  We define a subclass of Chemical Reaction Networks called Post-Translational
Modification systems. Important biological examples of such systems include
MAPK cascades and two-component systems which are well-studied experimentally
as well as theoretically. The steady states of such a system are solutions to a
system of polynomial equations with as many variables as equations. Even for
small systems the task of finding the solutions is daunting. We develop a
mathematical framework based on the notion of a cut, which provides a linear
elimination procedure to reduce the number of variables in the system. The
steady states are parameterized algebraically by a set of "core" variables, and
the non-negative steady states correspond to non-negative values of the core
variables. Further, minimal cuts are the connected components in the species
graph and provide conservation laws. A criterion for when a set of independent
conservation laws can be derived from cuts is given.
