A mathematical model of motorneuron dynamics in the heartbeat of the leech

Physica D: Nonlinear Phenomena

Volumn 188, Issue 3-4, 2004, Pages 292-313

  Buono, Pietro Luciano ^a   Palacios, A ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

Bifurcation; Coupled cell systems; Symmetry

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); BLOOD VESSELS; CARDIOVASCULAR SYSTEM; CELLS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MATHEMATICAL MODELS;

CENTRAL PATTERN GENERATORS (CPG); COUPLED CELL SYSTEMS;

NEUROLOGY;

EID: 0347128496     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.08.003     Document Type: Article

References (32)

1. Buono P.-L., Golubitsky M., Models of central pattern generators for quadruped locomotion. I. Primary gaits. J. Math. Biol. 42:2001;291-326.
2. Buono P.-L., Golubitsky M., Palacios A., Heteroclinic cycles in rings of coupled cell. Physica D. 143:2000;74-108.
3. Bressloff P.C., Coombes S., Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays. Physica D. 126:1999;99-122.
4. Bressloff P.C., Cowan J.D., Golubitsky M., Thomas P.J., Wiener M.C., Geometric visual hallucinations, Euclidean symmetry, and the functional architecture of striate cortex. Philos. Trans. R. Soc. London B. 356:2001;299-330.
5. Calabrese R., The neural control of alternate heartbeat coordination states in the leech, Hirudo medicinalis. J. Comp. Physiol. 122:1977;111-143.
6. R. Calabrese, J. Feldman, Intrinsic membrane properties and synaptic mechanisms in motor rhythm generators, in: P. Stein, S. Grillner, A. Selverston, D. Stuart (Eds.), Neurons, Networks, and Motor Behavior, MIT Press, Cambridge, MA, 1997, pp. 119-130.
7. Calabrese R., Nadim F., Olsen O., Heartbeat control in the medicinal leech: a model system for understanding the origin, coordination, and modulation of rhythmic motor patterns. J. Neurobiol. 27:1995;390-402.
8. A. Cohen, S. Rossignol, S. Grillner (Eds.), Neural Control of Rhythmic Movements in Vertebrates, Wiley, New York, 1988.
9. Epstein I., Golubitsky M., Symmetric patterns in linear arrays of coupled cells. Chaos. 3(1):1995;1-5.
10. M. Golubitsky, I.N. Stewart, Interior symmetries in coupled cell networks motivated by the leech heart, Preprint.
11. Golubitsky M., Stewart I.N., Buono P.-L., Collins J.J., A modular network for legged locomotion. Physica D. 115:1998;56-72.
12. Gramoll S., Schmidt J., Calabrese R., Switching in the activity state of an interneuron that controls coordination of the hearts in the medicinal leech (Hirudo Medicinalis). J. Exp. Biol. 186:1994;157-171.
13. M. Golubitsky, I.N. Stewart, D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. II, Applied Mathematical Science, vol. 69, Springer, New York, 1988.
14. S. Grillner, J. Buchanan, P. Wallen, L. Brodin, Neural control of locomotion in lower vertebrates, in: A.H. Cohen, S. Rossignol, S. Grillner (Eds.), Neural Control of Rhythmic Movements in Vertebrates, Wiley, New York, 1988, pp. 129-166.
15. Harris-Warrick R.M., Marder E., Modulation of neural networks for behavior. Annu. Rev. Neurosci. 14:1991;39-57.
16. Hodgkin A.L., Huxley A.F., A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. London. 117:1952;500-544.
17. Jonhston D., Magee J., Colbert C., Christie B., Active properties of neuronal dendrites. Annu. Rev. Neurosci. 19:1996;165-186.
18. Koch C., Computation and the single neuron. Nature. 385(16):1997;207-210.
19. Lu J., Gramoll S., Schmidt J., Calabrese R., Motor pattern switching in the heartbeat pattern generator of the medicinal leech: membrane properties and lack of synaptic interaction in switch interneurons. J. Comp. Physiol. A. 184:1999;311-324.
20. Magee J.C., Johnston D., A synaptically controlled associative signal for Hebbian plasticity in hippocampal neurons. Science. 275:1997;209-213.
21. Markram H., Lubke J., Frotscher M., Sakmann B., Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science. 275:1997;213-215.
22. Morton D.W., Chiel H.J., The timing of activity in motor neurons that produce radula movements distinguishes ingestion from rejection in Aplysia. J. Comp. Physiol. A. 173:1993;519-536.
23. Nadim F., Olsen O., De Schutter E., Calabrese R., Modeling the leech heartbeat elemental oscillator. I. Interactions of intrinsic and synaptic currents. J. Comp. Neurosci. 2:1995;216-235.
24. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University, New York, 2001.
25. Schmidt J., Calabrese R., Evidence that acetylcholine is an inhibitory transmitter of heart interneurons in the leech. J. Exp. Biol. 171:1992;329-347.
26. Stuart G., Sakmann B., Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature. 367:1994;69-72.
27. Stuart G., Spruston N., Sakmann B., Hausser M., Action potential initiation and backpropagation in neurons of the mammalian CNS. Trends Neurosci. 20:1997;125-131.
28. Thompson W., Stent G., Neuronal control of heartbeat in the medicinal leech. I. Generation of the vascular constriction rhythm by heart motorneurons. J. Comp. Physiol. 111:1976;261-279.
29. Thompson W., Stent G., Neuronal control of heartbeat in the medicinal leech. II. Intersegmental coordination of heart motor neuron activity by heart interneurons. J. Comp. Physiol. 111:1976;281-307.
30. Thompson W., Stent G., Neuronal control of heartbeat in the medicinal leech. III. Synaptic relations of heart interneurons. J. Comp. Physiol. 111:1976;309-333.
31. Wang X., Rinzel J., Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comput. 4:1992;84-97.
32. Westberg K., Kolta A., Clavelou P., Sandstrom G., Lund J., Evidence for functional compartmentalization of trigeminal muscle spindle afferents during fictive mastication in the rabbit. J. Neurosci. 12:2000;1145-1154.