Skip to main content
SpringerLink
Log in

Complexity of Network Connectivity Promotes Self-organized Criticality in Cortical Ensembles

  • Chapter
  • First Online:
The Functional Role of Critical Dynamics in Neural Systems

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 11))

Abstract

Large-scale dissociated in vitro cortical networks spontaneously exhibit recurrent events of propagating spiking and bursting activity, usually termed as neuronal avalanches, since their size and lifetime distributions can be described by a power law, as in critical sand pile models. Indeed, this spontaneous activity is originated by the synaptic interactions among neurons which are able to freely re-create networks exhibiting complex topological structures. However, experimental in vitro findings show that mature cortical assemblies not necessarily display a critical dynamics, but can follow two other different dynamic states, namely sub-critical and super-critical. Well-known factors that drive the network to these different states are the developmental stage and the excitation/inhibition balance. In this chapter, we will investigate the interplay between self-organized critical state and topological features of the underling cortical network. To investigate the role of connectivity in driving spontaneous activity towards critical, sub-critical or super-critical regimes, results achieved by combining both experimental and computational investigations will be presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The IEI is the probability density of time intervals between successive spikes of all the neurons. The average value of the IEI distribution gives an indication of the average time between two successive activations of any pair of neurons. Generally, the average IEI is calculated by averaging the values of the IEI distribution over a predefined time interval whose maximum value is determined as the average time interval corresponding to more the 99% of the area of the mean cross-correlogram (averaging cross-correlograms between all possible pairs of neurons).

  2. 2.

    The coincidence index is defined as the ratio of the integral of the cross-correlation function in a specified area (e.g., ±1 ms) around the zero bin to the integral of the total area [6].

  3. 3.

    Kruskal–Wallis non-parametric test was applied since the normality assumption was not verified by the considered dataset (Kolmogorov-Smirnov normality test).

  4. 4.

    The Small-World Index (SWI) is defined as: \( SWI = \frac{{CC_{net} }}{{CC_{rnd} }}/\frac{{PL_{net} }}{{PL_{rnd} }} \), where CCnet and PLnet are the cluster coefficient and the path length of the investigated network; while CCrnd and PLrnd correspond to the cluster coefficient and the path length of random networks equivalent to the original network (i.e., with the same number of nodes and links). A SWI higher than 1 suggests the emergence of a small-world topology.

  5. 5.

    It is used to measure the distance between the empirical distribution and the fitted model. When the p-value is close to 1, the data set is considered to be drawn from the fitted distribution, otherwise it should be rejected.

References

  1. O’Donovan, M.J.: The origin of spontaneous activity in developing networks of the vertebrate nervous system. Curr. Opin. Neurobiol. 9, 94–104 (1999)

    Article  Google Scholar 

  2. Buzsaki, G., Draguhn, A.: Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004)

    Article  CAS  Google Scholar 

  3. Marom, S., Shahaf, G.: Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy. Q. Rev. Biophys. 35, 63–87 (2002)

    Article  Google Scholar 

  4. Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003)

    Article  CAS  Google Scholar 

  5. Beggs, J.M., Plenz, D.: Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229 (2004)

    Article  CAS  Google Scholar 

  6. Pasquale, V., Massobrio, P., Bologna, L.L., Chiappalone, M., Martinoia, S.: Self-organization and neuronal avalanches in networks of dissociated cortical neurons. Neuroscience 153, 1354–1369 (2008)

    Article  CAS  Google Scholar 

  7. Petermann, T., Thiagarajan, T.C., Lebedev, M.A., Nicolelis, M.A., Chialvo, D.R., Plenz, D.: Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl. Acad. Sci. U.S.A. 106, 15921–15926 (2009)

    Article  CAS  Google Scholar 

  8. Gireesh, E.D., Plenz, D.: Neuronal avalanches organize as nested theta- and beta/gamma oscillations during development of cortical layer 2/3. Proc. Natl. Acad. Sci. U.S.A. 105, 7576–7581 (2008)

    Article  CAS  Google Scholar 

  9. Hahn, G., Petermann, T., Havenith, M.N., Yu, S., Singer, W., Plenz, D., et al.: Neuronal avalanches in spontaneous activity in vivo. J. Neurophysiol. 104, 3312–3322 (2010)

    Article  Google Scholar 

  10. Poil, S.S., van Ooyen, A., Linkenkaer-Hansen, K.: Avalanche dynamics of human brain oscillations: relation to critical branching processes and temporal correlations. Hum. Brain Mapp. 29, 770–777 (2008)

    Article  Google Scholar 

  11. Van Pelt, J., Corner, M.A., Wolters, P.S., Rutten, W.L.C., Ramakers, G.J.A.: Long-term stability and developmental changes in spontaneous network burst firing patterns in dissociated rat cerebral cortex cell cultures on multi-electrode arrays. Neurosci. Lett. 361, 86–89 (2004)

    Article  Google Scholar 

  12. Rolston, J.D., Wagenaar, D.A., Potter, S.M.: Precisely timed spatiotemporal patterns of neural activity in dissociated cortical cultures. Neuroscience 148, 294–303 (2007)

