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Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation.

David F Anderson1, Aidan S Howells2, Diego Rojas La Luz1

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

Bulletin of Mathematical Biology
|June 7, 2026
PubMed
Summary
This summary is machine-generated.

This study models dynamic cellular compartments where fragmentation depends on internal species. We provide new conditions for system stability, extending theories for content-mediated compartment dynamics.

Keywords:
Chemical reaction networksContinuous-time Markov chainsExplosivityPositive recurrence

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Area of Science:

  • Systems biology
  • Chemical kinetics
  • Mathematical modeling

Background:

  • Stochastic reaction networks (SRNs) with mass-action kinetics model homogeneous processes.
  • Cellular reactions are often non-homogeneous due to compartmentalization.
  • Existing models often assume static compartments or dynamics independent of contents.

Purpose of the Study:

  • To investigate a model of compartmentalization where compartment fragmentation rate depends on internal species abundance.
  • To extend the theoretical framework for compartmentalized chemistry with dynamic compartments.
  • To analyze the impact of content-mediated dynamics on compartment stability.

Main Methods:

  • Mathematical analysis of a compartmentalized stochastic reaction network model.
  • Investigating compartment fragmentation rates dependent on designated species abundance.
  • Developing new sufficient conditions for non-explosivity and positive recurrence.
  • Utilizing Lyapunov function analysis for system stability.

Main Results:

  • Demonstrated that previous explosivity characterizations fail when compartment dynamics depend on contents.
  • Established new sufficient conditions for non-explosivity and positive recurrence in content-mediated dynamic compartments.
  • Showcased the failure of static compartment assumptions in dynamic cellular environments.
  • Extended theoretical foundations for modeling complex cellular processes.

Conclusions:

  • Content-mediated compartment dynamics require specialized analytical approaches.
  • The developed conditions provide a theoretical basis for understanding systems like cell division and intracellular transport.
  • This work advances the modeling of non-homogeneous biological systems with dynamic structures.