Advertisement

Journal of Computational Neuroscience

, Volume 16, Issue 2, pp 87–112 | Cite as

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

  • Peter F. Rowat
  • Robert C. Elson
Article

Abstract

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.

During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.

During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.

We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.

bursting stochastic ion channels channel noise spike time jitter ISI variability chaotic bursting burst length distribution burst length variability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agmon A, Connors B (1989) Repetitive burst-firing neurons in the deep layers of mouse somatosensory cortex. Neurosci. Lett. 99: 137-141.Google Scholar
  2. Arvanitaki A, Chalazonitis N (1967) Electrical properties and temporal organization in oscillatory neurons (Aplysia). In: Neurobiology of Invertebrates. Plenum: Salanki, New York, pp. 169-199.Google Scholar
  3. Bal T, Nagy F, et al. (1988) The pyloric central pattern generator in crustacea: A set of conditional neuronal oscillators. J. Comp. Physiol. 163: 715-727.Google Scholar
  4. Braun H, Huber M, et al. (2000) Interactions between slow and fast conductances in the Huber/Braun model of cold-receptor discharges. Neurocomputing 32: 51-59.Google Scholar
  5. Braun H, Wissing H, et al. (1994) Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367: 270-273.Google Scholar
  6. Braun HA, Huber MT, et al. (2001) Noise-induced impulse pattern modifications at different period-one situations in a computer model of temperature encoding. Biosystems 62(1-3): 99-112.Google Scholar
  7. Braun HA, Huber MT, et al. (1998) Computer simulations of neuronal signal transduction: the role of nonlinear dynamics and noise. Int. J. Bifurcation and Chaos 8(5): 881-889.Google Scholar
  8. Calvin WH, Stevens CF (1968) Synaptic noise and other sources of randomness in motoneuron interspike intervals. J. Neurophysiol. 31: 574-587.Google Scholar
  9. Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys. J. 71: 3013-3021.Google Scholar
  10. Collins JJ, Chow CC, et al. (1995) Stochastic resonance without tuning. Nature 376: 236-238.Google Scholar
  11. Conti F, Wanke E (1975) Channel noise in nerve membranes and lipid bilayers. Quarterly Reviews of Biophysics 8(4): 451-506.Google Scholar
  12. Cymbalyuk GS, Gaudry Q, et al. (2002) Bursting in leech heart interneurons: Cell-autonomous and network-based mechanisms. J. Neurosci. 22(24): 10580-10592.Google Scholar
  13. Elson RC, Huerta R, et al. (1999) Dynamical control of irregular bursting in an identified neuron of an oscillatory circuit. J. Neurophysiol. 82: 115-122.Google Scholar
  14. Faure P, Korn H (1997) A nonrandom dynamic component in the synaptic noise of a central neuron. Proc. Natl. Acad. Sci. USA 94(12): 6506-6511.Google Scholar
  15. Feudel U, Neiman A, et al. (2000) Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos 10(1): 231-239.Google Scholar
  16. Fox RF (1997) Stochastic versions of the Hodgkin-Huxley equations. Biophysical Journal 72(5): 2068-2074.Google Scholar
  17. Fox RF, Lu Y (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phy. Rev. E 49(5): 3421-3431.Google Scholar
  18. Guckenheimer J, Rowat PF (1997) Dynamical systems analyses of real neuronal networks. In: PS Stein, S Grillner, AI Selverston and DG Stuart, eds. Neurons, Networks, Motor Behavior, MIT Press, pp. 151-163.Google Scholar
  19. Hartline DK, Russell DF (1984) Endogenous burst capability in a neuron of the gastric mill pattern generator of the spiny lobster Panulirus interruptus. J. Neurobiol. 15(5): 345-364.Google Scholar
  20. Hille B (2001) Ion Channels of Excitable Membranes, 3rd ed. Sunderland, Mass., Sinauer.Google Scholar
  21. Hodgkin AL, Huxley AF (1952) A quantitive description of membrane current and its applications to conductiion and excitation in nerve. J. Physiol. (Lond.) 116: 500-544.Google Scholar
  22. Hunter J, Milton J (2003) Amplitude and frequency dependence of spike timing: implications for dynamic regulation. J Neurophysiol. 90: 387-394.Google Scholar
  23. Hunter J, Milton J, Thomas PJ, Cowan JD (1998) Resonance effect for neural spike time reliability. J Neurophysiol. 80: 1427-1438.Google Scholar
  24. Hutcheon B, Yarom Y (2000) Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci. 23(5): 216-222.Google Scholar
  25. Izhikevich E (2000) Neural excitability, spiking, and bursting. Int. J. Bifurcations and Chaos 10(6): 1171-1266.Google Scholar
  26. Kandel E, Spencer W (1961) Electrophysiology of hippocampal neurons. II. After-potentials and repetitive firing. J. Neurophysiol. 24: 243-259.Google Scholar
  27. Kantz H, Schreiber T (1997) Nonlinear Time Series Analysis. Cambridge, Cambridge University Press.Google Scholar
