Journal of Computational Neuroscience

, Volume 10, Issue 3, pp 281–302 | Cite as

A Model of a Segmental Oscillator in the Leech Heartbeat Neuronal Network

  • A.A.V. Hill
  • J. Lu
  • M.A. Masino
  • O.H. Olsen
  • R.L. Calabrese


We modeled a segmental oscillator of the timing network that paces the heartbeat of the leech. This model represents a network of six heart interneurons that comprise the basic rhythm-generating network within a single ganglion. This model builds on a previous two cell model (Nadim et al., 1995) by incorporating modifications of intrinsic and synaptic currents based on the results of a realistic waveform voltage-clamp study (Olsen and Calabrese, 1996). Due to these modifications, the new model behaves more similarly to the biological system than the previous model. For example, the slow-wave oscillation of membrane potential that underlies bursting is similar in form and amplitude to that of the biological system. Furthermore, the new model with its expanded architecture demonstrates how coordinating interneurons contribute to the oscillations within a single ganglion, in addition to their role of intersegmental coordination.

Hirudo medicinalis half-center oscillator central pattern generator 


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  1. Abbott L, Marder E (1998) Modeling small networks. In: Koch C, Segev I, eds. Methods in Neuronal Modeling: From Ions to Networks (2nd ed.). MIT Press, Cambridge, MA, pp. 361-410.Google Scholar
  2. Angstadt JD, Calabrese RL (1989) A hyperpolarization-activated inward current in heart interneurons of the medicinal leech. J. Neurosci. 9:2846-2857.Google Scholar
  3. Angstadt JD, Calabrese RL (1991) Calcium currents and graded synaptic transmission between heart interneurons of the leech. J. Neurosci. 11:746-759.Google Scholar
  4. Arbas EA, Calabrese RL (1984) Rate modification in the heartbeat central pattern generator of the medicinal leech. J. Comp. Physiol. A 155:783-794.Google Scholar
  5. Arbas EA, Calabrese RL (1987) Slow oscillations of membrane potential in interneurons that control heartbeat in the medicinal leech. J. Neurosci. 7:3953-3960.Google Scholar
  6. Booth V, Rinzel J, Kiehn O (1997) Compartmental model of vertebrate motoneurons for Ca2+-dependent spiking and plateau potentials under pharmacological treatment. J. Neurophysiol. 78:3371-3385.Google Scholar
  7. Boroffka I, Hamp R (1969) Topographie des Kreislaufsystems und Zirkulation bei Hirudo medicinalis. Zeitschrift fur Morphologie der Tiere 64:59-76.Google Scholar
  8. Bower JM, Beeman D (1998) The Book of GENESIS: Exploring Realistic Neural Models with the GEneral Neural SImulation System (2nd ed.). Springer-Verlag, New York.Google Scholar
  9. Brodfuehrer PD, Debski EA, O'Gara BA, Friesen WO (1995) Neuronal control of leech swimming. J. Neurobiol. 27:403-418.Google Scholar
  10. Calabrese RL (1980) Control of multiple impulse-initiation sites in a leech interneuron. J. Neurophysiol. 44:878-896.Google Scholar
  11. Calabrese RL, Angstadt JD, Arbas EA (1989) A neural oscillator based on reciprocal inhibition, In: Carew TJ, Kelley D, eds. Perspectives in Neural Systems and Behavior. Liss, New York, pp. 33-50.Google Scholar
  12. Cohen AH, Ermentrout GB, Kiemel T, Kopell N, Sigvardt KA, Williams TL (1992) Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends Neurosci. 15:434-438.Google Scholar
  13. Cymbalyuk GS, Calabrese RL (2000) Oscillatory behaviors in pharmacologically isolated heart interneurons from the medicinal leech. Neurocomputing 32-33:97-104.Google Scholar
  14. De Schutter E, Angstadt JD, Calabrese RL (1993) A model of graded synaptic transmission for use in dynamic network simulations. J. Neurophysiol. 69:1225-1235.Google Scholar
