A Case Study on the Parametric Occurrence of Multiple Steady States

Russell Bradford, James Davenport, Matthew England, Hassan Errami, Vladimir P. Gerdt, Dima Grigoriev, Charles Hoyt, Marek Kosta, Ovidiu Radulescu, Thomas Sturm und Andreas Weber
In proceedings of Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation (ISSAC '17), Kaiserslautern, Germany, pages 45-52, ACM, Juli 2017
 

Abstract

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network 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, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.

Bibtex

@INPROCEEDINGS{BDEEGGHKRSW2017,
     author = {Bradford, Russell and Davenport, James and England, Matthew and Errami, Hassan and Gerdt, Vladimir
               P. and Grigoriev, Dima and Hoyt, Charles and Kosta, Marek and Radulescu, Ovidiu and Sturm, Thomas
               and Weber, Andreas},
      pages = {45--52},
      title = {A Case Study on the Parametric Occurrence of Multiple Steady States},
  booktitle = {Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation (ISSAC '17)},
       year = {2017},
      month = jul,
  publisher = {ACM},
   location = {Kaiserslautern, Germany},
   abstract = {We consider the problem of determining multiple steady states for positive real values in models of
               biological networks. Investigating the potential for these in models of the mitogen-activated
               protein kinases (MAPK) network has consumed considerable effort using special insights into the
               structure of corresponding models. Here we apply combinations of symbolic computation methods for
               mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization
               and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK
               network 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, 3 of which are of interest for
               symbolic treatment, and furthermore positivity conditions on all variables and parameters.},
       isbn = {978-1-4503-5064-8/17/07},
        doi = {10.1145/3087604.3087622}
}