Related papers: Translated Chemical Reaction Networks
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability…
In this work we consider the computation of Groebner bases of the steady state ideal of reaction networks equipped with mass-action kinetics. Specifically, we focus on the role of intermediate species and the relation between the extended…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
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 investigate the properties of large random conservative chemical reaction networks composed of elementary reactions endowed with either mass-action or saturating kinetics, assigning kinetic parameters in a thermodynamically-consistent…
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…
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…
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…
Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective…
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,…
We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks,…
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and the…
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this…
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective…
We show that discrete distributions on the $d$-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We…
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…