A global convergence result for processive multisite phosphorylation systems

DOI10.1007/s11538-014-0054-4zbMath1334.92169arXiv1404.5524OpenAlexW2135846414WikidataQ50987140 ScholiaQ50987140MaRDI QIDQ2352437

Carsten Conradi, Anne Shiu

Publication date: 1 July 2015

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.5524

zbMATH Keywords

global convergencesteady statemonotone systemsmass-action kineticsreaction networkmultisite phosphorylationmonomial parametrization

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Systems biology, networks (92C42)

Related Items (21)

Stability analysis of the Michaelis-Menten approximation of a mixed mechanism of a phosphorylation system ⋮ Sustained oscillations in the MAP kinase cascade ⋮ Dynamics of ERK regulation in the processive limit ⋮ Intermediates and generic convergence to equilibria ⋮ An all-encompassing global convergence result for processive multisite phosphorylation systems ⋮ Computing weakly reversible deficiency zero network translations using elementary flux modes ⋮ Emergence of oscillations in a mixed-mechanism phosphorylation system ⋮ A computational approach to steady state correspondence of regular and generalized mass action systems ⋮ Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks ⋮ Chemical reaction network approaches to biochemical systems theory ⋮ Families of toric chemical reaction networks ⋮ A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems ⋮ Algebra and Geometry in the Study of Enzymatic Cascades ⋮ Precluding oscillations in Michaelis-Menten approximations of dual-site phosphorylation systems ⋮ The effect of site-to-site variability in ultrasensitive dose responses ⋮ Global stability of a class of futile cycles ⋮ On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle ⋮ Complexity of model testing for dynamical systems with toric steady states ⋮ Oscillations and bistability in a model of ERK regulation ⋮ Lower bounds for positive roots and regions of multistationarity in chemical reaction networks ⋮ Algebra, geometry and topology of ERK kinetics

Uses Software

• CoNtRol
• crntwin

Cites Work

• Unnamed Item
• Unnamed Item
• Chemical reaction systems with toric steady states
• Translated chemical reaction networks
• \(n\)-site phosphorylation systems with \(2n-1\) steady states
• Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates
• A proof of bistability for the dual futile cycle
• On the number of steady states in a multiple futile cycle
• The rational parameterisation theorem for multisite post-translational modification systems
• Multiple steady states for chemical reaction networks of deficiency one
• Concordant chemical reaction networks
• Global convergence in systems of differential equations arising from chemical reaction networks
• MAPK's networks and their capacity for multistationarity due to toric steady states
• Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements
• Multistationarity in sequential distributed multisite phosphorylation networks
• Frequency spectra and probability distributions for quantum fluctuations
• Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles
• Multistationarity in the activation of a MAPK: parametrizing the relevant region in parameter space
• A Petri net approach to the study of persistence in chemical reaction networks
• Some Results on Injectivity and Multistationarity in Chemical Reaction Networks
• Local and Global Stability of Equilibria for a Class of Chemical Reaction Networks
• Power-Law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species
• A Geometric Approach to the Global Attractor Conjecture
• Simplifying the Jacobian Criterion for Precluding Multistationarity in Chemical Reaction Networks
• Global Asymptotic Stability for a Class of Nonlinear Chemical Equations
• Monotonicity in chemical reaction systems
• Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

This page was built for publication: A global convergence result for processive multisite phosphorylation systems