Figure 6.

Typical cases for the scaffold protein model shown in Fig. 5. (a) Plot, assuming eight phosphosites (n = 8), showing how the fraction of free B that is fully phosphorylated varies with the concentration of kinase A. The value α is the fold-change in the scaffold binding rates (i.e., $\alpha =k_{\mathrm{i}}^{\mathrm{a}}/k_{\mathrm{i}-1}^{\mathrm{a}}$). For each value of α, the corresponding effective Hill number n_H is also shown. Each curves is normalized by setting its EC50 to 1. (b) Hill coefficients as a function of number of phosphosites and fold change of scaffold binding rates with each phosphorylation. (c) Hill coefficients as a function of number of phosphosites and fold change of scaffold dissociation rates with each phosphorylation. (d) Hill coefficients as a function of number of phosphosites and simultaneous fold change of scaffold binding and dissociate rates at each phosphorylation, with λ_i = $k_{\mathrm{i}}^{\mathrm{a}}/k_{\mathrm{i}}^{\mathrm{d}}$ = 1. (e) The same as panel c except k_i/k_i−1 = 2 and d_i/d_i–1 = 1/2 for all i. (f) Hill coefficients as a function of the number of phosphorylation sites and the total amount scaffold. In this case, the parameters are α = β = 4, λ_i = $k_{\mathrm{i}}^{\mathrm{a}}/k_{\mathrm{i}}^{\mathrm{d}}$ = 1, k_i/k_i−1 = 2, and d_i/d_i–1 = 1/2. In panels a–f, S_t = 15, B_t = 10, with all other parameters equal to 1 except as specified otherwise in the figure.