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Spiking activities in chain neural network driven by channel noise with field coupling

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Abstract

The distribution of electromagnetic field in both intracellular and extracellular environments can be changed by fluctuations in the membrane potential, and the effects of electromagnetic induction should be considered in dealing with neuronal electrical activities, wherein field coupling plays a very important role in signal exchange between neurons. In this paper, basing on an improved electromagnetic induction model, a chain network is designed to investigate the responses of the neural system to channel noise under field coupling. Both the synchronization factor and coefficient of variation are numerically simulated, and it is found that (i) the weak field coupling strength is conducive to the regularity of discharge patterns in the neuronal network; (ii) the synchronization of neural spikes can be enhanced by selecting a suitable coupling intensity; and (iii) in the presence of the weak noise intensity, the discharge mode of neuron is easily affected by the inducing coefficient. Our results show that the regularity of discharge patterns in a stochastic neural network depends on the field coupling intensity, which reflects the importance of field coupling in the selection of neural discharge modes.

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References

  1. Barahona, M., Pecora, L.M.: Synchronization in small-world systems. Phys. Rev. Lett. 89, 054101 (2002)

    Article  Google Scholar 

  2. He, D., Shi, P., Stone, L.: Noise-induced synchronization in realistic models. Phys. Rev. E 67, 027201 (2003)

    Article  Google Scholar 

  3. Benzi, R., Sutera, A., Vulpiani, A.: The mechanism of stochastic resonance. J. Phys. A 14, L453–L457 (1981)

    Article  MathSciNet  Google Scholar 

  4. Moss, F., Pierson, D., O’Gorman, D.: Stochastic resonance: tutorial and update. Int. J. Bifurc. Chaos 4, 1383 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Guo, D., Matjaž, P., Zhang, Y., Yao, D.: Frequency-difference-dependent stochastic resonance in neural systems. Phys. Rev. E 96, 022415 (2017)

    Article  Google Scholar 

  6. Perc, M.: Spatial coherence resonance in excitable media. Phys. Rev. E 72, 016207 (2005)

    Article  MathSciNet  Google Scholar 

  7. Jung, P.: Periodically driven stochastic systems. Phys. Rep. 234, 175–295 (1993)

    Article  MathSciNet  Google Scholar 

  8. Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70, 223 (1998)

    Article  Google Scholar 

  9. Brunel, N., Chance, F.S., Fourcaud, N., Abbott, L.F.: Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys. Rev. Lett. 86, 2186–2189 (2001)

    Article  Google Scholar 

  10. Hille, B.: Ionic channels of excitable membranes. Neurology 42, 1439 (1992)

    Google Scholar 

  11. Lin, X., Gong, Y., Wang, L.: Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin–Huxley neuronal networks. Chaos 21, 043109 (2011)

    Article  MATH  Google Scholar 

  12. Maisel, B., Lindenberg, K.: Channel noise effects on first spike latency of a stochastic Hodgkin–Huxley neuron. Phys. Rev. E 95, 022414 (2017)

    Article  MathSciNet  Google Scholar 

  13. Schmid, G., Goychuk, I., Hänggi, P.: Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin–Huxley model. Phys. Biol. 1, 61 (2004)

    Article  Google Scholar 

  14. Jung, P., Shuai, J.W.: Optimal sizes of ion channel clusters. Europhys. Lett. 56, 29–35 (2007)

    Article  Google Scholar 

  15. Saikhedkar, N., Bhatnagar, M., Jain, A., Sukhwal, P., Sharma, C., Jaiswal, N.: Effects of mobile phone radiation (900 MHz radiofrequency) on structure and functions of rat brain. Neurol. Res. 36, 1072–1079 (2014)

    Article  Google Scholar 

  16. Kaprana, A.E., Karatzanis, A.D., Prokopakis, E.P., Panagiotaki, I.E., Vardiambasis, I.O., Adamidis, G., Christodoulou, P., Velegrakis, G.A.: Studying the effects of mobile phone use on the auditory system and the central nervous system: a review of the literature and future directions. Eur. Arch. Oto Rhino Laryngol. 265, 1011 (2008)

    Article  Google Scholar 

  17. Bao, B., Hu, A., Xu, Q., Bao, H., Wu, H., Chen, M.: AC-induced coexisting asymmetric bursters in the improved Hindmarsh–Rose model. Nonlinear Dyn. 92, 1695–1706 (2018)

    Article  Google Scholar 

  18. Ren, G., Xu, Y., Wang, C.: Synchronization behavior of coupled neuron circuits composed of memristors. Nonlinear Dyn. 88, 893–901 (2017)

    Article  Google Scholar 

  19. Yu, K., Wang, J., Deng, B., Wei, X.: Synchronization of neuron population subject to steady DC electric field induced by magnetic stimulation. Cognit. Neurodyn. 7, 237–252 (2013)

    Article  Google Scholar 

  20. Lu, L., Jia, Y., Liu, W., Yang, L.: Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity 2017, 7628537 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Ge, M., Jia, Y., Xu, Y., Yang, L.: Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn. 91, 515–523 (2018)

    Article  Google Scholar 

  22. Hodgkin, A.L., Huxley, A.F.: The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J. Physiol. 116, 497–506 (1952)

    Article  Google Scholar 

  23. Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35, 193–213 (1981)

    Article  Google Scholar 

  24. Hindmarsh, J.L., Rose, R.M.: A model of the nerve impulse using two first-order differential equations. Nature 296, 162–164 (1982)

