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Threshold fatigue and information transfer

  • Maurice J. Chacron
  • Benjamin Lindner
  • André Longtin
Article

Abstract

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin–Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies.

Keywords

Action potential threshold Variability Information theory Refractoriness 

Notes

Acknowledgement

We thank J. Benda for useful discussions. This research was supported by CIHR (M.J.C., A.L.) and NSERC (A.L.).

References

  1. Aizenman, C. D., & Linden, D. J. (1999). Regulation of the rebound depolarization and spontaneous firing patterns of deep nuclear neurons in slices of rat cerebellum. Journal of Neurophysiology, 82, 1697–1709.PubMedGoogle Scholar
  2. Azouz, R., & Gray, C. M. (1999). Cellular mechanisms contributing to response variability of cortical neurons in vivo. Journal of Neuroscience, 19, 2209–2223.PubMedGoogle Scholar
  3. Azouz, R., & Gray, C. M. (2000). Dynamic Spike Threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proceedings of the National Academy of Sciences of the United States of America, 97, 8110–8115.CrossRefPubMedGoogle Scholar
  4. Barlow, H. B., & Levick, W. R. (1969a). Changes in the maintained discharge with adaptation level in the cat retina. Journal of Physiology (London), 202, 699–718.Google Scholar
  5. Barlow, H. B., & Levick, W. R. (1969b). Three factors limiting the reliable detection of light by the retinal ganglion cells of the cat. Journal of Physiology (London), 200, 1–24.Google Scholar
  6. Bastian, J. (1981). Electrolocation I. How the electroreceptors of Apteronotus albifrons code for moving objects and other electrical stimuli. Journal of Comparative Physiology A, 144, 465–479.CrossRefGoogle Scholar
  7. Bastian, J., & Nguyenkim, J. (2001). Dendritic Modulation of Burst-like firing in sensory neurons. Journal of Neurophysiology, 85, 10–22.PubMedGoogle Scholar
  8. Bastian, J., Chacron. M. J., & Maler, L. (2002). Receptive field organization determines pyramidal cell stimulus-encoding capability and spatial stimulus selectivity. Journal of Neuroscience, 22, 4577–4590.PubMedGoogle Scholar
  9. Bastian, J., Chacron, M. J., & Maler, L. (2004). Plastic and non-plastic cells perform unique roles in a network capable of adaptive redundancy reduction. Neuron, 41, 767–779.CrossRefPubMedGoogle Scholar
  10. Borst, A., & Haag, J. (2001). Effects of mean firing on neural information rate. Journal of Computational Neuroscience, 10, 213–221.CrossRefPubMedGoogle Scholar
  11. Bryant, H. L., & Segundo, J. P. (1976). Spike initiation by transmembrane current: a white-noise analysis. Journal of Physiology, 260, 279–314.PubMedGoogle Scholar
  12. Burns, B. D., & Webb, A. C. (1970). Spread of responses in the cerebral cortex to meaningful stimuli. Nature, 225, 469–470.CrossRefPubMedGoogle Scholar
  13. Chacron, M. J. (2006). Nonlinear information processing in a model sensory system. Journal of Neurophysiology, 95, 2933–2946.CrossRefPubMedGoogle Scholar
  14. Chacron, M.J., Longtin, A., St-Hilaire, M., & Maler, L. (2000). Suprathreshold stochastic firing dynamics with memory in P-type electroreceptors. Physical Review Letters, 85, 1576–1579.CrossRefPubMedGoogle Scholar
  15. Chacron, M. J., Longtin, A., & Maler, L. (2001a). Simple models of bursting and non-bursting electroreceptors. Neurocomputing, 38, 129–139.CrossRefGoogle Scholar
  16. Chacron, M. J., Longtin, A., & Maler, L. (2001b). Negative interspike interval correlations increase the neuronal capacity for encoding time-varying stimuli. Journal of Neuroscience, 21, 5328–5343.Google Scholar
  17. Chacron, M. J., Pakdaman, K., & Longtin, A. (2003a). Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue. Neural Computation, 15, 253–278.CrossRefGoogle Scholar
  18. Chacron, M. J., Doiron, B., Maler, L., Longtin, A., & Bastian, J. (2003b). Non-classical receptive field mediates switch in a sensory neuron’s frequency tuning. Nature, 423, 77–81.CrossRefGoogle Scholar
  19. Chacron, M. J., Lindner, B., & Longtin, A. (2004a). Noise shaping by interval correlations increases information transfer. Physical Review Letters, 92, 080601.1–080601.4.CrossRefGoogle Scholar
  20. Chacron, M. J., Lindner, B., & Longtin, A. (2004b). ISI correlations and information transfer. Fluctuations and Noise Letters, 4, L195–L205.CrossRefGoogle Scholar
  21. Chacron, M. J., Longtin, A., & Maler, L. (2004c). To burst or not to burst? Journal of Computational Neuroscience, 17, 127–136.CrossRefGoogle Scholar
