Signal Processing in the TGF-β Superfamily Ligand-Receptor Network
Figure 4
Two-Compartment Model of Receptor Trafficking and Signaling
Graphical representation and equations for a model with one ligand that forms complexes with one type I and one type II receptor. Receptors are present in two main compartments: the plasma membrane (receptors at the cell surface) and the endosomes (internalized receptors). Receptors and ligand-receptor complexes traffic between these two compartments by internalization and recycling. Only internalized ligand-bound receptors have kinase activity. Active receptors can also be internalized in a degradation pathway (right). In addition, receptors in the plasma membrane can undergo constitutive degradation, independently of whether they are ligand-bound (left). A supply of new receptors is constantly produced by gene expression.
The concentration of the ligand is denoted by [ l ]; the numbers of type I and II receptor and ligand-receptor complexes in the plasma membrane, by [RI], [RII], and [l RIRII], respectively; and the numbers of internalized type I and II receptor and ligand-receptor complexes by [RI], [RII], and [l RIRII], respectively. (Note that type II receptors are not shown in the graphical representation.) kα is the rate constant of ligand-receptor complex formation; pRI and pRII are the rates of receptor production; ki, kr, kcd, and klid are the internalization, recycling, constitutive degradation, and ligand-induced degradation rate constants; α is the fraction of active receptors that are recycled back to the plasma membrane and can interact again with the ligand.
The signaling activity of the pathway is assumed to be proportional to the number of internalized ligand-receptor complexes, [lRIRII]. This assumption is based on the observations that R-Smad proteins become rapidly dephosphorylated after inhibition of the receptor kinase activity and that nuclear Smad localization closely follows Smad phosphorylation [16].