for small values of frac. C, Probability of obtaining surrogate networks with reduced fiber length (Pfl) as a function of frac. D, Same as (C) but for zoom for small values of frac. Blue curves correspond to weight-preserving geometric surrogate Gw, black curves correspond to strength preserving geometric surrogate Gs, and red curves correspond to strength-sequence preserving geometric surrogate Gss. For all panels probabilities are estimated from n=10,000 independent trials.

Supplementary Figure 4 The increase in wiring costs is enhanced in sparse connectomes.

A, Connectome representation of Gss as a function of the density of connections. B, Connectivity matrices lighter colors represent stronger connections. C, Increase in fiber length for the Gss connectome for different densities. D, Increase in wiring cost for the Gss connectome for different densities. Shaded regions correspond to the standard deviation. E, Maximum increase in fiber length for Gss surrogates as a function of connectome density. F, Maximum increase in wiring cost for Gss surrogates as a function of connectome density. Results of are an average of n=100 independent trials.

Supplementary Figure 5 Topological properties for different connectome densities.

A, Proportion of inter-hemispheric connections as a function of connectome density for Gs (black) and Gss (red). B, Proportion of homologous connections relative to the proportion of homologous connections in a geometry-ignoring random network (nHrand). C, Same as Fig. 3D but for clustering instead of small-world index. D, Same as Fig. 3D but for path length. Figure generated with n=100 independent trials. Shaded regions correspond to the standard deviation.

Supplementary Figure 6 Network susceptibility increases with the proportion of randomized edges.

A, Normalized network susceptibility after randomizing the empirical brain using geometry-ignoring randomization Rw. B: Normalized network susceptibility after randomizing the fully randomized Gs connectome using geometry-ignoring randomization Rw. C, Normalized network susceptibility after randomizing the empirical brain using strength-preserving geometry-ignoring randomization Rs. D: Normalized network susceptibility after randomizing the fully randomized Gs connectome using strength-preserving geometry-ignoring randomization Rs. Figure generated with n=100 trials.

Supplementary Figure 7 Relationship between fragility and the sum of the first two principal gradients shown in Fig. 5g.

Scatter plot of fragility and the sum of the first two gradients shown in Fig. 5G. Black line shows the linear regression between fragility and the sum of these gradients (r=0.43, p=0.00012, n=75 hubs).

Supplementary Figure 8 Hub strength is not a reliable predictor for gray matter deterioration in schizophrenia.

Same as Fig. 6 but for hub strength instead of fragility. Hub strength does not reach FDR-corrected significance (p<0.05, Pearson correlation, n=75 hubs).

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–8, Supplementary Tables 1 and 2

Reporting Summary

Supplementary Video 1

- One illustrative randomization trial using the geometry-preserving algorithm Gs. Connectomes as a function of the fraction of randomized edges (frac). Hubs are represented as large dots, inter-hub connections are shown in green, and other connection to non-hub regions are in gray. The empirical connectome (starting point) has hubs distant from each other. Hubs move towards the center of the brain as the fraction of randomized edges increases.

Supplementary Video 2

- An average over 100 independent randomization trials using the geometry-preserving algorithm Gs. The empirical connectome (starting point) has hubs distant from each other, which move towards the center of the brain as the fraction of randomized edges increases. Frontal and posterior hubs are disconnected earlier in the process.

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Gollo, L.L., Roberts, J.A., Cropley, V.L. et al. Fragility and volatility of structural hubs in the human connectome. Nat Neurosci 21, 1107–1116 (2018). https://doi.org/10.1038/s41593-018-0188-z

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