    Article  CAS  Google Scholar 

  13. Wagenaar, D.A., Pine, J., Potter, S.M.: An extremely rich repertoire of bursting patterns during the development of cortical cultures. BMC Neurosci. 7 (2006)

    Article  Google Scholar 

  14. Chiappalone, M., Bove, M., Vato, A., Tedesco, M., Martinoia, S.: Dissociated cortical networks show spontaneously correlated activity patterns during in vitro development. Brain Res. 1093, 41–53 (2006)

    Article  CAS  Google Scholar 

  15. Tetzlaff, C., Okujeni, S., Egert, U., Worgotter, F., Butz, M.: Self-organized criticality in developing neuronal networks. PLoS Comput. Biol. 6, e1001013 (2010)

    Article  Google Scholar 

  16. Taketani, M., Baudry, M. (eds.): Advances in Network Electrophysiology: Using Multi-Electrode Array. Springer, New York (2006)

    Google Scholar 

  17. Massobrio, P., Massobrio, G., Martinoia, S.: Interfacing cultured neurons to microtransducers arrays: a review of the neuro-electronic junction models. Front. Neurosci. 10 (2016)

    Google Scholar 

  18. Robinson, D.A.: The electrical properties of metal microelectrodes. Proc. IEEE 56, 1065–1071 (1968)

    Article  CAS  Google Scholar 

  19. Gross, G.W., Williams, A.N., Lucas, J.H.: Recording of spontaneous activity with photoetched microelectrode surfaces from mouse spinal neurons in culture. J. Neurosci. Methods 5, 13–22 (1982)

    Article  CAS  Google Scholar 

  20. Pine, J.: Recording action potentials from cultured neurons with extracellular microcircuit electrodes. J. Neurosci. Methods 2, 19–31 (1980, February)

    Article  CAS  Google Scholar 

  21. Canepari, M., Bove, M., Maeda, E., Cappello, M., Kawana, A.: Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity. Biol. Cybern. 77, 153–162 (1997)

    Article  CAS  Google Scholar 

  22. Jimbo, Y., Robinson, H.P.C., Kawana, A.: Strengthening of synchronized activity by tetanic stimulation in cortical cultures: application of planar electrode arrays. IEEE Trans. Biomed. Eng. 45, 1297–1304 (1998)

    Article  CAS  Google Scholar 

  23. Kamioka, H., Maeda, E., Jimbo, Y., Robinson, H.P.C., Kawana, A.: Spontaneous periodic synchronized bursting during formation of mature patterns of connections in cortical cultures. Neurosci. Lett. 206, 109–112 (1996)

    Article  CAS  Google Scholar 

  24. Le Feber, J., Stegenga, J., Rutten, W.L.C.: The effect of slow electrical stimuli to achieve learning in cultured networks of rat cortical neurons. PLoS ONE 5, e8871 (2010)

    Article  Google Scholar 

  25. Wagenaar, D.A., Pine, J., Potter, S.M.: Effective parameters for stimulation of dissociated cultures using multi-electrode arrays. J. Neurosci. Methods 138, 27–37 (2004)

    Article  Google Scholar 

  26. Defranchi, E., Novellino, A., Whelan, M., Vogel, S., Ramirez, T., van Ravenzwaay, B., et al.: Feasibility assessment of micro-electrode chip assay as a method of detecting neurotoxicity in vitro. Front. Neuroeng. 4, 6 (2011)

    Article  CAS  Google Scholar 

  27. Wagenaar, D.A., Madhavan, R., Pine, J., Potter, S.M.: Controlling bursting in cortical cultures with closed-loop multi-electrode stimulation. J. Neurosci. 25, 680–688 (2005)

    Article  CAS  Google Scholar 

  28. Martinoia, S., Sanguineti, V., Cozzi, L., Berdondini, L., Van Pelt, J., Tomas, J., et al.: Towards an embodied in-vitro electrophysiology: the NeuroBIT project. Neurocomputing 58–60, 1065–1072 (2004)

    Article  Google Scholar 

  29. Lewicki, M.S.: A review of methods for spike sorting: the detection and classification of neural action potentials. Netw. Comput. Neural Syst. 9, R53–R78 (1998)

    Article  CAS  Google Scholar 

  30. Wilson, S.B., Emerson, R.: Spike detection: a review and comparison of algorithms. Clin. Neurophysiol. 113, 1873–1881 (2002)

    Article  Google Scholar 

  31. Maccione, A., Gandolfo, M., Massobrio, P., Novellino, A., Martinoia, S., Chiappalone, M.: A novel algorithm for precise identification of spikes in extracellularly recorded neuronal signals. J. Neurosci. Methods 177, 241–249 (2009)

    Article  Google Scholar 

  32. Abbott, L.F., Rohrkemper, R.: A simple growth model constructs critical avalanche networks. Prog. Brain Res. 165, 13–19 (2007)

    Article  CAS  Google Scholar 

  33. Wagenaar, D.A., Nadasdy, Z., Potter, S.M.: Persistent dynamic attractors in activity patterns of cultured neuronal networks. Phys. Rev. E 73 (2006)

