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-Wiuf'12 , sequential distributive multisite phosphorylation networks, sequential processive multisite phosphorylation networks, most of the examples in Angeli et al. '07 , phosphorylation cascades, two component systems as in Kothamachu et al. '15 , the bacterial EnvZ/OmpR network in Shinar-Feinberg'10 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  (inspired by Feliu-Wiuf'12 , 13 and Thomson-Gunawardena'09)and we  define an important subclass of MESSI systems with toric steady states . 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.
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.
R
Feliu-Wiuf'12
Feliu and Wiuf (2012a)
R
multisite phosphorylation networks, sequential
and
R
'07
(2007)
R
'15
(2015)
R
Shinar-Feinberg'10 and
Shinar and Feinberg (2010)
A
, and
A
and we give conditions to ensure an explicit rational parametrization of the variety of steady states
R
Feliu-Wiuf'12
Feliu and Wiuf (2013a
R
13 and Thomson-Gunawardena'09)and we
2013b), Thomson and Gunawardena (2009)
A
). We
R
. We
P\'erez Mill\'an et al. (2012)
A
and we