Journal of Computational Neuroscience

, Volume 15, Issue 1, pp 91–103 | Cite as

Spike Generating Dynamics and the Conditions for Spike-Time Precision in Cortical Neurons

  • Boris Gutkin
  • G. Bard Ermentrout
  • Michael Rudolph


Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.

computational model cortical neurons Type I membrane frequency-locking 


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  1. Adrian ED, Zotterman Y (1926) The impulses produced by sensory nerve endings. Part. 2. The response of a single end organ. J. Physiol. 61: 151-171.Google Scholar
  2. Azouz R, Gray CM (1999) Cellular mechanisms contributing to response variability of cortical neurons in vivo. J. Neuroscience 19: 2209-2223.Google Scholar
  3. Azouz R, Gray CM (2000) Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proc. Natl. Acad. Sci. USA 97: 8110-8115.CrossRefPubMedGoogle Scholar
  4. Bair W, Koch C (1996) Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey. Neural Comp. 8: 1185-1202.Google Scholar
  5. Barlow H (1994) The neuron doctrine in perception. In: M Gazzaniga, ed. The Cognitive Neuroscience. MIT Press, Boston. pp. 415-435.Google Scholar
  6. Bialek W, Rieke F (1992) Reliability and information transmission in spiking neurons. Trends. Neurosci. 15: 428-434.CrossRefPubMedGoogle Scholar
  7. Bishop PO, Levick WR, Williams WO (1964) Statistical analysis of the dark discharge of lateral geniculate neurones. J. Physiol. 170: 598-612.PubMedGoogle Scholar
  8. Britten KH, Shadlen MN, Newsome WT, Movshon JA (1993) Response of neurons in macaque MT to stochastic motion signals. Visual Neurosci. 10: 1157-1169.Google Scholar
  9. Brunel N, Chance FS, Fourcard N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys. Rev. Lett. 86: 2186-2189.CrossRefPubMedGoogle Scholar
  10. Bryant HL, Segundo JP (1976) Spike initiation by transmembrane current: A white-noise analysis. J. Physiol. 260: 279-314.PubMedGoogle Scholar
  11. Bugmann G, Christodoulou C, Taylor JG (1997) Role of temporal integration and fluctuation detection in the highly irregular firing of a leaky integrator neuron model with partial reset. Neural Comp. 9: 985-1000.Google Scholar
  12. Calvin WH, Stevens CF (1968) Synaptic noise and other sources of randomness in motoneuron interspike intervals. J. Neurophysiol. 31: 574-587.PubMedGoogle Scholar
  13. Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends. Neurosci. 13: 99-104.CrossRefPubMedGoogle Scholar
  14. Coombes S, Bressloff P (1999) Mode locking and Arnold tongues in integrate-and-fire neural oscillators. Phys. Rev. E 60: 2086-2096.CrossRefGoogle Scholar
  15. Cox DR (1970) Analysis of Binary Data. Chapman and Hall, London.Google Scholar
  16. de Charms RC, Zador A (2000) Neural representation and the cortical code. Annu. Rev. Neurosci. 23: 613-647.CrossRefPubMedGoogle Scholar
  17. de Ruyter van Steveninck RR, Strong SP, Koberle R, Bialek W (1997) Reproducibility and variability in neural spike trains. Science 275: 1805-1808.CrossRefPubMedGoogle Scholar
  18. Destexhe A, Paré D (1999) Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J. Neurophysiol. 81: 1531-1547.PubMedGoogle Scholar
  19. Destexhe A, Rudolph M, Fellous J-M, Sejnowski TJ (2001) Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neurosci. 107: 13-24.CrossRefGoogle Scholar
  20. Engel AK, König P, Kreiter AK, Schillen TB, Singer W (1992) Temporal coding in the visual cortex: New vistas on integration in the nervous system. Trends Neurosci. 15: 218-226.CrossRefPubMedGoogle Scholar
  21. Ermentrout GB, Kopell NK (1984) Frequency plateaus in a chain of weakly coupled oscillators I. SIAM J. Math. Analysis 15: 215-237.Google Scholar
  22. Ermentrout GB, Kopell NK (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math. 46: 233-253.Google Scholar
  23. Ermentrout GB, Pascal M, Gutkin B (2001) The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comp. 13: 1285-1310.CrossRefGoogle Scholar
  24. Fellous J-M, Howeling AR, Modi RH, Rao RPN, Tiesinga PHE, Sejnowski T J (2000) Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons. J. Neurophys. 85: 1782-1787.Google Scholar
  25. Gray CM (2000) Synchronous oscillations in neuronal systems: Mechanisms and functions. J. Comp. Neurosci. 1: 11-38.Google Scholar
  26. Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comp. 10: 1047-1065.CrossRefGoogle Scholar
  27. Gutkin BS, Laing C, Colby C, Chow CC, Ermentrout GB (2001) Turning on and off with excitation: The role of spike-timing synchrony and asynchrony in sustained neural activity. J. Comp. Neurosci. 11: 121-134.CrossRefGoogle Scholar
  28. Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comp. 7: 307-337.Google Scholar
  29. Harsch A, Robinson HPC (2000) Postsynaptic variability of firing in rat cortical neurons: The role of input synchronization and synaptic NMDA receptor conductance. J. Neurosci. 20: 6181-6192.PubMedGoogle Scholar
  30. Hodgkin AL (1948) The local changes associated with repetitive action in non-medulated axon. J. Physiol. 107: 165-181.Google Scholar
