Related papers: Infinitesimal Homeostasis in Mass-Action Systems
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence,…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We develop tools from computational algebraic geometry for the study of steady state features of autonomous polynomial dynamical systems via elimination of variables. In particular, we obtain nontrivial bounds for the steady state…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a…
The notion of homeostasis typically conceptualises biological and artificial systems as maintaining stability by resisting deviations caused by environmental and social perturbations. In contrast, (social) allostasis proposes that these…
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…
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…
In this article we investigate the long time behavior of solutions to a class of infinitely many master equations defined from transition rates that are suitable for the description of a quantum system approaching thermodynamical…
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…
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural…
Reaction networks have been widely used as generic models in diverse areas of applied sciences, such as biology, chemistry, ecology, epidemiology, and computer science. A reaction network incorporating noisy effects is modeled as a…
Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…
How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent…
In this work we study, at the single molecular level, the thermodynamic and dynamic characteristics of an enzymatic reaction comprising a rate limiting step. We investigate how the stability of the enzyme-state stationary probability…
We studied metastability and extinction time of a finite system with a large number of interacting components in discrete time by means of analytical and numerical investigation. The system is markovian with respect to the potential profile…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More…
Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…