Phase response properties of half-center oscillators

We examine the phase response properties of half-center oscillators (HCOs) that are modeled by a pair of Morris-Lecar-type neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for half-center oscillations, “release” and “escape”, give rise to strikingly different phase response curves (PRCs). Release-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escape-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of Morris-Lecar-type HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying the shapes of the PRCs. To demonstrate the significance of the different shapes of the PRCs for the release-type and escape-type HCOs, we link the shapes of the PRCs to the different frequency modulation properties of release-type and escape-type HCOs, and we show that the different shapes of the PRCs for the release-type and escape-type HCOs can lead to fundamentally different phase-locking dynamics.

[1]  Tamara Joy Schlichter,et al.  Modeling the Dynamics of Central Pattern Generators and Anesthetic Action , 2011 .

[2]  Scott L. Hooper.  Central Pattern Generators , 2001 .

[3]  G. Ermentrout,et al.  Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator. , 1990, Journal of neurophysiology.

[4]  B. Mulloney,et al.  Coordination of Cellular Pattern-Generating Circuits that Control Limb Movements: The Sources of Stable Differences in Intersegmental Phases , 2003, The Journal of Neuroscience.

[5]  G. Ermentrout,et al.  Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion , 1992, Trends in Neurosciences.

[6]  Germán Mato,et al.  Synchrony in Excitatory Neural Networks , 1995, Neural Computation.

[7]  Brian Mulloney,et al.  Neurobiology of the crustacean swimmeret system , 2012, Progress in Neurobiology.

[8]  O. Kiehn.  Locomotor circuits in the mammalian spinal cord. , 2006, Annual review of neuroscience.

[9]  G Bard Ermentrout,et al.  Phase-response curves of coupled oscillators. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[11]  Kazuyuki Aihara,et al.  Synchronization of Firing in Cortical Fast-Spiking Interneurons at Gamma Frequencies: A Phase-Resetting Analysis , 2010, PLoS Comput. Biol..

[12]  Brian Mulloney,et al.  Local and intersegmental interactions of coordinating neurons and local circuits in the swimmeret system. , 2007, Journal of neurophysiology.

[13]  Robert Clewley,et al.  Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation , 2011, Journal of biological physics.

[14]  Eve Marder,et al.  Subharmonic Coordination in Networks of Neurons with Slow Conductances , 1994, Neural Computation.

[15]  R. Satterlie.  Reciprocal Inhibition and Postinhibitory Rebound Produce Reverberation in a Locomotor Pattern Generator , 1985, Science.

[16]  J C Smith,et al.  Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms. , 2007, Journal of neurophysiology.

[17]  Thelma L. Williams,et al.  The Calculation of Frequency-Shift Functions for Chains of Coupled Oscillators, with Application to a Network Model of the Lamprey Locomotor Pattern Generator , 2004, Journal of Computational Neuroscience.

[18]  Eve Marder,et al.  Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks , 1994, Journal of Computational Neuroscience.

[19]  Robert Clewley,et al.  Erratum to: Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation , 2011 .

[20]  S. Coombes.  Phase locking in networks of synaptically coupled McKean relaxation oscillators , 2001 .

[21]  John Guckenheimer,et al.  Dissecting the Phase Response of a Model Bursting Neuron , 2009, SIAM J. Appl. Dyn. Syst..

[22]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[23]  Ilya A. Rybak,et al.  Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis , 2009, Journal of Computational Neuroscience.

[24]  S. Grillner.  The motor infrastructure: from ion channels to neuronal networks , 2003, Nature Reviews Neuroscience.

[25]  Nava Rubin,et al.  Mechanisms for Frequency Control in Neuronal Competition Models , 2008, SIAM J. Appl. Dyn. Syst..

[26]  Idan Segev,et al.  Methods in neuronal modeling: From synapses to networks , 1989 .

[27]  Eugene M. Izhikevich,et al.  Phase Equations for Relaxation Oscillators , 2000, SIAM J. Appl. Math..

[28]  F. Nadim,et al.  Inhibitory feedback promotes stability in an oscillatory network , 2011, Journal of neural engineering.

[29]  Carson C. Chow,et al.  Role of mutual inhibition in binocular rivalry. , 2011, Journal of neurophysiology.

[30]  Robert J. Butera,et al.  Phase Response Curves in Neuroscience , 2012, Springer Series in Computational Neuroscience.

[31]  Donald M. Wilson,et al.  Behavioral Neuroscience , 2019 .

[32]  Michael A Schwemmer,et al.  Effects of dendritic load on the firing frequency of oscillating neurons. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[34]  E. Marder,et al.  Principles of rhythmic motor pattern generation. , 1996, Physiological reviews.

[35]  Ronald L. Calabrese,et al.  Half-center oscillators underlying rhythmic movements , 1998 .

[36]  Brian Mulloney,et al.  Coordination of Rhythmic Motor Activity by Gradients of Synaptic Strength in a Neural Circuit That Couples Modular Neural Oscillators , 2009, The Journal of Neuroscience.

[37]  Garrison W. Cottrell,et al.  Analysis of Oscillations in a Reciprocally Inhibitory Network with Synaptic Depression , 2002, Neural Computation.

[38]  John Rinzel,et al.  Synchronization of Electrically Coupled Pairs of Inhibitory Interneurons in Neocortex , 2007, The Journal of Neuroscience.

[39]  W. O. Friesen,et al.  Neuronal control of leech behavior , 2005, Progress in Neurobiology.

[40]  L. Schimansky-Geier,et al.  Kuramoto, Y., Chemical Oscillations, Waves, and Turbulence. Berlin-Heidelberg-New York-Tokyo, Springer-Verlag 1984. VIII, 156 S., 41 Abb., DM 79,—. US $ 28.80. ISBN 3-540-13322-4 (Springer Series in Synergetics 19) , 1986 .

[41]  Nancy Kopell,et al.  Rapid synchronization through fast threshold modulation , 1993, Biological Cybernetics.

[42]  Michael A. Schwemmer,et al.  Experimentally Estimating Phase Response Curves of Neurons: Theoretical and Practical Issues , 2012 .

[43]  G. Bard Ermentrout,et al.  Analytic approximations of statistical quantities and response of noisy oscillators , 2011 .

[44]  Michael A. Schwemmer,et al.  The Theory of Weakly Coupled Oscillators , 2012 .

[45]  T. Brown.  On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system , 1914, The Journal of physiology.

[46]  G. Ermentrout,et al.  Coupled oscillators and the design of central pattern generators , 1988 .

[47]  Philip Holmes,et al.  On the derivation and tuning of phase oscillator models for lamprey central pattern generators , 2008, Journal of Computational Neuroscience.

[48]  Allen I. Selverston,et al.  Oscillatory Mechanisms in Pairs of Neurons Connected with Fast Inhibitory Synapses , 1997, Journal of Computational Neuroscience.

[49]  Nava Rubin,et al.  Dynamical characteristics common to neuronal competition models. , 2007, Journal of neurophysiology.

[50]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[51]  Paul S. G. Stein,et al.  Motor pattern deletions and modular organization of turtle spinal cord , 2008, Brain Research Reviews.

[52]  Xiao-Jing Wang,et al.  Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons , 1992, Neural Computation.

[53]  J. Brumberg,et al.  Cortical pyramidal cells as non-linear oscillators: Experiment and spike-generation theory , 2007, Brain Research.

[54]  A. Selverston,et al.  Modeling the gastric mill central pattern generator of the lobster with a relaxation-oscillator network. , 1993, Journal of neurophysiology.

[55]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .