Abstract
Protein multivalency can provide increased affinity and specificity relative to monovalent counterparts, but these emergent biochemical properties and their mechanistic underpinnings are difficult to predict as a function of the biophysical properties of the multivalent binding partners. Here, we present a mathematical model that accurately simulates binding kinetics and equilibria of multivalent protein-protein interactions as a function of the kinetics of monomer-monomer binding, the structure and topology of the multidomain interacting partners, and the valency of each partner. These properties are all experimentally or computationally estimated a priori, including approximating topology with a worm-like chain model applicable to a variety of structurally disparate systems, thus making the model predictive without parameter fitting. We conceptualize multivalent binding as a protein-protein interaction network: ligand and receptor valencies determine the number of interacting species in the network, with monomer kinetics and structural properties dictating the dynamics of each species. As predicted by the model and validated by surface plasmon resonance experiments, multivalent interactions can generate several noncanonical macroscopic binding dynamics, including a transient burst of high-energy configurations during association, biphasic equilibria resulting from interligand competition at high concentrations, and multiexponential dissociation arising from differential lifetimes of distinct network species. The transient burst was only uncovered when extending our analysis to trivalent interactions due to the significantly larger network, and we were able to predictably tune burst magnitude by altering linker rigidity. This study elucidates mechanisms of multivalent binding and establishes a framework for model-guided analysis and engineering of such interactions.