# Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner System

@inproceedings{Rahkooy2021TestingBO, title={Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gr{\"o}bner System}, author={Hamid Rahkooy and Thomas Sturm}, booktitle={CASC}, year={2021} }

We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is binomial under every specialisation of the parameters if the conditions on the parameters hold. We approach the binomiality problem using Comprehensive Gröbner systems. Considering rate constants as parameters, we compute comprehensive Gröbner systems for various… Expand

#### References

SHOWING 1-10 OF 64 REFERENCES

The Multistationarity Structure of Networks with Intermediates and a Binomial Core Network

- Biology, Mathematics
- Bulletin of mathematical biology
- 2019

A new determinant criterion to decide whether a network is multistationary is provided, which applies when the network obtained by removing intermediates has a binomial steady-state ideal. Expand

Chemical Reaction Systems with Toric Steady States

- Mathematics, Medicine
- Bulletin 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. Expand

Multistationarity in Structured Reaction Networks

- Biology, Medicine
- Bulletin of mathematical biology
- 2019

This work builds on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain “critical function” changes sign, and allows for more general parametic changes, which make it much easier to determine the existence of a sign change. Expand

The Structure of MESSI Biological Systems

- Computer Science, Biology
- SIAM J. Appl. Dyn. Syst.
- 2018

A general framework for biological systems that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, called MESSI systems, is introduced, and general results based on the network structure are proved. Expand

Detecting binomiality

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2015

This work constructs a heuristic toolbox that can lead to simplifications even if the given ideal is not binomial, and gives an efficient, Grobner-free algorithm for binomiality detection, based on linear algebra only. Expand

Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-Action Kinetics

- Mathematics, Computer Science
- CASC
- 2012

We design an algorithm for finding solutions with nonzero coordinates of systems of polynomial equations which has a better complexity bound than for known algorithms when a system contains a few… Expand

On the number of steady states in a multiple futile cycle

- Mathematics, Biology
- Journal of mathematical biology
- 2008

The number of positive steady states of a general multisite phosphorylation–dephosphorylation cycle is studied, and it is shown that for some parameter ranges, there are at least n + 1 or n (if n is even) and there never are more than 2n − 1 steady states. Expand

Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks

- Computer Science, Mathematics
- CASC
- 2017

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent… Expand

Foundations of Chemical Reaction Network Theory

- Mathematics
- Applied Mathematical Sciences
- 2019

Part I: Preliminaries -- Anticipating the Big Picture: Some Clues -- Chemical and Notational Preliminaries -- Reaction Networks, Kinetics, and the Induced Differential Equations -- Open Systems: Why… Expand

Gröbner Systems Conversion

- Mathematics, Computer Science
- Math. Comput. Sci.
- 2017

The parametric variant of the generic Gröbner walk algorithm due to Fukuda et al. is developed, which takes as input a monomial ordering and a Gr Öbner basis w.r.t. another monomial order and outputs a decomposition of the given space of parameters as a finite set of cells. Expand