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.
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References
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
Lee S G, Kim S. Parameter dependence of stochastic resonance in the stochastic Hodgkin-Huxley neuron. Phys Rev E, 1999, 60: 826–830
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
Wang S T, Liu F, Wang W, Yu Y G. Impact of spatially correlated noise on neuronal firing. Phys Rev E, 2004, 69: 011909
Yu Y G, Liu F, Wang W. Frequency sensitivity in Hodgkin-Huxley systems. Biol Cybern, 2001, 84: 227–235
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
Lee S G, Neiman A, Kim S. Coherence resonance in a Hodgkin-Huxley neuron. Phys Rev E, 1998, 57: 3292–3297
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
Kwon O, Moon H T. Coherence resonance in small-world networks of excitable cells. Phys Lett A, 2002, 298: 319–324
Wang M S, Hou Z H, Xin H W. Optimal network size for Hodgkin-Huxley neurons. Phys Lett A, 2005, 334: 93–97
Lecar H, Nossal R. Theory of threshold fluctuations in nerves. Biophys J, 1971, 11:1048–1067
White J A, Rubinstein J T, Kay A R. Channel noise in neurons. Trends Neurosci, 2000, 23: 131–137
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
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
Gammaitoni L, Hänggi P, Jung P, Marchesoni F. Stochastic resonance. Rev Mod Phys, 1998, 70: 223–287
Jung P, Shuai J W. Optimal sizes of ion channel clusters. Europhys Lett, 2001, 56: 29–35
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
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
Shuai J W, Jung P. The dynamics of small excitable ion channel clusters. Chaos, 2006, 16: 026104
Schmid G, Goychuk I, Hänggi P. Channel noise and synchronization in excitable membranes. Physica A, 2003, 325: 165–175
Casado J M. Synchronization of two Hodgkin-Huxley neurons due to internal noise. Phys Lett A, 2003, 310: 400–406
Schmid G, Goychuk I, Hänggi P. Stochastic resonance as a collective property of ion channel assemblies. Europhys Lett, 2001, 56: 22–28
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
Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F. Stochastic resonance on a circle. Phys Rev Lett, 1994, 72: 2125–2129
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
Borland L. Ito-Langevin equations within generalized thermostatistics. Phys Lett A, 1998, 245: 67–72
Borland L. Microscopic dynamics of the nonlinear Fokker-Planck equation: a phenomenological model. Phys Rev E, 1998, 57: 6634–6642
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
Fuentes M A, Toral R, Wio H S. Enhancement of stochastic resonance: the role of non-Gaussian noises. Physica A, 2001, 295: 114–122
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
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
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
Wio H S, Toral R. Effect of non-Gaussian noise sources in a noise-induced transition. Physica D, 2004, 193: 161–168
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
Bouzat S, Wio H S. New aspects on current enhancement in Brownian motors driven by non-Gaussian noises. Physica A, 2005, 351: 69–78
Majee P, Goswami G, Bag B C. Colored non-Gaussian noise induced resonant activation. Chem Phys Lett, 2005, 416: 256–260
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
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
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
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
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
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
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
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
Liu F, Wang J F, Wang W. Frequency sensitivity in weak signal detection. Phys Rev E, 1999, 59: 3453–3460
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Supported by the Science Foundation of Ludong University (L20072805)
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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
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DOI: https://doi.org/10.1007/s11426-009-0177-x