# 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.

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