Computational models in systems biology are built from molecular interaction networks and rate laws, involving parameters, resulting in large systems of differential equations. These networks are foundational for systems medicine. One important problem is that the statistical estimation of model parameters is computationally expensive and many parameters are not identifiable from experimental data. In addition, there is typically a considerable uncertainty about the exact form of the mathematical model itself.
Parametric uncertainty with potential parameter variations over several orders of magnitudes leads to severe limitations of numerical approaches even for rather small and low dimensional models. Furthermore, existing model inference and analysis methods suffer from the curse of dimensionality that sets an upper limit of about ten variables for models to be tractable. Therefore, the currently prevailing numerical approaches shall be complemented with our novel algorithmic symbolic methods aiming at formal deduction of principle qualitative properties of relevant models.
The principle approach of SYMBIONT is to combine symbolic methods with model reduction methods for the analysis of biological networks. We propose new methods for symbolic analysis, which overcome the above mentioned obstacles and therefore can be applied to large networks. In order to cope more effectively with the parameter uncertainty problem we impose an entirely new paradigm replacing thinking about single instances with thinking about orders of magnitude.
Our computational methods are diverse and involve various branches of mathematics such as tropical geometry, real algebraic geometry, theories of singular perturbations, invariant manifolds, and symmetries of differential systems.