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Chemical synaptic coupling-induced delay-dependent synchronization transitions in scale-free neuronal networks

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Abstract

Chemical synaptic couplings are more common than electric (gap junction) connections in neurons. In this paper, the firing synchronizations induced by chemical synaptic coupling in chemically delayed scale-free networks of modified Hodgkin-Huxley neurons have been studied. It was found that the chemical coupling-induced synchronization transitions are delay-dependent and much different for various delay lengths. In the absence of delay, the neurons exhibit a transition from chaotic bursting (CB) to bursting synchronization (BS) with desynchronized spikes in each burst; for smaller delay lengths, the firing evolves from CB to spiking synchronization (SS), but for larger delay lengths, there are transitions from CB to intermittently multiple SS behaviors. These findings show that the chemical coupling-induced firing synchronization transitions strongly depend on the chemical delay lengths, and intermittently multiple SS can only occur for larger delay lengths. This result would be helpful for better understanding the joint roles of the chemical coupling and chemical delay in the firing activity of the neurons.

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References

  1. Singer W. Synchronization of cortical activity and its putative role in information processing and learning. Annu Rev Physiol, 1993, 55: 349–374

    Article  CAS  Google Scholar 

  2. Gray CM. The temporal correlation hypothesis of visual feature integration: still alive and well. Neuron, 1999, 24: 31–47

    Article  CAS  Google Scholar 

  3. Fries P, Nikolić D, Singer W. The gamma cycle. Trends Neurosci, 2007, 30: 309–316

    Article  CAS  Google Scholar 

  4. Levy R, Hutchison WD, Lozano AM, Dostrovsky JO. Highfrequency synchronization of neuronal activity in the sub-thalamic nucleus of Parkinsonian patients with limb tremor. J Neurosci, 2000, 20: 7766–7775

    CAS  Google Scholar 

  5. Mormann F, Kreuz T, Andrzejak RG, David P, Lehnertz K, Elger CE. Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Res, 2003, 53: 173–185

    Article  Google Scholar 

  6. Zhou CS, Kurths J. Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. Chaos, 2003, 13: 401–409

    Article  Google Scholar 

  7. Bahar S. Burst-enhanced synchronization in an array of noisy coupled neurons. Fluct Noise Lett, 2004, 4: L87–L96

    Article  Google Scholar 

  8. Yoshioka M. Chaos synchronization in gap-junction-coupled neurons. Phys Rev E, 2005, 71: 065203 (R)

    Google Scholar 

  9. Wang QY, Lu QS, Chen GR. Subthreshold stimulus-aided temporal order and synchronization in a square lattice noisy neuronal network. Europhys Lett, 2007, 77: 10004

    Article  Google Scholar 

  10. Hasegawa H. Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings. Phys Rev E, 2005, 72: 056139

    Article  Google Scholar 

  11. Gong YB, Wang MS, Hou ZH, Xin HW. Optimal spike coherence and synchronization on complex Hodgkin-Huxley neuron networks. ChemPhysChem, 2005, 6: 1042–1047

    Article  CAS  Google Scholar 

  12. Gong YB, Xu B, Xu Q, Yang CL, Ren TQ, Hou ZH, Xin HW. Ordering spatiotemporal chaos in complex thermosensitive neuron networks. Phys Rev E, 2006, 73: 046137

    Article  Google Scholar 

  13. Wei DQ, Luo XS. Ordering spatiotemporal chaos in discrete neural networks with small-world connections. Europhys Lett, 2007, 78: 68004

    Article  Google Scholar 

  14. Zheng YH, Lu QS. Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Physica A, 2008, 387: 3719–3728

    Google Scholar 

  15. Wang QY, Lu QS, Chen GR. Ordered bursting synchronization and complex wave propagation in a ring neuronal network. Physica A, 2007, 374: 869–878

    Article  Google Scholar 

  16. Ibarz B, Cao HJ, Sanjuán MAF. Bursting regimes in map-based neuron models coupled through fast threshold modulation. Phys Rev E, 2008, 77: 051918

    Article  Google Scholar 

  17. Perc M. Optimal spatial synchronization on scale-free networks via noisy chemical synapses. Biophys Chem, 2009, 141: 175–179

    Article  CAS  Google Scholar 

  18. Shen Y, Hou ZH, Xin HW. Transition to burst synchronization in coupled neuron networks. Phys Rev E, 2008, 77: 031920

    Article  Google Scholar 

  19. Postnova S, Voigt K, Braun HA. Neural synchronization at tonic-to-bursting transitions. J Biol Phys, 2007, 33: 129–143

    Article  Google Scholar 

  20. Sporns O, Chialvo DR, Kaiser M, Hilgetag CC. Organization, development and function of complex brain networks. Trends Cogn Sci, 2004, 8: 418–425

