  Many biochemical and industrial applications involve complicated networks of
simultaneously occurring chemical reactions. Under the assumption of mass
action kinetics, the dynamics of these chemical reaction networks are governed
by systems of polynomial ordinary differential equations. The steady states of
these mass action systems have been analysed via a variety of techniques,
including elementary flux mode analysis, algebraic techniques (e.g. Groebner
bases), and deficiency theory. In this paper, we present a novel method for
characterizing the steady states of mass action systems. Our method explicitly
links a network's capacity to permit a particular class of steady states,
called toric steady states, to topological properties of a related network
called a translated chemical reaction network. These networks share their
reaction stoichiometries with their source network but are permitted to have
different complex stoichiometries and different network topologies. We apply
the results to examples drawn from the biochemical literature.
