Boston University / Center for BioDynamics / Research / Neural Dynamics Research

Contents

1. Dynamics of cortical-like networks
   1. Principles of synchronization: biophysical details matter
   2. Behavior of Rhythmic Networks can be modulated
   3. Long-distance synchronization is different for different rhythms
   4. Propagating waves in cortical networks

2. Nonlinear dynamics in single neurons
   1. Dendrites of dopaminergic neurons behave like chains of oscillators
   2. Understanding dynamics of layer 1 cells of the neocortex
   3. Dynamics and spatial extent of channel block by zinc

3. Noise in the nervous system
   1. Noise-enhanced sensory dynamics
   2. Noise-shaping in a population of coupled neurons
   3. Neurons as a model of dynamical systems with intrinsic noise sources

4. Central Pattern Generators
   1. Synaptic properties can give rise to oscillations in passive cells
   2. Depressing synapses create a dynamical switch
   3. Fast and slow networks interact to create nested rhythms
   4. Decay of inhibition within a local circuit controls phase lags between the circuits
   5. Electrical synapses between cells of different type create unintuitive effects

2. Nonlinear dynamics in single neurons

A. Dendrites of dopaminergic neurons behave like chains of oscillators

Dopaminergic neurons from the basal ganglia have stereotypic firing patterns that are selected, but not altered, by synaptic input. C. Wilson and J. Callaway have suggested that these patterns require spatial integration within the neuron, and have constructed a model based on calcium concentration and voltage; the model describes the main dendrite as a chain of compartments, each compartment capable of oscillating, with a gradient in frequency along the chain. G Medvedev and Kopell, collaborating with Wilson and Callaway, have analyzed equations for chains of FitzHugh-Nagumo oscillators with electrical coupling between the voltage components of the oscillators. They have been able to reproduce the basic experimental results and have found surprising effects, including the result that stronger coupling can lead to longer lasting transients. In recent work, they have shown that the analysis of the FN oscillators can be extended to the original model of the Wilson and Calloway. The new work explains in physical terms what determines the time constants of the transient reaction.

Related Publications

C.J. Wilson and J.C. Callaway "A coupled oscillator model of the dopinerergic neuron of the Substantia Nigra", J. Neurophysiol 83 (2000) 3084-3110. G. Medvedev and N. Kopell, "Synchronization and transient dynamics in chains of Fitzhugh-Nagumo oscillators with strong electrical coupling", SIAM J. Appl. Math., 61 (2001) 1762-1801. G. Medvedev, C. Wilson, J. Callaway and N. Kopell, "Transient dynamics in the dendrite of a dopaminergic neuron as a consequence of spatial interactions of oscillatory compartments", preprint 2002.

B. Understanding the dynamics of layer 1 cells of the neocortex

Related Publications
	Budde, T. and White, J.A. (1998) "The voltage-dependent conductances of neocortical layer I neurons" Eur. J. Neurosci. 10: 2309-2321.

C. The dynamics and spatial extent of channel block by zinc

Several groups have postulated that molecular zinc serves as a novel neuromodulatory agent and/or endogenous neurotoxin in specific areas of the brain, including the hippocampal formation. G. Cuda, C. Mercogliano and J. White are measuring the spatial distributions of zinc-sensitive channels, as well as dynamics of channel block by molecular zinc, in order to understand the computational consequences of the pharmacology of zinc.

Related Publications
	J.A. White, A. Alonso, and A.R. Kay, "A heart-like Na+ current in the medial entorhinal cortex", Neuron 1993, 11: 1037-1047.

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