Related papers: Semigroup models for biochemical reaction networks
Oscillatory chemical reactions are functional components in a variety of biological contexts. In chemistry, the construction and identification of even rudimentary oscillators remain elusive and lack a general framework. Using…
Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…
Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…
The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…
Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…
At the microscopic scale, open chemical reaction networks are described by stochastic reactions that follow mass-action kinetics and are coupled to chemostats. We show that closed chemical reaction networks -- with specific stoichiometries…
We derive the Hessian geometric structure of nonequilibrium chemical reaction networks (CRN) on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow.…
Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…
In this paper we study a class of stochastic chemical reaction networks (CRNs) for which chemical species are created by a sequence of chain reactions. We prove that under some convenient conditions on the initial state, some of these…
We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action…
We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…
Quasi-steady state (QSS) reduction is a commonly used method to lower the dimension of a differential equation model of a chemical reaction network. From a mathematical perspective, QSS reduction is generally interpreted as a special type…
Biochemical systems that express certain chemical species of interest at the same level at any positive equilibrium are called "absolute concentration robust" (ACR). These species behave in a stable, predictable way, in the sense that their…
A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic theory to study such processes…
The complexity of molecular and cellular processes forces experimental studies to focus on subsystems. To study the functioning of biological systems across levels of structural and functional organisation, we require tools to compose and…
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…
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,…
Key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their…
We introduce KiNetX, a fully automated meta-algorithm for the kinetic analysis of complex chemical reaction networks derived from semi-accurate but efficient electronic structure calculations. It is designed to (i) accelerate the automated…
Thermodynamic aspects of chemical reactions have a long history in the Physical Chemistry literature. In particular, biochemical cycles - the building-blocks of biochemical systems - require a source of energy to function. However, although…