Related papers: Connectivity of Parameter Regions of Multistationa…
Multisite phosphorylation is a signaling mechanism well known to give rise to multiple steady states, a property termed multistationarity. When phosphorylation occurs in a sequential and distributive manner, we obtain a family of networks…
A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial…
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 distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and…
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…
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…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a…
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…
We apply tools from real algebraic geometry to the problem of multistationarity of chemical reaction networks. A particular focus is on the case of reaction networks whose steady states admit a monomial parametrization. For such systems we…
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…
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
In this paper we introduce a new representation for the multistationarity region of a reaction network, using polynomial superlevel sets. The advantages of using this polynomial superlevel set representation over the already existing…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative…
We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…
Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more…