  We introduce a general framework for biological systems, called MESSI
systems, that describe Modifications of type Enzyme-Substrate or Swap with
Intermediates, and we prove general results based on the network structure.
Many post-translational modification networks are MESSI systems. For example:
the motifs in [Feliu and Wiuf (2012a)], sequential distributive and processive
multisite phosphorylation networks, most of the examples in [Angeli et al.
(2007)], phosphorylation cascades, two component systems as in [Kothamachu et
al. (2015)], the bacterial EnvZ/OmpR network in [Shinar and Feinberg (2010)],
and all linear networks. We show that, under mass-action kinetics, MESSI
systems are conservative. We simplify the study of steady states of these
systems by explicit elimination of intermediate complexes and we give
conditions to ensure an explicit rational parametrization of the variety of
steady states (inspired by [Feliu and Wiuf (2013a, 2013b), Thomson and
Gunawardena (2009)]). We define an important subclass of MESSI systems with
toric steady states [P\'erez Mill\'an et al. (2012)] and we give for MESSI
systems with toric steady states an easy algorithm to determine the capacity
for multistationarity. In this case, the algorithm provides rate constants for
which multistationarity takes place, based on the theory of oriented matroids.
