Journal of Computational Neuroscience

, Volume 14, Issue 3, pp 329–342 | Cite as

Type I Burst Excitability

  • Carlo R. Laing
  • Brent Doiron
  • André Longtin
  • Liza Noonan
  • Ray W. Turner
  • Leonard Maler


We introduce the concept of “type I burst excitability”, which is a generalization of the “normal” excitability that is well-known in cardiac and neural systems. We demonstrate this type of burst excitability in a specific model system, a pyramidal cell from the electrosensory lateral line lobe of the weakly electric fish Apteronotus leptorhynchus. As depolarizing current is increased, a saddle-node bifurcation of periodic orbits occurs, which separates tonic and burst activity. This bifurcation is responsible for the excitable nature of the system, and is the basis for the “type I” designation. We verify the existence of this transition from in vitro recordings of a number of actual pyramidal cells. A scaling relationship between the magnitude and duration of a current pulse required to induce a burst is derived. We also observe this type of burst excitability and the scaling relationships in a multicompartmental model that is driven by realistic stochastic synaptic inputs mimicking sensory input. We conclude by discussing the relevance of burst excitability to communication between weakly electric fish.

bursting excitable systems pyramidal cells electric fish bifurcation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Assad C, Rasnow B, Stoddard PK (1999) Electric organ discharges and electric images during electrolocation J. Exp. Biol. 202: 1185-1193.Google Scholar
  2. Av-Ron E, Parnas H, Segel LA (1993) A basic biophysical model for bursting neurons. Biol. Cybern. 69: 87-95.CrossRefPubMedGoogle Scholar
  3. Bastian J, Chacron MJ, Maler L (2002) Receptive field organization determines pyramidal cell stimulus encoding capability and spatial stimulus selectivity. J. Neurosci. 22: 4577-4590.PubMedGoogle Scholar
  4. Bastian J, Courtright J (1991) Morphological correlates of pyramidal cell adaptation rate in the electrosensory lateral line lobe of weakly electric fish. J. Comp. Physiol. A 168(4): 393-407.PubMedGoogle Scholar
  5. Bastian J, Nguyenkim J (2001) Dendritic modulation of burst-like firing in sensory neurons. J. Neurophysiol. 85: 10-22.PubMedGoogle Scholar
  6. 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.PubMedGoogle Scholar
  7. Bub G, Shrier A, Glass L (2002) Spiral wave generation in heterogeneous excitable media. Phys. Rev. Lett. 88: 058101.CrossRefPubMedGoogle Scholar
  8. Butera RB, Clark JW, Byrne JH (1997) Transient responses of a modeled bursting neuron: Analysis with equilibrium and averaged nullclines. Biol. Cyber. 77: 307-322.CrossRefGoogle Scholar
  9. Butera RJ, Clark JW, Canavier CC, Baxter DA, Byrne JH (1995) Analysis of the effects of modulatory agents on a model bursting neuron: Dynamic interactions between voltage and calcium dependent systems. J. Comput. Neurosci. 2: 19-44.PubMedGoogle Scholar
  10. Carr C, Maler L, Sas E (1982) Peripheral organization and central projections of the electrosensory nerves in gymnotiform fish. J. Comp. Neurol. 211: 139-153.PubMedGoogle Scholar
  11. de Vreis G (1998) Multiple bifurcations in a polynomial model of bursting oscillations. J. Nonlinear Sci. 8: 281-316.CrossRefGoogle Scholar
  12. Doiron B, Laing CR, Longtin A, Maler L (2002) “Ghostbursting”: A novel bursting mechanism in pyramidal cells. J. Comput. Neurosci. 12(1): 5-25.CrossRefPubMedGoogle Scholar
  13. Doiron B, Longtin A, Turner RW, Maler L (2001a) Model of gamma frequency burst discharge generated by conditional backpropagation. J. Neurophysiol. 86(4): 1523-1545.PubMedGoogle Scholar
  14. Doiron B, Noonan L, Lemon N, Turner RW (2003) Persistant Na+ current modifies burst discharge by regulating conditional backpropagation of dendritic spikes. J. Neurophysiol. 89: 324-337.PubMedGoogle Scholar
  15. Doiron B, Noonan L, Turner RW, Longtin A, Maler L (2001b) Shifting burst threshold with dendritic conductances. XXXI Proc. Soc. Neurosci, San Diego.Google Scholar
  16. Ermentrout GB (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comp. 8: 979-1001.Google Scholar
