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Chemical synaptic multiplexing enhances rhythmicity in neuronal networks

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Abstract

Real-world networks are rarely isolated; rather, they constitute a large number of elements interacting through complex topologies and oscillation is essential for their proper functioning. But degradation may come up naturally in such large systems that can severely affect the dynamical activity of the entire network. This mandates us to prescribe some remedies to overcome such deterioration. In this work, we demonstrate this scenario using a neuronal model organized in a framework of multiplex structure composed of a mixture of active and inactive neurons, while interacting via both electrical gap junction and chemical synapse. Multiplex architecture being very much prominent in cortical networks, we explore the simultaneous effect of the electrical and chemical synapses in the persistence of global rhythmicity of a multiplex neuronal network. Our results suggest that although electrical synapse reduces the dynamical performance of the network, chemical synapse through interlayer connection is highly efficient in reviving the rhythmicity of the network. Moreover, we investigate the effect of demultiplexing on the resilience of the network and show that chemical synaptic coupling can revive global rhythmicity under progressive demultiplexing as well. We also demonstrate this effectiveness of the chemical synapses for the case of reverse transition from global rest state to dynamism.

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References

  1. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Science. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  2. Strogatz, S.H.: Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life. Hyperion, New York (2004)

    Google Scholar 

  3. Ghosh, D., Bhattacharya, S.: Projective synchronization of new hyperchaotic system with fully unknown parameters. Nonlinear Dyn. 61, 11–21 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Yao, Z., Ma, J., Yao, Y., Wang, C.: Synchronization realization between two nonlinear circuits via an induction coil coupling. Nonlinear Dyn. 96, 205–217 (2019)

    Google Scholar 

  5. Majhi, S., Ghosh, D., Kurths, J.: Emergence of synchronization in multiplex networks of mobile Rössler oscillators. Phys. Rev. E 99, 012308 (2019)

    MathSciNet  Google Scholar 

  6. Panaggio, M.J., Abrams, D.M.: Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity 28, R67 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Majhi, S., Bera, B.K., Ghosh, D., Perc, M.: Chimera states in neuronal networks: a review. Phys. Life Rev. 28, 100 (2019)

    Google Scholar 

  8. Koseka, A., Volkov, E., Kurths, J.: Oscillation quenching mechanisms: amplitude vs. oscillation death. Phys. Rep. 531, 173 (2013)

    MathSciNet  MATH  Google Scholar 

  9. Albert, R., Jeong, H., Barabási, A.-L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)

    Google Scholar 

  10. Cohen, R., Erez, K., ben-Avraham, D., Havlin, S.: Resilience of the internet to random breakdowns. Phys. Rev. Lett. 85, 4626 (2000)

    Google Scholar 

  11. Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S.: Catastrophic cascade of failures in interdependent networks. Nature 464, 1025 (2010)

    Google Scholar 

  12. Vespignani, A.: Complex networks: the fragility of interdependency. Nature 464, 984 (2010)

    Google Scholar 

  13. Gao, J., Barzel, B., Barabási, A.-L.: Universal resilience patterns in complex networks. Nature 530, 307–312 (2016)

    Google Scholar 

  14. Daido, H., Nakanishi, K.: Aging transition and universal scaling in oscillator networks. Phys. Rev. Lett. 93, 104101 (2004)

    Google Scholar 

  15. Daido, H., Nakanishi, K.: Aging and clustering in globally coupled oscillators. Phys. Rev. E 75, 056206 (2007)

    MathSciNet  Google Scholar 

  16. Morino, K., Tanaka, G., Aihara, K.: Robustness of multilayer oscillator networks. Phys. Rev. E 83, 056208 (2011)

    Google Scholar 

  17. Tanaka, G., Morino, K., Aihara, K.: Dynamical robustness in complex networks: the crucial role of low-degree nodes. Sci. Rep. 2, 232 (2012)

    Google Scholar 

  18. Tanaka, G., Morino, K., Daido, H., Aihara, K.: Dynamical robustness of coupled heterogeneous oscillators. Phys. Rev. E 89, 052906 (2014)

    Google Scholar 

  19. Thakur, B., Sharma, D., Sen, A.: Time-delay effects on the aging transition in a population of coupled oscillators. Phys. Rev. E 90, 042904 (2014)

    Google Scholar 

  20. Sasai, T., Morino, K., Tanaka, G., Almendral, J.A., Aihara, K.: Robustness of oscillatory behavior in correlated networks. PLoS ONE 10, e0123722 (2015)

    Google Scholar 

  21. Ranta, E., Fowler, M.S., Kaitala, V.: Population synchrony in small-world networks. Proc. R. Soc. B 275, 435 (2008)

    Google Scholar 

  22. Gilarranz, L.J., Bascompte, J.: Spatial network structure and metapopulation persistence. J. Theor. Biol. 297, 11 (2012)

