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

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.

Accepted into Proc. CASC 2017

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Cited by in corpus (11)

• Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
• Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks
• Cylindrical Algebraic Decomposition with Equational Constraints
• Using Machine Learning to Improve Cylindrical Algebraic Decomposition
• Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
• Algorithmic Reduction of Biological Networks With Multiple Time Scales
• Algorithmically generating new algebraic features of polynomial systems for machine learning
• Quantifier Elimination for Reasoning in Economics
• Parametric Toricity of Steady State Varieties of Reaction Networks
• Positive Solutions of Systems of Signed Parametric Polynomial Inequalities
• Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner Systems