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Chaos shapes transient synchrony activities and switchings in the excitatory-inhibitory networks

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Abstract

Chaotic dynamics have been evidenced in experimental data and numerical simulations ranging from the most straightforward individual neurons to the more complex neural groups. Nevertheless, whether chaotic behavior significantly contributes to the emergence of phase shift and spontaneous switchings between transient synchrony activities is subtle and remains elusive. We investigated the emergence of spontaneous transient synchrony activities and self-induced switchings in an excitatory-inhibitory network. We demonstrate that the dynamic nature of isolated neurons plays an essential role in the emergence of chaotic behavior, thereby affecting spontaneous transient synchrony and types of phase shift. We also show that the neural network of the cells with chaotic characteristics after synaptic interactions exhibits a broader range of excitatory transient synchronous dynamics. Our results offer several possibilities for explaining sensory perception and brain disease observed in experiments.

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References

  1. Hopfield, J.J., Brody, C.D.: What is a moment? transient synchrony as a collective mechanism for spatiotemporal integration. Proc. Natl. Acad. Sci. 98(3), 1282–1287 (2001)

    Google Scholar 

  2. Rabinovich, M., Huerta, R., Laurent, G.: Transient dynamics for neural processing. Science 321(5885), 48–50 (2008)

    Google Scholar 

  3. Duarte, R., Seeholzer, A., Zilles, K., Morrison, A.: Synaptic patterning and the timescales of cortical dynamics. Curr. Opin. Neurobiol. 43, 156–165 (2017)

    Google Scholar 

  4. Palmigiano, A., Geisel, T., Wolf, F., Battaglia, D.: Flexible information routing by transient synchrony. Nat. Neurosci. 20(7), 1014–1022 (2017)

    Google Scholar 

  5. Khona, M., Fiete, I.R.: Attractor and integrator networks in the brain. Nat. Rev. Neurosci. 1–23 (2022)

  6. Schirner, M., Xiaolu Kong, B.T., Yeo, T., Deco, G., Ritter, P.: Dynamic primitives of brain network interaction. Neuroimage 250, 118928 (2022)

    Google Scholar 

  7. Rabinovich, M.I., Varona, P., Selverston, A.I., Abarbanel, H.D.I.: Dynamical principles in neuroscience. Rev. Mod. Phys. 78(4), 1213 (2006)

    Google Scholar 

  8. Tang, G., Kesheng, X., Jiang, L.: Synchronization in a chaotic neural network with time delay depending on the spatial distance between neurons. Phys. Rev. E 84(4), 046207 (2011)

    Google Scholar 

  9. Kesheng, X., Maidana, J.P., Castro, S., Orio, P.: Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators. Sci. Rep. 8(1), 8370 (2018)

    Google Scholar 

  10. Fan, H., Kong, L.-W., Wang, X., Hastings, A., Lai, Y.-C.: Synchronization within synchronization: transients and intermittency in ecological networks. Natl. Sci. Rev. 8(10), nwaa269 (2021)

    Google Scholar 

  11. Faure, P., Korn, H.: Is there chaos in the brain? i. concepts of nonlinear dynamics and methods of investigation. Comptes Rendus de l’Académie des Sciences-Series III-Sciences de la Vie 324(9), 773–793 (2001)

    Google Scholar 

  12. Korn, H., Faure, P.: Is there chaos in the brain? ii. Experimental evidence and related models. C. R. Biol. 326(9), 787–840 (2003)

    Google Scholar 

  13. O’Byrne, J., Jerbi, K.: How critical is brain criticality? Trends Neurosci. (2022)

  14. Kesheng, X., Maidana, J.P., Caviedes, M., Quero, D., Aguirre, P., Orio, P.: Hyperpolarization-activated current induces period-doubling cascades and chaos in a cold thermoreceptor model. Front. Comput. Neurosci. 11, 12 (2017)

    Google Scholar 

  15. Pisarchik, A.N., Hramov, A.E.: Multistability in Physical and Living Systems. Springer, Berlin (2022)

    Google Scholar 

  16. Kesheng, X., Maidana, J.P., Orio, P.: Diversity of neuronal activity is provided by hybrid synapses. Nonlinear Dyn. 105, 2693–2710 (2021)

    Google Scholar 

  17. Zhou, X., Tian, C., Zhang, X., Zheng, M., Kesheng, X.: Short-term plasticity as a mechanism to regulate and retain multistability. Chaos Solitons Fractals 165, 112891 (2022)

