Journal of Computational Neuroscience

, Volume 12, Issue 1, pp 5–25 | Cite as

Ghostbursting: A Novel Neuronal Burst Mechanism

  • Brent Doiron
  • Carlo Laing
  • André Longtin
  • Leonard Maler


Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish have been observed to produce high-frequency burst discharge with constant depolarizing current (Turner et al., 1994). We present a two-compartment model of an ELL pyramidal cell that produces burst discharges similar to those seen in experiments. The burst mechanism involves a slowly changing interaction between the somatic and dendritic action potentials. Burst termination occurs when the trajectory of the system is reinjected in phase space near the “ghost” of a saddle-node bifurcation of fixed points. The burst trajectory reinjection is studied using quasi-static bifurcation theory, that shows a period doubling transition in the fast subsystem as the cause of burst termination. As the applied depolarization is increased, the model exhibits first resting, then tonic firing, and finally chaotic bursting behavior, in contrast with many other burst models. The transition between tonic firing and burst firing is due to a saddle-node bifurcation of limit cycles. Analysis of this bifurcation shows that the route to chaos in these neurons is type I intermittency, and we present experimental analysis of ELL pyramidal cell burst trains that support this model prediction. By varying parameters in a way that changes the positions of both saddle-node bifurcations in parameter space, we produce a wide gallery of burst patterns, which span a significant range of burst time scales.

