Queuing theory models of competitive protein-protein interactions

Many processes including cell signaling, gene regulation, and cellular metabolism rely on molecular binding events, where a receptor can transiently bind a number of different proteins, and thus regulate an aspect of a cell's state. The kinetic complexities of competitive protein-protein interactions mediated by subcellular protein hubs often require detailed and computationally-rich approaches. We developed an analytically accessible model anchored in queuing theory to predict binding site occupancies as a function of ligand concentrations. Remarkably, we find that the theoretically predicted receptor occupancy with no free fit parameters aligns well with the measurements acquired in experiments using nanopore sensors that can detect multiple ligand types. Building on this result, we apply mean-field approaches to compartmentalize large numbers of ligands competing for a single site. By extending the method to multiple binding sites we consider allosteric regulation, where the state of one site can impact binding affinity of the distant other. Our models provide a rich mechanistic understanding of competitive protein-protein interactions that broadly applies to protein analytics, drug development, and biosensor technology.