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Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling

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Abstract

Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage (p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.

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References

  1. Gorelova N A, Bureš J. Spiral waves of spreading depression in the isolated chicken retina. J Neurobiol, 1983, 14: 353–363

    Article  Google Scholar 

  2. Salomonsz R, Pertsov A V, Davidenko J M, et al. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature, 1992, 355: 349–351

    Article  Google Scholar 

  3. Prechtl J C, Cohen L B, Pesaran B, et al. Visual stimuli induce waves of electrical activity in turtle cortex. Proc Natl Acad Sci U S A, 1997, 94: 7621–7626

    Article  Google Scholar 

  4. Engel A K, König P, Kreiter A K, et al. Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex. Science, 1991, 252: 1177–1179

    Article  Google Scholar 

  5. Cobb S R, Buhl E H, Halasy K, et al. Synchronization of neuronal activity in hippocampus by individual GABAergic interneurons. Nature, 1995, 378: 75–78

    Article  Google Scholar 

  6. Uhlhaas P J, Roux F, Rodriguez E, et al. Neural synchrony and the development of cortical networks. Trends Cogn Sci, 2010, 14: 72–80

    Article  Google Scholar 

  7. Huang X Y, Troy W C, Yang Q, et al. Spiral waves in disinhibited mammalian neocortex. J Neurosci, 2004, 24: 9897–9902

    Article  Google Scholar 

  8. Schiff S J, Huang X Y, Wu J Y. Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. Phys Rev Lett, 2007, 98: 178102

    Article  Google Scholar 

  9. Huang X Y, Xu W F, Liang J M, et al. Spiral wave dynamics in neocortex. Neuron, 2010, 68: 978–990

    Article  Google Scholar 

  10. Jalife J. Rotors and spiral waves in atrial fibrillation. J Cardiovasc Electrophysiol, 2003, 14: 776–780

    Article  Google Scholar 

  11. Stiefel K M, Gutkin B S, Sejnowski T J. Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons. PLoS One, 2008, 3: e3947

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Liu Z Q, Zhang H M, Li Y Y, et al. Multiple spatial coherence resonance induced by the stochastic signal in neuronal networks near a saddle-node bifurcation. Physica A, 2010, 389: 2642–2653

    Article  Google Scholar 

  14. Sun X J, Lu Q S. Spatial coherence resonance induced by colored noise and parameter diversity in a neuronal network. Chin Phys B, 2010, 19: 040504

    Article  Google Scholar 

  15. Tang Z, Li Y Y, Xi L, et al. Spiral waves and multiple spatial coherence resonances induced by colored noise in neuronal network. Commun Theor Phys, 2012, 57: 61–67

    Article  MATH  Google Scholar 

  16. Gu H G, Jia B, Li Y Y, et al. White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability. Physica A, 2013, 392: 1361–1374

    Article  MathSciNet  Google Scholar 

  17. Wu Y, Li J J, Liu S B, et al. Noise-induced spatiotemporal patterns in Hodgkin–Huxley neuronal network. Cogn Neurodyn, 2013, 7: 431–440

    Article  MathSciNet  Google Scholar 

  18. Perc M. Spatial decoherence induced by small-world connectivity in excitable media. New J Phys, 2005, 7: 252

    Article  Google Scholar 

  19. Sun X J, Perc M, Lu Q S, et al. Spatial coherence resonance on diffusive and small-world networks of Hodgkin—Huxley neurons. Chaos, 2008, 18: 023102

    Article  MathSciNet  Google Scholar 

  20. Glatt E, Gassel M, Kaiser F. Variability-sustained pattern formation in sub-excitable media. Phys Rev E, 2007, 75: 026206

    Article  Google Scholar 

  21. Tang J, Yang L, Ma J, et al. Ca2+ spiral waves in a spatially discrete and random medium. Eur Biophys J Biophys Lett, 2009, 38: 1061–1068

    Article  Google Scholar 

  22. Tang J, Yi M, Chen P, et al. The influence of diversity on spiral wave in the cardiac tissue. Europhys Lett, 2012, 97: 28003

    Article  Google Scholar 

  23. Li Y Y, Jia B, Gu H G, et al. Parameter diversity induced multiple spatial coherence resonances and spiral waves in neuronal network with and without noise. Commun Theor Phys, 2012, 57: 817–824

    Article  MATH  Google Scholar 

  24. Qin H X, Ma J, Wang C N, et al. Autapse-induced target wave, spiral wave in regular network of neurons. Sci China-Phys Mech Astron, 2014, 57: 1918–1926

    Article  Google Scholar 

  25. Qin H X, Ma J, Jin W Y, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936–946

    Article  Google Scholar 

  26. Qin H X, Ma J, Wang C N, et al. Autapse-induced spiral wave in network of neurons under noise. PloS One, 2014, 9: e100849

    Article  Google Scholar 

  27. Ma J, Song X, Tang J, et al. Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomputing, 2015, 167: 378–389

    Article  Google Scholar 

  28. Song X L, Wang C N, Ma J, et al. Transition of electric activity of neurons induced by chemical and electric autapses. Sci China Tech Sci, 2015, 58: 1007–1014

    Article  Google Scholar 

  29. Liu S B, Wu Y, Li J J, et al. The dynamic behavior of spiral waves in stochastic Hodgkin–Huxley neuronal networks with ion channel blocks. Nonlinear Dyn, 2013, 73: 1055–1063

