Canard Induced Mixed-Mode Oscillations in a Medial Entorhinal Cortex Layer II Stellate Cell Model

Stellate cells (SCs) of the medial entorhinal cortex (layer II) display mixed-mode oscillatory activity, subthreshold oscillations (small-amplitude) interspersed with spikes (large amplitude), at theta frequencies (8–12 Hz). In this paper we study the mechanism of generation of such patterns in an SC biophysical (conductance-based) model. In particular, we show that the mechanism is based on the three-dimensional canard phenomenon and that the subthreshold oscillatory phenomenon is intrinsically nonlinear, involving the participation of both components (fast and slow) of a hyperpolarization-activated current in addition to the voltage and a persistent sodium current. We discuss some consequences of this mechanism for the SC intrinsic dynamics as well as for the interaction between SCs and external inhibitory inputs.

[1]  Y. Yarom,et al.  Resonance, oscillation and the intrinsic frequency preferences of neurons , 2000, Trends in Neurosciences.

[2]  Jianzhong Su,et al.  Analysis of a Canard Mechanism by Which Excitatory Synaptic Coupling Can Synchronize Neurons at Low Firing Frequencies , 2004, SIAM J. Appl. Math..

[3]  Bard Ermentrout,et al.  Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students , 2002, Software, environments, tools.

[4]  Nancy Kopell,et al.  Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics , 2003, Journal of Computational Neuroscience.

[5]  Michael E. Hasselmo,et al.  A biophysical simulation of intrinsic and network properties of entorhinal cortex , 1999, Neurocomputing.

[6]  Lisa M. Giocomo,et al.  Temporal Frequency of Subthreshold Oscillations Scales with Entorhinal Grid Cell Field Spacing , 2007, Science.

[7]  J. Miller.  Numerical Analysis , 1966, Nature.

[8]  Eugene M. Izhikevich,et al.  Resonate-and-fire neurons , 2001, Neural Networks.

[9]  Wiktor Eckhaus,et al.  Relaxation oscillations including a standard chase on French ducks , 1983 .

[10]  M. Hasselmo,et al.  Properties and role of I(h) in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. , 2000, Journal of neurophysiology.

[11]  H. Scharfman,et al.  The parahippocampal region. Implications for neurological and psychiatric diseases. Introduction. , 2000, Annals of the New York Academy of Sciences.

[12]  Martin Wechselberger,et al.  Existence and Bifurcation of Canards in ℝ3 in the Case of a Folded Node , 2005, SIAM J. Appl. Dyn. Syst..

[13]  Heiko Richter,et al.  Developmental changes of inward rectifier currents in neurons of the rat entorhinal cortex , 1997, Neuroscience Letters.

[14]  Christopher Jones,et al.  Geometric singular perturbation theory , 1995 .

[15]  Martin Wechselberger,et al.  Bifurcations of mixed-mode oscillations in a stellate cell model , 2009 .

[16]  Eric Vanden-Eijnden,et al.  Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle. , 2008, Chaos.

[17]  A. Alonso,et al.  Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. , 1998, Journal of neurophysiology.

[18]  Horacio G. Rotstein,et al.  Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. , 2008, Chaos.

[19]  J. Winson.  Loss of hippocampal theta rhythm results in spatial memory deficit in the rat. , 1978, Science.

[20]  M. Fyhn,et al.  Spatial Representation in the Entorhinal Cortex , 2004, Science.

[21]  A. Alonso,et al.  Oscillatory Activity in Entorhinal Neurons and Circuits: Mechanisms and Function , 2000, Annals of the New York Academy of Sciences.

[22]  Horacio G. Rotstein,et al.  The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells , 2006, Journal of Computational Neuroscience.

[23]  S. Siegelbaum,et al.  Hyperpolarization-activated cation currents: from molecules to physiological function. , 2003, Annual review of physiology.

[24]  R. A. Davidoff.  Neural Control of Rhythmic Movements in Vertebrates , 1988, Neurology.

[25]  Neil Fenichel.  Persistence and Smoothness of Invariant Manifolds for Flows , 1971 .

