Related papers: A Computational Approach to Multistationarity in P…
This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the…
This work introduces a novel approach to study properties of positive equilibria of a chemical reaction network $\mathscr{N}$ endowed with Hill-type kinetics $K$, called a Hill-type kinetic (HTK) system $\left(\mathscr{N},K\right)$,…
Poly-PL kinetic systems (PYK) are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law…
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…
Poly-PL kinetic systems are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law…
Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides statements about uniqueness, existence, and stability of…
Studies about the set of positive equilibria ($E_+$) of kinetic systems have been focused on mass action, and not that much on power law kinetic (PLK) systems, even for PL-RDK systems (PLK systems where two reactions with identical reactant…
This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and 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…
There have been recent theoretic results that provide sufficient conditions for the existence of a species displaying absolute concentration robustness (ACR) in a power law kinetic (PLK) system. One such result involves the detection of ACR…
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…
Mitogen-activated protein kinase (MAPK) signaling pathways play an essential role in the transduction of environmental stimuli to the nucleus, thereby regulating a variety of cellular processes, including cell proliferation, differentiation…
We characterize completely the capacity for (nondegenerate) multistationarity of mass action reaction networks with one-dimensional stoichiometric subspace in terms of reaction structure. Specifically, we show that networks with two or more…
Robustness against the presence of environmental disruptions can be observed in many systems of chemical reaction network. However, identifying the underlying components of a system that give rise to robustness is often elusive. The…
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 present determinant criteria for the preclusion of non-degenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation…
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…
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…
We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can…
The fundamental decomposition of a chemical reaction network (also called its "$\mathscr{F}$-decomposition") is the set of subnetworks generated by the partition of its set of reactions into the "fundamental classes" introduced by Ji and…