Projects per year
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.
|Number of pages||36|
|Journal||Journal of Symbolic Computation|
|Early online date||15 Jul 2019|
|Publication status||Published - 1 May 2020|
- Biological networks
- Mixed equation/inequality solving
- Real quantifier elimination
- Signalling pathways
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
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- 1 Finished
Real Geometry and Connectedness via Triangular Description
Davenport, J., Bradford, R., England, M. & Wilson, D.
Engineering and Physical Sciences Research Council
1/10/11 → 31/12/15
Project: Research council
- Department of Computer Science - Senior Lecturer
- Mathematical Foundations of Computation
Person: Research & Teaching