A Case Study on the Parametric Occurrence of Multiple Steady States

Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Kosta, Ovidiu Radulescu, Thomas Sturm, Andreas Weber

  • 1 Citations

Abstract

The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual
substitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methods
when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters
Original languageEnglish
Title of host publicationProceedings of the 42nd International Symposium on Symbolic and Algebraic Computation
Subtitle of host publicationISSAC '17
PublisherAssociation for Computing Machinery
Pages45-52
Number of pages8
DOIs
StatePublished - 25 Jul 2017
Event42nd International Symposium on Symbolic and Algebraic Computation - Kaiserslautern, Germany

Conference

Conference42nd International Symposium on Symbolic and Algebraic Computation
Abbreviated titleISSAC '17
CountryGermany
CityKaiserslautern
Period25/07/1728/07/17
Internet address

Fingerprint

Model
Protein kinase
Biological networks
Symbolic computation
Numerics
Positivity
Substitution
Equality
Decompose
Demonstrate

Keywords

  • Applied computing
  • Biological networks
  • Computing Methodologies
  • Equation and inequality solving algorithms

Cite this

Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., ... Weber, A. (2017). A Case Study on the Parametric Occurrence of Multiple Steady States. In Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17 (pp. 45-52). Association for Computing Machinery. DOI: 10.1145/3087604.3087622

A Case Study on the Parametric Occurrence of Multiple Steady States. / Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Kosta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas.

Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery, 2017. p. 45-52.

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

Bradford, R, Davenport, JH, England, M, Errami, H, Gerdt, V, Grigoriev, D, Hoyt, C, Kosta, M, Radulescu, O, Sturm, T & Weber, A 2017, A Case Study on the Parametric Occurrence of Multiple Steady States. in Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery, pp. 45-52, 42nd International Symposium on Symbolic and Algebraic Computation, Kaiserslautern, Germany, 25-28 July. DOI: 10.1145/3087604.3087622
Bradford R, Davenport JH, England M, Errami H, Gerdt V, Grigoriev D et al. A Case Study on the Parametric Occurrence of Multiple Steady States. In Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery. 2017. p. 45-52. Available from, DOI: 10.1145/3087604.3087622

Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Kosta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas / A Case Study on the Parametric Occurrence of Multiple Steady States.

Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation: ISSAC '17. Association for Computing Machinery, 2017. p. 45-52.

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

@inbook{b947cb9dcb8643ee85cbaf90a34584ad,
title = "A Case Study on the Parametric Occurrence of Multiple Steady States",
abstract = "The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtualsubstitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methodswhen numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters",
keywords = "Applied computing, Biological networks, Computing Methodologies, Equation and inequality solving algorithms",
author = "Russell Bradford and Davenport, {James H.} and Matthew England and Hassan Errami and Vladimir Gerdt and Dima Grigoriev and Charles Hoyt and Marek Kosta and Ovidiu Radulescu and Thomas Sturm and Andreas Weber",
year = "2017",
month = "7",
doi = "10.1145/3087604.3087622",
pages = "45--52",
booktitle = "Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation",
publisher = "Association for Computing Machinery",

}

TY - CHAP

T1 - A Case Study on the Parametric Occurrence of Multiple Steady States

AU - Bradford,Russell

AU - Davenport,James H.

AU - England,Matthew

AU - Errami,Hassan

AU - Gerdt,Vladimir

AU - Grigoriev,Dima

AU - Hoyt,Charles

AU - Kosta,Marek

AU - Radulescu,Ovidiu

AU - Sturm,Thomas

AU - Weber,Andreas

PY - 2017/7/25

Y1 - 2017/7/25

N2 - The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtualsubstitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methodswhen numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters

AB - The determination of multiple steady states for positive values is very important in the analysis of biological networks. The investigation of the potential of models of the mitogen-activated protein kinases (MAPK) network for such multistationarity has consumed considerable effort using special insights into the structure of corresponding models. We apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtualsubstitution, lazy real triangularization and cylindrical algebraic decomposition. We demonstrate that the determination of multistationarity of an 11-dimensional MAPK network with can be achieved by currently available methodswhen numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters and furthermore positivity conditions on all variables and parameters

KW - Applied computing

KW - Biological networks

KW - Computing Methodologies

KW - Equation and inequality solving algorithms

U2 - 10.1145/3087604.3087622

DO - 10.1145/3087604.3087622

M3 - Conference proceeding

SP - 45

EP - 52

BT - Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation

PB - Association for Computing Machinery

ER -