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Attractor Stability in Finite Asynchronous Biological System Models.

Henning S Mortveit1, Ryan D Pederson2

  • 1Engineering Systems and Environment and Network Systems Science & Advanced Computing, University of Virginia, Charlottesville, VA, USA.

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|January 19, 2019
PubMed
Summary

This study introduces mathematical techniques to analyze biological system dynamics, reducing computational costs for studying asynchronous models. It reveals distinct attractor structures in the lac operon and C. elegans cell cycle models, enhancing understanding of their robustness.

Keywords:
Attractor structuresBoolean networksClassificationDiscrete dynamical systemsEnumerationLong-term behaviorSequential dynamical systemsUpdate schedules

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Area of Science:

  • Computational Biology
  • Dynamical Systems Theory
  • Mathematical Modeling

Background:

  • Analyzing long-term dynamics of asynchronous biological systems is computationally challenging.
  • Previous work focused on comparing exact states and transitions, limiting scalability.
  • Understanding attractor configurations is crucial for biological system robustness.

Purpose of the Study:

  • To develop novel mathematical techniques for exhaustive studies of asynchronous biological system dynamics.
  • To extend existing methods for analyzing attractor configurations under varying update orders.
  • To computationally assess the robustness of biological models by characterizing their attractor structures.

Main Methods:

  • Extended the notion of [Formula: see text]-equivalence for graph dynamical systems.
  • Adapted combinatorial theory for dynamical systems to reduce computational complexity.
  • Developed and applied a detailed algorithm to specific biological models (lac operon, C. elegans cell cycle).

Main Results:

  • Significantly reduced the number of update orders to consider for the lac operon model (from [Formula: see text] to 344).
  • Identified 4 distinct attractor structures for the lac operon model and 125 for the C. elegans model.
  • Demonstrated the computational tractability of analyzing attractor structures up to topological conjugation.

Conclusions:

  • The developed methods provide efficient tools for analyzing complex biological system dynamics.
  • The characterization of attractor structures offers insights into the robustness of biological networks.
  • This approach enables a more comprehensive understanding of system behavior under asynchronous updates.