Frequency cluster formation and slow oscillations in neural populations with plasticity


Autoři: Vera Röhr aff001;  Rico Berner aff002;  Ewandson L. Lameu aff004;  Oleksandr V. Popovych aff006;  Serhiy Yanchuk aff003
Působiště autorů: Neurotechnology Group, Technische Universität Berlin, Berlin, Germany aff001;  Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany aff002;  Institut für Mathematik, Technische Universität Berlin, Berlin, Germany aff003;  National Institute for Space Research (INPE), São José dos Campos, São Paulo, Brazil aff004;  Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany aff005;  Institute of Neuroscience and Medicine - Brain & Behaviour (INM-7), Research Centre Jülich, Jülich, Germany aff006;  Institute for Systems Neuroscience - Medical Faculty, Heinrich-Heine University Düsseldorf, Düsseldorf, Germany aff007
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
doi: 10.1371/journal.pone.0225094

Souhrn

We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different frequencies. In this regime, the amplitude of the mean field undergoes low-frequency modulations, which may contribute to the mechanism of the emergence of slow oscillations of neural activity observed in spectral power of local field potentials or electroencephalographic signals at high frequencies. In addition to numerical simulations of such multi-clusters, we investigate the mechanisms of the observed phenomena using the simplest case of two clusters. In particular, we propose a phenomenological model which describes the dynamics of two clusters taking into account the adaptation of coupling weights. We also determine the set of plasticity functions (update rules), which lead to multi-clustering.

Klíčová slova:

Action potentials – Functional magnetic resonance imaging – Neural networks – Neurons – Population dynamics – Synapses – Synaptic plasticity – Neuronal plasticity


Zdroje

1. Cole MW, Bassett DS, Power JD, Braver TS, Petersen SE. Intrinsic and Task-Evoked Network Architectures of the Human Brain. Neuron. 2014;83(1):238–251. doi: 10.1016/j.neuron.2014.05.014 24991964

2. Marrelec G, Messe A, Giron A, Rudrauf D. Functional Connectivity’s Degenerate View of Brain Computation. PLoS Comput Biol. 2016;12(10):e1005031. doi: 10.1371/journal.pcbi.1005031

3. Bolt T, Nomi JS, Rubinov M, Uddin LQ. Correspondence Between Evoked and Intrinsic Functional Brain Network Configurations. Hum Brain Mapp. 2017;38(4):1992–2007. doi: 10.1002/hbm.23500 28052450

4. Zhou Y, Friston KJ, Zeidman P, Chen J, Li S, Razi A. The Hierarchical Organization of the Default, Dorsal Attention and Salience Networks in Adolescents and Young Adults. Cereb Cortex. 2018;28(2):726–737. doi: 10.1093/cercor/bhx307 29161362

5. Fornito A, Harrison BJ, Zalesky A, Simons JS. Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection. Proc Natl Acad Sci U S A. 2012;109(31):12788–12793. doi: 10.1073/pnas.1204185109 22807481

6. Leonardi N, Richiardi J, Gschwind M, Simioni S, Annoni JM, Schluep M, et al. Principal components of functional connectivity: A new approach to study dynamic brain connectivity during rest. Neuroimage. 2013;83:937–950. doi: 10.1016/j.neuroimage.2013.07.019 23872496

7. Allen EA, Damaraju E, Plis SM, Erhardt EB, Eichele T, Calhoun VD. Tracking Whole-Brain Connectivity Dynamics in the Resting State. Cereb Cortex. 2014;24(3):663–676. doi: 10.1093/cercor/bhs352 23146964

8. Damaraju E, Allen EA, Belger A, Ford JM, McEwen S, Mathalon DH, et al. Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia. Neuroimage-clinical. 2014;5:298–308. doi: 10.1016/j.nicl.2014.07.003 25161896

9. Uhlhaas PJ, Singer W. Neural Synchrony in Brain Disorders: Relevance for Cognitive Dysfunctions and Pathophysiology. Neuron. 2006;52(1):155–168. doi: 10.1016/j.neuron.2006.09.020 17015233

10. Gerstner W, Kistler WM, Naud R, Paninski L. Neuronal dynamics: From single neurons to networks and models of cognition; 2014.