  28. Kay AR, Sugimori M, Llinas R (1998) Kinetic and stochastic properties of a persistent sodium current in mature guinea pig cerebellar purkinje cells. J. Neurophysiol. 80(3): 1167-1179.Google Scholar
  29. Kepecs A, Wang X-J (2000) Analysis of complex bursting in cortical pyramidal neuron models. Neurocomputing 32/33: 181-187.Google Scholar
  30. Kepler TB, Marder E, Abbott LF (1990) The effect of electrical coupling on the frequency of model neuronal oscillators. Science 248(4951): 83-85.Google Scholar
  31. Kiehn O (1991) Plateau potentials and active integration in the 'final common pathway' for motor behavior. TINS 14(2): 68-73.Google Scholar
  32. Klink R, Alonso A (1993) Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer-II neurons. J Neurophysiol. 70: 144-157.Google Scholar
  33. LeCar H, Nossal R (1971) Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. Biophysical. J 11: 1068-1084.Google Scholar
  34. Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268(9 June): 1503-1506.Google Scholar
  35. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382(6589): 363-366.Google Scholar
  36. Mino H, Rubinstein JT, White JA (2002) Comparison of algorithms for simulation of action potentials with stochastic sodium channels. Annals of Biomed. Eng. 30: 578-587.Google Scholar
  37. Neiman A, Schimansky-Geier L, Moss F, Shulgin B, Collins JJ (1999) Synchronization of noisy systems by stochastic signals. Phys. Rev. E 60: 284-292.Google Scholar
  38. Oldeman BE, Krauskpof B, et al. (2000) Death of period-doublings: Locating the homoclinic-doubling cascade. Physica. D 146(1-4): 100-120.Google Scholar
  39. Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons [published erratum appears in J. Comput. Neurosci., 1995 Sep; 2(3): 275]. Journal of Computational Neuroscience 1(1/2): 39-60.Google Scholar
  40. Rinzel J (1987) A Formal Classification of Bursting Mechanisms in Excitable Systems. In: 1986 International Congress of Mathematicians, American Mathematics Society.Google Scholar
  41. Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. In: Koch C, Segev I, eds. Methods in Neuronal Modelling, Cambridge, Mass., MIT Press.Google Scholar
  42. Rubinstein J (1995) Threshold fluctuations in N sodium channel model of the node of Ranvier. Biophys. J 68: 779-785.Google Scholar
  43. Russell DF, Hartline DK (1982) Slow active potentials and bursting motor patterns in pyloric network of the lobster, Panulirus interruptus. J. Neurophysiol. 48(4): 914-937.Google Scholar
  44. Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10: 1679-1703.Google Scholar
  45. Selverston AI, Moulins M, eds. (1987) The Crustacean Stomatogastric System. Berlin Heidelberg, Springer-Varlag.Google Scholar
  46. Sigworth FJ (1980) The variance of sodium current fluctuations at the node of Ranvier. J. Physiol. 307: 97-129.Google Scholar
  47. Simiu E (2002) Chaotic Transitions in Deterministic and Stochastic Dynamical Systems. Princeton, New jersey, Princeton University Press.Google Scholar
  48. Skaugen E, Walløe L (1979) Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiologica Scandinavica 107(4): 343-363.Google Scholar
  49. Stevens C, Zador A (1998) Input synchrony and the irregular firing of cortical neurons. Nature Neurosci. 1: 210-217.Google Scholar
  50. Strassberg AF, DeFelice LJ (1993) Limitations of the Hodgkin-Huxley formalism: Effects of single channel kinetics on transmembrane voltage dynamics. Neural Computation 5(6): 843-855.Google Scholar
  51. Terman D (1991) Chaotic spikes arising from a model of bursting in excitable membranes. SIAM J. Appl. Math. 51(5): 1418-1450.Google Scholar
  52. Terman D (1992) The transition from bursting to continuous in excitable membrane models. J. Nonlinear Science 2: 135-182.Google Scholar
  53. Traub RD, Wong RK, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophysiol. 66(2): 635-650.Google Scholar
  54. Ulrich D (2002) Dendritic resonance in rat neocortical pyramidal cells. J Neurophysiol. 87: 2753-2759.Google Scholar
  55. Wang X-J (1993) Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle. Physica D 62: 263-274.Google Scholar
  56. Wang X-J, Rinzel J (1995). Oscillatory and bursting properties of neurons. In: MA Arbib, ed. Handbook of Brain Theory and Neural Networks, MIT Press. pp. 686-691.Google Scholar
  57. White J, Budde T, Kay AR (1995) A bifurcation analysis of neuronal subthreshold oscillations. Biophys J. 69: 1203-1217.Google Scholar
  58. White JA, Klink R, Alonso A, Kay AR (1998) Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J. Neurophysiol. 80: 262-269.Google Scholar
  59. White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci. 23(3): 131-137.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Peter F. Rowat
    • 1
  • Robert C. Elson
    • 2
  1. 1.Institute for Neural ComputationUniversity of California at San DiegoLa JollaUSA
  2. 2.Institute for Nonlinear ScienceUniversity of California at San DiegoLa JollaUSA

Personalised recommendations