相关论文: Sign patterns for chemical reaction networks

It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-balanced equilibrium (in every stoichiometric class and for…

Genes are connected in regulatory networks, often modelled by ordinary differential equations. Changes in expression of a gene propagate to other genes along paths in the network. At a stable state, the system's Jacobian matrix confers…

This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions…

We present a computational procedure to characterize the signs of sensitivities of steady states to parameter perturbations in chemical reaction networks.

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,…

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,…

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.…

Motivated by investigating multistationarity in biochemical systems, we address saddle-node bifurcations for chemical reaction networks endowed with general kinetics. At positive equilibria, we identify structural network conditions that…

Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as…

We mathematically prove that chemical reaction networks without hidden layers can solve tasks for which spiking neural networks require hidden layers. Our proof uses the deterministic mass-action kinetics formulation of chemical reaction…

In complex molecular systems, the reaction coordinate (RC) that characterizes transition pathways is essential to understand underlying molecular mechanisms. This review surveys a framework for identifying the RC by applying deep learning…

The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and…

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address…

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…

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…

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at…

The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however,…

The random transitions of ion channels between conducting and non-conducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling fluctuations in the states of ion channels…