Skip to main content
Log in

Enhancement of spike coherence by the departure from Gaussian noise in a Hodgkin-Huxley neuron

  • Published:
Science in China Series B: Chemistry Aims and scope Submit manuscript

Abstract

Experimental study has shown that non-Gaussian noise exists in sensory systems like neurons. The departure from Gaussian behavior is a characteristic parameter of non-Gaussian noise. In this paper, we have numerically studied the effect of a particular kind of non-Gaussian colored noise (NGN), especially its departure q from Gaussian noise (q = 1), on the spiking activity in a deterministic Hodgkin-Huxley (HH) neuron driven by sub-threshold periodic stimulus. Simulation results show that the departure q can affect the spiking activity induced by noise intensity D. For smaller q values, the minimum in the variation coefficient (CV) as a function of noise intensity (D) becomes smaller, showing that D-induced stochastic resonance (SR) becomes strengthened. Meanwhile, depending on the value of D, q can either enhance or reduce the spiking regularity. Interestingly, CV changes non-monotonously with varying q and passes through a minimum at an intermediate q, representing the presence of “departure-induced SR”. This result shows that appropriate departures of the NGN can enhance the spike coherence in the HH neuron. Since the departure of the NGN determines the probability distribution and hence may denote the type of the noise, “departure-induced SR” shows that different types of noise can enhance the spike coherence, and hence may improve the timing precision of sub-threshold signal encoding in the HH neuron.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952, 117: 500–544

    CAS  Google Scholar 

  2. Lee S G, Kim S. Parameter dependence of stochastic resonance in the stochastic Hodgkin-Huxley neuron. Phys Rev E, 1999, 60: 826–830

    Article  CAS  Google Scholar 

  3. Chik D T W, Wang Y Q, Wang Z D. Stochastic resonance in a Hodgkin-Huxley neuron in the absence of external noise. Phys Rev E, 2001, 64: 021913

    Google Scholar 

  4. Wang S T, Liu F, Wang W, Yu Y G. Impact of spatially correlated noise on neuronal firing. Phys Rev E, 2004, 69: 011909

    Google Scholar 

  5. Yu Y G, Liu F, Wang W. Frequency sensitivity in Hodgkin-Huxley systems. Biol Cybern, 2001, 84: 227–235

    Article  CAS  Google Scholar 

  6. Yu Y G, Wang W, Wang J F, Liu F. Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems. Phys Rev E, 2001, 63: 021907

    Google Scholar 

  7. Lee S G, Neiman A, Kim S. Coherence resonance in a Hodgkin-Huxley neuron. Phys Rev E, 1998, 57: 3292–3297

    Article  CAS  Google Scholar 

  8. Wang Y Q, Chik D W T, Wang Z D. Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons. Phys Rev E, 2000, 61: 740–746

    Article  CAS  Google Scholar 

  9. Kwon O, Moon H T. Coherence resonance in small-world networks of excitable cells. Phys Lett A, 2002, 298: 319–324

    Article  CAS  Google Scholar 

  10. Wang M S, Hou Z H, Xin H W. Optimal network size for Hodgkin-Huxley neurons. Phys Lett A, 2005, 334: 93–97

    Article  CAS  Google Scholar 

  11. Lecar H, Nossal R. Theory of threshold fluctuations in nerves. Biophys J, 1971, 11:1048–1067

    Article  CAS  Google Scholar 

  12. White J A, Rubinstein J T, Kay A R. Channel noise in neurons. Trends Neurosci, 2000, 23: 131–137

    Article  CAS  Google Scholar 

  13. Fox R F, Lu Y. Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E, 1994, 49: 3421–3431

    Article  CAS  Google Scholar 

  14. Schneidman E, Freedman B, Segev I. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neuronal Comput, 1998, 10: 1679–1703

    Article  CAS  Google Scholar 

  15. Gammaitoni L, Hänggi P, Jung P, Marchesoni F. Stochastic resonance. Rev Mod Phys, 1998, 70: 223–287

    Article  CAS  Google Scholar 

  16. Jung P, Shuai J W. Optimal sizes of ion channel clusters. Europhys Lett, 2001, 56: 29–35

    Article  CAS  Google Scholar 

  17. Hänggi P. Stochastic resonance in biology-how noise can enhance detection of weak signals and help improve biological information processing. ChemPhysChem, 2002, 3: 285–290

    Article  Google Scholar 

  18. Gong Y B, Wang M S, Hou Z H, Xin H W. Optimal spike coherence and synchronization on complex Hodgkin-Huxley neuron networks. ChemPhysChem, 2005, 6: 1042–1047

    Article  CAS  Google Scholar 

  19. Shuai J W, Jung P. The dynamics of small excitable ion channel clusters. Chaos, 2006, 16: 026104

    Google Scholar 

  20. Schmid G, Goychuk I, Hänggi P. Channel noise and synchronization in excitable membranes. Physica A, 2003, 325: 165–175

    Article  Google Scholar 

  21. Casado J M. Synchronization of two Hodgkin-Huxley neurons due to internal noise. Phys Lett A, 2003, 310: 400–406

    Article  CAS  Google Scholar 

  22. Schmid G, Goychuk I, Hänggi P. Stochastic resonance as a collective property of ion channel assemblies. Europhys Lett, 2001, 56: 22–28