11. Hebb DO. The organization of behavior: A neuropsychological approach. John Wiley & Sons; 1949.

12. Brown T, Chapman P, Kairiss E, Keenan C. Long-term synaptic potentiation. Science (80-). 1988;242(4879):724–728. doi: 10.1126/science.2903551

13. Bliss TVP, Collingridge GL. A synaptic model of memory: long-term potentiation in the hippocampus. Nature. 1993;361(6407):31–39. doi: 10.1038/361031a0 8421494

14. Gerstner W, Kempter R, van Hemmen JL, Wagner H. A neuronal learning rule for sub-millisecond temporal coding. Nature. 1996;383(6595):76–78. doi: 10.1038/383076a0 8779718

15. Markram H. Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs. Science (80-). 1997;275(5297):213–215. doi: 10.1126/science.275.5297.213

16. Bi Gq, Poo Mm. Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type. J Neurosci. 1998;18(24):10464–10472. doi: 10.1523/JNEUROSCI.18-24-10464.1998

17. Abbott LF, Nelson SB. Synaptic plasticity: Taming the beast. Nat Neurosci. 2000;3(11s):1178–1183. doi: 10.1038/81453 11127835

18. Bi Gq, Poo Mm. Synaptic Modification by Correlated Activity: Hebb’s Postulate Revisited. Annu Rev Neurosci. 2001;24(1):139–166. doi: 10.1146/annurev.neuro.24.1.139

19. Hoppensteadt FC, Izhikevich EM. Synaptic organizations and dynamical properties of weakly connected neural oscillators II. Learning phase information. Biol Cybern. 1996;75(2):129–135. doi: 10.1007/s004220050280

20. Seliger P, Young SC, Tsimring LS. Plasticity and learning in a network of coupled phase oscillators. Phys Rev E. 2002;65(4):041906. doi: 10.1103/PhysRevE.65.041906

21. Clopath C, Büsing L, Vasilaki E, Gerstner W. Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nat Neurosci. 2010;13(3):344–352. doi: 10.1038/nn.2479 20098420

22. Tass PA, Popovych OV. Unlearning tinnitus-related cerebral synchrony with acoustic coordinated reset stimulation: theoretical concept and modelling. Biol Cybern. 2012;106:27–36. doi: 10.1007/s00422-012-0479-5 22350536

23. Tass PA, Majtanik M. Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study. Biol Cybern. 2006;94(1):58–66. doi: 10.1007/s00422-005-0028-6 16284784

24. Popovych O, Yanchuk S, Tass PAPA. Self-organized noise resistance of oscillatory neural networks with spike timing-dependent plasticity. Sci Rep. 2013;3(1):2926. doi: 10.1038/srep02926 24113385

25. Lücken L, Popovych OV, Tass PA, Yanchuk S. Noise-enhanced coupling between two oscillators with long-term plasticity. Phys Rev E. 2016;93(3):032210. doi: 10.1103/PhysRevE.93.032210 27078347

26. Ashourvan A, Telesford QK, Verstynen T, Vettel JM, Bassett DS. Multi-scale detection of hierarchical community architecture in structural and functional brain networks. PLOS ONE. 2019;14(5):1–36. doi: 10.1371/journal.pone.0215520

27. Bassett DS, Bullmore E, Verchinski BA, Mattay VS, Weinberger DR, Meyer-Lindenberg A. Hierarchical Organization of Human Cortical Networks in Health and Schizophrenia. Journal of Neuroscience. 2008;28(37):9239–9248. doi: 10.1523/JNEUROSCI.1929-08.2008 18784304

28. Bassett DS, Greenfield DL, Meyer-Lindenberg A, Weinberger DR, Moore SW, Bullmore ET. Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits. PLOS Computational Biology. 2010;6(4):1–14. doi: 10.1371/journal.pcbi.1000748

29. Betzel RF, Medaglia JD, Papadopoulos L, Baum GL, Gur R, Gur R, et al. The modular organization of human anatomical brain networks: Accounting for the cost of wiring. Network Neuroscience. 2017;1(1):42–68. doi: 10.1162/NETN_a_00002 30793069

30. Lohse C, Bassett DS, Lim KO, Carlson JM. Resolving Anatomical and Functional Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations. PLOS Computational Biology. 2014;10(10):1–17. doi: 10.1371/journal.pcbi.1003712

31. Aoki T, Aoyagi T. Self-organized network of phase oscillators coupled by activity-dependent interactions. Phys Rev E. 2011;84(6):66109. doi: 10.1103/PhysRevE.84.066109

32. Kasatkin DV, Yanchuk S, Schöll E, Nekorkin VI. Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings. Phys Rev E. 2017;96(6):062211. doi: 10.1103/PhysRevE.96.062211 29347359

33. Berner R, Schöll E, Yanchuk S. Multi-clusters in networks of adaptively coupled phase oscillators networks. SIAM J Appl Dyn Syst (to appear).

34. Berner R, Fialkowski J, Kasatkin D, Nekorkin V, Yanchuk S, Schöll E. Hierarchical frequency clusters in adaptive networks of phase oscillators. Chaos (to appear).

