A Global Convergence Result for Processive Multisite Phosphorylation Systems

@article{Conradi2015AGC,
  title={A Global Convergence Result for Processive Multisite Phosphorylation Systems},
  author={Carsten Conradi and Anne Shiu},
  journal={Bulletin of Mathematical Biology},
  year={2015},
  volume={77},
  pages={126-155}
}
Multisite phosphorylation plays an important role in intracellular signaling. There has been much recent work aimed at understanding the dynamics of such systems when the phosphorylation/dephosphorylation mechanism is distributive, that is, when the binding of a substrate and an enzyme molecule results in the addition or removal of a single phosphate group and repeated binding therefore is required for multisite phosphorylation. In particular, such systems admit bistability. Here, we analyze a… 
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References

SHOWING 1-10 OF 55 REFERENCES
Multistationarity in Sequential Distributed Multisite Phosphorylation Networks
TLDR
A systematic exploration of the region in parameter space where multistationarity occurs has become possible and one consequence of this work is that, for any pair of steady states, the ratio of the steady state concentrations of kinase- substrate complexes equals that of phosphatase-substrate complexes.
Distributivity and processivity in multisite phosphorylation can be distinguished through steady-state invariants.
TLDR
By mathematical analysis, it is shown by mathematical analysis that steady-state invariants enable the mechanism of the kinase or the phosphatase to be determined from steady- state measurements.
Unlimited multistability in multisite phosphorylation systems
TLDR
It is shown that, when kinase and phosphatase act in opposition on a multisite substrate, the system can exhibit distinct stable phospho-form distributions at steady state and that the maximum number of such distributions increases with n, reducing the complexity of calculating steady states from simulating 3 × 2n differential equations to solving two algebraic equations, while treating parameters symbolically.
Catalytic constants enable the emergence of bistability in dual phosphorylation
TLDR
Algebraic conditions present a practical way to determine the capacity for bistability and will be a useful tool for examining the origin of bistable in many models containing dual phosphorylation.
Multisite protein phosphorylation makes a good threshold but can be a poor switch.
  • J. Gunawardena
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 2005
TLDR
It is pointed out that conventional measures of ultrasensitivity must be modified to discriminate between thresholding and switching; additional factors that influence switching efficiency are discussed and new directions for experimental investigation are suggested.
Enzyme-sharing as a cause of multi-stationarity in signalling systems
TLDR
This paper determines conditions for the emergence of multi-stationarity in small motifs without feedback that repeatedly occur in signalling pathways and derives an explicit mathematical relationship φ between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available.
The geometry of multisite phosphorylation.
TLDR
A kinase-phosphatase-substrate system with two sites with no restrictions on the order of phosphorylation or dephosphorylation is considered, and it is shown that the concentrations of the four phosphoforms at steady state satisfy an algebraic formula-an invariant-that is independent of the other chemical species.
On the number of steady states in a multiple futile cycle
TLDR
The number of positive steady states of a general multisite phosphorylation–dephosphorylation cycle is studied, and it is shown that for some parameter ranges, there are at least n + 1 or n (if n is even) and there never are more than 2n − 1 steady states.
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