  Weak multivalent interactions govern a large variety of biological processes
like cell-cell adhesion and virus-host interactions. These systems distinguish
sharply between surfaces based on receptor density, known as superselectivity.
Earlier experimental and theoretical work provided insights into the control of
selectivity: Weak interactions and a high number of ligands facilitate
superselectivity. Present experimental studies typically involve tens or
hundreds of interactions, resulting in a high entropic contribution leading to
high selectivities. However, if, and if so how, systems with few ligands, such
as multi-domain proteins and virus binding to a membrane, show superselective
behavior is an open question. Here, we address this question with a multivalent
experimental model system based on star shaped branched DNA nanostructures (DNA
nanostars) with each branch featuring a single stranded overhang that binds to
complementary receptors on a target surface. Each DNA nanostar possesses a
fluorophore, to directly visualize DNA nanostar surface adsorption by total
internal reflection fluorescence microscopy (TIRFM). We observe that DNA
nanostars can bind superselectively to surfaces and bind optimally at a valency
of three. We quantitatively explain this optimum by extending the current
theory with interactions between DNA nanostar binding sites (ligands). Our
results add to the understanding of multivalent interactions, by identifying
microscopic mechanisms that lead to optimal selectivity, and providing
quantitative values for the relevant parameters. These findings inspire
additional design rules which improve future work on selective targeting in
directed drug delivery.
