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Related papers: Multistationarity questions in reduced vs extended…

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We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…

Dynamical Systems · Mathematics 2021-08-24 Kexin Lin , Xiaoxian Tang , Zhishuo Zhang

Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…

Molecular Networks · Quantitative Biology 2012-03-28 Jost Neigenfind , Sergio Grimbs , Zoran Nikoloski

Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…

Algebraic Geometry · Mathematics 2014-12-30 Elisenda Feliu

We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize…

Probability · Mathematics 2007-05-23 David Anderson , Jonathan Mattingly , H. Frederik Nijhout , Michael Reed

The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an…

Molecular Networks · Quantitative Biology 2017-11-01 David F. Klosik , Anne Grimbs , Stefan Bornholdt , Marc-Thorsten Hütt

James et al. (2012) presented simulations that apparently falsify the analytical result by Bastolla et al. (2009), who showed that nested mutualistic interactions decrease interspecific competition and increase biodiversity in model…

Populations and Evolution · Quantitative Biology 2013-01-17 Rudolf P. Rohr , Miguel A. Fortuna , Bartolo Luque , Jordi Bascompte

We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can…

Dynamical Systems · Mathematics 2017-09-11 Murad Banaji , Casian Pantea

Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction…

Statistical Mechanics · Physics 2007-10-12 Baruch Barzel , Ofer Biham , Raz Kupferman

Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…

Molecular Networks · Quantitative Biology 2025-11-03 Juan David Marmolejo Lozano , Nikola Popovic , Ramon Grima

The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…

Combinatorics · Mathematics 2023-04-03 Jane Ivy Coons , Mark Curiel , Elizabeth Gross

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…

Dynamical Systems · Mathematics 2008-09-09 Gheorghe Craciun , J. William Helton , Ruth J. Williams

Reconstruction of biochemical reaction networks is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and…

Systems and Control · Computer Science 2016-11-18 Wei Pan , Ye Yuan , Guy-Bart Stan

Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…

Dynamical Systems · Mathematics 2013-08-15 Stefan Müller , Georg Regensburger

A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following…

Dynamical Systems · Mathematics 2023-02-23 Murad Banaji

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…

Molecular Networks · Quantitative Biology 2011-07-19 Elisenda Feliu , Carsten Wiuf

New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…

Molecular Networks · Quantitative Biology 2009-05-12 David Angeli , Patrick De Leenheer , Eduardo Sontag

Processes involving multi-input multi-step reaction cascades are used in developing novel biosensing, biocomputing, and decision making systems. In various applications different changes in responses of the constituent processing steps…

Molecular Networks · Quantitative Biology 2016-08-16 Sergii Domanskyi , Vladimir Privman

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…

Quantitative Methods · Quantitative Biology 2022-06-08 Lorenzo Duso , Christoph Zechner

We provide a sufficient and necessary condition in terms of the stoichiometric coefficients for a bi-reaction network to admit multistability. Also, this result completely characterizes the bi-reaction networks according to if they admit…

Dynamical Systems · Mathematics 2024-05-09 Yixuan Liang , Xiaoxian Tang , Qian Zhang

Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…

Dynamical Systems · Mathematics 2018-05-22 Daniele Cappelletti , Carsten Wiuf