## 10 Citations

### Dynamical Features of the MAP Kinase Cascade

- Mathematics
- 2017

The MAP kinase cascade is an important signal transduction system in molecular biology for which a lot of mathematical modelling has been done. This paper surveys what has been proved mathematically…

### Dynamics of ERK regulation in the processive limit

- BiologyJournal of mathematical biology
- 2021

This work considers a model of extracellular signal-regulated kinase regulation by dual-site phosphorylation and dephosphorylation, and suggests that anywhere along the way to becoming processive, the model remains bistable and oscillatory.

### A proof of unlimited multistability for phosphorylation cycles

- MathematicsNonlinearity
- 2020

This paper proves the conjecture that parameter values can be chosen such that [n/2]+1 out of 2[n/ 2]+1 steady states are asymptotically stable and the remaining steadyStates are unstable.

### Algebra and Geometry in the Study of Enzymatic Cascades

- BiologyAssociation for Women in Mathematics Series
- 2019

A general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates and include many post-translational modification networks is described.

### Symbolic hunt of instabilities and bifurcations in reaction networks

- Mathematics
- 2023

The localization of bifurcations in large parametric systems is still a challenge where the combination of rigorous criteria and informal intuition is often needed. With this motivation, we address…

### The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation

- MathematicsNonlinearity
- 2023

We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov–Hopf bifurcation (from here on abbreviated to ‘Hopf bifurcation’). It is…

### Structural obstruction to the simplicity of the eigenvalue zero in chemical reaction networks

- Mathematics
- 2022

. Multistationarity is the property of a system to exhibit two distinct equilibria (steady-states) under otherwise identical conditions, and it is a phenomenon of recognized importance for…

### Dynamics of ERK regulation in the processive limit

- BiologyJournal of Mathematical Biology
- 2021

This work considers a model of extracellular signal-regulated kinase regulation by dual-site phosphorylation and dephosphorylation, and suggests that anywhere along the way to becoming processive, the model remains bistable and oscillatory.

## References

SHOWING 1-10 OF 36 REFERENCES

### Intrinsic Feedbacks in MAPK Signaling Cascades Lead to Bistability and Oscillations

- BiologyActa biotheoretica
- 2013

The existence of interesting phenomena—oscillations and bistability—in signaling cascades possessing at least one stage with a double-phosphorylation cycle as in MAPK cascades is shown.

### Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

- BiologyEuropean journal of biochemistry
- 2000

It is demonstrated that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation, which can range from minutes to hours.

### A Hidden Feedback in Signaling Cascades Is Revealed

- BiologyPLoS Comput. Biol.
- 2008

A key feature of the new model is that a negative feedback emerges naturally, exerted between each cycle and its predecessor, and the system displays damped temporal oscillations under constant stimulation and propagates perturbations both forwards and backwards.

### Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades

- BiologyThe Journal of cell biology
- 2004

It is demonstrated that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation.

### Using chemical reaction network theory to discard a kinetic mechanism hypothesis.

- BiologySystems biology
- 2005

It is shown that, unexpectedly, multilayered protein kinase cascades can exhibit multistationarity, even on a single cascade level, and that their assumption of a distributive mechanism for double phosphorylation and dephosphorylation is crucial for multistatedarity on the single cascadelevel.

### Ultrasensitivity in the mitogen-activated protein kinase cascade.

- BiologyProceedings of the National Academy of Sciences of the United States of America
- 1996

It is demonstrated that the cascade arrangement has unexpected consequences for the dynamics of MAPK signaling, and MAPK is predicted to behave like a highly cooperative enzyme, even though it was not assumed that any of the enzymes in the cascade were regulated cooperatively.

### A Global Convergence Result for Processive Multisite Phosphorylation Systems

- BiologyBulletin of mathematical biology
- 2015

This work analyze a different class of multisite systems, in which the binding of a substrate and an enzyme molecule results in the addition or removal of phosphate groups at all phosphorylation sites, and shows that processive systems modeled with mass-action kinetics do not admit bistability and exhibit rigid dynamics.

### Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling

- PhysicsPLoS Comput. Biol.
- 2007

A methodology for the statistical analysis of mechanistic signaling models based on the combination of random parameter search and continuation algorithms is developed and it is argued that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics.

### Competing docking interactions can bring about bistability in the MAPK cascade.

- BiologyBiophysical journal
- 2007

The feedback mechanism proposed in this article synergizes with such enzyme depletion effects to bring about a much larger bistable range than either mechanism alone, and shows that stable docking interactions and competition effects, which are common in protein kinase cascades, can result in sequestration-based feedback, and thus can have profound effects on the qualitative behavior of signaling pathways.