  We discuss the symbolic dynamics of biochemical networks with separate
timescales. We show that symbolic dynamics of monomolecular reaction networks
with separated rate constants can be described by deterministic, acyclic
automata with a number of states that is inferior to the number of biochemical
species. For nonlinear pathways, we propose a general approach to approximate
their dynamics by finite state machines working on the metastable states of the
network (long life states where the system has slow dynamics). For networks
with polynomial rate functions we propose to compute metastable states as
solutions of the tropical equilibration problem. Tropical equilibrations are
defined by the equality of at least two dominant monomials of opposite signs in
the differential equations of each dynamic variable. In algebraic geometry,
tropical equilibrations are tantamount to tropical prevarieties, that are
finite intersections of tropical hypersurfaces.
