Figures and data
Reaction scheme of kinetic proofreading models.
Chemical species and rate constants are shown in the figure. R denote ligand-free receptors, B denote ligand-bound inactive receptors, and Pn, n ∈ [1, N] are phosphorylated receptors. The ultimate phosphorylated species PN (marked red) is assumed to be signaling competent. (a) shows the traditional model first proposed by McKeithan (McKeithan, 1995). (b, c) show the sustained signaling model and the limited signaling model (Lever et al., 2014) which introduce additional receptor states, 
Ligand discrimination in kinetic proofreading models.
(a) Activity PN plotted as a function of non-dimensional ligand dissociation rate δ for the traditional KPR scheme (Fig. 1a). (b) Activity PN plotted as a function of non-dimensional ligand dissociation rate δ for the limited signaling model (Fig. 1b). (c) The dependence of the activity on the dimensionless phosphorylation rate ω for the limited signaling model. All figures plotted for a sequence of N = 1, 5, and 10 phosphorylation sites.
Kinetic sorting of receptor species.
Abundances of networks species B (ligand bound inactive receptor) and Pn, n ∈ [1, 5] for a signaling receptor with N = 5 phosphorylation sites. Abundances are shown for ligands of three different affinities. The inset shows the activity of the first phosphorylation site A1. Species abundances below 10−3 are not shown.
Kinetic sorting model predicts ligand specificity.
(a) The activity An of the nth phosphorylation site as a function of dimensionless dissociation rate δ. The activity is normalized to the maximum activity. The maximum An as a function of n is shown in the inset. (b) Activity of the first phosphorylation site A1 plotted as a function of the dissociation rate δ for different values of the phosphorylation rate ω. (c, d) Activity of the first phosphorylation site A1 plotted as a function of phosphorylation rate ω (dephosphorylation rate ρ in panel d) for different values of the dissociation rate δ.
Multiple phosphorylation sites and receptor degradation dictate ligand specificity.
(a) Activity A1 of the first phosphorylation site as a function of the dissociation rate δ for signaling networks with different number of phosphorylation sites. (b) The optimal dissociation rate δopt that leads to maximum phosphorylation activity as a function of dimensionless degradation rate β for different values of ω. δopt is shown only if δopt ∈ [1, 1000]. (c) The relative activity of a ligand with dissociation rate that differs by kBT compared to δopt plotted as a function of β for different values of ω (see inset). Of the two ligands that differ in stability by kBT, the ligand exhibiting maximum activity is considered.
