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Multistationarity in Structured Reaction Networks.

Alicia Dickenstein1, Mercedes Pérez Millán1, Anne Shiu2

  • 1Departamento de Matemática, FCEN, Universidad de Buenos Aires e IMAS (UBA-CONICET), Ciudad Universitaria, Pab.I, 1428, Buenos Aires, Argentina.

Bulletin of Mathematical Biology
|February 22, 2019
PubMed
Summary
This summary is machine-generated.

This study develops new methods to determine if biological systems can have multiple steady states (multistationarity) and find specific parameters that cause this behavior. These techniques simplify the analysis of complex dynamical systems.

Keywords:
Binomial idealBrouwer degreeGröbner basisMass-action kineticsMultistationarityParametrizationReaction network

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Area of Science:

  • Computational Biology
  • Biochemistry
  • Dynamical Systems Theory

Background:

  • Many biological systems exhibit multistationarity, characterized by multiple positive steady states.
  • Determining multistationarity and identifying specific parameter values (witnesses) for this phenomenon is computationally challenging.

Purpose of the Study:

  • To develop novel methods for identifying multistationarity in dynamical systems.
  • To provide techniques for finding witnesses to multistationarity in biological networks.

Main Methods:

  • Utilizing generalized parametrizations of steady states to simplify sign change analysis.
  • Applying concepts from degree theory and Gröbner bases.
  • Developing methods for explicit rational parametrization of steady states.

Main Results:

  • Established conditions for multistationarity based on the sign change of a critical function with generalized parametrizations.
  • Identified necessary conditions for steady-state equations to be linearly equivalent to binomials.
  • Provided a sufficient condition for multistationarity using triangular-form equations.
  • Demonstrated effective methods for finding witnesses to multistationarity in structured biological networks.

Conclusions:

  • The developed methods offer a more accessible approach to determining multistationarity and finding witnesses.
  • These techniques are particularly applicable to reaction networks common in biological signaling pathways.
  • The study advances the understanding and computational analysis of multistationary dynamical systems.