  31. Hoppensteadt F, Izhikevich E (1997) Weakly Connected Neural Nets. Springer-Verlag, Berlin.Google Scholar
  32. Howeling AR, Modi RH, Granter P, Fellous J-M, Sejnowski TJ (2001) Models of frequency preferences of prefrontal cortical neurons. Neurocomputing 38: 231-238.CrossRefGoogle Scholar
  33. Hunter JD, Milton JG, Thomas PJ, Cowan JD (1998) Resonance effect for neural spike time reliability. J. Neurophysiol. 80: 1427-1438.PubMedGoogle Scholar
  34. Jensen R, Jones L, Gartner DH (1998) Synchronization of randomly driven nonlinear oscillators and the reliable firing of cortical neurons. In: JM Bower, ed. Computational Neuroscience: Trends in Research 1998. New York: Plenum.Google Scholar
  35. Kretzberg J, Egelhaaf M, Warzecha AK (2001) Membrane potential fluctuations determine the precision of spike timing and asynchronous activity: A model study. J. Comp. Neurosci. 10: 79-97.CrossRefGoogle Scholar
  36. Krüger J, Becker JD (1991) Recognizing the visual stimulus from neuronal discharges. Trends Neurosci. 14: 282-286.CrossRefPubMedGoogle Scholar
  37. Latham PE, Richmond BJ, Nelson PG, Nirenberg S (2000) Intrinsic dynamics in neuronal networks. I. Theory. J. Neurophysiol. 83: 808-827.PubMedGoogle Scholar
  38. MacKay D, McCulloch W (1952) The limiting information capacity of a neuronal link. Bull. Math. Biophys. 14: 127-135.Google Scholar
  39. Mainen ZF, Sejnowski T J (1995) Reliability of spike timing in neocortical neurons. Science 268: 1503-1506.PubMedGoogle Scholar
  40. McClurkin JW, Optican LM, Richmond BJ, Gawne TJ (1991) Concurrent processing and complexity of temporally encoded neuronal messages in visual perception. Science 253: 675-677.PubMedGoogle Scholar
  41. McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J. Neurophysiol. 54: 782-806.PubMedGoogle Scholar
  42. Needleman DJ, Tisienga PHE, Sejnowski TJ (2001) Collective enhancement of precision in networks of coupled oscillators. Physica D 155: 324-336.Google Scholar
  43. Nowak LG, Sanchaez-Vives MV, McCormick DA (1997) Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cerebral Cortex 7: 487-501.CrossRefPubMedGoogle Scholar
  44. Panzeri S, Petersen RS, Schultz SR, Lebedev M, Diamond ME (2001) The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron 29: 769-777.CrossRefPubMedGoogle Scholar
  45. Paré D, Shrink E, Gaudreau H, Destexhe A, Lang EJ (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo. J. Neurophysiol. 79: 1450-1460.PubMedGoogle Scholar
  46. Prut Y, Vaadia E, Bergman H, Haalman I, Slovin H, Abeles M (1998) Spatiotemporal structure of cortical activity: Properties and behavioral relevance. J. Neurophysiol. 79: 2857-2874.PubMedGoogle Scholar
  47. Reinagel P, Reid RC (2000) Temporal coding of visual information in the thalamus. J Neurosci. 20: 5392-5400.PubMedGoogle Scholar
  48. Rinzel JM, Ermentrout GB (1998) Analysis of Neuronal Excitability, in Methods in Neuronal Modeling, 2nd edn. C Koch, I Segev, eds. MIT Press Cambridge, MA.Google Scholar
  49. Rudolph M, Destexhe A (2002) Gain modulation and frequency locking under conductance noise. CNS 2002 Abstract.Google Scholar
  50. Salinas E, Sejnowski TJ (2000) Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J. Neurosci. 20: 6193-6209.PubMedGoogle Scholar
  51. Shadlen M, Newsome WT (1998) The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J. Neurosci. 18: 3870-3896.PubMedGoogle Scholar
  52. Stafstrom CE, Schwindt PC, Crill WE (1984) Repetitive fring in layer V neurons from cat neocortex in vitro. J. Neurophysiol. 52: 264-277.PubMedGoogle Scholar
  53. Tang A (1997) Effects of cholinergic modulation on responses of neocortical neurons to fluctuating input. Cereb. Cortex 7: 502-509.CrossRefPubMedGoogle Scholar
  54. Teich MC, Henegan C, Lowen SB, Ozaki T, Kaplan E (1997) Fractal character of the neural spike train in the visual system of the cat. J. Opt. Soc. Am. 14: 529-546.Google Scholar
  55. Theunissen F, Miller JP (1995) Temporal encoding in nervous systems: A rigorous definition. J. Comp. Neurosci. 2: 149-162.Google Scholar
  56. Thorpe S, Fize D, Marlot C (1996) Speed of processing in the human visual system. Nature 381: 520-522.CrossRefPubMedGoogle Scholar
  57. Tovée MJ, Rolls ET, Treves A, Bellis RP (1993) Information encoding and the responses of single neurons in the primate temporal visual cortex. J. Neurophysiol. 70: 640-654.PubMedGoogle Scholar
  58. Van Rossum MCW (2001) The transient precision of integrate and fire neurons: Effects of background activity and noise. J. Comp. Neurosci. 10: 303-311.CrossRefGoogle Scholar
  59. Wang X-J (1998) Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J. Neurophysiol. 79: 1549-1566.PubMedGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Boris Gutkin
    • 1
  • G. Bard Ermentrout
    • 2
  • Michael Rudolph
    • 1
    • 3
  1. 1.Unité de Neurosciences Intégratives et ComputationnellesGif-sur-YvetteFrance
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA
  3. 3.Gatsby Computational Neuroscience UnitUniversity College of LondonLondonUK

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