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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.…

Molecular Networks · Quantitative Biology 2011-07-13 Daniele De Martino , Matteo Figliuzzi , Andrea De Martino , Enzo Marinari

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…

Pattern Formation and Solitons · Physics 2016-11-15 N. E. Kouvaris , M. Sebek , A. S. Mikhailov , I. Z. Kiss

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…

Molecular Networks · Quantitative Biology 2021-02-24 Muruhan Rathinam , Mingkai Yu

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…

Analysis of PDEs · Mathematics 2024-04-22 Ningning Zhu , Dongpo Hu , Huili Bi

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…

Statistical Mechanics · Physics 2013-05-29 David K. Lubensky

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…

Dynamical Systems · Mathematics 2021-02-22 Xiaoxian Tang , Zhishuo Zhang

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…

Molecular Networks · Quantitative Biology 2007-05-23 Feng Yang , Feng Qi , Daniel A. Beard

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…

Dynamical Systems · Mathematics 2019-08-23 Xiaoyu Zhang , Chuanhou Gao

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,…

Probability · Mathematics 2014-01-20 David F. Anderson , German Enciso , Matthew Johnston

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…

Machine Learning · Computer Science 2026-05-07 Sreejata Dey , Guoxiang Grayson Tong , Jonathan F. MacArt , Daniele E. Schiavazzi

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…

Molecular Networks · Quantitative Biology 2007-05-23 Elchanan Mossel , Mike Steel

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…

Rings and Algebras · Mathematics 2017-04-11 Wolfram Decker , Christian Eder , Viktor Levandovskyy , Sharwan K. Tiwari

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,…

Numerical Analysis · Mathematics 2014-10-14 Andreychenko Alexander , Mikeev Linar , Wolf Verena

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…

Machine Learning · Computer Science 2023-01-04 Tung Nguyen , Mona Bavarian

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…

Dynamical Systems · Mathematics 2020-06-05 Gheorghe Craciun , Maya Mincheva , Casian Pantea , Polly Y. Yu

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…

Chemical Physics · Physics 2017-12-19 Gregor N. Simm , Markus Reiher

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…

Quantitative Methods · Quantitative Biology 2014-07-14 Mercedes Pérez Millán , Alicia Dickenstein

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…

Molecular Networks · Quantitative Biology 2025-11-19 Richard Golnik , Thomas Gatter , Peter F. Stadler , Nicola Vassena

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…

Number Theory · Mathematics 2007-05-23 Mathias Lederer

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…

Molecular Networks · Quantitative Biology 2021-01-05 Tomislav Plesa