A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems

@article{Johnston2016ACA,
  title={A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems},
  author={M. D. Johnston and C. Pantea and P. Donnell},
  journal={Journal of Mathematical Biology},
  year={2016},
  volume={72},
  pages={467-498}
}
  • M. D. Johnston, C. Pantea, P. Donnell
  • Published 2016
  • Computer Science, Mathematics, Medicine
  • Journal of Mathematical Biology
  • We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same result is conjectured but as yet unproved for general endotactic networks. The algorithms we present are the first capable of verifying… CONTINUE READING
    12 Citations

    Figures and Topics from this paper

    A computational approach to extinction events in chemical reaction networks with discrete state spaces.
    • M. D. Johnston
    • Computer Science, Mathematics
    • Mathematical biosciences
    • 2017
    • 3
    • PDF
    Endotactic Networks and Toric Differential Inclusions
    • 4
    • PDF
    Symbolic analysis of multiple steady states in a MAPK chemical reaction network
    • D. Lichtblau
    • Computer Science, Mathematics
    • J. Symb. Comput.
    • 2021
    • 5
    Large Deviations Theory for Chemical Reaction Networks
    • 1
    • PDF
    Robust Persistence and Permanence of Polynomial and Power Law Dynamical Systems
    • 16
    • PDF
    Large deviations theory for Markov jump models of chemical reaction networks
    • 26
    • PDF
    Persistence of Some Delayed Complex Balanced Systems
    • 1
    • PDF
    Identifying parameter regions for multistationarity
    • 50
    • PDF

    References

    SHOWING 1-10 OF 39 REFERENCES
    A Petri net approach to the study of persistence in chemical reaction networks.
    • 161
    • PDF
    Persistence and Permanence of Mass-Action and Power-Law Dynamical Systems
    • 95
    • PDF
    Translated Chemical Reaction Networks
    • M. D. Johnston
    • Mathematics, Biology
    • Bulletin of mathematical biology
    • 2014
    • 23
    • PDF
    The existence and uniqueness of steady states for a class of chemical reaction networks
    • 324
    CoNtRol: an open source framework for the analysis of chemical reaction networks
    • 33
    • PDF
    Necessary and sufficient conditions for complex balancing in chemical kinetics
    • 283
    On the Persistence and Global Stability of Mass-Action Systems
    • C. Pantea
    • Mathematics, Computer Science
    • SIAM J. Math. Anal.
    • 2012
    • 63
    • PDF
    The rational parameterization theorem for multisite post-translational modification systems.
    • 84
    • PDF