Table 3 Biological observations and mathematical translation

Constraint 1

an increase of R-Smads phosphorylation and an increase of the transcription of some SMAD regulated genes is observed upon addition of ADAM12 [8]

at stable state, with TGF-β, the amount of LRCs present in the endosome is increased by at least a factor 2

Constraint 2

cells transfected with Tβ RII and increasing amounts of ADAM12 proved that the more ADAM12 there was, the higher the steady state level of Tβ RII was [8]

at stable state, without TGF-β, the total amount of receptors present in the system is increased by at least a factor 2

Constraint 3

immunofluorescence studies showed that ADAM12 modifies the ratio of the Tβ RII present at the cell surface membrane out of those internalized, favoring the intracellular compartments [8]

at stable state, without TGF-β, the ratio of internalized receptors out of those present in the membrane is increased by at least a factor 2

Constraint 4

ADAM12 expression decreases the amount of SMAD7 complexed with ligand-receptor complexes, and thus their ubiquitination [8]

at stable state, with TGF-β, the ligand induced degradation flow is decreased by at least a factor 2

Constraint 5

overexpression studies with ADAM12 and gene reporter assay showed that ADAM12 does not maintain transcriptional activity after TGF-β removal (unpublished data)

after stabilization with TGF-β, and removal of TGF-β, the amount of LRCs present in the endosome becomes negligible within the first 200 minutes