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BIBO stability of continuous and discrete -time systems

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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Dynamical instability in Boolean networks as a percolation problem.

Shane Squires1, Edward Ott, Michelle Girvan

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742, USA. squires@umd.edu

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Boolean networks, used in gene regulation, show a phase transition. This transition maps to a static percolation problem, predicting perturbation effects on gene circuits.

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Area of Science:

  • Systems biology
  • Computational biology
  • Network dynamics

Background:

  • Boolean networks are a key tool for modeling gene regulatory networks.
  • These networks exhibit critical dynamics characterized by a phase transition.
  • Understanding perturbation effects is crucial for predicting network behavior.

Purpose of the Study:

  • To map the phase transition in Boolean network dynamics to a static percolation problem.
  • To establish a predictive framework for the long-time behavior of perturbed gene regulatory networks.

Main Methods:

  • Analysis of Boolean network dynamics.
  • Numerical verification of theoretical mappings.
  • Application of concepts from percolation theory.

Main Results:

  • The phase transition in Boolean network dynamics is shown to be equivalent to a static percolation problem.
  • This mapping accurately predicts the long-time average Hamming distance between perturbed and unperturbed network states.
  • The study provides a novel link between dynamical transitions and static network properties.

Conclusions:

  • Percolation theory offers a powerful framework for understanding Boolean network dynamics.
  • The findings facilitate predictions of gene regulatory network robustness and sensitivity to perturbations.
  • This work bridges concepts from statistical physics and systems biology.