Hub Occupancy by Competitively Interacting Proteins Obeys a Simple Queuing Law

Coordinated interactions between a protein hub, or receptor, and its cognate protein ligands are at the heart of cell signaling. Any significant perturbations in their kinetic and dynamic complexities result in major alterations in biochemical traffic at the subcellular and extracellular levels. The coexistence of multiple ligands with varying local concentrations and affinity constants, as well as the transient nature of their underlying protein-protein interactions (PPIs), makes predicting hub occupancy a challenging task. Here, we develop models of PPIs anchored in queuing theory to determine hub occupancy as a function of the kinetic rate constants and concentrations in complex mixtures of protein ligands. We find that in a ternary mixture of protein ligands spanning a range of kinetic rate constants, the concentration of one ligand can significantly influence the competitive PPIs between the other two ligands and the protein receptor, thereby impacting its overall occupancy. Further, for more complex mixtures, we developed a coarse-graining approach to compartmentalize large numbers of ligands competing for the same binding site of the receptor. Our analytical strategy provides a mechanistic and quantitative understanding of competitive PPIs, with broad applicability to biochemical processes, protein analytics, and drug development.