    Article  CAS  Google Scholar 

  23. Schmid G, Goychuk I, Hänggi P, Zeng S, Jung P. Stochastic resonance and optimal clustering for assemblies of ion channels. Fluct Noise Lett, 2004, 4: L33–L42

    Article  Google Scholar 

  24. Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F. Stochastic resonance on a circle. Phys Rev Lett, 1994, 72: 2125–2129

    Article  Google Scholar 

  25. Nozaki D, Mar D J, Grigg P, Collins J J. Effects of colored noise on stochastic resonance in sensory neurons. Phys Rev Lett, 1999, 82: 2402–2405

    Article  CAS  Google Scholar 

  26. Borland L. Ito-Langevin equations within generalized thermostatistics. Phys Lett A, 1998, 245: 67–72

    Article  CAS  Google Scholar 

  27. Borland L. Microscopic dynamics of the nonlinear Fokker-Planck equation: a phenomenological model. Phys Rev E, 1998, 57: 6634–6642

    Article  CAS  Google Scholar 

  28. Castro F J, Kuperman M N, Fuentes M A, Wio H S. Experimental evidence of stochastic resonance without tuning due to non-Gaussian noises. Phys Rev E, 2001, 64: 051105

    Google Scholar 

  29. Fuentes M A, Toral R, Wio H S. Enhancement of stochastic resonance: the role of non-Gaussian noises. Physica A, 2001, 295: 114–122

    Article  Google Scholar 

  30. Fuentes M A, Wio H S, Toral R. Effective Markovian approximation for non-Gaussian noises: a path integral approach. Physica A, 2002, 303: 91–104

    Article  Google Scholar 

  31. Wio H S, Revelli J A, Sánchez A D. Effect of non-Gaussian noises on the stochastic resonance-like phenomenon in gated traps. Physica D, 2002, 168: 165–170

    Article  Google Scholar 

  32. Fuentes M A, Tessone C J, Wio H S, Toral R. Stochastic resonance in bistable and excitable systems: Effect of non-Gaussian noises. Fluct Noise Lett, 2003, 3: L365–L371

    Article  Google Scholar 

  33. Wio H S, Toral R. Effect of non-Gaussian noise sources in a noise-induced transition. Physica D, 2004, 193: 161–168

    Article  Google Scholar 

  34. Bouzat S, Wio H S. Current and efficiency enhancement in Brownian motors driven by non-Gaussian noises. Eur Phys J B, 2004, 41: 97–105

    Article  CAS  Google Scholar 

  35. Bouzat S, Wio H S. New aspects on current enhancement in Brownian motors driven by non-Gaussian noises. Physica A, 2005, 351: 69–78

    Article  Google Scholar 

  36. Majee P, Goswami G, Bag B C. Colored non-Gaussian noise induced resonant activation. Chem Phys Lett, 2005, 416: 256–260

    Article  CAS  Google Scholar 

  37. Goswami G, Majee P, Kumar Ghosh P, Bag B C. Colored multiplicative and additive non-Gaussian noise-driven dynamical system: Mean first passage time. Physica A, 2007, 374: 549–558

    Article  Google Scholar 

  38. Bag B C, Hu C K. Escape through an unstable limit cycle driven by multiplicative colored non-Gaussian and additive white Gaussian noises. Phys Rev E, 2007, 75: 042101

    Google Scholar 

  39. Wu D, Luo X Q, Zhu S Q. Stochastic system with coupling between non-Gaussian and Gaussian noise terms. Physica A, 2007, 373: 203–214

    Article  Google Scholar 

  40. Wu D, Zhu S Q. Stochastic resonance in a bistable system with time-delayed feedback and non-Gaussian noise. Phys Lett A, 2007, 363: 202–212

    Article  CAS  Google Scholar 

  41. Mangioni S E, Wio H S. A random walker on a ratchet potential: effect of a non-Gaussian noise. Eur Phys J B, 2008, 61: 67–73

    Article  CAS  Google Scholar 

  42. Wang M S, Hou Z H, Xin H W. Double-system size resonance for spiking activity of coupled Hodgkin-Huxley neurons. ChemPhysChem, 2004, 5: 1602–1605

    Article  CAS  Google Scholar 

  43. Gong Y B, Xu B, Xu Q, Yang C L, Ren T Q, Hou Z H, Xin H W. Ordering spatiotemporal chaos in complex thermo-sensitive neuron networks. Phys Rev E, 2006, 73: 046137

    Google Scholar 

  44. Lee DeVille R E, Vanden-Eijnden E, Muratov C B. Two distinct mechanisms of coherence in randomly perturbed dynamical systems. Phys Rev E, 2005, 72: 031105

  45. Liu F, Wang J F, Wang W. Frequency sensitivity in weak signal detection. Phys Rev E, 1999, 59: 3453–3460

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to YuBing Gong.

Additional information

Supported by the Science Foundation of Ludong University (L20072805)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xie, Y., Gong, Y. & Hao, Y. Enhancement of spike coherence by the departure from Gaussian noise in a Hodgkin-Huxley neuron. Sci. China Ser. B-Chem. 52, 1186–1191 (2009). https://doi.org/10.1007/s11426-009-0177-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11426-009-0177-x

Keywords

Navigation