Multiple steady states for chemical reaction networks of deficiency one

1995 ◽  
Vol 132 (4) ◽  
pp. 371-406 ◽  
Author(s):  
Martin Feinberg
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Multiple Steady States

scholarly journals Families of toric chemical reaction networks

2020 ◽  
Vol 58 (9) ◽  
pp. 2061-2093
Author(s):  
Michael F. Adamer ◽  
Martin Helmer
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Core Network ◽  
Entire Family ◽  
Data Set ◽  
The Family ◽  
Positive Steady States ◽  
State Behaviour

Abstract We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks.

scholarly journals Structural simplification of chemical reaction networks in partial steady states

Biosystems ◽  
2016 ◽  
Vol 149 ◽  
pp. 34-49 ◽  
Author(s):  
Guillaume Madelaine ◽  
Cédric Lhoussaine ◽  
Joachim Niehren ◽  
Elisa Tonello
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Reaction Networks ◽  
Structural Simplification

scholarly journals Independent, Incidence Independent and Weakly Reversible Decompositions of Chemical Reaction Networks

2021 ◽  
Vol 87 (2) ◽  
pp. 367-396
Author(s):  
Bryan Hernandez ◽  
◽  
Deza Amistas ◽  
Ralph John De la Cruz ◽  
Lauro Fontanil ◽  
...  
Keyword(s):  
Chemical Reaction ◽  
Linear Span ◽  
Directed Graphs ◽  
Chemical Reaction Networks ◽  
Steady States ◽  
Connected Components ◽  
Reaction Networks ◽  
Positive Steady States ◽  
Underlying Network ◽  
Strongly Connected

Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks can be considered as the most important class of reaction networks. Now, the stoichiometric subspace of a network is the linear span of the reaction vectors (i.e., difference between the product and the reactant complexes). A decomposition of a CRN is independent (incidence independent) if the direct sum of the stoichiometric subspaces (incidence maps) of the subnetworks equals the stoichiometric subspace (incidence map) of the whole network. Decompositions can be used to study relationships between positive steady states of the whole system (induced from partitioning the reaction set of the underlying network) and those of its subsystems. In this work, we revisit our novel method of finding independent decomposition, and use it to expand applicability on (vector) components of steady states. We also explore CRNs with embedded deficiency zero independent subnetworks. In addition, we establish a method for finding incidence independent decomposition of a CRN. We determine all the forms of independent and incidence independent decompositions of a network, and provide the number of such decompositions. Lastly, for weakly reversible networks, we determine that incidence independence is a sufficient condition for weak reversibility of a decomposition, and we identify subclasses of weakly reversible networks where any independent decomposition is weakly reversible.

A Positive Real Eigenvalue Condition for the Determination of Unstable Steady States in Chemical Reaction Networks

2008 ◽  
Vol 63 (12) ◽  
pp. 778-790
Author(s):  
An-Chong Chao ◽  
Hsing-Ya Li ◽  
Guo-Syong Chuang ◽  
Pang-Yen Ho
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Steady States ◽  
Reaction Networks ◽  
Real Eigenvalue ◽  
Multiple Steady States ◽  
Positive Real ◽  
Unstable Steady State ◽  
Eigenvalue Condition

The interesting dynamical behaviours exhibiting in chemical reaction systems, such as multiple steady states and undamped oscillations, often result from unstable steady states. A positive real eigenvalue condition is proposed which gives a necessary and sufficient condition for the determination of an unstable steady state having a positive real eigenvalue in general isothermal reaction networks. Formulas are developed to construct an unstable steady state and a set of positive rate constants. The applications are illustrated by three examples. Two give rise to oscillations and one admits multiple steady states.

An Observer for Mass-action Chemical Reaction Networks

2009 ◽  
Vol 15 (5) ◽  
pp. 578-597
Author(s):  
Marcello Farina ◽  
Sergio Bittanti
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Mass Action ◽  
Reaction Networks

scholarly journals A chemically consistent graph architecture for massive reaction networks applied to solid-electrolyte interphase formation

2021 ◽  
Author(s):  
Samuel M. Blau ◽  
Hetal D Patel ◽  
Evan Walter Clark Spotte-Smith ◽  
Xiaowei Xie ◽  
Shyam Dwaraknath ◽  
...  
Keyword(s):  
Energy Storage ◽  
Solid Electrolyte ◽  
Chemical Reaction ◽  
Solid Electrolyte Interphase ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Mechanistic Understanding

Modeling reactivity with chemical reaction networks could yield fundamental mechanistic understanding that would expedite the development of processes and technologies for energy storage, medicine, catalysis, and more. Thus far, reaction...

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