Title :

Identifying the parametric occurrence of multiple steady states for some biological networks

Author(s) :

Bradford, Russell [Auteur]
Department of Computer Science [Bath]
Davenport, James Harold [Auteur]
Department of Computer Science [Bath]
England, Matthew [Auteur]
Coventry University
Errami, Hassan [Auteur]
Institut für Informatik II [Bonn]
Gerdt, Vladimir [Auteur]
Joint Institute for Nuclear Research [JINR]
Grigoriev, Dima [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Hoyt, Charles [Auteur]
Bonn-Aachen International Center for Information Technology [B-IT]
Košta, Marek [Auteur]
Slovak Academy of Sciences [SAS]
Radulescu, Ovidiu [Auteur]
Université de Montpellier [UM]
Sturm, Thomas [Auteur]
Centre National de la Recherche Scientifique [CNRS]
Modeling and Verification of Distributed Algorithms and Systems [VERIDIS]
Proof-oriented development of computer-based systems [MOSEL]
Max-Planck-Institut für Informatik [MPII]
Saarland University [Saarbrücken]
Weber, Andreas [Auteur]
Institut für Informatik II [Bonn]

Journal title :

Journal of Symbolic Computation

Pages :

84-119

Publisher :

Elsevier

Publication date :

2020-05

ISSN :

0747-7171

English keyword(s) :

Mixed equation/inequality solving
Real quantifier elimination
Biological networks
Signalling pathways
MAPK
Mixed Equation / Inequality Solving
Real Quantifier Elimination
Biological Networks
Signaling Pathways

HAL domain(s) :

Informatique [cs]
Mathématiques [math]
Sciences du Vivant [q-bio]

English abstract : [en]

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple ...
Show more >We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic and numerical methods.The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters.We apply combinations of symbolic computation methods designed for mixed equality / inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine semi-algebraic conditions for multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Méthodes symboliques pour les réseaux biologiques

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL