Abstract
This paper describes a mathematical model of the neuronal central pattern generator (CPG) that controls the rhythmic body motion of the swimming leech. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG. We show through numerical simulations that the values of a few parameters can be estimated within physiologically reasonable ranges to achieve good fit of the data with respect to the phase, amplitude, and period. This parameter estimation leads to predictions regarding the synaptic coupling strength and intrinsic period gradient along the nerve cord, the latter of which agrees qualitatively with experimental observations.
Similar content being viewed by others
References
Angstadt JD, Friesen WO (1993) Modulation of swimming behavior in the medicinal leech. I. Effects of serotonin on the electrical properties of swim-gating cell 204. J. Comp. Physiol. A 59: 223–234.
Brodfuehrer PD, Debski EA, O’Gara BA, Friesen WO (1995) Neuronal control of swimming. J. Neurobiol. 27: 403–418.
Buchanan JT (1992) Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord. Biol. cybern. 66: 367–374.
Cang J, Friesen WO (2002) Model for intersegmental coordination of leech swimming: Central and sensory mechanisms. J. Neurophysiol. 87: 2760–2769.
Cang J, Yu X, Friesen WO (2001) Sensory modification of leech swimming: interactions between ventral stretch receptors and swim-related neurons. J. Comp. Physiol. A 187: 569–579.
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.
Debski EA, Friesen WO (1986) Role of central interneurons in habituation of swimming activity in the medicinal leech. J. Neurophysiol. 55: 977–994.
Ekeberg O (1993) A combined neuronal and mechanical model of fish swimming. Biological Cybernetics. 69: 363–374.
Ekeberg O, Grillner S (1999) Simulations of neuromuscular control in lamprey swimming. Phil. Trans. R. Soc. Lond. B 354: 895–902.
Ekeberg O, Wallén P, Lansner A, Traven H, Brodin L, Grillner S (1991) A computer based model for realistic simulations of neural networks. I. The single neuron and synaptic interaction. Biol. Cybern. 65: 81–90.
Ermentrout GB, Chow CC (2002) Modeling neural oscillations. Physiology and Behavior. 77: 629–633.
Friesen WO (1985) Neuronal control of leech swimming movements: Interactions between cell 60 and previously described oscillator neurons. J. Comp. Physiol. A 156: 231–242.
Friesen WO (1989a) Neuronal control of leech swimming movements. In JW Jacklet (Ed.) Cellular and Neuronal Oscillators, Marcel Dekker, New York, pp. 269–316.
Friesen WO (1989b) Neuronal control of leech swimming movements I. Inhibitory interactions between motor neurons. J. Comp. Physiol. A 166: 195–203.
Friesen WO, Hocker CG (2001) Functional analyses of the leech swim oscillator. J. Neurophysiol. 86: 824–835.
Friesen WO, Pearce RA (1993) Mechanisms of intersegmental coordination in leech locomotion. Seminars in the Neurosciences 5: 41–47.
Friesen WO, Stent GS (1977) Generation of a locomotory rhythm by a neural network with recurrent cyclic inhibition. Biol. Cybern. 28: 27–40.
Friesen WO, Poon M, Stent GS (1978) Neuronal control of swimming in the medicinal leech IV. I dentification of a network of oscillatory interneurones. J. Exp. Biol. 75: 25–43.
Granzow BL, Friesen WO, Kristan Jr. WB (1985) Physiological and morphological analysis of synaptic transmission between leech motor neurons. J. Neurosci. 5: 2035–2050.
Hill AAV, Masino MA, Calabrese RL (2003) Intersegmental coordination of rhythmic motor patterns. J. Neurophysiol. 90: 531–538.
Hocker CG, Yu X, Friesen WO (2000) Functionally heterogeneous segmental oscillators generate swimming in the medicinal leech. J. Comp. Physiol. A 186: 871–883.
Kiehn O, Harris-Warrick RM, Jordan LM, Hultborn H, Kudo N (Eds.) (1998) Neuronal Mechanisms for Generating Locomotor Activity. The New York Academy of Sciences.
Koch C, Segev I (1989) Methods in Neuronal Modeling: From Synapses to Networks. The MIT Press.
Kristan Jr. WB, Stent GS, Ort CA (1974) Neuronal control of swimming in the medicinal leech. I Dynamics of the swimming rhythm. J. Comp. Physiol. A 94: 97–119.
Mangan PS, Curran GA, Hurney CA, Friesen WO (1994) Modulation of swimming behavior in the medicinal leech. III. Control of cellular properties in motor neurons by serotonin. J. Comp. Physiol. A 175: 709–722.
Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol. Rev. 76(3): 687–717.
Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol. Cybern. 52: 367–376.
Margulis M, Tang CM (1998) Temporal integration can readily switch between sublinear and supralinear summation. J. Neurophysiol. 79: 2809–2813.
Nusbaum MP, Friesen WO, Kristan Jr. WB, Pearce RA (1987) Neural mechanisms generating the leech swimming rhythm: Swim-initiator neurons excite the network of swim oscillator neurons. J. Comp. Physiol. A 161: 355–366.
Orlovsky GN, Deliagina TG, Grillner S (1999) Neuronal Control of Locomotion: From Mollusc to Man. Oxford University Press.
Pearce RA, Friesen WO (1984) Intersegmental coordination of leech swimming: comparison of in situ and isolated nerve cord activity with body wall movement. Brain Res. 299: 363–366.
Pearce RA, Friesen WO (1985a) Intersegmental coordination of the leech swimming rhythm. I. Roles of cycle period gradient and coupling strength. J. Neurophysiol. 54(6): 1444–1459.
Pearce RA, Friesen WO (1985b) Intersegmental coordination of the leech swimming rhythm. II. Comparison of long and short chains of ganglia. J. Neurophysiol. 54: 1460–1472.
Pearce RA, Friesen WO (1988) A model for intersegmental coordination in the leech nerve cord. Biol. Cybern. 58: 301–311
Poon M, Friesen WO, Stent GS (1978) Neuronal control of swimming in the medicinal leech V. Connexions between the oscillatory interneurones and the motor neurones. J. Exp. Biol. 75: 45–63.
Selverston AI (Ed.) (1985) Model Neural Networks and Behavior. Plenum Press.
Skinner FK, Mulloney B (1998a) Intersegmental coordination in invertebrates and vertebrates. Curr. Opin. Neurobiol. 8: 725–732.
Skinner FK, Mulloney B (1998b) Intersegmental coordination of limb movements during locomotion: Mathematical models predict circuits that drive swimmeret beating. J. Neurosci. 18: 3831–3842.
Taylor A, Cottrell GW, Kristan Jr. WB (2000) A model of the leech segmental swim central pattern generator. Neurocomputing, 32-33: 573–584.
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.
Wallen P, Ekeberg O, Lansner A, Brodin L, Traven H, Grillner S (1992) A computer-based model for realistic simulations of neural networks. II. The segmental network generating locomotor rhythmicity in the lamprey. J. Neurophysiol. 68(6): 1939–1950.
Weeks JC (1982a) Synaptic basis of swim initiation in the leech I Connections of a swim-initiating neuron (cell 204) with motor neurons and pattern-generating “oscillator” neurons. J. Comp. Physiol. A 148: 253–263.
Weeks JC (1982b) Synaptic basis of swim initiation in the leech II. A pattern-generating neuron (cell 208) which mediates motor effects of swim-initiating neurons. J. Comp. Physiol. A, 148: 265–279.
Wessel R, Kristan WB Jr, Kleinfeld D (1990) Supralinear summation of synaptic inputs by an invertebrate neuron: Dendritic gain is mediated by an “inward rectifier” \(K^+\) current. J. Neurosci. 19: 5875–5888.
Williams TL (1992) Phase coupling by synaptic spread in chains of coupled neuronal oscillators. Science 258: 662–665.
Author information
Authors and Affiliations
Corresponding author
Additional information
Action Editor:
F. Skinner
Rights and permissions
About this article
Cite this article
Zheng, M., Friesen, W.O. & Iwasaki, T. Systems-level modeling of neuronal circuits for leech swimming. J Comput Neurosci 22, 21–38 (2007). https://doi.org/10.1007/s10827-006-9648-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10827-006-9648-7