35. Popovych OV, Xenakis MN, Tass PA. The Spacing Principle for Unlearning Abnormal Neuronal Synchrony. PLoS One. 2015;10(2):e0117205. doi: 10.1371/journal.pone.0117205 25714553

36. Wittenberg GM, Wang SSH. Malleability of Spike-Timing-Dependent Plasticity at the CA3-CA1 Synapse. J Neurosci. 2006;26(24):6610–6617. doi: 10.1523/JNEUROSCI.5388-05.2006 16775149

37. Kepecs A, van Rossum MCW, Song S, Tagner J. Spike-timing-dependent plasticity: common themes and divergent vistas. Biol Cybern. 2002;87:446–458. doi: 10.1007/s00422-002-0358-6 12461634

38. Monto S, Palva S, Voipio J, Palva JM. Very Slow EEG Fluctuations Predict the Dynamics of Stimulus Detection and Oscillation Amplitudes in Humans. Journal of Neuroscience. 2008;28(33):8268–8272. doi: 10.1523/JNEUROSCI.1910-08.2008 18701689

39. Alvarado-Rojas C, Valderrama M, Fouad A, Ihle M, Teixeira C, Sales F, et al. Slow modulations of high-frequency activity (40-140 Hz) discriminate preictal changes in human focal epilepsy. Scientific reports. 2014;4:4545. doi: 10.1038/srep04545

40. Mantini D, Perrucci MG, Del Gratta C, Romani GL, Corbetta M. Electrophysiological signatures of resting state networks in the human brain. Proc Natl Acad Sci U S A. 2007;104(32):13170–13175. doi: 10.1073/pnas.0700668104 17670949

41. Magri C, Schridde U, Murayama Y, Panzeri S, Logothetis NK. The Amplitude and Timing of the BOLD Signal Reflects the Relationship between Local Field Potential Power at Different Frequencies. J Neurosci. 2012;32(4):1395–1407. doi: 10.1523/JNEUROSCI.3985-11.2012 22279224

42. Maistrenko YL, Lysyansky B, Hauptmann C, Burylko O, Tass PA. Multistability in the Kuramoto model with synaptic plasticity. Phys Rev E. 2007;75(6):066207. Nonlinearity 2016; 29(5):1468–1486. doi: 10.1103/PhysRevE.75.066207

43. Cateau H, Kitano K, Fukai T. Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering. Phys Rev E. 2008;77(5):051909. doi: 10.1103/PhysRevE.77.051909

44. Hodgkin A, Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. Bull Math Biol. 1990;52(1-2):25–71. doi: 10.1007/bf02459568 2185861

45. Hansel D, Mato G, Meunier C. Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons. Europhys Lett. 1993;23(5):367–372. doi: 10.1209/0295-5075/23/5/011

46. Hoppensteadt FC, Izhikevich EM. Weakly Connected Neural Networks. Springer-Verlag, New York; 1997.

47. Pikovsky A, Rosenblum M, Kurths J. Synchronization. {A} Universal Concept in Nonlinear Sciences. Cambridge University Press; 2001.

48. Guckenheimer J. Isochrons and phaseless sets. J Math Biol. 1975;1(3):259–273. doi: 10.1007/BF01273747 28303309

49. Winfree AT. The Geometry of Biological Time. vol. 12. Springer; 2001. Available from: http://link.springer.com/10.1007/978-1-4757-3484-3.

50. Song S, Miller KD, Abbott LF. Competitive Hebbian learning through spike-timing-dependent synapticplasticity. Nat Neurosci. 2000;3(9):919–926. doi: 10.1038/78829 10966623

51. Rubin J, Lee DD, Sompolinsky H. Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity. Phys Rev Lett. 2001;86(2):364–367. doi: 10.1103/PhysRevLett.86.364 11177832

52. Deco G, Jirsa V, McIntosh AR, Sporns O, Kotter R. Key role of coupling, delay, and noise in resting brain fluctuations. Proc Natl Acad Sci U S A. 2009;106(25):10302–10307. doi: 10.1073/pnas.0901831106 19497858

53. Ponce-Alvarez A, Deco G, Hagmann P, Romani GL, Mantini D, Corbetta M. Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity. PLoS Comput Biol. 2015;11(2):UNSP e1004100. doi: 10.1371/journal.pcbi.1004100 25692996

54. Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ. Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J Neurosci. 2002;22(19):8691–8704. doi: 10.1523/JNEUROSCI.22-19-08691.2002 12351744

55. Compte A, Sanchez-Vives MV, McCormick DA, Wang XJ. Cellular and network mechanisms of slow oscillatory activity (< 1 Hz) and wave propagations in a cortical network model. J Neurophysiol. 2003;89(5):2707–2725. doi: 10.1152/jn.00845.2002 12612051

56. Ashwin P, Burylko O. Weak chimeras in minimal networks of coupled phase oscillators. Chaos 2015;25(1):13106. doi: 10.1063/1.4905197

57. Bick C, Ashwin P. Chaotic weak chimeras and their persistence in coupled populations of phase oscillators. Nonlinearity 2016;29(5):1468–1486. doi: 10.1088/0951-7715/29/5/1468


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