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Intermediates, catalysts, persistence, and boundary steady states.

Michael Marcondes de Freitas1, Elisenda Feliu1, Carsten Wiuf2

  • 1Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.

Journal of Mathematical Biology
|August 3, 2016
PubMed
Summary

This study introduces graphical methods to simplify chemical reaction networks, ensuring species persistence. These techniques efficiently reduce network complexity while preserving essential properties for dynamical systems analysis.

Keywords:
Boundary steady statesCatalystsIntermediatesModel reductionPersistencePost-translational modificationReaction network theory

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Area of Science:

  • Chemical kinetics
  • Dynamical systems theory
  • Systems biology

Background:

  • Persistence in chemical reaction networks is crucial for biological systems.
  • Simplifying complex networks is essential for analysis.
  • Existing methods for assessing persistence can be computationally intensive.

Purpose of the Study:

  • To develop graphical procedures for simplifying chemical reaction networks.
  • To maintain necessary and sufficient conditions for network persistence.
  • To provide a tool for checking boundary steady states.

Main Methods:

  • Iterative removal of intermediates and catalysts from reaction networks.
  • Graphical analysis of network structures.
  • Characterization using graph strong connectivity properties.

Main Results:

  • Two graphical procedures for network simplification were developed.
  • Simplified networks often exhibit structures like monomolecular networks.
  • Persistence conditions were shown to be equivalent for specific network classes.
  • Connectivity properties of related graphs characterize persistence.

Conclusions:

  • Graphical simplification methods preserve network persistence properties.
  • The methods are applicable to various systems, including post-translational modification cascades.
  • This approach offers an efficient graphical tool for analyzing network dynamics and boundary states.