Related papers: What makes a reaction network "chemical"?
Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields…
Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a…
Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet,…
The process of genetic recombination can be seen as a chemical reaction network with mass-action kinetics. We review the known results on existence, uniqueness, and global stability of an equilibrium in every compatibility class and for all…
We establish a new relationship between monotonicity and contractivity and use this connection to describe a new general class of weakly contractive reaction networks. The new class is characterized by the stoichiometry matrix of the…
Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…
Some results are presented on how oscillation is inherited by chemical reaction networks (CRNs) when they are built in natural ways from smaller oscillatory networks. The main results describe four important ways in which a CRN can be…
Persistency is the property, for differential equations in $\R^n$, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction property:…
Retrosynthesis is one of the fundamental problems in organic chemistry. The task is to identify reactants that can be used to synthesize a specified product molecule. Recently, computer-aided retrosynthesis is finding renewed interest from…
We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary -- linear or nonlinear -- open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
We establish a generalized work theorem for stochastic chemical reaction networks (CRNs). By using a compensated Poisson jump process, we identify a martingale structure in a generalized entropy defined relative to an auxiliary backward…
This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems…
At the microscopic scale, open chemical reaction networks are described by stochastic reactions that follow mass-action kinetics and are coupled to chemostats. We show that closed chemical reaction networks -- with specific stoichiometries…
The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible…
In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal…