Related papers: What makes a reaction network "chemical"?
Associated with a chemical reaction network is a natural labelled bipartite multigraph termed an SR graph, and its directed version, the DSR graph. These objects are closely related to Petri nets. The construction of SR and DSR graphs for…
We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…
Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks…
We derive the nonequilibrium conductance matrix for open stationary Chemical Reaction Networks (CRNs) described by a deterministic mass action kinetic equation. As an illustration, we determine the nonequilibrium conductance matrix of a CRN…
Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
The automated inference of physically interpretable (bio)chemical reaction network models from measured experimental data is a challenging problem whose solution has significant commercial and academic ramifications. It is demonstrated,…
Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be…
Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology,…
A reaction system exhibits "absolute concentration robustness" (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
The construction of a reaction network containing all relevant intermediates and elementary reactions is necessary for the accurate description of chemical processes. In the case of a complex chemical reaction (involving, for instance, many…
Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector…
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…
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…
Chemical reaction networks (CRN) comprise an important class of models to understand biological functions such as cellular information processing, the robustness and control of metabolic pathways, circadian rhythms, and many more. However,…
Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…
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…
Certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) which is achieved by imposing network-related…