  It has been recently observed that the dynamical properties of mass action
systems arising from many models of biochemical reaction networks can be
derived by considering the corresponding properties of a related generalized
mass action system. The correspondence process known as network translation in
particular has been shown to be useful in characterizing a system's steady
states. In this paper, we further develop the theory of network translation
with particular focus on a subclass of translations known as improper
translations. For these translations, we derive conditions on the network
topology of the translated network which are sufficient to guarantee the
original and translated systems share the same steady states. We then present a
mixed-integer linear programming (MILP) algorithm capable of determining
whether a mass action system can be corresponded to a generalized system
through the process of network translation.
