A reduced model for medial entorhinal cortex stellate cell : subthreshold oscillations , spiking and synchronization

Entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the interspike interval (ISI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOS. This mechanism is based on the “canard structure”, in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking is controlled in the ISI by the same structure. The same mechanism is invoked to explain why noise increases the robustness of the STO

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

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

[3]  J. R. Kline.  Memoirs of the American Mathematical Society , 1949 .

[4]  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.

[5]  Nancy Kopell,et al.  Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network. , 2005, Journal of neurophysiology.

[6]  N. Kopell,et al.  Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[7]  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.

[8]  R. Llinás,et al.  Oscillatory properties of guinea‐pig inferior olivary neurones and their pharmacological modulation: an in vitro study. , 1986, The Journal of physiology.

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

[10]  Fiona E. N. LeBeau,et al.  A Model of Atropine‐Resistant Theta Oscillations in Rat Hippocampal Area CA1 , 2002, The Journal of physiology.

[11]  A. Alonso,et al.  Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer II neurons. , 1993, Journal of neurophysiology.

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

[13]  A. Alonso,et al.  High Conductance Sustained Single-Channel Activity Responsible for the Low-Threshold Persistent Na+ Current in Entorhinal Cortex Neurons , 1999, The Journal of Neuroscience.

[14]  Terrence J. Sejnowski,et al.  Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism , 1994, Journal of Computational Neuroscience.

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

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

[17]  Carson C. Chow,et al.  Spontaneous action potentials due to channel fluctuations. , 1996, Biophysical journal.

[18]  U. Heinemann,et al.  Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold , 2004, The Journal of physiology.

[19]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

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

[21]  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..

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

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

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

[25]  R. Llinás,et al.  Electrophysiology of mammalian inferior olivary neurones in vitro. Different types of voltage‐dependent ionic conductances. , 1981, The Journal of physiology.

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

[27]  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.

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

[29]  A. Alonso,et al.  Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. , 1993, Journal of neurophysiology.

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

[31]  R. Miura,et al.  Subthreshold membrane resonance in neocortical neurons. , 1996, Journal of neurophysiology.

[32]  J. White,et al.  Channel noise in neurons , 2000, Trends in Neurosciences.