    Google Scholar 

  23. Kundu, S., Majhi, S., Sasmal, S.K., Ghosh, D., Rakshit, B.: Survivability of a metapopulation under local extinctions. Phys. Rev. E 96, 062212 (2017)

    Google Scholar 

  24. Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89, 1569–1578 (2017)

    MathSciNet  Google Scholar 

  25. Ge, M., Jia, Y., Kirunda, J.B., Xu, Y., Shen, J., Lu, L., Liu, Y., Pei, Q., Zhan, X., Yang, L.: Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh–Rose neural network. Neurocomputing 320, 60–68 (2018)

    Google Scholar 

  26. Lu, L., Jia, Y., Kirunda, J.B., Xu, Y., Ge, M., Pei, Q., Yang, L.: Effects of noise and synaptic weight on propagation of subthreshold excitatory postsynaptic current signal in a feed-forward neural network. Nonlinear Dyn. 95, 1673–1686 (2019)

    Google Scholar 

  27. Xu, Y., Jia, Y., Wang, H., Liu, Y., Wang, P., Zhao, Y.: Spiking activities in chain neural network driven by channel noise with field coupling. Nonlinear Dyn. 95, 3237–3247 (2019)

    Google Scholar 

  28. Ge, M., Jia, Y., Xu, Y., Lu, L., Wang, H., Zhao, Y.: Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh–Rose neural network. Appl. Math. Comput. 352, 136–145 (2019)

    MathSciNet  Google Scholar 

  29. Lisman, J., Buzsáki, G.: A neural coding scheme formed by the combined function of gamma and theta oscillations. Schizophr. Bull. 34, 974–980 (2008)

    Google Scholar 

  30. Jalife, J., Gray, R.A., Morley, G.E., Davidenko, J.M.: Self-organization and the dynamical nature of ventricular fibrillation. Chaos 8, 79 (1998)

    MATH  Google Scholar 

  31. Engel, A.K., Singer, W.: Temporal binding and the neural correlates of sensory awareness. Trends Cogn. Sci. 5, 16–25 (2001)

    Google Scholar 

  32. Varela, F., Lachaux, J.P., Rodriguez, E., Martinerie, J.: The brainweb: phase synchronization and large-scale integration. Nat. Rev. Neurosci. 2, 229 (2001)

    Google Scholar 

  33. Burrow, T.: The neurodynamics of behavior: a phylobiological foreword. Philos. Sci. 10, 271–288 (1943)

    Google Scholar 

  34. Ma, J., Yang, Z., Yang, L., Tang, J.: A physical view of computational neurodynamics. J. Zhejiang Univ. Sci. A 20, 639–659 (2019)

    Google Scholar 

  35. Xu, Y., Ying, H., Jia, Y., Ma, J., Hayat, T.: Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7, 43452 (2017)

    Google Scholar 

  36. Ma, J., Zhang, G., Hayat, T., Ren, G.: Model electrical activity of neuron under electric field. Nonlinear Dyn. 95, 1585–1598 (2019)

    Google Scholar 

  37. Xu, Y., Jia, Y., Ma, J., Hayat, T., Alsaedi, A.: Collective responses in electrical activities of neurons under field coupling. Sci. Rep. 8, 1349 (2018)

    Google Scholar 

  38. Rakshit, S., Ray, A., Bera, B.K., Ghosh, D.: Synchronization and firing patterns of coupled Rulkov neuronal map. Nonlinear Dyn. 94, 785–805 (2018)

    Google Scholar 

  39. Lv, M., Wang, C., Ren, G., Ma, J., Song, X.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)

    Google Scholar 

  40. Levanova, T.A., Kazakov, A.O., Osipov, G.V., Kurths, J.: Dynamics of ensemble of inhibitory coupled Rulkov maps. Eur. Phys. J. Spec. Top. 225, 147–157 (2016)

    Google Scholar 

  41. Korotkov, A.G., Kazakov, A.O., Levanova, T.A., Osipov, G.V.: The dynamics of ensemble of neuron-like elements with excitatory couplings. Commun. Nonlinear Sci. Numer. Simul. 71, 38–49 (2019)

    MathSciNet  Google Scholar 

  42. Morino, K., Tanaka, G., Aihara, K.: Efficient recovery of dynamic behavior in coupled oscillator networks. Phys. Rev. E 88, 032909 (2013)

    Google Scholar 

  43. Liu, Y., Zou, W., Zhan, M., Duan, J., Kurths, J.: Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators. Europhys. Lett. 114, 40004 (2016)

    Google Scholar 

  44. Sun, Z., Ma, N., Xu, W.: Aging transition by random errors. Sci. Rep. 7, 42715 (2017)

    Google Scholar 

  45. Kundu, S., Majhi, S., Ghosh, D.: Resumption of dynamism in damaged networks of coupled oscillators. Phys. Rev. E 97, 052313 (2018)

    Google Scholar 

  46. Bera, B.K.: Low pass filtering mechanism enhancing dynamical robustness in coupled oscillatory networks. Chaos 29, 041104 (2019)

