Related papers: Multiple positive steady states in subnetworks def…
We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and for any production factor, the fully open extension of a…
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…
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…
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of…
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…
We provide a sufficient and necessary condition in terms of the stoichiometric coefficients for a bi-reaction network to admit multistability. Also, this result completely characterizes the bi-reaction networks according to if they admit…
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,…
We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
Thomas's necessary conditions for the existence of multiple steady states in gene networks have been proved by Soul\'e with high generality for dynamical systems defined by differential equations. When applied to (protein) reaction networks…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
One important question that interests those who work in chemical reaction network theory (CRNT) is this: Does the system obtained from a reaction network admit a positive equilibrium and if it does, can there be more than one within a…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…
Here we propose a generic mechanism - networked buffering - for generating robust traits in complex systems that requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role…
Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…
This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
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…