Related papers: Testing Binomiality of Chemical Reaction Networks …
The analysis of non-equilibrium steady states of biochemical reaction networks relies on finding the configurations of fluxes and chemical potentials satisfying stoichiometric (mass balance) and thermodynamic (energy balance) constraints.…
Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular…
In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In…
For the reaction networks with one-dimensional stoichiometric subspaces, we show the following results. (1) If the maximum number of positive steady states is an even number N, then the maximum number of stable positive steady states is…
Thermodynamic constraints on reactions directions are inherent in the structure of a given biochemical network. However, concrete procedures for determining feasible reaction directions for large-scale metabolic networks are not well…
In this paper, we derive two sufficient conditions to diagnose the persistence of two classes of delayed complex balanced chemical reaction network systems equipped with mass-action kinetics. One class is identified by $\dim…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for…
We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient `food' source. Such systems have previously been investigated for their…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Here, we demonstrate how machine learning enables the prediction of comonomers reactivity ratios based on the molecular structure of monomers. We combined multi-task learning, multi-inputs, and Graph Attention Network to build a model…
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition…
The construction of a reaction network containing all relevant intermediates and elementary reactions is necessary for the accurate description of chemical processes. In the case of a complex chemical reaction (involving, for instance, many…
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…
Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…
We construct a Gr\"obner Basis of the relation ideal of a polynomial, give an interpolation formula for the basis elements and explain the connection of the interpolation formula to the Buchberger--M\"oller algorithm. We present a situation…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…