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Related Experiment Videos

Stable and unstable attractors in Boolean networks.

Konstantin Klemm1, Stefan Bornholdt

  • 1Department of Bioinformatics, University of Leipzig, Härtelstr. 16-18, D-04107 Leipzig, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

Boolean network attractors are often artifacts of synchronous updates. Noise-resilient attractors in these systems exhibit sublinear scaling with size, offering insights for biological modeling.

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Area of Science:

  • Computational biology
  • Complex systems theory
  • Dynamical systems

Background:

  • Boolean networks are widely used to model gene regulatory networks and other complex systems.
  • Attractor dynamics in Boolean networks, particularly at critical points, are crucial for understanding system stability and behavior.
  • Previous studies suggested superpolynomial scaling of attractors with system size under deterministic parallel updates.

Purpose of the Study:

  • To re-evaluate attractor stability in Boolean networks, considering the impact of update schemes.
  • To investigate the significance of attractors for biological systems where noise is prevalent.
  • To determine how attractor numbers scale with system size when considering noise resilience.

Main Methods:

  • Analysis of Boolean networks using deterministic parallel update.

Related Experiment Videos

  • Testing attractor stability against infinitesimal deviations from synchronous updates.
  • Investigating the impact of fluctuating delays on attractor stability.
  • Numerical simulations to assess scaling of stable attractors with system size.

    • Main Results:

    • A significant fraction of attractors identified through deterministic parallel updates are artifacts of the synchronous updating scheme.
    • Only attractors stable against fluctuating delays are considered robust.
    • The number of these stable attractors grows sublinearly with system size within the numerically tractable range.

    Conclusions:

    • The superpolynomial scaling of attractors reported in prior studies may be an artifact of the deterministic parallel update method.
    • Robust attractors, resilient to noise and update fluctuations, exhibit sublinear scaling, aligning better with expectations for biological systems.
    • This revised understanding of attractor dynamics is critical for developing more realistic simplified models of biological systems.