    Google Scholar 

  18. Wang, X., Zhang, X., Zheng, M., Leijun, X., Kesheng, X.: Noise-induced coexisting firing patterns in hybrid-synaptic interacting networks. Physica A 615, 128591 (2023)

    Google Scholar 

  19. Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. 81(10), 3088–3092 (1984)

    Google Scholar 

  20. Xie, X., Hahnloser, R.H.R., Sebastian Seung, H.: Double-ring network model of the head-direction system. Phys. Rev. E 66(4), 041902 (2002)

    Google Scholar 

  21. Wang, X.-J.: Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36(5), 955–968 (2002)

    Google Scholar 

  22. Kesheng, X., Zhang, X., Wang, C., Liu, Z.: A simplified memory network model based on pattern formations. Sci. Rep. 4(1), 1–8 (2014)

    Google Scholar 

  23. Kesheng, X., Huang, W., Li, B., Dhamala, M., Liu, Z.: Controlling self-sustained spiking activity by adding or removing one network link. Europhys. Lett. 102(5), 50002 (2013)

    Google Scholar 

  24. Yao, Y., Yao, C.: Autapse-induced logical resonance in the Fitzhugh–Nagumo neuron. Nonlinear Dyn. 111(5), 4807–4821 (2023)

    MathSciNet  Google Scholar 

  25. Yao, C., Xu, F., Tang, X., Zou, W., Yang, D., Shuai, J.: A physical understanding and quantification for the regulation of orexin on sleep. Chaos Interdiscip. J. Nonlinear Sci. 33(7) (2023)

  26. Durstewitz, D., Deco, G.: Computational significance of transient dynamics in cortical networks. Eur. J. Neurosci. 27(1), 217–227 (2008)

    Google Scholar 

  27. Hastings, A., Abbott, K.C., Cuddington, K., Francis, T., Gellner, G., Lai, Y.-C., Morozov, A., Petrovskii, S., Scranton, K., Zeeman, M.L.: Transient phenomena in ecology. Science 361(6406), eaat6412 (2018)

    Google Scholar 

  28. Velez, A., Carlson, B.A.: Detection of transient synchrony across oscillating receptors by the central electrosensory system of mormyrid fish. Elife 5, e16851 (2016)

    Google Scholar 

  29. Shengdun, W., Zhou, K., Ai, Y., Zhou, G., Yao, D., Guo, D.: Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity. Cogn. Neurodyn. 15, 53–64 (2021)

    Google Scholar 

  30. Wens, V., Bourguignon, M., Ghinst, M.V., Mary, A., Marty, B., Coquelet, N., Naeije, G., Peigneux, P., Goldman, S., De Tiège, X.: Synchrony, metastability, dynamic integration, and competition in the spontaneous functional connectivity of the human brain. Neuroimage 199, 313–324 (2019)

    Google Scholar 

  31. Morozov, A., Abbott, K., Cuddington, K., Francis, T., Gellner, G., Hastings, A., Lai, Y.-C., Petrovskii, S., Scranton, K., Zeeman, M.L.: Long transients in ecology: theory and applications. Phys. Life Rev. 32, 1–40 (2020)

    Google Scholar 

  32. Hastings, A.: Transients: the key to long-term ecological understanding? Trends Ecol. Evol. 19(1), 39–45 (2004)

    Google Scholar 

  33. Bogacz, R.: Optimal decision-making theories: linking neurobiology with behaviour. Trends Cogn. Sci. 11(3), 118–125 (2007)

    Google Scholar 

  34. Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT press, New York (2007)

    Google Scholar 

  35. McCann, K., Yodzis, P.: Nonlinear dynamics and population disappearances. Am. Nat. 144(5), 873–879 (1994)

    Google Scholar 

  36. Kuehn, C.: Multiple Time Scale Dynamics, vol. 191. Springer, Berlin (2015)

    Google Scholar 

  37. Reimer, J.R., Arroyo-Esquivel, J., Jiang, J., Scharf, H.R., Wolkovich, E.M., Zhu, K., Boettiger, C.: Noise can create or erase long transient dynamics. Thyroid Res. 14(4), 685–695 (2021)

