Related papers: Geometry of nonequilibrium reaction networks
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and…
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 develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical…
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework…
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
In this paper, we provide a graphic formulation of non-isothermal reaction systems and show that a non-isothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold…
Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…
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…
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…
Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…
The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network…
Rapid discovery of new reactions and molecules in recent years has been facilitated by the advancements in high throughput screening, accessibility to a much more complex chemical design space, and the development of accurate molecular…
It is fundamental for science and technology to be able to predict chemical reactions and their properties. To achieve such skills, it is important to develop good representations of chemical reactions, or good deep learning architectures…
In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…