Related papers: Testing Binomiality of Chemical Reaction Networks …
We present a new conjecture about a necessary condition that a (bio)chemical network has to satisfy for it to exhibit multistationarity. According to a Theorem of Feliu and Wiuf [27, 12], the conjecture is known for strictly monotonic…
Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind…
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…
This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high…
Key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their…
Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
Recent work of M.D. Johnston et al. has produced sufficient conditions on the structure of a chemical reaction network which guarantee that the corresponding discrete state space system exhibits an extinction event. The conditions consist…
Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…
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…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…
Despite their noted potential in polynomial-system solving, there are few concrete examples of Newton-Okounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of Newton-Okounkov body theory to…
We investigate, via Brownian dynamics simulations, the reaction dynamics of a simple, non-linear chemical network (the Willamowski-Rossler network) under spatial confinement and crowding conditions. Our results show that the presence of…
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…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…