Boston University / Center for BioDynamics / Research / Neural Dynamics 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


4. Central pattern generators

A. Synaptic properties can give rise to oscillations in passive cells

Manor et al (1999) looked in detail at the mechanism that produces the gastric mill oscillation in the crustacean stomatogastric system. There are a pair of cells with mutual inhibition, but they oscillate only in the presence of excitation to one of the cells gated by the voltage of that cell. Provided that synapses are graded, the system can then oscillate even if the two primary cells are entirely passive; the inhibitory synapses provide the equivalent of a negative slope resistance in the I-V curves of the cells.

Related Publications
 

Y. Manor, F. Nadim, S. Epstein, J. Ritt, E. Marder, N. Kopell, "Network oscillations generated by balancing asymmetric inhibition in passive neurons", J. Neurosci., 19 (1999) 2765-2779.

B. Depressing synapses create a dynamical switch

For a subnetwork of the crustacean STG, Nadim et al showed that a depressing inhibitory synapse can produce a switch in control of frequency of the network. A small change in the conductance of this synapse can lead, via network interactions, to an order of magnitude change in the strength of the synapse. For low values of the conductance the frequency is controlled by intrinsic processes; for higher values, the kinetics of the synapse become important.

Related Publications
 

F. Nadim, Y. Manor, N. Kopell and E. Marder, "Synaptic depression creates a switch that controls the frequency of an oscillator circuit". Proc. of Nat Acad. Sci. USA 96 (1999) 8206-8211.

C. Fast and slow networks interact to create nested rhythms

LoFaro and Kopell analyzed a 3-cell network of the crustacean STG that displays nested rhythms in two frequencies. They developed a method to reduce the dynamics to a one-dimensional map. The explicit reduction procedure enables one to see how changing parameters (such has conductance of the h-current) changes the network behavior.

Related Publications
 

T. LoFaro and N. Kopell, "Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map", J. Math Biol., 38: 479-533 (1999)

F. Nadim, Y. Manor, M.P. Nusbaum, E. Marder, "Frequency regulation of a slow rhythm by a fast periodic input", J. Neurosci. 18 (1998) 5053-5067.

D. Decay of inhibition within a local circuit controls phase lags between the circuits

The crayfish swimmeret CPG network is able to keep intersegmental phase lags and individual cell duty cycles constant at different frequencies. F. Skinner and B. Mulloney (1998) created a biophysically-based model that reproduced this invariance with realistic intersegmental phase lags. In recent work, S.R. Jones, T. Kaper and N. Kopell use a modified version of the Skinner/Mulloney model to reveal, numerically and analytically, that the rate of decay of the inhibition within a local circuit is a critical factor in determining both intersegmental phase lags and duty cycle in this model.

Related Publications
 

F. Skinner and B. Mulloney, "Intersegmental coordination of limb movements during locomotion: Mathematical models predict circuits that drive swimmeret beating", J. Neurosci 18:3831-3842 (1998).

F. Skinner, N. Kopell and B. Mulloney, "How does the crayfish swimmeret system work: Insights from nearest neighbor coupled models", J. Comp. Neuro., 4 (1997) 151-160.

S.R. Jones, B. Mulloney, T. Kaper, and N.Kopell, "Coordination of cellular pattern-generating circuits that control limb movements: the sources of stable differences in intersegmental phases" Preprint 2002

E. Electrical coupling between cells of different type create unintuitive effects

Electrical synapses can have unintuitive effects when coupling cells with different dynamical properties. Motivated by a subnetwork of the STG, Kopell et al analyzed a two-cell network consisting of a pacemaker cell and a bistable cell, coupled electrically. The work includes new geometric methods for understanding how the wave form of the coupled network depends on the intrinsic properties of the neurons and coupling strength. The techniques can be generalized to somewhat larger networks containing both electrical coupling and chemical synapses.

Related Publications
 

N. Kopell, L. Abbott and C. Soto-Trevino, "On the behavior of a neural oscillator electrically coupled to a bistable element", Physica D. 121 (1998) 367-395..

Further information is available from Dr. Kopell's homepage in the mathematics department.


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