Interspike interval statistics in the stochastic Hodgkin-Huxley model: Coexistence of gamma frequency bursts and highly irregular firing

Neural Computation

Volumn 19, Issue 5, 2007, Pages 1215-1250

  Rowat, Peter ^a  

^a UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SODIUM CHANNEL;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; ELECTROSTIMULATION; METHODOLOGY; NERVE CELL; NONLINEAR SYSTEM; NORMAL DISTRIBUTION; PERIODICITY; PHYSIOLOGY; PROBABILITY; RADIATION EXPOSURE; STATISTICS; TIME;

ACTION POTENTIALS; ANIMALS; ELECTRIC STIMULATION; MODELS, NEUROLOGICAL; NEURONS; NONLINEAR DYNAMICS; NORMAL DISTRIBUTION; PERIODICITY; PROBABILITY; SODIUM CHANNELS; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 34247898815     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2007.19.5.1215     Document Type: Article

References (73)

1. Armstrong-James, M. (1975). Functional status and columnar organization of single cells responding to cutaneous stimulation in neonatal rat somatosensory cortex S1. J. Physiol., 246, 501-538.
2. Azouz, R., & Gray, C. (2000). Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proc. Natl. Acad. Sci., 97(14), 8110-8115.
3. Bassant, M. (1976). Analyse statistique de l'activité des cellules pyramidales de l'hippocampe dorsal du lapin. Electroencephal. Clinical Neurophysiology, 40, 585-603.
4. Berglund, N., & Gentz, B. (2003). Geometric singular perturbation theory for stochastic differential equations. J. Differential Equations, 191, 1-54.
5. Best, E. (1979). Null space in the Hodgkin-Huxley equations. Biophysical J., 27, 87-104.
6. Brette, R. (2003). Reliability of spike timing is a general property of spiking model neurons. Neural Computation, 15, 279-308.
7. Burns, B., & Webb, A. (1976). The spontaneous activity of neurones in the cat's cerebral cortex. Proc. R. Soc. Lond. B, 194, 211-223.
8. Cauli, B., Audinat, E., Lambolez, B., Angulo, M. C., Ropert, N., Tsuzuki, K., Hestrin, S., & Rossier, J. (1997). Molecular and physiological diversity of cortical nonpyramidal cells. J. Neuroscience, 17(10), 3894-3906.
9. Chow, C. C., & White, J. A. (1996). Spontaneous action potentials due to channel fluctations. Biophysical J., 71, 3013-3021.
10. de Ruyter van Steveninck, R., Lewen, G., Strong, S. P., Koberle, R., & Bialek, W. (1997). Reproducibility and variability in neural spike trains. Science, 275, 1805-1808.
11. Dean, A. (1981). The variability of discharge of simple cells in the cat striate cortex. Experimental Brain Research, 44, 437-440.
12. Destexhe, A., M. Rudolph, Fellous, J., & Sejnowski, T. J. (2001). Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience, 107(1), 13-24.
13. Dorval, A., & White, J. (2005). Channel noise is essential for perithreshold oscillations in entorhinal stellate neurons. J. Neurosci., 25(43), 10025-10028.
14. Duchamp-Viret, P., Kostal, L., Chaput, M., Lansky, P., & Rospars, J.-P. (2005). Patterns of spontaneous activity in single rat olfactory receptor neurons are different in normally breathing and tracheotomized animals. J. Neurobiology, 65(2), 97-14.
15. Fitzhugh, R. (1961). Impulses and physiological states in models of nerve membrane. Biophys. J., 1, 445-166.
16. Gerstein, G., & Kiang, N. Y.-S. (1960). Approach to the quantitative analysis of electrophysiological data from single neurons. Biophys. J., 6, 15-28.
17. Gerstein, G., & Mandelbrot, B. (1964). Random walk models for the spike activity of a single neuron. Biophys. J., 4, 41-68.
18. Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Physical Chemistry, 81(25), 2340-2361.
19. Guckenheimer, J., & Labouriau, I. S. (1993). Bifurcation of the Hodgkin-Huxley equations: A new twist. Bull. Math. Biol., 55, 937-952.
