Related papers: Semigroup models for biochemical reaction networks
We show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity for multiple nondegenerate equilibria and/or periodic…
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…
In the field of complex systems, self-organization magnifies the compounding effects of element interactions by propagating, modifying, and enhancing functionality, ultimately leading to emergent system properties. The intricacies of…
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Living systems contain intricate biochemical networks whose structure is closely related to their function and allows them to exhibit robust behavior in the presence of external stimuli. Such networks typically involve catalytic enzymes,…
The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions are usually…
The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of…
Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as…
It is becoming widely accepted that very early in the origin of life, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and…
Emergent behavior in complex systems arises from nonlinear interactions among components, yet the intricate nature of self-organization often obscures the underlying causal relationships, long regarded as the "holy grail" of complexity…
The Chemical Reaction Network (CRN) is a well-studied model that describes the interaction of molecules in well-mixed solutions. In 2014, Qian and Winfree [22] proposed the abstract surface chemical reaction network model (sCRN), which…
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 present a thermodynamically consistent model describing the dynamics of a multi-component mixture where one enzyme component catalyzes a reaction between other components. We find that the catalytic activity alone can induce phase…
Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of…
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…
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…
Similarly to gear systems in vehicles, most chemical reaction networks (CRNs) involved in energy transduction have at their disposal multiple transduction pathways, each characterized by distinct efficiencies. We conceptualize these…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
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…