    Google Scholar 

  34. Van Pelt, J., Wolters, P.S., Corner, M.A., Rutten, W.L.C., Ramakers, G.J.A.: Long-term characterization of firing dynamics of spontaneous bursts in cultured neural networks. IEEE Trans. Biomed. Eng. 51, 2051–2062 (2004)

    Article  Google Scholar 

  35. Sporns, O., Chialvo, D.R., Kaiser, M., Hilgetag, C.C.: Organization, development and function of complex brain networks. Trends Cogn. Sci. 8, 418–425 (2004)

    Article  Google Scholar 

  36. Massobrio, P., Pasquale, V., Martinoia, S.: Self-organized criticality in cortical assemblies occurs in concurrent scale-free and small-world networks. Sci. Rep. 5 (2015)

    Google Scholar 

  37. Eytan, D., Marom, S.: Dynamics and effective topology underlying synchronization in networks of cortical neurons. J. Neurosci. 26, 8465–8476 (2006)

    Article  CAS  Google Scholar 

  38. Berdondini, L., Imfeld, K., Maccione, A., Tedesco, M., Neukom, S., Koudelka-Hep, M., et al.: Active pixel sensor array for high spatio-temporal resolution electrophysiological recordings from single cell to large scale neuronal networks. Lab Chip 9, 2644–2651 (2009)

    Article  CAS  Google Scholar 

  39. Eversmann, B., Jenker, M., Hofmann, F., Paulus, C., Brederlow, R., Holzapfl, B., et al.: A 128 x 128 CMOS biosensor array for extracellular recording of neural activity. IEEE J. Solid-State Circuits 38, 2306–2317 (2003)

    Article  Google Scholar 

  40. Frey, U., Egert, U., Heer, F., Hafizovic, S., Hierlemann, A.: Microelectronic system for high-resolution mapping of extracellular electric fields applied to brain slices. Biosens. Bioelectron. 24, 2191–2198 (2009)

    Article  CAS  Google Scholar 

  41. Pastore, V.P., Godjoski, A., Martinoia, S., Massobrio, P.: SpiCoDyn: a toolbox for the analysis of neuronal network dynamics and connectivity from multi-site spike signal recordings. Neuroinformatics 16, 15–30 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. Sporns, O.: Graph theory methods for the analysis of neural connectivity patterns. In: Kotter, R. (ed.) Neuroscience Databases. A Practical Guide. Klüwer (2002)

    Google Scholar 

  44. Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 1569–1572 (2003)

    Article  CAS  Google Scholar 

  45. Erdős, P., Rényi, A.: On random graphs I. Publ. Math. 6, 290–297 (1959)

    Google Scholar 

  46. Barabasi, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  CAS  Google Scholar 

  47. Dorogovtsev, S., Mendes, J.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)

    Article  Google Scholar 

  48. Timofeev, I., Grenier, F., Bazhenov, M., Sejnowski, T.J., Steriade, M.: Origin of slow cortical oscillations in deafferented cortical slabs. Cereb. Cortex 10, 1185–1199 (2000)

    Article  CAS  Google Scholar 

  49. Friedman, N., Ito, S., Brinkman, B.A., Shimono, M., DeVille, R.E., Dahmen, K.A., et al.: Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108, 208102 (2012, 18 May)

    Google Scholar 

  50. Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009)

    Article  Google Scholar 

  51. Priesemann, V., Wibral, M., Valderrama, M., Pröpper, R., Le Van Quyen, M., Geisel, T., et al.: Spike avalanches in vivo suggest a driven, slightly subcritical brain state. Front. Syst. Neurosci. 8, 2014-June-24 (2014)

    Google Scholar 

  52. Tomen, N., Rotermund, D., Ernst, U.: Marginally subcritical dynamics explain enhanced stimulus discriminability under attention. Front. Syst. Neurosci. 8, 2014-August-25 (2014)

    Google Scholar 

  53. Pastore, V.P., Massobrio, P., Godjoski, A., Martinoia, S.: Identification of excitatory-inhibitory links and network topology in large scale neuronal assemblies from multi-electrode recordings. PLoS Comput. Biol. (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, Bioengineering, Robotics, System Engineering (DIBRIS), University of Genova, Genova, Italy

    Paolo Massobrio

  2. Optical Approaches to Brain Function Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy

    Valentina Pasquale

Authors
  1. Paolo Massobrio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valentina Pasquale
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paolo Massobrio .

Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Nergis Tomen

  2. Institute of Perception, Action and Behaviour, University of Edinburgh, Edinburgh, UK

    J. Michael Herrmann

  3. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Udo Ernst

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Massobrio, P., Pasquale, V. (2019). Complexity of Network Connectivity Promotes Self-organized Criticality in Cortical Ensembles. In: Tomen, N., Herrmann, J., Ernst, U. (eds) The Functional Role of Critical Dynamics in Neural Systems . Springer Series on Bio- and Neurosystems, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-20965-0_3

Download citation

Publish with us

Policies and ethics

Search

Navigation