Designing super-selectivity in multivalent nano-particle binding

A key challenge in nano-science is to design ligand-coated nano-particles that can bind selectively to surfaces that display the cognate receptors above a threshold (surface) concentration. Nano-particles that bind monovalently to a target surface do not discriminate sharply between surfaces with high and low receptor coverage. In contrast, ``multivalent'' nano-particles that can bind to a larger number of ligands simultaneously, display regimes of ``super-selectivity'' where the fraction of bound particles varies sharply with the receptor concentration. We present numerical simulations that show that multivalent nano-particles can be designed such that they approach the ``on-off'' binding behavior ideal for receptor-concentration selective targeting. We propose a simple analytical model that accounts for the super-selective behavior of multi-valent nano-particles. We propose a simple rule of thumb to predict the conditions under which super-selectivity can be achieved. We validate our model predictions against the Monte Carlo simulations. Finally, we investigate the role of multi-component ligand-receptor interactions in the enhancement of targeting selectivity.