Abstract
We describe a novel computational approach to reduce detailed models of central pattern generation to an equationless mapping that can be studied geometrically. Changes in model parameters, coupling properties, or external inputs produce qualitative changes in the mapping. These changes uncover possible biophysical mechanisms for control and modulation of rhythmic activity. Our analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying detailed models, applicable to a variety of biological phenomena beyond motor control. We demonstrate our technique on a motif of three reciprocally inhibitory cells that is able to produce multiple patterns of bursting rhythms. In particular, we examine the qualitative geometric structure of two-dimensional maps for phase lag between the cells.
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References
E. Marder, R.L. Calabrese, Principles of rhythmic motor pattern generation. Physiol. Rev. 76, 687–717 (1996)
F. Skinner, N. Kopell, E. Marder, Mechanisms for oscillation and frequency control in networks of mutually inhibitory relaxation oscillators. J. Comput. Neurosci. 1, 69–97 (1994)
A. Selverston, Model Neural Networks and Behavior (Plenum Press, New York, 1985)
K.L. Briggman, W.B. Kristan, Multifunctional pattern generating circuits. Annu. Rev. Neurosci. 31, 271–294 (2008)
W.B. Kristan, R.L. Calabrese, W.O. Friesen, Neuronal basis of leech behaviors. Prog. Neurobiol. 76, 279–327 (2005)
C.C. Canavier, D.A. Baxter, J.W. Clark, J.H. Byrne, Control of multistability in ring circuits of oscillators. Biol. Cybern. 80, 87–102 (1999)
G.B. Ermentrout, K. Kopell, Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc. Natl. Acad. Sci. USA 95, 1259–1264 (1998)
R. Milo, et al., Science 298, 824–827 (2002)
A. Prinz, D. Bucher, E. Marder, Similar network activity from disparate circuit parameters. Nat. Neurosci. 7(12), 1345–1352 (2004)
M.I. Rabinovich, P. Varona, A.I. Selverston, H.D. Abarbanel, Dynamical principles in neuroscience. Rev. Modern. Phys. 78(4), 1213–1265 (2006)
O. Sporns, R. Kötter, Motifs in brain networks. PLoS Biol. 2(11), 1910–1918 (2004)
A. Shilnikov, R. Gordon, I. Belykh, Polyrhythmic synchronization in bursting network motif. Chaos 18, 037120 (2008)
N. Kopell, D. Somers, Rapid synchronization through fast threshold modulation. Biol. Cybern. 68(5), 393–407 (1993)
A. Shilnikov, G. Cymbalyuk, Transition between tonic-spiking and bursting in a neuron model via the blue-sky catastrophe. Phys. Rev. Lett. 94, 048101-4 (2005)
I. Belykh, A. Shilnikov, When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons. Phys. Rev. Lett. 101, 078102-4 (2008)
J. Wojcik, A.L. Shilnikov, Order parameter for bursting polyrhythms in multifunctional central pattern generators. Phys. Rev. E 83, 056209-6 (2011)
J. Wojcik, Neural Cartography: Computer Assisted Poincaré Return Mappings for Biological Oscillations Mathematics Dissertations. Paper 10. http://digitalarchive.gsu.edu/math_diss/10 (2012)
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Wojcik , J., Clewley, R., Shilnikov, A. (2014). The Role of Duty Cycle in a Three Cell Central Pattern Generator. In: In, V., Palacios, A., Longhini, P. (eds) International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012). Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-02925-2_29
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DOI: https://doi.org/10.1007/978-3-319-02925-2_29
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