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Spatiotemporal activities of a pulse-coupled biological neural network

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A Correction to this article was published on 27 March 2018

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Abstract

The present work is on the spatiotemporal activities and effects of chaotic neurons in a pulse-coupled biological neural network. The biological neural network used is that of Caenorhabditis elegans. Because of its similarity to human neural network, it can be used to understand the simple dynamics of human brain. Within the network the neurons are found to exhibit chaotic nature, even though their parameters are that of normal neurons. It is observed that when the strength of synaptic conductance is increased, initially the bursting synchronization, entropy of the network and the average firing rate decrease slightly and then increase. Since chaotic dynamics of neuron plays an important role in human brain functions, the neurons of the network are intentionally made chaotic and the dynamics is studied. As the neurons of the network are made chaotic, ‘near-death’-like surges of neuron activity before ending firing is observed throughout the network. Also, the brain dynamics changes from alert to rest state. When most of the neurons of the network are made chaotic, their activities become independent of the coupling strength.

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  • 27 March 2018

    There is a typographical error in Eq. (1) of the original article, where ‘w’, the membrane potential, should be squared in the first term on the right-hand side.

References

  1. Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT Press, Cambridge (2014)

    Google Scholar 

  2. Resmi, V., Ambika, G., Amritkar, R.E.: General mechanism for amplitude death in coupled systems. Phys. Rev. E 84, 46212 (2011)

    Article  Google Scholar 

  3. Zou, W., Senthilkumar, D.V., Koseska, A., Kurths, J.: Generalizing the transition from amplitude to oscillation death in coupled oscillators. Phys. Rev. E 88, 50901 (2013)

    Article  Google Scholar 

  4. Banerjee, T., Biswas, D.: Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion. Chaos Interdiscip. J. Nonlinear Sci. 23, 43101 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Thottil, S.K., Ignatius, R.P.: Nonlinear feedback coupling in Hindmarsh–Rose neurons. Nonlinear Dyn. 87(3), 1879–1899 (2017)

    Article  Google Scholar 

  6. Ma, J., Tang, J.: A review for dynamics of collective behaviors of network of neurons. Sci. China Technol. Sci. 58(12), 2038–2045 (2015)

    Article  Google Scholar 

  7. Hizanidis, J., Kouvaris, N.E., Gorka, Z.-L., Díaz-Guilera, A., Antonopoulos, C.G.: Chimera-like states in modular neural networks. Sci. Rep. 6, 19845 (2016)

    Article  Google Scholar 

  8. Tsigkri-DeSmedt, N.D., Hizanidis, J., Hovel, P., Provata, A.: Multi-chimera states in the Leaky Integrate-and-Fire model. Procedia Comput. Sci. 66, 13–22 (2015)

    Article  Google Scholar 

  9. Ermentrout, B.: Neural networks as spatio-temporal pattern-forming systems. Rep. Prog. Phys. 61, 4 (1998)

    Article  Google Scholar 

  10. Ma, J., Wang, C., Jin, W.: Pattern selection and self-organization induced by random boundary initial values in a neuronal network. Phys. A Stat. Mech. Appl. 461, 586–594 (2016)

    Article  MathSciNet  Google Scholar 

  11. Panaggio, M.J., Abrams, D.M.: Chimera states: Coexistance of coherence and incoherence in networks of coupled oscillators. Nonlinearity 28, 3 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bogaard, A., Parent, J., Zochowski, M., Booth, V.: Interaction of cellular and network mechanisms in spatiotemporal pattern formation in neuronal networks. J. Neurosci. 29(6), 1677–1687 (2009)

    Article  Google Scholar 

  13. Wang, Q., Zheng, Y., Ma, J.: Cooperative dynamics in neuronal networks. Chaos Solitons Fractals 56, 19–27 (2013)

    Article  Google Scholar 

  14. Erichsen Jr., R., Brunnet, L.G.: Multistability in networks of Hindmarsh–Rose neurons. Phys. Rev. E. 78, 61917 (2008)

    Article  Google Scholar 

  15. Jia, Y., Gu, H.: Transition from double coherence resonances to single coherence resonance in a neuronal network with phase noise. Chaos An Interdiscip. J. Nonlinear Sci. 25, 123124 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Feng, Y., Li, W.: Analysis on the synchronized network of Hindmarsh–Rose neuronal models. J. Phys. Conf. Ser. 604, 12006 (2015)

    Article  Google Scholar 

  17. Acker, C.D., Kopell, N., White, J.A.: Synchronization of strongly coupled excitatory neurons: relating network behavior to Biophysics. J. Comput. Neurosci. 15(1), 71–90 (2003)

    Article  Google Scholar 

  18. Luccioli, S., Politi, A.: Collective behavior of heterogeneous neural networks. Phys. Rev. Lett. 105, 158104 (2010)

    Article  Google Scholar 

  19. Cichy, R.M., Khosla, A., Pantazis, D., Torralba, A., Oliva, A.: Comparison of deep neural networks to spatio-temporal cortical dynamics of human visual object recognition reveals hierarchical correspondence. Sci. Rep. 6, 27755 (2016)

    Article  Google Scholar 

  20. Chen, Y., Rangarajan, G., Ding, M.: Stability of synchronized dynamics and pattern formation in coupled systems: review of some recent results. Commun. Nonlinear Sci. Numer. Simul. 11, 934–960 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Destexhe, A.: Stability of periodic oscillations in a network of neurons with time delay. Phys. Lett. A. 187(4), 309–316 (1994)

    Article  Google Scholar 

  22. Wang, H., Chen, Y.: Spatiotemporal activities of neural network exposed to external electric fields. Nonlinear Dyn. 85(2), 881–891 (2016)