  15. Friesen WO, Pearce RA (1993) Mechanisms of intersegmental coordination in leech locomotion. Semin. Neurosci. 5:41-47.Google Scholar
  16. Grillner S (1999) Bridging the gap-from ion channels to networks and behavior. Curr. Opin. Neurobiol. 9:663-669.Google Scholar
  17. Grillner S, Wallén P (1980) Does the central pattern generation for locomotion in lamprey depend on glycine inhibition? Acta Physiol. Scand. 110:103-105.Google Scholar
  18. Grillner S, Wallén P, Brodin L, Lansner A (1991) Neuronal network generating locomotor behavior in lamprey: Circuitry, transmitters, membrane properties and simulation. Ann. Rev. Neurosci. 14:169-199.Google Scholar
  19. Hille (1992) Ionic channels of excitable membranes. Sinauer Associates, Sunderland, MA.Google Scholar
  20. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117:500-544.Google Scholar
  21. Ikeda K, Wiersma CAG (1964) Autogenic rhythmicity in the abdominal ganglia of the crayfish: The control of swimmeret movements. Comp. Biochem. Physiol. 12:107-115.Google Scholar
  22. Ivanov AI, Calabrese RL (1999) Correlation of presynaptic intracelluar Ca2+ concentration with homosynaptic plasticity between leech inhibitory heart interneurons. Soc. Neurosci. Abs. 25:658.1.Google Scholar
  23. Kopell N, Ermentrout GB (1988) Coupled oscillators and the design of central pattern generators. Math. Biosci. 90:87-109.Google Scholar
  24. Krahl B, Zerbst-Boroffka I (1983) Blood pressure in the leech, Hirudo medicinalis. J. Exp. Biol. 107:163-168.Google Scholar
  25. Lu J, Dalton JF, Stokes DR, Calabrese RL (1997) Functional role of Ca2+ currents in graded and spike-mediated synaptic transmission between leech heart interneurons. J. Neurophysiol. 77:1779-1794.Google Scholar
  26. Maranto AR (1982) Neuronal mapping: A photoxidation reaction makes Lucifer yellow useful for electron microscopy. Science 217:953-955.Google Scholar
  27. Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol. Rev. 76:687-717.Google Scholar
  28. Masino MA, Calabrese RL (1999) Differences in inherent cycle periods between coupled segmental oscillators can produce phase differences in the leech heartbeat central pattern generator. Soc. Neurosci. Abst. 25:659.13.Google Scholar
  29. Mulloney B, Skinner FK, Namba H, Hall WM (1998) Intersegmental coordination of swimmeret movements: Mathematical models and neural circuits. Ann. N.Y. Acad. Sci. 860:266-280.Google Scholar
  30. Murchison D, Chrachri A, Mulloney B (1993) A separate local pattern-generating circuit controls the movements of each swimmeret in crayfish. J. Neurophysiol. 70:2620-2631.Google Scholar
  31. Nadim F, Calabrese RL (1997) A slow outward current activated by FMRFamide in heart interneurons of the medicinal leech. J. Neurosci. 17:4461-4472.Google Scholar
  32. Nadim F, Olsen OH, De Schutter E, Calabrese RL (1995) Modeling the leech heartbeat elemental oscillator: I. Interactions of intrinsic and synaptic currents. J. Comput. Neurosci. 2:215-235.Google Scholar
  33. Namba H, Mulloney B (1999) Coordination of limb movements: Three types of intersegmental interneurons in the swimmeret system and their responses to changes in excitation. J. Neurophysiol. 81:2437-2450.Google Scholar
  34. Nicholls JG, Baylor DA (1968) Specific modalities and receptive fields of sensory neurons in the CNS of the leech. J. Physiol. (Lond.) 31:740-756.Google Scholar
  35. Nicholls JG, Wallace BG (1978a) Modulation of transmission at an inhibitory synapse in the central nervous system of the leech. J. Physiol. (Lond.) 281:157-170.Google Scholar