    Article  Google Scholar 

  21. Zhou C, Zemanova L, Zamora G, Hilgetag CC, Kurths J. Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys Rev Lett, 2006, 97: 238103

    Article  Google Scholar 

  22. EguÍluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Phys Rev Lett, 2005, 94: 018102

    Article  Google Scholar 

  23. Kandel ER, Schwartz JH, Jessell TM. Principles of Neural Science. Amsterdam: Elsevier, 1991

    Google Scholar 

  24. Dhamala M, Jirsa VK, Ding MZ. Enhancement of neural synchrony by time delay. Phys Rev Lett, 2004, 92: 074104

    Article  Google Scholar 

  25. Rossoni E, Chen YH, Ding MZ, Feng JF. Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling. Phys Rev E, 2005, 71: 061904

    Article  Google Scholar 

  26. Ko T-W, Ermentrout GB. Effects of axonal time delay on synchronization and wave formation in sparsely coupled neuronal oscillators. Phys Rev E, 2007, 76: 056206

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Wang QY, Perc M, Duan ZS, Chen GR. Delay-induced multiple stochastic resonances on scale-free neuronal networks. Chaos, 2009, 19: 023112

    Article  Google Scholar 

  29. Wang QY, Perc M, Duan ZS, Chen GR. Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks. Phys Lett A, 2008, 372: 5681–5687

    Article  CAS  Google Scholar 

  30. Wang QY, Duan ZS, Perc M, Chen GR. Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability. Europhys Lett, 2008, 83: 50008

    Article  Google Scholar 

  31. Wang QY, Perc M, Duan ZS, Chen GR. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E, 2009, 80: 026206

    Article  Google Scholar 

  32. BuriĆ N, TodoroviĆ K, VasoviĆ N. Synchronization of bursting neurons with delayed chemical synapses. Phys Rev E, 2008, 78: 036211

    Article  Google Scholar 

  33. Wang QY, Lu QS, Chen GR, Feng ZS, Duan LX. Bifurcation and synchronization of synaptically coupled FHN models with time delay. Chaos, Solitons & Fractals, 2009, 39: 918–925

    Article  Google Scholar 

  34. Wang QY, Lu QS, Chen GR. Synchronization transition by synaptic delay in coupled fast spiking neurons. Int J Bifurcat Chaos, 2008, 18: 1189–1198

    Article  Google Scholar 

  35. Wang QY, Perc M, Duan ZS, Chen GR. Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling. Physica A, 2010, 389: 3299–3306

    Article  Google Scholar 

  36. Goh K-I, Kahng B, Kim D. Universal behavior of load distribution in scale-free networks. Phys Rev Lett, 2001, 87: 278701

    Article  CAS  Google Scholar 

  37. Braun HA, Huber MT, Dewald M, Schafer K, Voigt K. Computer simulations of neuronal signal transduction: the role of nonlinear dynamics and noise. Int J Bifurcation Chaos, 1998, 8: 881–889

    Article  Google Scholar 

  38. Destexhe A, Mainen ZF, Sejnowski TJ. An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comput, 1994, 6: 14–18

    Article  Google Scholar 

  39. Feudel U, Neiman A, Pei X, Wojtenek W, Braun H, Huber M, Moss F. Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos, 2000, 10: 231–239

    Article  Google Scholar 

  40. Steriade M, McCormick DA, Sejnowski TJ. Thalamocortical oscillations in the sleeping and aroused brain. Science, 1993, 262: 679–685

    Article  CAS  Google Scholar 

  41. Amzica F, Steriade M. Electrophysiological correlates of sleep delta waves. Electroencephalogr Clin Neurophysiol, 1998, 2: 69–83

    Google Scholar 

  42. Riehle A, Grün S, Diesmann M, Aertsen A. Spike synchronization and rate modulation differentially involved in motor cortical function. Science, 1997, 278: 1950–1953

    Article  CAS  Google Scholar 

  43. Grammont F, Riehle A. Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time. Biol Cybern, 2003, 88: 360–373

    Article  CAS  Google Scholar 

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  1. School of Physics, Ludong University, Yantai, 264025, China

    YuBing Gong, Xiu Lin, Li Wang & YingHang Hao

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  1. YuBing Gong
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  2. Xiu Lin
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  3. Li Wang
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  4. YingHang Hao
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Correspondence to YuBing Gong.

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Gong, Y., Lin, X., Wang, L. et al. Chemical synaptic coupling-induced delay-dependent synchronization transitions in scale-free neuronal networks. Sci. China Chem. 54, 1498–1503 (2011). https://doi.org/10.1007/s11426-011-4363-2

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  • DOI: https://doi.org/10.1007/s11426-011-4363-2

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