bursting electric fish compartmental model backpropagation pyramidal cell 


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  1. Adams WB(1985) Slowdepolarization and hyperpolarizing currents which mediate bursting in an Aplysia neurone R15. J. Physiol. (Lond.) 360: 51–68.Google Scholar
  2. Aldrich R, Getting P, Thomson S (1979) Mechanism of frequencydependent broadening of molluscan neuron soma spikes. J. Physiol. (Lond.) 291: 531–544.Google Scholar
  3. Bastian J, Nguyenkim J (2001) Dendritic modulation of burst-like firing in sensory neurons. J. Neurophysiol. 85: 10–22.Google Scholar
  4. Berman NJ, Maler L (1999) Neural architecture of the electrosensory lateral line lobe: Adaptations for coincidence detection, a sensory searchlight and frequency-dependent adaptive filtering. J. Exp. Biol. 202: 1243–1253.Google Scholar
  5. Bertram R, Butte MJ, Kiemel T, Sherman A (1995) Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57: 413–439.Google Scholar
  6. Bland BH, Colom LV(1993) Extrinsic and intrinsic properties underlying oscillation and synchrony in limbic cortex. Prog. Neurobiol. 41: 157–208.Google Scholar
  7. Booth V, Bose A (2001) Neural mechanisms for generating rate and temporal codes in model CA3 pyramidal cells. J. Neurophysiol. 85: 2432–2445.Google Scholar
  8. Bressloff PC (1995) Dynamics of a compartmental model integrateand fire neuron with somatic potential reset. Physica D 80: 399–412.Google Scholar
  9. Brumberg JC, Nowak LG, McCormick DA (2000) Ionic mechanisms underlying repetitive high-frequency burst firing in supragranular cortical neurons. J. Neurosci. 20: 4829–4843.Google Scholar
  10. Carpenter GA (1979) Bursting phenomena in excitable membranes. SIAM J. Appl. Math. 36: 334–372.Google Scholar
  11. Chay TR, Rinzel J (1985) Bursting, beating, and chaos in an excitable membrane model. Biophys. J. 48: 815–827.Google Scholar
  12. Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. TINS 13: 99–104.Google Scholar
  13. Connors BW, Gutnick MJ, Prince DA (1982) Electrophysiological properties of neocortical neurons in vitro. J. Neurophysiol. 48: 1302–1320.Google Scholar
  14. de Vries G (1998) Multiple bifurcations in a polynomial model of bursting oscillations. J. Nonlinear Sci. 8: 281–316.Google Scholar
  15. Doedel E (1981) A program for the automatic bifurcation analysis of autonomous systems. Congr. Nemer. 30: 265–484.Google Scholar
  16. Doiron B, Longtin A, Berman NJ, Maler L (2001a) Subtractive and divisive inhibition: Effect of voltage-dependent inhibitory conductances and noise. Neural. Comp. 13: 227–248.Google Scholar
  17. Doiron B, Longtin A, Turner RW, Maler L (2001b) Model of gamma frequency burst discharge generated by conditional backpropagation. J. Neurophysiol. 86: 1523–1545.Google Scholar
  18. Eguia MC, Rabinovich MI, Abarbanel HDI (2000) Information transmission and recovery in neural communication channels. Phys. Rev. E62: 7111–7122.Google Scholar
  19. Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comp. 8: 979–1001.Google Scholar
  20. Franceschetti S, Guateo E, Panzica F, Sancini G, Wanke E, Avanzini A (1995) Ionic mechanism underlying burst firing in pyramidal neurons: Intracellular study in rat sensorimotor cortex. Brain Res. 696: 127–139.Google Scholar
  21. Gabbiani F, Metzner W (1999) Encoding and processing of sensory information in neuronal spike trains. J. Exp. Biol. 202: 1267–1279.Google Scholar
  22. Gabbiani F, Metzner W, Wessel R, Koch C (1996) From stimulus encoding to feature extraction in weakly electric fish. Nature 384: 564–567.Google Scholar
  23. Giannakopoulos F, Hauptmann C, Zapp A (2000) Bursting activity in a model of a neuron with recurrent synaptic feedback. Fields Instit. Comm. 29.Google Scholar
  24. Golubitsky M, Kreŝimir J, Kaper TJ (2001) An unfolding theory approach to bursting in fast-slow systems. In: Festschrift Dedicated to Floris Takens, Global Analysis of Dynamical Systems. pp. 277–308.Google Scholar
  25. Gray CM, McCormick DA (1996) Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274: 109–113.Google Scholar
  26. Grebogi E, Ott E, Yorke JA (1983) Crises, sudden changes in chaotic attractors and transient chaos. Physica D. 7: 181–200.Google Scholar
  27. Guckenheimer J, Holmes P (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, New York.Google Scholar
  28. Häusser M, Spruston N, Stuart G (2000) Diversity and dynamics of dendritic signaling. Science 290: 739–744.Google Scholar
  29. Hayashi H, Izhizuka S (1992) Chaotic nature of bursting discharges in the Onchidium pacemaker neuron. J. Theor. Biol. 156: 269–291.Google Scholar
  30. Heiligenburg W (1991) Neural Nets in Electric Fish. MIT Press, Cambridge, MA.Google Scholar
  31. 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.Google Scholar
  32. Hoppensteadt FC, Izhikevich EM (1997) Weakly Connected Neural Networks. Springer-Verlag, New York.Google Scholar
  33. Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int. J. Bifurc. Chaos 10: 1171–1269.Google Scholar
  34. Jensen M, Azouz R, Yaari Y (1996) Spike after-depolarization and burst generation in adult rat hippocampal CA1 pyramdial cells. J. Physiol. 492: 199–210.Google Scholar
  35. Keener J, Sneyd J (1998) Mathematical Physiology. Springer-Verlag, New York.Google Scholar
  36. Kepecs A, Wang XJ (2000) Analysis of complex bursting in cortical pyramidal neuron models. Neurocomput. 32- 33: 181–187.Google Scholar
  37. Komendantov AO, Kononenko NI (1996) Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia. J.Theor. Biol. 183: 219–230.Google Scholar
  38. Lánsky P, Rodriguez R (1999) The spatial properties of a model neuron increase its coding range. Biol. Cybern. 81: 161–167.Google Scholar
  39. Lemon N, Turner RW (2000) Conditional spike backpropagation generates burst discharge in a sensory neuron. J. Neurophysiol. 84: 1519–1530.Google Scholar