  36. Nicholls JG, Wallace BG (1978b) Quantal analysis of transmitter release at an inhibitory synapse in the central nervous system of the leech. J. Physiol. (Lond.) 281:171-185.Google Scholar
  37. Olsen OH, Calabrese RL (1996) Activation of intrinsic and synaptic currents in leech heart interneurons by realistic waveforms. J. Neurosci. 16:4958-4970.Google Scholar
  38. Olsen OH, Nadim F, Calabrese RL (1995) Modeling the leech heartbeat elemental oscillator: II. Exploring the parameter space. J. Comput. Neurosci. 2:237-257.Google Scholar
  39. Opdyke CA, Calabrese RL (1994) A persistent sodium current contributes to oscillatory activity in heart interneurons of the medicinal leech. J. Comp. Physiol. A 175:781-789.Google Scholar
  40. Paul DH, Mulloney B (1986) Intersegmental coordination of swimmeret rhythms in isolated nerve cords of crayfish. J. Comp. Physiol. A 158:215-224.Google Scholar
  41. Peterson EL (1983a) Generation and coordination of heartbeat timing oscillation in the medicinal leech. I. Oscillation in isolated ganglia. J. Neurophysiol. 49:611-626.Google Scholar
  42. Peterson EL (1983b) Generation and coordination of heartbeat timing oscillation in the medicinal leech. II. Intersegmental coordination. J. Neurophysiol. 49:627-638.Google Scholar
  43. Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1:39-60.Google Scholar
  44. Roberts A, Soffe SR, Wolf ES, Yoshida M, Zhao FY (1998) Central circuits controlling locomotion in young frog tadpoles. Ann. N.Y. Acad. Sci. 860:19-34.Google Scholar
  45. Schmidt J, Calabrese RL (1992) Evidence that acetylcholine is an inhibitory transmitter of heart interneurons in the leech. J. Exp. Biol. 171:329-347.Google Scholar
  46. Schweighofer N, Doya K, Kawato M (1999) Electrophysiological properties of inferior olive neurons: A compartmental model. J. Neurophysiol. 82:804-817.Google Scholar
  47. Simon TW, Opdyke CA, Calabrese RL (1992) Modulatory effects of FMRF-NH2 on outward currents and oscillatory activity in heart interneurons of the medicinal leech. J. Neurosci. 12:525-537.Google Scholar
  48. Simon TW, Schmidt J, Calabrese RL (1994) Modulation of highthreshold transmission between heart interneurons of the medicinal leech by FMRF-NH2. J. Neurophysiol. 71:454-466.Google Scholar
  49. Skinner FK, Kopell N, Marder E (1994) Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J. Comput. Neurosci. 1:69-87.Google Scholar
  50. Skinner FK, Kopell N, Mulloney B (1997) How does the crayfish swimmeret system work? Insights from nearest-neighbor coupled oscillator models. J. Comput. Neurosci. 4:151-160.Google Scholar
  51. Stein PSG (1971) Intersegmental coordination of swimmeret motor neuron activity in crayfish. J. Neurophysiol. 34:310-318.Google Scholar
  52. Thompson WJ, Stent GS (1976) Neuronal control of heartbeat in the medicinal leech. III. Synaptic relations of the heart interneurons. J. Comp. Physiol. 111:309-333.Google Scholar
  53. Tolbert LP, Calabrese RL (1985) Anatomical analysis of contacts between identified neurons that control heartbeat in the leech Hirudo medicinalis. Cell Tissue Res. 242:257-267.Google Scholar
  54. Wadden T, Hellgren J, Lansner A, Grillner S (1997) Intersegmental coordination in the lamprey: Simulations using a network model without segmental boundaries. Biol. Cybern. 76:1-9.Google Scholar
  55. Wang X-J, Rinzel J (1992) Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comp. 4:84-97.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A.A.V. Hill
    • 1
  • J. Lu
    • 1
  • M.A. Masino
    • 1
  • O.H. Olsen
    • 1
  • R.L. Calabrese
    • 1
  1. 1.Biology DepartmentEmory UniversityAtlanta

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