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Cited by 104Neural dynamics and brain functionTheoretical and Computational PhysicsNonlinear Dynamics and Pattern Formation

Sustained activity in hierarchical modular neural networks: self-organized criticality and oscillations

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Wang·2011·Frontiers in Computational Neuroscience
DOI 10.3389/fncom.2011.00030PMC PMC3151620
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Abstract

Cerebral cortical brain networks possess a number of conspicuous features of structure and dynamics. First, these networks have an intricate, non-random organization. In particular, they are structured in a hierarchical modular fashion, from large-scale regions of the whole brain, via cortical areas and area subcompartments organized as structural and functional maps to cortical columns, and finally circuits made up of individual neurons. Second, the networks display self-organized sustained activity, which is persistent in the absence of external stimuli. At the systems level, such activity is characterized by complex rhythmical oscillations over a broadband background, while at the cellular level, neuronal discharges have been observed to display avalanches, indicating that cortical networks are at the state of self-organized criticality (SOC). We explored the relationship between hierarchical neural network organization and sustained dynamics using large-scale network modeling. Previously, it was shown that sparse random networks with balanced excitation and inhibition can sustain neural activity without external stimulation. We found that a hierarchical modular architecture can generate sustained activity better than random networks. Moreover, the system can simultaneously support rhythmical oscillations and SOC, which are not present in the respective random networks. The mechanism underlying the sustained activity is that each dense module cannot sustain activity on its own, but displays SOC in the presence of weak perturbations. Therefore, the hierarchical modular networks provide the coupling among subsystems with SOC. These results imply that the hierarchical modular architecture of cortical networks plays an important role in shaping the ongoing spontaneous activity of the brain, potentially allowing the system to take advantage of both the sensitivity of critical states and the predictability and timing of oscillations for efficient information processing.

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  • Free energy may be most effectively minimized-and integrated information maximized-if synchronized couplings take the form of hierarchically organized modules, thus affording robustness, separable optimization, balanced integration and differentiation, evolvability via degeneracy, efficient communication via small-world connectivity, and flexible multi-scale responsivity via critical dynamics.

    “Free energy may be most effectively minimized—and integrated information maximized (Marshall et al., 2016)—if synchronized couplings take the form of hierarchically organized modules, thus affording robustness, separable optimization, balanced integration and differentiation, evolvability via degeneracy, efficient communication via small-world connectivity, and flexible multi-scale responsivity”

    From An Integrated World Modeling Theory (IWMT) of Consciousness (2020) · cites this paper as Wang et al., 2011

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Research works printed but not linked: 56