    Article  MathSciNet  Google Scholar 

  30. Sun X J, Shi X. Effects of channel blocks on the spiking regularity in clustered neuronal networks. Sci China Tech Sci, 2014, 57: 879–884

    Article  Google Scholar 

  31. Li Y Y, Gu H G. The influence of initial values on spatial coherence resonance in neuronal networks. Int J Bifurcat Chaos, 2015, 25: 1550104

    Article  MathSciNet  MATH  Google Scholar 

  32. Hodgkin A L. The local electric changes associated with repetitive action in a non-medullated axon. J Physiol, 1948, 107: 165–181

    Article  Google Scholar 

  33. Rinzel J, Ermentrout G B. Analysis of neural excitability and oscillations. In: Methods in Neural Modeling. Cambridge: The MIT Press, 1989. 135–171

    Google Scholar 

  34. Izhikevich E M. Neural excitability, spiking and bursting. Int J Bifurcat Chaos, 2000, 10: 1171–1266

    Article  MathSciNet  MATH  Google Scholar 

  35. Hansel D, Mato G, Meunier C. Synchrony in excitatory neural networks. Neural Comput, 1995, 7: 307–337

    Article  Google Scholar 

  36. Tateno T, Harsch A, Robinson H P C. Threshold firing frequency- current relationships of neurons in rat somatosensory cortex: Type 1 and type 2 dynamics. J Neurophysiol, 2004, 92: 2283–2294

    Article  Google Scholar 

  37. Tateno T, Robinson H P C. Rate coding and spike-time variability in cortical neurons with two types of threshold dynamics. J Neurophysiol, 2006, 95: 2650–2663

    Article  Google Scholar 

  38. Tsubo Y, Takada M, Reyes A D, et al. Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex. Eur J Neurosci, 2007, 25: 3429–3441

    Article  Google Scholar 

  39. Jia B, Gu H G, Li Y Y. Coherence-resonance-induced neuronal firing near a saddle-node and homoclinic bifurcation corresponding to type-I excitability. Chin Phys Lett, 2011, 28: 090507

    Article  Google Scholar 

  40. Jia B, Gu H G. Identifying type I excitability using dynamics of stochastic neural firing patterns. Cogn Neurodyn, 2012, 6: 485–497

    Article  Google Scholar 

  41. Prescott S A, Ratté S, Koninck Y D, et al. Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions. J Neurophysiol, 2008, 100: 3030–3042

    Article  Google Scholar 

  42. Gu H G, Chen S G. Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker. Sci China Tech Sci, 2014, 57: 864–871

    Article  Google Scholar 

  43. Gu H G, Zhao Z G. Dynamics of time delay-induced multiple synchronous behaviors in inhibitory coupled bursting neurons. PLoS One, 2015, 10: e0138593

    Google Scholar 

  44. Ermentrout G B. Type I membranes, phase resetting curves, and synchrony. Neural Comput, 1996, 8: 979–1001

    Article  Google Scholar 

  45. Galán R F, Bard Ermentrout G, Urban N N. Reliability and stochastic synchronization in type I vs type II neural oscillators. Neurocomputing, 2007, 70: 2102–2106

    Article  Google Scholar 

  46. Marella S, Ermentrout G. Class-II neurons display a higher degree of stochastic synchronization than class-I neurons. Phys Rev E, 2008, 77: 041918

    Article  MathSciNet  Google Scholar 

  47. Aushra A, Ermentrout G B. Type-II phase resetting curve is optimal for stochastic synchrony. Phys Rev E, 2009, 80: 011911

    Article  MathSciNet  Google Scholar 

  48. Bogaard A, Parent J, Zochowski M, et al. Interaction of cellular and network mechanisms in spatiotemporal pattern formation in neuronal networks. J Neurosci, 2009, 29: 1677–1687

    Article  Google Scholar 

  49. Smeal R M, Ermentrout G B, White J A. Phase-response curves and synchronized neural networks. Philos T Roy Soc B, 2010, 365: 2407–2422

    Article  Google Scholar 

  50. Jiao X F, Zhu D F. Phase-response synchronization in neuronal population. Sci China Tech Sci, 2014, 57: 923–928

    Article  Google Scholar 

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

    Article  Google Scholar 

  52. Tateno T, Pakdaman K. Random dynamics of the Morris-Lecar neural model. Chaos, 2004, 14: 511–530

    Article  MathSciNet  MATH  Google Scholar 

  53. Tsumoto K, Kitajima H, Yoshinaga T, et al. Bifurcations in Morris- Lecar neuron model. Neurocomputing, 2006, 69: 293–316

    Article  Google Scholar 

  54. Shen Y, Hou Z, Xin H. Transition to burst synchronization in coupled neuron networks. Phys Rev E, 2008, 77: 03192

    Article  Google Scholar 

  55. Gutkin B S, Ermentrout G B. Dynamics of membrane excitability determine inter-spike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comput, 1998, 10: 1047–1065

    Article  Google Scholar 

  56. Feng J F, Brown D. Coefficient of variation of interspike intervals greater than 0.5. How and when? Biol Cybern, 1999, 80: 291–297

    Article  MATH  Google Scholar 

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Xiao, W., Gu, H. & Liu, M. Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling. Sci. China Technol. Sci. 59, 1943–1952 (2016). https://doi.org/10.1007/s11431-016-6046-x

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  • DOI: https://doi.org/10.1007/s11431-016-6046-x

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