  17. Glass L, Mackey MC (1988) From Clocks to Chaos: The Rhythms of Life. Princeton University Press.Google Scholar
  18. Goldbeter A (1996) Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press.Google Scholar
  19. Guckenheimer J, Holmes P (1990) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Applied Mathematical Sciences, Springer-Verlag, Vol. 42.Google Scholar
  20. Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine inter-spike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comp. 10: 1047-1065.CrossRefGoogle Scholar
  21. Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int. J. Bifn. Chaos 10: 1171-1266.CrossRefGoogle Scholar
  22. Keener J, Sneyd J (1998) Mathematical Physiology. Interdisciplinary Applied Mathematics, Vol. 8. Springer-Verlag, New York.Google Scholar
  23. Koch C (1999) Biophysics of Computation: Information Processing in Single Neurons. Oxford University Press.Google Scholar
  24. Kuznetsov YA (1995) Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, Springer-Verlag, Vol. 112.Google Scholar
  25. Laing CR, Doiron B, Longtin A, Maler L (2002) Ghostbursting: The effects of dendrites on spike patterns. Neurocomputing 44-46: 127-132.CrossRefGoogle Scholar
  26. Laing CR, Longtin A (2002) A two-variable model of somaticdendritic interactions in a bursting neuron. Bull. Math. Biol, 64: 829-860.CrossRefPubMedGoogle Scholar
  27. Lemon N, Turner R (2000) Conditional spike backpropagation generates burst discharge in a sensory neuron. J Neurophysiol 84: 1519-1530.PubMedGoogle Scholar
  28. Lisman JE (1997) Bursts as units of neural information: Making unreliable synapses reliable. Trends Neurosci 20: 38-43.CrossRefPubMedGoogle Scholar
  29. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382: 363-366.CrossRefPubMedGoogle Scholar
  30. Metzner W (1999) Neural circuitry for communication and jamming avoidance in gymnotiform electric fish. J. Exp. Biol. 202: 1365-1375.PubMedGoogle Scholar
  31. Metzner W, Heiligenberg W (1991) The coding of signals in the electric communication of the gymnotiform fish Eigenmannia: From electroreceptors to neurons in the torus semicircularis of the midbrain. J. Comp. Physiol. [A] 169: 135-150.Google Scholar
  32. Nelson, ME, Xu Z, Payne JR (1997) Characterization and modeling of P-type electrosensory afferent responses to amplitude modulations in a wave-type electric fish. J. Comp. Physiol. A. 181: 532-544.CrossRefPubMedGoogle Scholar
  33. Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1: 39-60.PubMedGoogle Scholar
  34. Rinzel J, Ermentrout GB (1998) Analysis of neural excitability and oscillations. In: C Koch, I Segev, eds. Methods in Neuronal Modeling: From Ions to Networks. MIT Press.Google Scholar
  35. Smith GD, Cox CL, Sherman SM, Rinzel J (2000) Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. J. Neurophysiol. 83: 588-610.PubMedGoogle Scholar
  36. Steriade M, Timofeev I, Dürmüller N, Grenie F (1998) Dynamic properties of corticothalamic neurons and local cortical interneurons generating fast rhythmic (30-40 Hz) spike bursts. J. Neurophysiol. 79: 483-490.PubMedGoogle Scholar
  37. Terman D (1992) The transition from bursting to continuous spiking in excitable membrane models. J. Nonlinear Sci. 2(2): 135-182.Google Scholar
  38. Turner RW, Maler L (1999) Oscillatory and burst discharge in the Apteronotid electrosensory lateral line lobe. J. Exp. Biol. 202: 1255-1265.PubMedGoogle Scholar
  39. Xu Z, Payne JR, Nelson ME (1996) Logarithmic time course of sensory adaptation in electrosensory afferent nerve fibers in a weakly electric fish. J. Neurophysiol. 76: 2020-2032.PubMedGoogle Scholar
  40. Zupanc GKH, Maler L (1993) Evoked chirping in the weakly electric fish (Apteronotus leptorhynchus): Aquantitative biophysical analysis. Can. J. Zool. 71: 2301-2310.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Carlo R. Laing
    • 1
  • Brent Doiron
    • 1
  • André Longtin
    • 1
  • Liza Noonan
    • 2
  • Ray W. Turner
    • 2
  • Leonard Maler
    • 3
  1. 1.Department of PhysicsUniversity of OttawaOttawaCanada
  2. 2.Department of Cell Biology and AnatomyUniversity of CalgaryCalgaryCanada
  3. 3.Department of Cellular and Molecular MedicineUniversity of OttawaOttawaCanada

Personalised recommendations