  22. Chacron, M. J., Maler, L., & Bastian, J. (2005a). Feedback and feedforward control of frequency tuning to naturalistic stimuli. Journal of Neuroscience, 25, 5521–5532.CrossRefGoogle Scholar
  23. Chacron, M. J., Maler, L., & Bastian, J. (2005b). Electroreceptor neuron dynamics shape information transmission. Nature Neuroscience, 8, 673–678.CrossRefGoogle Scholar
  24. Cover, T., & Thomas, J. (1991). Elements of information theory. New York: Wiley.CrossRefGoogle Scholar
  25. Cox, D. R., & Lewis, P. A. W. (1966). The statistical analysis of series of events. London: Methuen.Google Scholar
  26. Doiron, B., Laing, C., Longtin, A., & Maler, L. (2002). Ghostbursting: a novel neuronal burst mechanism. Journal of Computational Neuroscience, 12, 5–25.CrossRefPubMedGoogle Scholar
  27. Doiron, B., Chacron, M. J., Maler, L., Longtin, A., & Bastian, J. (2003). Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature, 421, 539–543.CrossRefPubMedGoogle Scholar
  28. Fernandez, F. R., Mehaffey, W. H., & Turner, R. W. (2005). Dendritic Na+ current inactivation can increase cell excitability by delaying a somatic depolarizing afterpotential. Journal of Neurophysiology, 94, 3836–3848.CrossRefPubMedGoogle Scholar
  29. Gabbiani, F., & Koch, C. (1996). Coding of time-varying signals in spike trains of integrate-and-fire neurons with random threshold. Neural Computation, 8, 44–66.CrossRefGoogle Scholar
  30. Gabbiani, F., Metzner, W., Wessel, R., & Koch, C. (1996). From stimulus encoding to feature extraction in weakly electric fish. Nature, 384, 564–567.CrossRefPubMedGoogle Scholar
  31. Geisler, C. D., & Goldberg, J. M. (1966). A stochastic model of the repetitive activity of neurons. Biophysical Journal, 6, 53–69.CrossRefPubMedGoogle Scholar
  32. Gestri, G., Masterbroek, H. A. K., & Zaagman, W. H. (1980). Stochastic constancy, variability and adaptation of spike generation: performance of a giant neuron in the visual system of the fly. Biological Cybernetics, 38, 31–40.CrossRefGoogle Scholar
  33. Goldberg, J. M. (2000). Afferent diversity and the organisation of central vestibular pathways. Experimental Brain Research, 130, 277–297.CrossRefGoogle Scholar
  34. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology London, 117, 500–544.Google Scholar
  35. Holden, A. V. (1976). Models of the stochastic activity of neurons. Berlin: Springer.Google Scholar
  36. Jaeger, D., & Bauer, J. M. (1994). Prolonged responses in rat cerebellar Purkinje cells following activation of the granule cell layer: an intracellular in vitro and in vivo investigation. Experimental Brain Research, 100, 200–214.CrossRefGoogle Scholar
  37. Jolivet, R., Rauch, A., Luscher, H. R., & Gerstner, W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. Journal of Computational Neuroscience, 21, 35–49.Google Scholar
  38. Koch, C. (1999). Biophysics of computation. New York: Oxford University Press.Google Scholar
  39. Köppl, C. (1997). Frequency tuning and spontaneous activity in the auditory nerve and Cochlear Nucleus Magnocellularis of the Barn Owl Tyto alba. Journal of Neurophysiology, 77, 364–377.PubMedGoogle Scholar
  40. Lebedev, M. A., & Nelson, R. J. (1996). High-frequency vibratory sensitive neurons in monkey primate somatosensory cortex: entrained and nonentrained responses to vibration during the performance of vibratory-cued hand movements. Experimental Brain Research, 111, 313–325.CrossRefGoogle Scholar
  41. Lemon, N., & Turner, R. W. (2000). Conditional spike backpropagation generates burst discharge in a sensory neuron. Journal of Neurophysiology, 84, 1519–1530.PubMedGoogle Scholar
  42. Lindner, B., Chacron, M. J., & Longtin, A. (2005). Integrate-and-fire neurons with threshold noise: A tractable model of how interspike interval correlations affect neuronal signal transmission. Physical Review E, 72, 021911.CrossRefGoogle Scholar
  43. Liu, Y. H., & Wang, X. J. (2001). Spike Frequency adaptation of a generalized leaky integrate-and-fire neuron. Journal of Computational Neuroscience, 10, 25–45.CrossRefPubMedGoogle Scholar
  44. Mainen, Z. F., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503–1506.CrossRefPubMedGoogle Scholar
  45. Manwani, A., & Koch, C. (1999). Detecting and estimating signals in noisy cable structure, I: neuronal noise sources. Neural Computation, 11, 1797–1829.CrossRefPubMedGoogle Scholar
  46. Mar, D. J., Chow, C. C., Gerstner, W., Adams, R. W., & Collins, J. J. (1999). Noise Shaping in populations of coupled model neurons. Proceedings of the National Academy of Sciences, 96, 10450–10455.CrossRefGoogle Scholar
