Related papers: Homotopy methods for counting reaction network equ…

In this paper we study how to determine if a linear biochemical network satisfies the detailed balance condition, without knowing the details of all the reactions taking place in the network. To this end, we use the formalism of response…

This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…

The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same…

It is useful to have complete lists of nonisomorphic chemical reaction networks (CRNs) of a given size, with or without various restrictions. One may, for example, be interested in exploring how often certain dynamical behaviours occur in…

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…

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…

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,…

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The…

Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however,…

High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…

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…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

We consider stochastic models of chemical reaction networks with time dependent input rates and several types of molecules. We prove that, in despite of strong time dependence of input rates, there is a kind of homeostasis phenomenon: far…

Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…

In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…

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…

Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is…

Polymer models are a widely used tool to study the prebiotic formation of metabolism at the origins of life. Counts of the number of reactions in these models are often crucial in probabilistic arguments concerning the emergence of…