相关论文: Graphical Requirements for Multistationarity in Re…

We discuss properties which must be satisfied by a genetic network in order for it to allow differentiation. These conditions are expressed as follows in mathematical terms. Let $F$ be a differentiable mapping from a finite dimensional real…

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…

Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult,…

Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like…

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been…

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we…

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…

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…

We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…

The sheer amounts of biological data that are generated in recent years have driven the development of network analysis tools to facilitate the interpretation and representation of these data. A fundamental challenge in this domain is the…

For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We…

We study binomiality of the steady state ideals of chemical reaction networks. Considering rate constants as indeterminates, the concept of unconditional binomiality has been introduced and an algorithm based on linear algebra has been…

In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…

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…

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…

Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address…

Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…

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…

Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…