Figure 1. Models of n-site (de)phosphorylation of substrate with scaffold protein .

A) Phosphorylation occurs only on scaffold-bound substrates, and dephosphorylation can take place both on and off scaffold except when stated otherwise. represents a protein that has been phosphorylated times, and represents the scaffold-bound protein. Phosphorylation is mediated by a kinase , and dephosphorylation is facilitated by a phosphatase . B) Full enzymatic (de)phosphorylation mechanism using standard mass action kinetics (MA). The parameters represent the on, off, and catalytic rates for the phosphorylation reaction. For the dephosphorylation reaction these rates are , and , respectively. C) Mechanism for scaffold binding. The substrate binds with the scaffold to form a heterodimer that can also unbind back to its original form. The parameters and represent the on and off rates, respectively. D–G) We distinguish between models with a scaffold (S) and models with no scaffold (NS), as well as models with full mass action enzymatic reactions (MA) and models with simplified, linear enzymatic reaction rates (LR). This gives rise to the four models MA-S (D), LR-S (E), MA-NS (F), and N LR-S (G). The reactions in the dotted squares are omitted when dephosphorylation only takes place off-scaffold.