# Translated Chemical Reaction Networks

@article{Johnston2014TranslatedCR, title={Translated Chemical Reaction Networks}, author={Matthew D. Johnston}, journal={Bulletin of Mathematical Biology}, year={2014}, volume={76}, pages={1081-1116} }

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In…

## 33 Citations

Chemical reaction network approaches to Biochemical Systems Theory.

- BiologyMathematical biosciences
- 2015

Network Translation and Steady-State Properties of Chemical Reaction Systems

- Computer ScienceBulletin of mathematical biology
- 2018

It is shown that network translation can often provide a method for deriving the steady-state value of the robust species and is presented with a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

Analysis of mass-action systems by split network translation

- Computer ScienceJournal of Mathematical Chemistry
- 2021

We introduce the notion of corresponding a chemical reaction network to a split network translation , and use this novel process to extend the scope of existing network-based theory for…

Computing Weakly Reversible Deficiency Zero Network Translations Using Elementary Flux Modes

- Computer ScienceBulletin of mathematical biology
- 2019

A computational method for performing structural translation is presented, which has been studied recently in the context of analyzing the steady states and dynamical behavior of mass-action systems derived from biochemical reaction networks, and how it can be incorporated into recently proposed algorithms for establishing mono- and multistationarity in biochemical reaction systems.

On classes of reaction networks and their associated polynomial dynamical systems

- Computer ScienceJournal of Mathematical Chemistry
- 2020

This work completely characterize the inclusions between reversible, weakly reversible, endotactic, and strongly endotactic network, as well as other less well studied network types and introduces a new class of source-only networks.

A Computational Approach to Steady State Correspondence of Regular and Generalized Mass Action Systems

- Computer ScienceBulletin of mathematical biology
- 2015

This paper develops the theory of network translation with particular focus on a subclass of translations known as improper translations, and presents a mixed-integer linear programming algorithm capable of determining whether a mass action system can be corresponded to a generalized system through the process of networktranslation.

The disguised toric locus and affine equivalence of reaction networks

- Mathematics
- 2022

Under the assumption of mass-action kinetics, a dynamical system may be induced by several diﬀerent reaction networks and/or parameters. It is therefore possible for a mass-action system to exhibit…

Conditions for extinction events in chemical reaction networks with discrete state spaces

- Computer ScienceJournal of mathematical biology
- 2018

This work presents sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event and suggests sequences of reactions which may lead to extinction events.

An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems

- MathematicsSIAM J. Appl. Math.
- 2020

This work describes a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex- balanced, detailed-balanced, weakly reversible, and reversible mass-action systems.

Joining and decomposing reaction networks

- Computer ScienceJournal of mathematical biology
- 2020

Results are proved that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can be inferred from or can imply similar property of the original network.

## References

SHOWING 1-10 OF 56 REFERENCES

Algebraic methods for biochemical reaction network theory

- Mathematics
- 2010

This dissertation develops the algebraic study of chemical reaction networks endowed with mass-action kinetics, and develops a new method for determining whether given initial concentrations allow for various boundary steady states.

Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph

- ChemistrySIAM J. Appl. Math.
- 2006

A new graph-theoretical method is suggested for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot, which associates with each network a species-reaction graph, which is similar to reaction network representations drawn by biochemists.

The existence and uniqueness of steady states for a class of chemical reaction networks

- Chemistry
- 1995

My purpose here is to draw some general relationships between the structure of a chemical reaction network and the nature of the set of equilibrium states for the corresponding system of nonlinear…

Chemical Reaction Systems with Toric Steady States

- MathematicsBulletin of mathematical biology
- 2012

The main result gives sufficient conditions for a chemical reaction system to have toric steady states, and the capacity of such a system to exhibit positive steady states and multistationarity is analyzed.

Multiple steady states for chemical reaction networks of deficiency one

- Mathematics
- 1995

This article is intended as an addendum to The Existence and Uniqueness of Steady States for a Class of Chemical Reaction Networks [F1]. Readers are presumed to be familiar with the terminology and…

Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems

- Mathematics
- 1987

Topics in Chemical Reaction Network Theory

- Mathematics
- 2011

This thesis focuses on three topics within the scope of Chemical Reaction Network theory, and calls the theory Linear Conjugacy theory, which states that under the mass-action assumption two reaction networks with disparate topological structure may give rise to the same set of differential equations and therefore exhibit the same qualitative dynamical behaviour.

Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces

- MathematicsSIAM J. Appl. Math.
- 2012

A notion of generalized mass action systems that admits arbitrary power-law rate functions and serves as a more realistic model for reaction networks in intracellular environments is suggested.

A Family of Sparse Polynomial Systems Arising in Chemical Reaction Systems

- MathematicsJ. Symb. Comput.
- 2002

The positive steady states of chemical reaction systems modeled by mass action kinetics are investigated and it is shown that the simplest cases are equivalent to binomial systems and are explained with the help of toric varieties.