Related papers: Modeling of chemical reaction systems with detaile…
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…
The temporal evolution of the levels in a three-level laser is macroscopically described by a closed set of rate equations. Here, we complement this picture by providing a model which describes through chemical reactions how the levels are…
The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the…
We obtain bounds on the Kullback--Leibler divergence to equilibrium for mass-action chemical reaction networks (CRNs) with equilibrium. The associated decay rates are characterized in terms of the singular values of the stoichiometric…
We formulate and study computationally the fluctuating compressible Navier-Stokes equations for reactive multi-species fluid mixtures. We contrast two different expressions for the covariance of the stochastic chemical production rate in…
Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…
The evolution of chemical reaction networks is often analyzed through kinetic models and energy landscapes, but these approaches fail to capture the deeper structural constraints governing complexity growth. In chemical reaction networks,…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…
A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes,…
It is shown that certain classes of differential equations arising from the modelling of chemical reaction networks have the following property: the state space is foliated by invariant subspaces each of which contains a unique equilibrium…
The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
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…