    Article  MathSciNet  Google Scholar 

  23. Sprott, J.C.: Chaotic dynamics on large networks. Chaos Interdiscip. J. Nonlinear Sci. 18, 23135 (2008)

    Article  MathSciNet  Google Scholar 

  24. Wu, J., Xu, Y., Ma, J.: Levy noise improves the electrical activity in a neuron under electromagnetic radiation. PLoS One 12(3), e0174330 (2017)

    Article  Google Scholar 

  25. Roxin, A., Brunel, N., Hansel, D.: Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks. Phys. Rev. Lett. 94, 238103 (2005)

    Article  Google Scholar 

  26. Keplinger, K., Wackerbauer, R.: Transient spatiotemporal chaos in the Morris–Lecar neuronal ring network. Chaos Interdiscip. J. Nonlinear Sci. 24, 13126 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. Truccolo, W., Hochberg, L.R., Donoghue, J.P.: Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes. Nat. Neurosci. 13(1), 105–111 (2010)

    Article  Google Scholar 

  28. Fink, C.G., Booth, V., Zochowski, M.: Cellularly-driven differences in network synchronization propensity are differentially modulated by firing frequency. PLoS Comput. Biol. 7(5), e1002062 (2011)

    Article  MathSciNet  Google Scholar 

  29. Garbo, A.Di, Barbi, M., Chillemi, S., Alloisio, S., Nobile, M.: Calcium signalling in astrocytes and modulation of neural activity. BioSystems 89, 74–83 (2007)

    Article  Google Scholar 

  30. Guo, S., Tang, J., Ma, J., Wang, C.: Autaptic modulation of electrical activity in a network of neuron-coupled astrocyte. Compexity 2017, 4631602 (2017)

    MathSciNet  Google Scholar 

  31. Tang, J., Zhang, J., Ma, J., Zhang, G., Yang, X.: Astrocyte calcium wave induces seizure-like behavior in neuron network. Sci. China Technol. Sci. 60(7), 1011–1018 (2017)

    Article  Google Scholar 

  32. Freeman, W.J.: Role of chaotic dynamics in neural plasticity. Prog. Brain Res. 102, 319–333 (1994)

    Article  Google Scholar 

  33. Sato, W., Kochiyama, T., Uono, S.: Spatiotemporal neural network dynamics for the processing of dynamic facial expressions. Sci. Rep. 5, 12432 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  35. Varshney, L.R., Chen, B.L., Paniagua, E., Hall, D.H., Chklovskii, D.B.: Structural properties of the Caenorhabditis elegans neuronal network. PLoS Comput. Biol. 7(2), e1001066 (2011)

    Article  Google Scholar 

  36. Antonopoulos, C.G., Fokas, A.S., Bountis, T.C.: Dynamical complexity in the C. elegans neural network. Eur. Phys. J. Spec. Top 225(6–7), 1255–1269 (2016)

    Article  Google Scholar 

  37. Kosinski, R.A., Zaremba, M.: Dynamics of the model of the Caenorhabditis elegans neural network. Acta Phys. Pol. B. 38(6), 2201–2210 (2007)

    Google Scholar 

  38. Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 6 (2003)

    Article  Google Scholar 

  39. Izhikevich, E.M.: Which model to use for Cortical spiking neurons. IEEE Trans. Neural Netw. 15, 5 (2004)

    Article  Google Scholar 

  40. Izhikevich, E.M.: Hybrid spiking models. Philos. Trans. R. Soc. A. 368, 5061–5070 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. Altun, Z.F., Hall, D.H.: Nervous System, General Description. http://www.wormatlas.org/hermaphrodite/nervous/Neuroframeset.html

  42. Kaiser, M., Hilgetag, C.C.: Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2(7), e95 (2006)

    Article  Google Scholar 

  43. Kotter, R.: Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database. Neuroinformatics 2(2), 127–144 (2004)

    Article  Google Scholar 

  44. Choe, Y., McCormick, B., Koh, W.: Network connectivity analysis on the temporally augmented C. elegans web : A pilot study. Soc. Neurosci. Abstr. 30, 921.9 (2004)

  45. Dorval, A.D.: Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets. J. Neurosci. Methods. 173(1), 129–139 (2008)

    Article  Google Scholar 

  46. Dur-e-Ahmad, M., Nicola, W., Campbell, S.A., Skinner, F.K.: Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation. J. Comput. Neurosci. 33(1), 21–40 (2012)

    Article  MathSciNet  Google Scholar 

  47. Jin, W., Lin, Q., Wang, A., Wang, C.: Computer simulation of noise effects of the neighborhood of stimulus threshold for a Mathematical model of homeostatic regulation of sleep-wake cycles. Compexity 2017, 4797545 (2017)

    MathSciNet  MATH  Google Scholar 

  48. Chawla, L.S., Akst, S., Junker, C., Jacobs, B.R.N., Seneff, M.G.: Surges of Electroencephalogram activity at the time of death: a case series. J. Palliat. Med. 12(12), 1095–1100 (2009)

    Article  Google Scholar 

  49. Norton, L., Gibson, R.M., Gofton, T., Benson, C., Dhanani, S., Shemie, S.D., Hornby, L., Ward, R., Young, G.B.: Electroencephalographic recordings during withdrawal of life-sustaining therapy until 30 minutes after declaration of death. Can. J. Neurol. Sci. 44(2), 139–145 (2017)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, St. Teresa’s college, Ernakulam, Kerala, India

    K. K. Mineeja & Rose P. Ignatius

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  1. K. K. Mineeja
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Correspondence to K. K. Mineeja.

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Mineeja, K.K., Ignatius, R.P. Spatiotemporal activities of a pulse-coupled biological neural network. Nonlinear Dyn 92, 1881–1897 (2018). https://doi.org/10.1007/s11071-018-4169-2

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