[26]  Horacio G. Rotstein,et al.  A reduced model for medial entorhinal cortex stellate cell : subthreshold oscillations , spiking and synchronization , 2005 .

[27]  Peter Szmolyan,et al.  Multiple Time Scales and Canards in a Chemical Oscillator , 2001 .

[28]  Boris S. Gutkin,et al.  The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators , 2001, Neural Computation.

[29]  É. Benoît.  Chasse au canard , 1980 .

[30]  Miles A. Whittington,et al.  Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus , 2006, Neural Computation.

[31]  P. Szmolyan,et al.  Canards in R3 , 2001 .

[32]  T. Hafting,et al.  Microstructure of a spatial map in the entorhinal cortex , 2005, Nature.

[33]  M. Krupa,et al.  Relaxation Oscillation and Canard Explosion , 2001 .

[34]  Jonathan E. Rubin,et al.  Giant squid-hidden canard: the 3D geometry of the Hodgkin–Huxley model , 2007, Biological Cybernetics.

[35]  A. Alonso,et al.  Ionic mechanisms of muscarinic depolarization in entorhinal cortex layer II neurons. , 1997, Journal of neurophysiology.

[36]  Irina Erchova,et al.  Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. , 2004, Journal of neurophysiology.

[37]  Freddy Dumortier,et al.  Canard Cycles and Center Manifolds , 1996 .

[38]  N. Brunel,et al.  From subthreshold to firing-rate resonance. , 2003, Journal of neurophysiology.

[39]  John Guckenheimer,et al.  Asymptotic analysis of subcritical Hopf-homoclinic bifurcation , 2000 .

[40]  John Guckenheimer,et al.  Bifurcation, Bursting, and Spike Frequency Adaptation , 1997, Journal of Computational Neuroscience.

[41]  V I Nekorkin,et al.  Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. , 2001, Physical review letters.

[42]  R. Llinás,et al.  Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II , 1989, Nature.

[43]  J. White,et al.  Frequency selectivity of layer II stellate cells in the medial entorhinal cortex. , 2002, Journal of neurophysiology.

[44]  Helwig Löffelmann,et al.  GEOMETRY OF MIXED-MODE OSCILLATIONS IN THE 3-D AUTOCATALATOR , 1998 .

[45]  S. Rossignol,et al.  Neural Control of Rhythmic Movements in Vertebrates , 1988 .

[46]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[47]  Michael E Hasselmo,et al.  Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons , 2004, Hippocampus.

[48]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[49]  Corey D. Acker,et al.  Synchronization in hybrid neuronal networks of the hippocampal formation. , 2005, Journal of neurophysiology.

[50]  R. Larter,et al.  Chaos via mixed-mode oscillations , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[51]  Françoise Argoul,et al.  Homoclinic chaos in chemical systems , 1993 .

[52]  N. Kopell,et al.  Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron. , 2008, Chaos.

[53]  R. Morris.  Foundations of cellular neurophysiology , 1996 .

[54]  A. Alonso,et al.  Neuronal sources of theta rhythm in the entorhinal cortex of the rat , 1987, Experimental Brain Research.

[55]  A. Alonso,et al.  Biophysical Properties and Slow Voltage-Dependent Inactivation of a Sustained Sodium Current in Entorhinal Cortex Layer-II Principal Neurons , 1999, The Journal of general physiology.

[56]  Martin Krupa,et al.  Mixed Mode Oscillations due to the Generalized Canard Phenomenon , 2006 .

[57]  Kenneth Showalter,et al.  False bifurcations in chemical systems: canards , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[58]  A. Alonso,et al.  Neuronal sources of theta rhythm in the entorhinal cortex of the rat , 1987, Experimental Brain Research.

[59]  Horacio G. Rotstein,et al.  A Canard Mechanism for Localization in Systems of Globally Coupled Oscillators , 2003, SIAM J. Appl. Math..

[60]  Torkel Hafting,et al.  Conjunctive Representation of Position, Direction, and Velocity in Entorhinal Cortex , 2006, Science.

[61]  K. Bar-Eli,et al.  Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction , 1991 .