    Google Scholar 

  38. Ohira, T., Milton, J.: Mathematics As a Laboratory Tool: Dynamics. Delays and Noise. Springer, Berlin (2021)

    Google Scholar 

  39. Poil, S.-S., Hardstone, R., Mansvelder, H.D., Linkenkaer-Hansen, K.: Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neuronal networks. J. Neurosci. 32(29), 9817–9823 (2012)

    Google Scholar 

  40. Deco, G., Kringelbach, M.L.: Metastability and coherence: extending the communication through coherence hypothesis using a whole-brain computational perspective. Trends Neurosci. 39(3), 125–135 (2016)

    Google Scholar 

  41. Dahmen, D., Grün, S., Diesmann, M., Helias, M.: Second type of criticality in the brain uncovers rich multiple-neuron dynamics. Proc. Natl. Acad. Sci. 116(26), 13051–13060 (2019)

    Google Scholar 

  42. Li, J., Shew, W.L.: Tuning network dynamics from criticality to an asynchronous state. PLoS Comput. Biol. 16(9), e1008268 (2020)

    Google Scholar 

  43. Nowotny, T., Rabinovich, M.I.: Dynamical origin of independent spiking and bursting activity in neural microcircuits. Phys. Rev. Lett. 98(12), 128106 (2007)

    Google Scholar 

  44. Buckley, C.L., Nowotny, T.: Multiscale model of an inhibitory network shows optimal properties near bifurcation. Phys. Rev. Lett. 106(23), 238109 (2011)

    Google Scholar 

  45. Nakatani, H., van Leeuwen, C.: Transient synchrony of distant brain areas and perceptual switching in ambiguous figures. Biol. Cybern. 94, 445–457 (2006)

    Google Scholar 

  46. Creaser, J., Ashwin, P., Tsaneva-Atanasova, K.: Sequential escapes and synchrony breaking for networks of bistable oscillatory nodes. SIAM J. Appl. Dyn. Syst. 19(4), 2829–2846 (2020)

    MathSciNet  Google Scholar 

  47. Park, C., Worth, R.M., Rubchinsky, L.L.: Neural dynamics in parkinsonian brain: the boundary between synchronized and nonsynchronized dynamics. Phys. Rev. E 83(4), 042901 (2011)

    Google Scholar 

  48. Tinkhauser, G., Torrecillos, F., Pogosyan, A., Mostofi, A., Bange, M., Fischer, P., Tan, H., Hasegawa, H., Glaser, M., Muthuraman, M., et al.: The cumulative effect of transient synchrony states on motor performance in Parkinson’s disease. J. Neurosci. 40(7), 1571–1580 (2020)

    Google Scholar 

  49. Carr, M.F., Karlsson, M.P., Frank, L.M.: Transient slow gamma synchrony underlies hippocampal memory replay. Neuron 75(4), 700–713 (2012)

    Google Scholar 

  50. Xing, D., Shen, Y., Burns, S., Yeh, C.-I., Shapley, R., Li, W.: Stochastic generation of gamma-band activity in primary visual cortex of awake and anesthetized monkeys. J. Neurosci. 32(40), 13873–13880a (2012)

    Google Scholar 

  51. Orio, P., Gatica, M., Herzog, R., Maidana, J.P., Castro, S., Kesheng, X.: Chaos versus noise as drivers of multistability in neural networks. Chaos Interdiscip. J. Nonlinear Sci. 28(10), 106321 (2018)

    MathSciNet  Google Scholar 

  52. Fell, J., Axmacher, N.: The role of phase synchronization in memory processes. Nat. Rev. Neurosci. 12(2), 105–118 (2011)

    Google Scholar 

  53. Ray, S., Maunsell, J.H.R.: Do gamma oscillations play a role in cerebral cortex? Trends Cogn. Sci. 19(2), 78–85 (2015)

    Google Scholar 

  54. Ray, S., Maunsell, J.H.R.: Differences in gamma frequencies across visual cortex restrict their possible use in computation. Neuron 67(5), 885–896 (2010)

    Google Scholar 

  55. Ed Bullmore, Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)

    Google Scholar 

  56. Hansen, E.C.A., Battaglia, D., Spiegler, A., Deco, G., Jirsa, V.K.: Functional connectivity dynamics: modeling the switching behavior of the resting state. Neuroimage 105, 525–535 (2015)