  1. Albert R. Barabási A. (2002). Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47– 97 10.1103/RevModPhys.74.47 · DOI · Paper page
  2. Albus K. Wahle P. (1994). The topography of tangential inhibitory connections in the postnatally developing and mature striate cortex of the cat. Eur. J. Neurosci. 6, 779– 792 10.1111/j.1460-9568.1994.tb00989.x 7521250 · DOI
  3. Arenas A. Díaz-Guilera A. Kurths J. Moreno Y. Zhou C. (2008). Synchronization in complex networks. Phys. Rep. 469, 93– 153 10.1016/j.physrep.2008.09.002 · DOI · Paper page
  4. Bak P. (1996). How Nature Works: The Science of Self-Organized Criticality (Copernicus), 1st Edn New York, NY: Springer-Verlag
  5. Bak P. Tang C. Wiesenfeld K. (1987). Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381– 384 10.1103/PhysRevLett.59.381 10035754 · DOI
  6. Bak P. Tang C. Wiesenfeld K. (1988). Self-organized criticality. Phys. Rev. A 38, 364– 374 10.1103/PhysRevA.38.364 9900174 · DOI
  7. Bassett D. Bullmore E. (2006). Small-world brain networks. Neuroscientist 12, 512 10.1177/1073858406293182 17079517 · DOI · Paper page
  8. Bassett D. S. Greenfield D. L. Meyer-Lindenberg A. Weinberger D. R. Moore S. W. Bullmore E. T. (2010). Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, e1000748 10.1371/journal.pcbi.1000748 20421990 PMC2858671 · DOI
  9. Battaglia D. Brunel N. Hansel D. (2007). Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation. Phys. Rev. Lett. 99, 238106 10.1103/PhysRevLett.99.238106 18233419 · DOI
  10. Bedard C. Kroeger H. Destexhe A. (2006). Does the 1/f frequency scaling of brain signals reflect self-organized critical states? Phys. Rev. Lett. 97, 118102 10.1103/PhysRevLett.97.118102 17025932 · DOI
  11. Beggs J. Plenz D. (2003). Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167 14657176 PMC6741045
  12. Beggs J. Plenz D. (2004). Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216 10.1523/JNEUROSCI.0540-04.2004 15175392 PMC6729198 · DOI
  13. Belykh I. de Lange E. Hasler M. (2005). Synchronization of bursting neurons: what matters in the network topology. Phys. Rev. Lett. 94, 188101 10.1103/PhysRevLett.94.188101 15904412 · DOI
  14. Boccaletti S. Latora V. Moreno Y. Chavez M. Hwang D.-U. (2006). Complex networks: structure and dynamics. Phys. Rep. 424, 175– 308 10.1016/j.physrep.2005.10.009 · DOI · Paper page
  15. Bonifazi P. Goldin M. Picardo M. Jorquera I. Cattani A. Bianconi G. Represa A. Ben-Ari Y. Cossart R. (2009). GABAergic hub neurons orchestrate synchrony in developing hippocampal networks. Science 326, 1419 10.1126/science.1175509 19965761 · DOI · Paper page
  16. Bosking W. Zhang Y. Schofield B. Fitzpatrick D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17, 2112 9045738 PMC6793759
  17. Brunel N. (2000). Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons. J. Physiol. Paris 94, 445– 463 10.1016/S0928-4257(00)01084-6 11165912 · DOI
  18. Bullmore E. Sporns O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186– 198 10.1038/nrn2618 19190637 · DOI
  19. Buzsáki G. (2006). Rhythms of the Brain. New York, NY: Oxford University Press
  20. Buzsáki G. Geisler C. Henze D. Wang X. (2004). Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186– 193 10.1016/j.tins.2004.02.007 15046877 · DOI
  21. Cossart R. Aronov D. Yuste R. (2003). Attractor dynamics of network UP states in the neocortex. Nature 423, 283– 288 10.1038/nature01614 12748641 · DOI · Paper page
  22. de Arcangelis L. Perrone-Capano C. Herrmann H. (2006). Self-organized criticality model for brain plasticity. Phys. Rev. Lett. 96, 28107 10.1103/PhysRevLett.96.051102 16486652 · DOI
  23. Engel A. Fries P. Singer W. (2001). Dynamic predictions: oscillations and synchrony in top–down processing. Nat. Rev. Neurosci. 2, 704– 716 10.1038/35094565 11584308 · DOI · Paper page
  24. Eurich C. Herrmann J. Ernst U. (2002). Finite-size effects of avalanche dynamics. Phys. Rev. E 66, 66137 10.1103/PhysRevE.66.066137 12513377 · DOI
  25. Fries P. (2005). A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cogn. Sci. (Regul. Ed.) 9, 474– 480 10.1016/j.tics.2005.08.011 16150631 · DOI · Paper page
  26. Galán R. (2008). On how network architecture determines the dominant patterns of spontaneous neural activity. PLoS ONE 3, e2148 10.1371/journal.pone.0002148 18478091 PMC2374893 · DOI
  27. Grinstein G. Linsker R. (2005). Synchronous neural activity in scale-free network models versus random network models. Proc. Natl. Acad. Sci. U.S.A. 102, 9948 10.1073/pnas.0504127102 15998732 PMC1175007 · DOI
  28. Hilgetag C. Burns G. O'Neill M. Scannell J. Young M. (2000). Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos. Trans. R. Soc. Lond. B Biol. Sci 355, 91 10.1098/rstb.2000.0551 10703046 PMC1692723 · DOI
  29. Hilgetag C. Kaiser M. (2004). Clustered organization of cortical connectivity. Neuroinformatics 2, 353– 360 10.1385/NI:2:3:353 15365196 · DOI
  30. Hill S. Tononi G. (2005). Modeling sleep and wakefulness in the thalamocortical system. J. Neurophysiol. 93, 1671– 1698 10.1152/jn.00915.2004 15537811 · DOI · Paper page
  31. Honey C. Kötter R. Breakspear M. Sporns O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl. Acad. Sci. U.S.A. 104, 10240 10.1073/pnas.0701519104 17548818 PMC1891224 · DOI
  32. Jensen H. J. (1998). Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Cambridge, MA: Cambridge University Press
  33. Kaiser M. Görner M. Hilgetag C. (2007). Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9, 110 10.1088/1367-2630/9/5/110 · DOI
