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Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally power-law systems) are very common in chemistry, biology, and engineering, and are often used to… (More)

—Bistability plays a key role in important biological processes, such as cell division, differentiation, and apoptosis. Examples show that there is a very delicate relationship between the structure of a reaction network and its capacity for bistable behavior. We describe mathematical methods that discriminate between networks that have the capacity for… (More)

This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of chemical reaction network theory: the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of… (More)

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental… (More)

Dynamical system models of complex biochemical reaction networks are high-dimensional, nonlinear, and contain many unknown parameters. The capacity for multiple equilibria in such systems plays a key role in important biochemical processes. Examples show that there is a very delicate relationship between the structure of a reaction network and its capacity… (More)

Chemical mechanisms for even simple reaction networks involve many highly reactive and short-lived species (intermediates), present in small concentrations , in addition to the main reactants and products, present in larger concentrations. The chemical mechanism also often contains many rate constants whose values are unknown a priori and must be determined… (More)

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We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to… (More)

We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the… (More)

We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the… (More)