The optimal docking strength for reversibly tethered kinases

Many kinases use reversible docking interactions to augment the specificity of their catalytic domains. Such docking interactions are often structurally independent of the catalytic domain, which allow for a flexible combination of modules in evolution and in bioengineering. The affinity of docking interactions spans several orders of magnitude. This led us to ask how the affinity of the docking interaction affects enzymatic activity and how to pick the optimal interaction module to complement a given substrate. Here, we develop equations that predict the optimal binding strength of a kinase docking interaction and validate it using numerical simulations and steady-state phosphorylation kinetics for tethered protein kinase A. We show that a kinase-substrate pair has an optimum docking strength that depends on their enzymatic constants, the tether architecture, the substrate concentration, and the kinetics of the docking interactions. We show that a reversible tether enhances phosphorylation rates most when 1) the docking strength is intermediate, 2) the substrate is nonoptimal, 3) the substrate concentration is low, 4) the docking interaction has rapid exchange kinetics, and 5) the tether optimizes the effective concentration of the intramolecular reaction. This work serves as a framework for interpreting mutations in kinase docking interactions and as a design guide for engineering enzyme scaffolds.