  34. Kaiser M. Hilgetag C. (2010). Optimal hierarchical modular topologies for producing limited sustained activation of neural networks. Front. Neuroinform. 4: 8 10.3389/fninf.2010.00112 20514144 PMC2876872 · DOI · Paper page
  35. Kinouchi O. Copelli M. (2006). Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2, 348– 351 10.1038/nphys289 · DOI · Paper page
  36. Knight R. (2007). Neural networks debunk phrenology. Science 316, 1578 10.1126/science.1144677 17569852 · DOI
  37. Levina A. Herrmann J. M. Geisel T. (2007). Dynamical synapses causing self-organized criticality in neural networks. Nat. Phys. 3, 857– 860 10.1038/nphys758 · DOI
  38. Lewis C. Baldassarre A. Committeri G. Romani G. Corbetta M. (2009). Learning sculpts the spontaneous activity of the resting human brain. Proc. Natl. Acad. Sci. U.S.A. 106, 17558 10.1073/pnas.0905999106 19805061 PMC2762683 · DOI
  39. Mao B. Hamzei-Sichani F. Aronov D. Froemke R. Yuste R. (2001). Dynamics of spontaneous activity in neocortical slices. Neuron 32, 883– 898 10.1016/S0896-6273(01)00518-9 11738033 · DOI
  40. Mountcastle V. (1997). The columnar organization of the neocortex. Brain 120, 701 10.1093/brain/120.4.701 9153131 · DOI
  41. Müller-Linow M. Hilgetag C. C. Hütt M. T. (2008). Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4, e1000190 10.1371/journal.pcbi.1000190 18818769 PMC2542420 · DOI
  42. Reijneveld J. Ponten S. Berendse H. Stam C. (2007). The application of graph theoretical analysis to complex networks in the brain. Clin. Neurophysiol. 118, 2317– 2331 10.1016/j.clinph.2007.08.010 17900977 · DOI
  43. Robinson P. A. Henderson J. A. Matar E. Riley P. Gray R. T. (2009). Dynamical reconnection and stability constraints on cortical network architecture. Phys. Rev. Lett. 103, 108104 10.1103/PhysRevLett.103.108104 19792345 · DOI
  44. Roxin A. Riecke H. Solla S. (2004). Self-sustained activity in a small-world network of excitable neurons. Phys. Rev. Lett. 92, 198101 10.1103/PhysRevLett.92.198101 15169447 · DOI
  45. Scannell J. Burns G. Hilgetag C. O'Neil M. Young M. (1999). The connectional organization of the cortico-thalamic system of the cat. Cereb. Cortex 9, 277 10.1093/cercor/9.3.277 10355908 · DOI · Paper page
  46. Somogyi P. Tamas G. Lujan R. Buhl E. (1998). Salient features of synaptic organisation in the cerebral cortex1. Brain Res. Rev. 26, 113– 135 10.1016/S0165-0173(97)00061-1 9651498 · DOI
  47. Sporns O. Chialvo D. Kaiser M. Hilgetag C. (2004). Organization, development and function of complex brain networks. Trends Cogn. Sci. (Regul. Ed.) 8, 418– 425 10.1016/j.tics.2004.07.008 15350243 · DOI · Paper page
  48. Sporns O. Tononi G. Edelman G. (2000). Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10, 127 10.1093/cercor/10.2.127 10667981 · DOI
  49. Strogatz S. (2001). Exploring complex networks. Nature 410, 268– 276 10.1038/35065725 11258382 · DOI
  50. Vogels T. P. Abbott L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. J. Neurosci. 25, 10786– 10795 10.1523/JNEUROSCI.3508-05.2005 16291952 PMC6725859 · DOI
  51. Vreeswijk C. Sompolinsky H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724 10.1126/science.274.5293.1724 8939866 · DOI
  52. Vreeswijk C. Sompolinsky H. (1998). Chaotic balanced state in a model of cortical circuits. Neural. Comput. 10, 1321– 1371 10.1162/089976698300017214 9698348 · DOI
  53. Worrell G. Cranstoun S. Echauz J. Litt B. (2002). Evidence for self-organized criticality in human epileptic hippocampus. Neuroreport 13, 2017 10.1097/00001756-200211150-00005 12438917 · DOI
  54. Zhao M. Zhou C. Chen Y. Hu B. Wang B. (2010). Complexity versus modularity and heterogeneity in oscillatory networks: combining segregation and integration in neural systems. Phys. Rev. E 82, 046225 10.1103/PhysRevE.82.046225 21230383 · DOI
  55. Zhou C. Zemanová L. Zamora G. Hilgetag C. Kurths J. (2006). Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett. 97, 238103 10.1103/PhysRevLett.97.155704 17280251 · DOI
  56. Zhou C. Zemanová L. Zamora-Lopez G. Hilgetag C. Kurths J. (2007). Structure–function relationship in complex brain networks expressed by hierarchical synchronization. New J. Phys. 9, 178 10.1088/1367-2630/9/6/173 · DOI

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Authors
Wang
Affiliations
Hong Kong Baptist University (HK)
Corresponding author
Wang
Venue
Frontiers in Computational Neuroscience
Publisher
Frontiers Media SA
Published
2011
Volume
5
Pages
30-30
ISSN
1662-5188 (ISSN-L)
DOI
10.3389/fncom.2011.00030
PMC
PMC3151620
OpenAlex
W2165895470
Cited by
104
References
1
Citations by year
2025: 4 · 2024: 6 · 2023: 3 · 2022: 1 · 2021: 6 · 2020: 7 · 2019: 11 · 2018: 5 · 2017: 8 · 2016: 12 · 2015: 12 · 2014: 9 · 2013: 8 · 2012: 10
FWCI
4.71
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Frontiers in Computational Neuroscience (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • HKBU Institutional Repository (Hong Kong Baptist University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • Deutscher Akademischer Austauschdienst
  • Hong Kong Baptist University
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
  • Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
Keywords
self-organized criticality, sustained neural activity, spontaneous brain activity, cortical oscillations, neuronal avalanches, excitation-inhibition balance

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