20. Guckenheimer, J., & Oliva, R. A. (2002). Chaos in the Hodgkin-Huxley model. SIAM J. Applied Dynamical Systems, 1(1), 105-114.
21. Gutkin, B. S., & Ermentrout, G. B. (1998). Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Computation, 10(5), 1047-1065.
22. Guttman, R., & Barnhill, R. (1970). Oscillation and repetitive firing in squid axons. Journal of general Physiology, 55, 104-118.
23. Guttman, R., Lewis, S., & Rinzel, J. (1980). Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator. J. Physiology, 305, 377-395.
24. Hassard, B. (1978). Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon. J. Theor. Biology, 71, 401-420.
25. Hille, B. (2001). Ion channels of excitable membranes (3rd ed.). Sunderland, MA: Sinauer.
26. Hodgkin, A. (1948). The local electrical changes associated with repetitive action in a non-medullated axon. J. Physiol., 107, 165-181.
27. Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117, 500-544.
28. Holt, G., Softky, W., Koch, C., & Douglas, R. J. (1996). Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. J. Neurophysiol., 75(5), 1806-1814.
29. Kiang, N. Y.-S. (1965). Discharge patterns of single fibers in the cat's auditory nerve. Cambridge, MA: MIT Press.
30. Klink, R., & Alonso, A. (1993). Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer II neurons. J. Neurosci., 70(1), 144-157.
31. h channels in pyramidal neuron dendrites: Properties, distribution, and impact on action potential output. J. Neurosci., 26(6), 1677-1687.
32. Labouriau, I. S. (1985). Degenerate Hopf bifurcation and nerve impulse. SIAM J. Math. Anal., 16(6), 1121-1133.
33. Lamarre, Y., Filion, M., & Cordeau, J. P. (1971). Neuronal discharges of the ventral nucleus of the thalamus during sleep and wakefulness in the cat. I. Spontaneous activity. Experimental Brain Research, 12, 480-498.
34. Lee, S.-G., Neiman, A., & Kim, S. (1998). Coherence resonance in a Hodgkin-Huxley neuron. Physical Review E, 57(3), 3292-3297.
35. Lindner, B., Garica-Ojalvo, J., Nerman, A., & Schimansky-Geier, L. (2004). Effects of noise in excitable systems. Physics Reports, 392(6), 321-424.
36. Lynch, J., & Barry, P. (1989). Action potentials initiated by single channels opening in a small neuron (rat olfactory receptor). Biophys. J., 55, 755-768.
37. Mainen, Z., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503-1506.
38. Mann-Metzer, P., & Yarom, Y. (2002). Jittery trains induced by synaptic-like currents in cerebellar inhibitory interneurons. J. Neurophysiol., 87, 149-156.
39. Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., & Caizhi, W. (2004). Interneurons of the neocortical inhibitory system. Nature Reviews Neuroscience, 5, 793-807.
40. Matsumoto, M., & Nishimura, T. (1998). Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. on Modeling and Computer Simulation, 8(1), 3-30.
41. McDonald, S. W., Grebogi, C., Ott, E., & Yorke, J. A. (1985). Fractal basin boundaries. Physica D, 17, 125-153.
42. Meunier, C., & Segev, I. (2002). Playing the devil's advocate: Is the Hodgkin-Huxley model useful? TINS, 25(11), 558-563.
43. Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophys. J., 35, 193-213.
44. Nakahama, H., Suzuki, H., Yamamoto, M., & Aikawa, S. (1968). A statistical analysis of spontaneous activity of central single neurons. Physiology and Behavior, 3(5), 745-752.
45. Noda, H., & Adey, R. (1970). Firing variability in cat association cortex during sleep and wakefulness. Brain Research, 18, 513-526.
46. Pfeiffer, R., & Kiang, N. Y.-S. (1965). Spike discharge patterns of spontaneous and continuously stimulated activity in the cochlear nucleus of anaesthetized cats. Biophysical Journal, 5, 301-316.
47. Poggio, G., & Viernstein, J. (1964). Time series analysis of impulse sequences of thalamic somatic sensory neurons. J. Neurophysiol., 27, 517-545.