    Article  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Xu, F., Zhang, J., Fang, T., Huang, S., Wang, M.: Synchronous dynamics in neural system coupled with memristive synapse. Nonlinear Dyn. 92, 1395–1402 (2018)

    Article  Google Scholar 

  27. 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)

    Article  Google Scholar 

  28. Gu, H., Pan, B., Li, Y.: The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain. Nonlinear Dyn. 82, 1191–1210 (2015)

    Article  MathSciNet  Google Scholar 

  29. Bartsch, R., Kantelhardt, J.W., Penzel, T., Havlin, S.: Experimental evidence for phase synchronization transitions in the human cardiorespiratory system. Phys. Rev. Lett. 98, 054102 (2007)

    Article  Google Scholar 

  30. Xu, Y., Jia, Y., Ge, M., Lu, L., Yang, L., Zhan, X.: Effects of ion channel blocks on electrical activity of stochastic Hodgkin–Huxley neural network under electromagnetic induction. Neurocomputing 283, 196–204 (2018)

    Article  Google Scholar 

  31. Ma, J., Wu, F., Alsaedi, A., Tang, J.: Crack synchronization of chaotic circuits under field coupling. Nonlinear Dyn. 93, 2057–2069 (2018)

    Article  Google Scholar 

  32. Casado, J.M., Baltanás, J.P.: Phase switching in a system of two noisy Hodgkin–Huxley neurons coupled by a diffusive interaction. Phys. Rev. E 68, 061917 (2003)

    Article  MathSciNet  Google Scholar 

  33. Xu, X., Ni, L., Wang, R.: A neural network model of spontaneous up and down transitions. Nonlinear Dyn. 84, 1541–1551 (2016)

    Article  MathSciNet  Google Scholar 

  34. Gutierrez, G.J., O’Leary, T., Marder, E.: Multiple mechanisms switch an electrically coupled, synaptically inhibited neuron between competing rhythmic oscillators. Neuron 77, 845–858 (2013)

    Article  Google Scholar 

  35. Dhamala, M., Jirsa, V.K., Ding, M.: Enhancement of neural synchrony by time delay. Phys. Rev. Lett. 92, 074104 (2004)

    Article  Google Scholar 

  36. Yao, C., Zhan, M., Shuai, J., Ma, J., Kurths, J.: Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling. Chaos 27, 126702 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  38. Lu, L., Jia, Y., Kirunda, J., 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. (2018). https://doi.org/10.1007/s11071-018-4652-9

  39. Mesin, L.: Dynamics of spiral waves in a cardiac electromechanical model with a local electrical inhomogeneity. Chaos Solitons Fractals 45, 1220–1230 (2012)

    Article  MathSciNet  Google Scholar 

  40. Ozer, M., Uzuntarla, M.: Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network. Phys. Lett. A 372, 4603–4609 (2008)

    Article  MATH  Google Scholar 

  41. Yu, L., Chen, Y., Zhang, P.: Frequency and phase synchronization of two coupled neurons with channel noise. Eur. Phys. J. B 59, 249–257 (2007)

    Article  Google Scholar 

  42. Ma, J., Xu, Y., Ren, G., Wang, C.: Prediction for breakup of spiral wave in a regular neuronal network. Nonlinear Dyn. 84, 497–509 (2016)

    Article  MathSciNet  Google Scholar 

  43. Braun, H.A., Wissing, H., Schäfer, K., Hirsch, M.C.: Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367, 270–273 (1994)

    Article  Google Scholar 

  44. Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  46. Li, Q., Zeng, H., Li, J.: Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria. Nonlinear Dyn. 79, 2295–2308 (2015)

    Article  MathSciNet  Google Scholar 

  47. Wu, F., Wang, C., Jin, W., Ma, J.: Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Phys. A 469, 81–88 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  48. Ozer, M.: Frequency-dependent information coding in neurons with stochastic ion channels for subthreshold periodic forcing. Phys. Lett. A 354, 258–263 (2006)

    Article  Google Scholar 

  49. Li, J., Liu, S., Liu, W., Yu, Y., Wu, Y.: Suppression of firing activities in neuron and neurons of network induced by electromagnetic radiation. Nonlinear Dyn. 83, 801–810 (2016)

    Article  MathSciNet  Google Scholar 

  50. 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)

    Article  Google Scholar 

  51. Xu, Y., Jia, Y., Kirunda, J.B., Shen, J., Ge, M., Lu, L., Pei, Q.: Dynamic behaviors in coupled neuron system with the excitatory and inhibitory autapse under electromagnetic induction. Complexity 2018, 3012743 (2018)

    Google Scholar 

  52. Ge, M., Jia, Y., Kirunda, J.B., Xu, Y., Shen, J., Lu, L.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)

    Article  Google Scholar 

  53. Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001)

    Article  Google Scholar 

  54. Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge Prof. Jun Ma from Lanzhou University of Technology for his constructive suggestions. This work was supported by the National Natural Science Foundation of China, under Grant Nos. 11775091 and 11474117.

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Authors and Affiliations

  1. School of Physics and Institute of Biophysics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Ying Xu, Ya Jia, Huiwen Wang, Ying Liu, Ping Wang & Yunjie Zhao

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  1. Ying Xu
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Correspondence to Ya Jia.

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Xu, Y., Jia, Y., Wang, H. et al. Spiking activities in chain neural network driven by channel noise with field coupling. Nonlinear Dyn 95, 3237–3247 (2019). https://doi.org/10.1007/s11071-018-04752-2

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