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The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles…
Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
Stochastic models of reaction networks are becoming increasingly important in Systems Biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
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…
We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…
This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…