    Google Scholar 

  57. Coombes, S., Wedgwood, K.C.A.: Neurodynamics: An Applied Mathematics Perspective, vol. 75. Springer, Berlin (2023)

    Google Scholar 

  58. Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B 221(1222), 87–102 (1984)

    Google Scholar 

  59. Coombes, S., Bressloff, P.C.: Bursting: The Genesis of Rhythm in the Nervous System. World Scientific, Singapore (2005)

    Google Scholar 

  60. Alreja, A., Nemenman, I., Rozell, C.J.: Constrained brain volume in an efficient coding model explains the fraction of excitatory and inhibitory neurons in sensory cortices. PLoS Comput. Biol. 18(1), e1009642 (2022)

    Google Scholar 

  61. Marín, O.: Interneuron dysfunction in psychiatric disorders. Nat. Rev. Neurosci. 13(2), 107–120 (2012)

    Google Scholar 

  62. Marom, S., Shahaf, G.: Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy. Q. Rev. Biophys. 35(1), 63–87 (2002)

    Google Scholar 

  63. Sahara, S., Yanagawa, Y., O’Leary, D.D.M., Stevens, C.F.: The fraction of cortical gabaergic neurons is constant from near the start of cortical neurogenesis to adulthood. J. Neurosci. 32(14), 4755–4761 (2012)

    Google Scholar 

  64. Wonders, C.P., Anderson, S.A.: The origin and specification of cortical interneurons. Nat. Rev. Neurosci. 7(9), 687–696 (2006)

    Google Scholar 

  65. Liu, G.: Local structural balance and functional interaction of excitatory and inhibitory synapses in hippocampal dendrites. Nat. Neurosci. 7(4), 373–379 (2004)

    Google Scholar 

  66. Van Vreeswijk, C., Sompolinsky, H.: Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274(5293), 1724–1726 (1996)

    Google Scholar 

  67. Moreau, A.W., Amar, M., Le Roux, N., Morel, N., Fossier, P.: Serotoninergic fine-tuning of the excitation-inhibition balance in rat visual cortical networks. Cereb. Cortex 20(2), 456–467 (2010)

    Google Scholar 

  68. Ebsch, C.L.: Excitatory-Inhibitory Balance, Imbalance, and Amplification In Cortical Network Models. University of Notre Dame, New York (2019)

    Google Scholar 

  69. Gerstner, W., Kistler, W.M., Naud, R., Paninski, L.: Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  70. Destexhe, A., Rudolph-Lilith, M.: Neuronal Noise, vol. 8. Springer, Berlin (2012)

    Google Scholar 

  71. Zador, A.: Spikes: exploring the neural code. Science 277(5327), 772–773 (1997)

    Google Scholar 

  72. Koch, C., Segev, I.: Methods in Neuronal Modeling: From Ions to Networks. MIT press, New York (1998)

    Google Scholar 

  73. Sterratt, D., Graham, B., Gillies, A., Willshaw, D.: Principles of Computational Modelling in Neuroscience. Cambridge University Press, Cambridge (2011)

    Google Scholar 

  74. Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Courier Corporation, North Chelmsford (2003)

    Google Scholar 

  75. Bertolotti, E., Burioni, R., di Volo, M., Vezzani, A.: Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity. Phys. Rev. E 95(1), 012308 (2017)

    Google Scholar 

  76. Golomb, D., Rinzel, J.: Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. Rev. E 48(6), 4810 (1993)

    Google Scholar 

  77. Mulansky, M., Kreuz, T.: Pyspike a python library for analyzing spike train synchrony. SoftwareX 5, 183–189 (2016)

    Google Scholar 

  78. Kreuz, T., Mulansky, M., Bozanic, N.: Spiky: a graphical user interface for monitoring spike train synchrony. J. Neurophysiol. 113(9), 3432–3445 (2015)

    Google Scholar 

  79. Brunel, N., Wang, X.-J.: What determines the frequency of fast network oscillations with irregular neural discharges? i. Synaptic dynamics and excitation-inhibition balance. J. Neurophysiol. 90(1), 415–430 (2003)

    Google Scholar 

  80. Ahmadian, Y., Miller, K.D.: What is the dynamical regime of cerebral cortex? Neuron 109(21), 3373–3391 (2021)

    Google Scholar 

  81. Zerlaut, Y., Zucca, S., Panzeri, S., Fellin, T.: The spectrum of asynchronous dynamics in spiking networks as a model for the diversity of non-rhythmic waking states in the neocortex. Cell Rep. 27(4), 1119–1132 (2019)

