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Multistationarity in Cyclic Sequestration-Transmutation Networks.

Gheorghe Craciun1, Badal Joshi2, Casian Pantea3

  • 1Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA.

Bulletin of Mathematical Biology
|May 11, 2022
PubMed
Summary
This summary is machine-generated.

This study characterizes multistationarity in reaction networks with sequestration and transmutation feedback cycles. These networks serve as fundamental "atoms of multistationarity," demonstrating minimal systems capable of multiple positive steady states.

Keywords:
Atoms of multistationarityGeneral kineticsMass-action kineticsMultistationarityReaction networksSequestration-transmutation networksVEGFR dimerization

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Area of Science:

  • Systems biology
  • Biochemical reaction networks
  • Nonlinear dynamics

Background:

  • Reaction networks are fundamental to understanding biological processes.
  • Multistationarity, the ability to exhibit multiple stable steady states, is a key feature in biological regulation.
  • Understanding the minimal network structures that give rise to multistationarity is crucial for systems biology.

Purpose of the Study:

  • To investigate and fully characterize the capacity for multistationarity in a specific class of reaction networks.
  • To identify and analyze simple network motifs, termed "atoms of multistationarity," that exhibit multiple positive steady states.
  • To provide a theoretical framework for understanding complex behaviors in biological systems.

Main Methods:

  • Analysis of reaction networks involving sequestration (mutual inactivation) and transmutation (species transformation).
  • Mathematical characterization of the conditions leading to multistationarity.
  • Identification of minimal network structures capable of generating multiple steady states.

Main Results:

  • Complete characterization of the multistationarity capacity for the considered class of reaction networks.
  • Demonstration that these networks act as fundamental "atoms of multistationarity."
  • Identification of specific network structures that guarantee multiple positive steady states.

Conclusions:

  • The studied reaction networks, featuring sequestration and transmutation with feedback, can exhibit multistationarity.
  • These networks represent the simplest building blocks for generating multiple positive steady states.
  • The findings contribute to a deeper understanding of the fundamental principles governing complex behaviors in biological systems.