Abstract
Multivalent binding interactions are commonly found throughout biology to enhance weak monovalent binding such as between glycoligands and protein receptors. Designing multivalent polymers to bind to viruses and toxic proteins is a promising avenue for inhibiting their attachment and subsequent infection of cells. Several studies have focused on oligomeric multivalent inhibitors and how changing parameters such as ligand shape, size, linker length, and flexibility affect binding. However, experimental studies of how larger structural parameters of multivalent polymers, such as degree of polymerization, affect binding avidity to targets have mixed results, with some finding an improvement with longer polymers and some finding no effect. Here, we use Brownian dynamics simulations to provide a theoretical understanding of how the degree of polymerization affects the binding avidity of multivalent polymers. We show that longer polymers increase binding avidity to multivalent targets but reach a limit in binding avidity at high degrees of polymerization. We also show that when interacting with multiple targets simultaneously, longer polymers are able to use intertarget interactions to promote clustering and improve binding efficiency. We expect our results to narrow the design space for optimizing the structure and effectiveness of multivalent inhibitors as well as be useful to understand biological design strategies for multivalent binding.