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Gap junctions destroy persistent states in excitatory networks.

Bard Ermentrout1

  • 1Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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Gap junctions disrupt neuronal persistent states by destabilizing asynchronous network activity. This study analyzes bifurcations using a partial differential equation (PDE), revealing complex dynamics and chaotic behavior.

Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Mathematical Biology

Background:

  • Persistent neural states are crucial for cognitive functions.
  • Gap junctions mediate electrical coupling between neurons, influencing network dynamics.
  • Understanding how neuronal coupling affects network stability is essential.

Purpose of the Study:

  • To investigate the impact of gap junctions between excitatory neurons on network persistent states.
  • To analyze the mechanisms of destabilization of asynchronous neural activity.
  • To develop a mathematical model for studying bifurcations in neural networks.

Main Methods:

  • Development of a partial differential equation (PDE) model to represent neural network dynamics.
  • Analysis of Hopf and homoclinic bifurcations.

Related Experiment Videos

  • Comparison of PDE model with a biophysical model.
  • Application of averaging techniques to study network stability.

    • Main Results:

    • Gap junctions were shown to disrupt the persistent state of excitatory neuronal networks.
    • Asynchronous network states lose stability through Hopf and homoclinic bifurcations.
    • The PDE model exhibited complex and potentially chaotic dynamics, especially in low noise conditions.
    • A criterion for the destabilization of the asynchronous persistent state was derived.

    Conclusions:

    • Neuronal gap junctions play a critical role in disrupting persistent neural states.
    • Mathematical modeling, including PDEs, provides valuable insights into neural network bifurcations and stability.
    • The findings contribute to understanding the mechanisms underlying neural synchrony and potential chaotic dynamics in the brain.