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This study reveals how line attractors in neuronal networks enable graded information processing through pulse gating. These dynamics, arising from a cusp catastrophe, ensure robust information propagation in the brain.

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Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Neural Network Modeling

Background:

  • Line attractors are hypothesized to underlie various brain functions, including memory and sensory processing.
  • Their neutral stability allows for time-translational invariance, crucial for propagating graded information.
  • Understanding their manifestation in complex feed-forward networks remains a challenge.

Purpose of the Study:

  • To connect line attractors with pulse gating mechanisms in feed-forward neuronal networks.
  • To analyze the dynamics of pulse-gated information propagation in a nonlinear integrate-and-fire network.
  • To identify the structural and dynamical basis of line attractors in biologically realistic neural systems.

Main Methods:

  • Utilized a Fokker-Planck approach to analyze the system dynamics of a high-dimensional, nonlinear feed-forward network.
  • Connected pulse-gated propagation in Fokker-Planck models with population-averaged mean-field (firing rate) models.
  • Identified and analyzed an approximate line attractor in state space, characterized by specific fixed points and dynamics.

Main Results:

  • An approximate line attractor was identified as the core structure for graded information propagation.
  • This line attractor emerges at a cusp catastrophe, involving a fold bifurcation dependent on synaptic noise.
  • Ghost dynamics near the cusp's fold were shown to underlie the robustness of the line attractor.

Conclusions:

  • Line attractors can persist in biologically realistic neuronal networks through the dynamics of cusp catastrophes.
  • The interplay of pulse gating, synaptic coupling, and neuronal stochasticity enables one-dimensional attracting manifolds.
  • This mechanism dynamically controls the processing and propagation of graded information in neural circuits.