    Google Scholar 

  82. Devroye, L., Lugosi, G.: Combinatorial Methods in Density Estimation. Springer, Berlin (2001)

    Google Scholar 

  83. Gramacki, A.: Nonparametric Kernel Density Estimation and Its Computational Aspects, vol. 37. Springer, Berlin (2018)

    Google Scholar 

  84. Geisler, C., Brunel, N., Wang, X.-J.: Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. J. Neurophysiol. 94(6), 4344–4361 (2005)

    Google Scholar 

  85. Holden, A.V., Winlow, W., Haydon, P.G.: The induction of periodic and chaotic activity in a molluscan neurone. Biol. Cybern. 43(3), 169–173 (1982)

    MathSciNet  Google Scholar 

  86. Aihara, K., Matsumoto, G.: Temporally coherent organization and instabilities in squid giant axons. J. Theor. Biol. 95(4), 697–720 (1982)

    MathSciNet  Google Scholar 

  87. Makarenko, V., Llinás, R.: Experimentally determined chaotic phase synchronization in a neuronal system. Proc. Natl. Acad. Sci. 95(26), 15747–15752 (1998)

    Google Scholar 

  88. Abarbanel, H.D.I., Huerta, R., Rabinovich, M.I., Rulkov, N.F., Rowat, P.F., Selverston, A.I.: Synchronized action of synaptically coupled chaotic model neurons. Neural Comput. 8(8), 1567–1602 (1996)

    Google Scholar 

  89. Faure, P., Kaplan, D., Korn, H.: Synaptic efficacy and the transmission of complex firing patterns between neurons. J. Neurophysiol. 84(6), 3010–3025 (2000)

    Google Scholar 

  90. Crevier, D.W., Meister, M.: Synchronous period-doubling in flicker vision of salamander and man. J. Neurophysiol. 79(4), 1869–1878 (1998)

    Google Scholar 

  91. Fisahn, A., Pike, F.G., Buhl, E.H., Paulsen, O.: Cholinergic induction of network oscillations at 40 hz in the hippocampus in vitro. Nature 394(6689), 186–189 (1998)

    Google Scholar 

  92. Isaacson, J.S., Scanziani, M.: How inhibition shapes cortical activity. Neuron 72(2), 231–243 (2011)

  93. Ansmann, G., Lehnertz, K., Feudel, U.: Self-induced switchings between multiple space-time patterns on complex networks of excitable units. Phys. Rev. X 6(1), 011030 (2016)

    Google Scholar 

  94. Nunes Machado, J., Selingardi Matias, F.: Phase bistability between anticipated and delayed synchronization in neuronal populations. Phys. Rev. E 102(3), 032412 (2020)

    Google Scholar 

  95. Battaglia, D., Witt, A., Wolf, F., Geisel, T.: Dynamic effective connectivity of inter-areal brain circuits. PLoS Comput. Biol. 8(3), e1002438 (2012)

    Google Scholar 

  96. Lumer, E.D., Friston, K.J., Rees, G.: Neural correlates of perceptual rivalry in the human brain. Science 280(5371), 1930–1934 (1998)

    Google Scholar 

  97. Freyer, F., Roberts, J.A., Becker, R., Robinson, P.A., Ritter, P., Breakspear, M.: Biophysical mechanisms of multistability in resting-state cortical rhythms. J. Neurosci. 31(17), 6353–6361 (2011)

    Google Scholar 

  98. Freyer, F., Aquino, K., Robinson, P.A., Ritter, P., Breakspear, M.: Bistability and non-gaussian fluctuations in spontaneous cortical activity. J. Neurosci. 29(26), 8512–8524 (2009)

    Google Scholar 

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Funding

This work was supported by National Natural Science Foundation of China (Grants Nos. 12165016, 12005079 and 12305043), the funding for the Scientific Research Startup of Jiangsu University, China (Grant Nos.  4111190017 and 4111710001), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20220511). M. Zheng. appreciates the support from the Jiangsu Specially-Appointed Professor Program.

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Zhu, G., Zhang, Y., Wu, J. et al. Chaos shapes transient synchrony activities and switchings in the excitatory-inhibitory networks. Nonlinear Dyn 112, 7555–7570 (2024). https://doi.org/10.1007/s11071-024-09471-5

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