Using Methods of Tropical Geometry for Model Reduction and Model Analysis of Biological and Chemical Networks

Model reduction of bio-chemical networks relies on the knowledge of slow
and fast variables. We provide a geometric method, which is
based on the Newton polytopes,  to identify slow variables of a
bio-chemical network with polynomial rate functions.
The gist of the method is the notion of tropical equilibration that
provides approximate descriptions of slow invariant manifolds.
Compared to extant numerical algorithms such as the intrinsic low
dimensional manifold method, our approach is symbolic
Application of this method to a large collection of biochemical network
models supports the idea that the number of
dynamical variables in minimal models  of cell physiology can be small,
in spite of the large number of molecular regulatory actors.
Moreover, the the computed solution polytopes can be related to
metastable regimes allowing to describe the qualitative dynamics
of chemical reactions networks.