相关论文: A proof of bistability for the dual futile cycle
The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory…
Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the…
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological…
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In…
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…
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecules where each molecule regulates its successor in a cycle.…
The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This papers…
Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…
This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and…
Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying…
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are…
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…
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,…
Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles, limit cycle bifurcations and multistability. The results…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates, are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory and…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
Multisite phosphorylation networks are encountered in many intracellular processes like signal transduction, cell-cycle control or nuclear signal integration. In this contribution networks describing the phosphorylation and…
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…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…