  47. Metzner, W., Koch, C., Wessel, R., & Gabbiani, F. (1998). Feature extraction by burst-like spike patterns in multiple sensory maps. Journal of Neuroscience, 18, 2283–2300.PubMedGoogle Scholar
  48. Mickus, T., Jung, H. Y., & Spruston, N. (1999). Properties of slow cumulative sodium channel inactivation in rat hippocampal CA1 pyramidal neurons. Biophysical Journal, 76, 846–860.CrossRefPubMedGoogle Scholar
  49. Norsworthy, S. R., Schreier, R., & Temes, G. C. (Eds.) (1997). Delta-sigma data converters. Piscataway, NJ: IEEE Press.Google Scholar
  50. Oswald, A. M. M., Chacron, M. J., Doiron, B., Bastian, J., & Maler, L. (2004). Parallel processing of sensory input by bursts and isolated spikes. Journal of Neuroscience, 24, 4351–4362.CrossRefPubMedGoogle Scholar
  51. Reinagel, P., & Reid, R. C. (2000). Temporal coding of visual information in the thalamus. Journal of Neuroscience, 20, 5392–5400.PubMedGoogle Scholar
  52. Rieke, F., Warland, D., de Ruyter van Steveninck, R. R., & Bialek, W. (1996). Spikes: Exploring the neural code. Cambridge, MA: MIT.Google Scholar
  53. Rudolph, M., & Destexhe, A. (2003). The discharge variability of neocortical neurons during high-conductance states. Neuroscience, 119, 855–873.CrossRefPubMedGoogle Scholar
  54. Sadeghi, S. G., Chacron, M. J., Taylor, M. C., & Cullen, K. E. (2007). Neural variability, detection thresholds, and information transmission in the vestibular system. Journal of Neuroscience, 27, 771–781.CrossRefPubMedGoogle Scholar
  55. Sah, P. (1996). Ca2+-activated K+ currents in neurones: types, physiological roles and modulation. Trends in Neurosciences, 19, 150–154.CrossRefPubMedGoogle Scholar
  56. Shannon, C. E. (1948). The mathematical theory of communication. Bell Systems Technical Journal, 27, 379–423, 623–656.Google Scholar
  57. Sherman, S. M. (2001). Tonic and burst firing: dual modes of thalamocortical relay. Trends in Neurosciences, 24, 122–126.CrossRefPubMedGoogle Scholar
  58. Shin, J. (1993). Novel neural circuits based on stochastic pulse coding noise feedback pulse coding. International Journal of Electronics, 74, 359–368.CrossRefGoogle Scholar
  59. Shin, J. (2001). Adaptation in spiking neurons based on the noise shaping neural coding hypothesis. Neural Networks, 14, 907–919.CrossRefPubMedGoogle Scholar
  60. Shinomoto, S., Sakai, Y., & Funahashi, S. (1999). The Ornstein–Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neural Computation, 11, 935–951.CrossRefPubMedGoogle Scholar
  61. Softky, W. R., & Koch, C. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. Journal of Neuroscience, 13, 334–350.PubMedGoogle Scholar
  62. Stein, R. B., Gossen, E. R., & Jones, K. E. (2005). Neuronal variability: noise or part of the signal. Nature Reviews Neuroscience, 6, 4766–4778.CrossRefGoogle Scholar
  63. Steriade, M. (1978). Cortical long-axoned cells and putative interneurons during the sleep-waking cycle. Behavioural Brain Research, 3, 465–514.Google Scholar
  64. Teich, M. C. (1992). Fractal neuronal firing patterns. In: T. McKenna, J. Davis, & S. F. Zornetzer (Eds) Single neuron computation (pp. 589–622). San Diego: Academic Press.Google Scholar
  65. Teich, M. C., & Khanna, S. M. (1985). Pulse-number distributions for the neural spike train in the cat’s auditory nerve. Journal of the Accoustical Society of America 77, 1110–1128.CrossRefGoogle Scholar
  66. Treves, A. (1996). Mean-field analysis of neuronal spike dynamics. Network: Computation in Neural Systems, 4, 259–284.CrossRefGoogle Scholar
  67. Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. Journal of Neurophysiology, 79, 1549–1566.PubMedGoogle Scholar
  68. Wiesenfeld, K., & Satija, I. (1987). Noise tolerance of frequency-locked dynamics. Physical Review B, 36, 2483–2492.CrossRefGoogle Scholar
  69. Yacomotti, A. M., Eguia, M. C., Aliaga, J., Martinez, O. E., & Mindlin, G. B. (1999). Interspike time distribution in noise driven excitable systems. Physical Review Letters, 83, 292–295.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Maurice J. Chacron
    • 1
  • Benjamin Lindner
    • 2
    • 3
  • André Longtin
    • 2
  1. 1.Departments of Physiology and Physics, Center for Nonlinear DynamicsMcGill UniversityMontrealCanada
  2. 2.Department of PhysicsUniversity of OttawaOttawaCanada
  3. 3.Max Planck Institute for the Physics of Complex SystemsDresdenGermany

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