Dynamical response of the Hodgkin-Huxley model in the high-input regime.

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability, and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for the different features appearing in the interspike-interval distributions (like multimodality and exponential tails) are clearly identified in the various regimes.

[1]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[2]  H. Hasegawa,et al.  Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  J. Leroy Folks,et al.  The Inverse Gaussian Distribution , 1989 .

[4]  Jian-Xue Xu,et al.  Resonance in a noise-driven excitable neuron model , 2002 .

[5]  Jianfeng Feng,et al.  Impact of Poisson synaptic inputs with a changing rate on weak-signal processing , 2003 .

[6]  Lutz Schimansky-Geier,et al.  Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  E. Manjarrez,et al.  Internal stochastic resonance in the coherence between spinal and cortical neuronal ensembles in the cat , 2002, Neuroscience Letters.

[8]  Adrienne L. Fairhall,et al.  Computation in a Single Neuron: Hodgkin and Huxley Revisited , 2002, Neural Computation.

[9]  Jianfeng Feng,et al.  Variability of Firing of Hodgkin-Huxley and FitzHugh-Nagumo Neurons with Stochastic Synaptic Input , 1999 .

[10]  Anishchenko,et al.  Dynamical Entropies Applied to Stochastic Resonance , 1996, Physical review letters.

[11]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[12]  Idan Segev,et al.  Playing the Devil's advocate: is the Hodgkin–Huxley model useful? , 2002, Trends in Neurosciences.

[13]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[14]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[15]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[16]  H. Haken,et al.  Stochastic resonance without external periodic force. , 1993, Physical review letters.

[17]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[18]  B. M. Fulk.  MATH , 1992 .

[19]  W. Precht.  The synaptic organization of the brain G.M. Shepherd, Oxford University Press (1975). 364 pp., £3.80 (paperback) , 1976, Neuroscience.

[20]  R B Stein,et al.  The threshold conditions for initiation of action potentials by excitable cells , 1966, The Journal of physiology.

[21]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[22]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[23]  P. Parmananda,et al.  Experimental evidence of coexisting periodic stochastic resonance and coherence resonance phenomena. , 2004, Physical review letters.

[24]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[25]  H. Tuckwell.  Introduction to Theoretical Neurobiology: Linear Cable Theory and Dendritic Structure , 1988 .

[26]  Christof Koch,et al.  Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience Series) , 1998 .

[27]  P. Grassberger.  Entropy Estimates from Insufficient Samplings , 2003, physics/0307138.

[28]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[29]  T. Sejnowski,et al.  Correlated neuronal activity and the flow of neural information , 2001, Nature Reviews Neuroscience.

[30]  G. Shepherd.  The Synaptic Organization of the Brain , 1979 .

[31]  Claude E. Shannon,et al.  A mathematical theory of communication , 1948, MOCO.

[32]  J. Rinzel,et al.  Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations , 1980 .

[33]  Tetsuya Shimokawa,et al.  Coherence resonance and discharge time reliability in neurons and neuronal models , 2001, Neural Networks.

[34]  Alexander B. Neiman,et al.  Coherence resonance in a Hodgkin-Huxley neuron , 1998 .

[35]  J Rinzel,et al.  A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions. , 1983, Journal of theoretical biology.

[36]  F. Liu,et al.  Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[38]  奥仲 哲弥,et al.  肺門部早期肺癌に対する光線力学的治療法(肺門部早期癌の診断と治療)(第 18 回日本気管支学会総会特集号) , 1995 .

[39]  A. Longtin.  AUTONOMOUS STOCHASTIC RESONANCE IN BURSTING NEURONS , 1997 .

[40]  Minying Chen,et al.  187 , 2022 .

[41]  T. Sejnowski,et al.  Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  I. Raman,et al.  The kinetics of the response to glutamate and kainate in neurons of the avian cochlear nucleus , 1992, Neuron.

[43]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[44]  D. Signorini,et al.  Neural networks , 1995, The Lancet.