  40. Lisman JE (1997) Bursts as a unit of neural information: Making unreliable synapses reliable. TINS 20: 28–43.Google Scholar
  41. Ma M, Koester J (1995) Consequences and mechanisms of spike broadening of R20 cells in Aplysia californica. J. Neurosci. 15: 6720–6734.Google Scholar
  42. Mainen ZF, Joerges J, Huguenard JR, Sejnowski TJ (1995) A model of spike initiation in neocortical pyramidal cells. Neuron 15: 1427–1439.Google Scholar
  43. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382: 363–365.Google Scholar
  44. 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.Google Scholar
  45. Metzner W, Koch C, Wessel R, Gabbiani F (1998) Feature extraction of burst-like spike pat-terns in multiple sensory maps. J. Neurosci. 15: 2283–2300.Google Scholar
  46. Noonan LM, Morales E, Rashid AJ, Dunn RJ, Turner RW (2000) Kv3.3 channels have multiple roles in regulating somatic and dendritic spike discharge. Proc. Soc. Neurosci. 26(2): 1638.Google Scholar
  47. Paré D, Shink E, Gaudreau H, Destexhe A, Lang EJ (1998) Impact of spontaneous synaptic activity on the resting properties of cat neocortical neurons in vivo. J. Neurophysiol. 79: 1450–1460.Google Scholar
  48. Pinault D, Deschênes M (1992) Voltage-dependent 40 Hz oscillations in rat reticular thalamic neurons in vivo. Neurosci. 51: 245–258.Google Scholar
  49. Pinsky P, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1: 39–60.Google Scholar
  50. Pomeau Y, Manneville P (1980) Intermittent transition to turbulence in dissipative dynamical systems. Comm. Math. Phys. 74: 189–197.Google Scholar
  51. Rashid AJ, Morales E, Turner RW, Dunn RJ (2001) Dendritic Kv3 K+ channels regulate burst threshold in a sensory neuron. J. Neurosci. 21: 125–135.Google Scholar
  52. Rinzel J (1987) A formal classification of bursting in excitable systems. In: E Teramoto, M Yamaguti, eds. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences. Lecture Notes in Biomathematics. Vol. 71, Springer-Verlag, Berlin.Google Scholar
  53. Rinzel J, Ermentrout B (1989) Analysis of neural excitability and oscillations. In: C Koch, I Segev, eds. Methods in Neuronal Modeling. MIT Press, Cambridge, MA. pp. 251–291.Google Scholar
  54. Shao LR, Halvorsrud R, Borg-Graham L, Strom J (1999) The role of BK-type Ca2+ dependent K+ channels in spike broadening during repetitive firing in rat hippocampal pyramidal cells. J. Physiol. (Lond.) 521: 135–146.Google Scholar
  55. Sherman A, Carrol P, Santos RM, Atwater I (1990) Glucose dose response of pancreatic beta-cells: Experimental and theoretical results. In: C Hidalgo, ed. Transduction in Biological Systems. Plenum Press, New York.Google Scholar
  56. Sherman SM (2001) Tonic and burst firing: Dual modes of thalmocortical relay. TINS 24: 122–127.Google Scholar
  57. Shorten PR, Wall D (2000) A Hodgkin-Huxley model exhibiting bursting oscillations. Bull. Math. Biol. 62: 695–715.Google Scholar
  58. Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262: 679–685.Google Scholar
  59. Steriade M, Timofeev I, Dürmüller N, Grenier F (1998) Dynamic properties of corticothalamic neurons and local cortical interneurons generating fast rhythmic (30- 40 Hz) spike bursts. J. Neurophysiol. 79: 483–490.Google Scholar
  60. Strogatz SH (1994) Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering. Addison-Wesley, Reading, MA.Google Scholar
  61. Stuart G, Häusser M (2001) Dendritic coincidence detection of EPSPs and action potentials. Nature Neurosci. 4: 63–71.Google Scholar
  62. Stuart G, Sakmann B (1994) Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature 367: 69–72.Google Scholar
  63. Stuart G, Spruston N, Sakmann B, Häusser M (1997) Action potential initiation and backpropagation in neurons of the mammalian CNS. TINS 20: 125–131.Google Scholar
  64. Terman D (1991) Chaotic spikes arising from a model of bursting in excitable membranes. SIAM J. Appl. Math. 51: 1418–1450.Google Scholar
  65. Terman D (1992) The transition from bursting to continuous spiking in excitable membrane models. J. Nonlinear Sci. 2: 135–182.Google Scholar
  66. Traub R, Wong R, Miles R, Michelson H (1994) A model of a CA3 hippocampal neuron incorporating voltage-clamp data on intrinsic conductances. J. Neurophysiol. 66: 635–650.Google Scholar
  67. Turner RW, Maler L (1999) Oscillatory and burst discharge in the apteronotid electrosensory lateral line lobe. J. Exp. Biol. 202: 1255–1265.Google Scholar
  68. Turner RW, Maler L, Deerinck T, Levinson SR, Ellisman M (1994) TTX-sensitive dendritic sodium channels underlie oscillatory discharge in a vertebrate sensory neuron. J. Neurosci. 14: 6453–6471.Google Scholar
  69. Turner RW, Plant J, Maler L (1996) Oscillatory and burst discharge across electrosensory topographic maps. J. Neurophysiol. 76: 2364–2382.Google Scholar
  70. Vetter P, Roth A, Häusser M (2001) Propagation of action potentials in dendrites depends on dendritic morphology. J. Neurophysiol. 85: 926–937.Google Scholar
  71. Wang XJ (1993) Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle. Physica D. 62: 263–274.Google Scholar
  72. Wang XJ (1999) Fast burst firing and short-term synaptic plasticity: A model of neocortical chattering neurons. Neurosci. 89: 347–362.Google Scholar
  73. Wang XJ, Rinzel J (1995) Oscillatory and bursting properties of neurons. In: MA Arbib, ed. The Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge, MA. pp. 686–691.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Brent Doiron
    • 1
  • Carlo Laing
    • 1
  • André Longtin
    • 1
  • Leonard Maler
    • 2
  1. 1.Physics DepartmentUniversity of OttawaOttawaCanada
  2. 2.Department of Cellular and Molecular MedicineUniversity of OttawaOttawaCanada

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