Figure 1.

Cooperative stability allows protein complex formation systems to overcome systematic constraints on stoichiometric balance arising from synthesis rate variations. (A–C) For heterodimers, the abundance of each protein species—dimer $p_3$ (green), monomer $p_1$ (blue) and monomer $p_2$ (orange)—in response to synthesis rate variations is plotted. Protein abundance is normalized to dimer $p_3$ abundance ($C_1$ = $C_2$). The $p_2$ synthesis rate $C_2$ is fixed at 50 nM/h and the $p_1$ synthesis rate $C_1$ varies from 0 to 100 nM/h (0–200% relative to the $p_2$ synthesis rate $C_2$). The response curves of each protein species in the absence of cooperative stability (${\lambda }_{\mathit{monomer}}{/\lambda }_{\mathit{dimer}}=1$) are plotted when the binding affinity is either (A) low ($K_a=0.001{\mathit{nM}}^{-1}$) or (B) high ($K_a=1{\mathit{nM}}^{-1}$). Response curves of each protein species subjected to cooperative stability (${\lambda }_{\mathit{monomer}}{/\lambda }_{\mathit{dimer}}=5$) and with high binding affinity ($K_a=1{\mathit{nM}}^{-1}$) are shown in (C). (D–F). The heatmap of the tolerance range with parameter configurations in the physiological range. The x-axis is the reference protein synthesis rate ($C_2$) from 1 to 1000 nM/h and the y-axis is the association constant $K_a$ from 0.001 to 1 nM⁻¹, both axes are at log scale. (G–I) The heatmap of the tolerance score within 0 to two-fold synthesis rate variation range in the same parameter space of $K_a$ and $C_2$ as (D–F). For heterodimers without cooperative stability, the heatmap is plotted in (D and G). For heterodimer with cooperative stability, the heatmaps are plotted for different extent of differential degradation rate using ${\lambda }_{\mathit{monomer}}{/\lambda }_{\mathit{dimer}}=5$ (E and H) and ${\lambda }_{\mathit{monomer}}{/\lambda }_{\mathit{dimer}}=10$ (F and I).