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Symbolic dynamics and computation in model gene networks.

R. Edwards1, H. T. Siegelmann, K. Aziza

  • 1Department of Mathematics and Statistics, University of Victoria, P. O. Box 3045, STN CSC, Victoria, British Columbia, Canada V8W 3P4.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

This study models genetic networks using differential equations and graph theory. It translates system dynamics into a symbolic language, enabling analysis of chaotic behavior and network identification.

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Area of Science:

  • Computational biology
  • Nonlinear dynamics
  • Systems biology

Background:

  • Genetic networks involve complex interactions influencing cellular functions.
  • Modeling these networks is crucial for understanding gene regulation and dynamics.
  • Simplified models are needed to analyze complex genetic regulatory mechanisms.

Purpose of the Study:

  • To develop a novel framework for analyzing the dynamics of genetic networks.
  • To connect differential equation models of gene regulation to computational language theory.
  • To investigate bifurcations in chaotic dynamics and solve the inverse problem of network inference.

Main Methods:

  • Analysis of ordinary differential equations for a simplified genetic network model.
  • Representation of system dynamics using a directed graph on an n-dimensional hypercube (n-cube).

Related Experiment Videos

  • Symbolic representation of dynamics through cycle analysis and generation of a formal language.

    • Main Results:

    • Developed a symbolic language where cycles correspond to words and letters represent orthant traversals.
    • Established a connection between Poincaré maps and the generated language.
    • Demonstrated that bifurcations in chaotic dynamics correspond to changes in the language structure.

    Conclusions:

    • The developed formalism provides a new method for studying genetic network dynamics.
    • This approach integrates nonlinear dynamics with computation theory for analyzing biological systems.
    • The framework aids in understanding chaotic dynamics and inferring underlying genetic network structures.