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

Matthew England, Hassan Errami, Dima Grigoriev, Ovidiu Radulescu, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 19th International Workshop (CASC 2017), Beijing, China, Springer, Sept. 2017
 

Abstract

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 progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.

Bibtex

@INPROCEEDINGS{eegrsw2017,
     author = {England, Matthew and Errami, Hassan and Grigoriev, Dima and Radulescu, Ovidiu and Weber, Andreas},
      title = {Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity
               of Biological Networks},
  booktitle = {Computer Algebra in Scientific Computing - 19th International Workshop (CASC 2017)},
     series = {Lecture Notes in Computer Science},
     volume = {10490},
       year = {2017},
      month = sep,
  publisher = {Springer},
   location = {Beijing, China},
   abstract = {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
               progress which combines various symbolic computation methods for mixed systems of equalities and
               inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented
               graph theoretical symbolic preprocessing method. We compare computation times and quality of results
               of numerical continuation methods with our symbolic approach before and after the application of our
               preprocessing.},
       isbn = {978-3-319-66320-3},
        url = {https://doi.org/10.1007/978-3-319-66320-3_8},
        doi = {10.1007/978-3-319-66320-3_8}
}