48. Rinzel, J., & Ermentrout, G. B. (1998). Analysis of neural excitability and oscillations. K. Koch & I. Segev (Eds.), In Methods in neuronal modeling (pp. 251-291). Cambridge, MA: MIT Press.
49. Rinzel, J., & Miller, R. (1980). Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Mathematical Biosciences, 49, 27-59.
50. Rospars, J.-P., Lansky, P., Vaillant, J., Duchamp-Viret, P., & Duchamp, A. (1994). Spontaneous activity of first- and second-order neurons in the frog olfactory system. Brain Research, 662, 31-44.
51. Rowat, P., & Elson, R. (2004). State-dependent effects of Na-channel noise on neuronal burst generation. J. Comput. Neuroscience, 16, 87-112.
52. Rudolph, M., & Destexhe, A. (2002). Point-conductance models of cortical neurons with high discharge variability. Neurocomputing, 44-46, 147-152.
53. Ruggero, M. (1973). Response to noise of auditory nerve fibers in the squirrel monkey. J. Neurophysiol., 36, 569-587.
54. Schneidman, E., Freedman, B., & Segev, I. (1998). Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Computation, 10(7), 1679-1703.
55. Shadlen, M., & Newsome, W. (1998). The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J. Neuroscience, 18(10), 3870-3896.
56. Siebler, M., Koller, H., Stichel, C. C., Muller, H. W., & Freund, H. J. (1993). Spontaneous activity and recurrent inhibition in cultured hippocampal networks. Synapse, 14, 206-213.
57. Sigworth, F. (1980). The variance of sodium current fluctuation at the node of Ranvier. J. Physiol., 307, 97-129.
58. Softky, W., & Koch, K. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neuroscience, 13(1), 334-350.
59. Stein, R. (1965). A theoretical analysis of neuronal variability. Biophys. J., 5, 173-194.
60. Stevens, C. F., & Zador, A. M. (1998). Input synchrony and the irregular firing of cortical neurons. Nature Neuroscience, 1(3), 210-217.
61. +-kinetics. Manuscript in preparation.
62. Su, J., Rubin, J., & Terman, D. (2004). Effects of noise on elliptic bursters. Nonlinearity, 17, 133-157.
63. Tateno, T., Harsch, A., & Robinson, H. P. C. (2004). Threshold firing frequency-current relationships of neurons in rat somatosensory cortex: Type 1 and type 2 dynamics. J. Neurophysiol., 92, 2283-2294.
64. Tateno, T., & Pakdaman, K. (2004). Random dynamics of the Morris-Lecar model. Chaos, 14(3), 511-530.
65. Tiesenga, P., Jose, J., & Sejnowski, J. (2000). Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltagegated channels. Phys. Review E, 62(6), 8413-8419.
66. Troy, W. C. (1978). The bifurcation of periodic solutions in the Hodgkin-Huxley equations. Quarterly Journal of Applied Mathematics, 36, 73-83.
67. Troyer, T., & Miller, K. (1997). Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Computation, 9(5), 971-983.
68. Werner, G., & Mountcastle, V. (1963). The variability of central neural activity in a sensory system, and its implications for the central reflection of sensory events. J. Neurophysiol., 26, 958-977.
69. White, J. A., Klink, R., Alonso, A., & Kay, A. P. (1998). Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J. Neurophysiol., 80, 262-269.
70. White, J. A., Rubinstein, J. T., & Kay, A. P. (2000). Channel noise in neurons. Trends in Neurosciences, 23(3), 131-137.
71. Whitsel, B., Schreiner, R., & Essick, G. K. (1977). An analysis of variability in somatosensory cortical neuron discharge. J. Neurophysiol., 40(3), 589-607.
72. Wilbur, W., & Rinzel, J. (1983). A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distribution. J. Theoretical Biology, 105, 345-368.
73. Yu, X., & Lewis, E. R. (1989). Studies with spike initiators: Linearization by noise allows continuous signal modulation in neural networks. IEEE Trans. Biomedical Eng., 36(1), 36-43.