    MathSciNet  Google Scholar 

  47. Kundu, S., Majhi, S., Karmakar, P., Ghosh, D., Rakshit, B.: Augmentation of dynamical persistence in networks through asymmetric interaction. Europhys. Lett. 123, 30001 (2018)

    Google Scholar 

  48. Boccaletti, S., Bianconi, G., Criado, R., del Genio, C.I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544, 1–122 (2014)

    MathSciNet  Google Scholar 

  49. Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2, 203–271 (2014)

    Google Scholar 

  50. Domenico, M.D., Solé-Ribalta, A., Cozzo, E., Kivelä, M., Moreno, Y., Porter, M.A., Gómez, S., Arenas, A.: Mathematical formulation of multilayer networks. Phys. Rev. X 3, 041022 (2013)

    Google Scholar 

  51. Nicosia, V., Bianconi, G., Latora, V., Barthelemy, M.: Growing multiplex networks. Phys. Rev. Lett. 111, 058701 (2013)

    Google Scholar 

  52. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821 (2002)

    MathSciNet  MATH  Google Scholar 

  53. Cardillo, A., Zanin, M., Gómez-Gardeñes, J., Romance, M., Garcia del Amo, A., Boccaletti, S.: Modeling the multi-layer nature of the European air transport network: resilience and passengers re-scheduling under random failures. Eur. Phys. J. Spec. Top. 215, 23 (2013)

    Google Scholar 

  54. Brummitt, C.D., D’Souza, R.M., Leicht, E.A.: Suppressing cascades of load in interdependent networks. Proc. Natl. Acad. Sci. USA 109, E680 (2012)

    Google Scholar 

  55. Pilosof, S., Porter, M.A., Pascual, M., Kéfi, S.: The multilayer nature of ecological networks. Nat. Ecol. Evol. 1, 0101 (2017)

    Google Scholar 

  56. Bentley, B., Branicky, R., Barnes, C.L., Chew, Y.L., Yemini, E., Bullmore, E.T., Vtes, P.E., Schafer, W.R.: The multilayer connectome of Caenorhabditis elegans. PLoS Comput. Biol. 12, e1005283 (2016)

    Google Scholar 

  57. Battiston, F., Nicosia, V., Chavez, M., Latora, V.: Multilayer motif analysis of brain networks. Chaos 27, 047404 (2017)

    MathSciNet  Google Scholar 

  58. Pereda, A.E.: Electrical synapses and their functional interactions with chemical synapses. Nat. Rev. Neurosci. 15, 250 (2014)

    Google Scholar 

  59. Rakshit, S., Bera, B.K., Ghosh, D.: Synchronization in a temporal multiplex neuronal hypernetwork. Phys. Rev. E 98, 032305 (2018)

    MathSciNet  Google Scholar 

  60. Rakshit, S., Majhi, S., Bera, B.K., Sinha, S., Ghosh, D.: Time-varying multiplex network: intralayer and interlayer synchronization. Phys. Rev. E 96, 062308 (2017)

    Google Scholar 

  61. Rakshit, S., Bera, B.K., Ghosh, D., Sinha, S.: Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks. Phys. Rev. E 97, 052304 (2018)

    Google Scholar 

  62. Majhi, S., Perc, M., Ghosh, D.: Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos 27, 073109 (2017)

    MathSciNet  Google Scholar 

  63. Majhi, S., Kapitaniak, T., Ghosh, D.: Solitary states in multiplex networks owing to competing interactions. Chaos 29, 013108 (2019)

    MathSciNet  Google Scholar 

  64. Bassett, D.S., Bullmore, E.T.: Small-world brain networks. Neuroscientist 12, 512 (2006)

    Google Scholar 

  65. Bassett, D.S., Bullmore, E.T.: Small-world brain networks revisited. Neuroscientist 23, 499 (2017)

    Google Scholar 

  66. Sporns, O., Honey, C.J.: Small worlds inside big brains. Proc. Natl. Acad. Sci. USA 103, 19219 (2006)

    Google Scholar 

  67. Hilgetag, C.C., O’Neill, M.A., Young, M.P.: Hierarchical organization of macaque and cat cortical sensory systems explored with a novel network processor. Philos. Trans. R. Soc. Lond. B Biol. Sci. 355, 71 (2000)

    Google Scholar 

  68. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature (London) 393, 440 (1998)

    MATH  Google Scholar 

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  1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    Srilena Kundu, Soumen Majhi & Dibakar Ghosh

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  1. Srilena Kundu
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  2. Soumen Majhi
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  3. Dibakar Ghosh
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Correspondence to Dibakar Ghosh.

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Kundu, S., Majhi, S. & Ghosh, D. Chemical synaptic multiplexing enhances rhythmicity in neuronal networks. Nonlinear Dyn 98, 1659–1668 (2019). https://doi.org/10.1007/s11071-019-05277-y

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