## Models

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.

## Objectives

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.

## Approach

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.

## Methods

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.