Related papers: Sustained oscillations in the MAP kinase cascade
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 about the qualitative properties of…
Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site phosphorylated first…
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely, the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for…
Phosphorylation networks, representing the mechanisms by which proteins are phosphorylated at one or multiple sites, are ubiquitous in cell signalling and display rich dynamics such as unlimited multistability. Dual-site phosphorylation…
We mathematically modeled the receptor-activated MAP kinase signaling by incorporating the regulation through cellular phosphatases. Activation induced the alignment of a phosphatase cascade in parallel with the MAP kinase pathway. A novel…
Interconvertible enzyme cascades, exemplified by the mitogen activated protein kinase (MAPK) cascade, are a frequent mechanism in signal transduction pathways. There has been much speculation as to the role of these pathways, and how their…
The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system…
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
Systems of ODEs coupled with the topology of a closed ring are common models in biology, robotics, electrical engineering, and many other areas of science. When the component systems and couplings are identical, the system has a cyclic…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade, where in each layer of the cascade a protein is phosphorylated at two sites. It has…
Double phosphorylation of protein kinases is a common feature of signalling cascades. This motif may reduce cross-talk between signalling pathways, as the second phosphorylation site allows for proofreading, especially when phosphorylation…
Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex…
We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…