Designing super selectivity in multivalent nano-particle binding

Abstract

A key challenge in nano-science is to design ligand-coated nanoparticles that can bind selectively to surfaces that display the cognate receptors above a threshold (surface) concentration. Nanoparticles 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 multivalent nano-particles. The model shows that the super selectivity is due to the fact that the number of distinct ligand-receptor binding arrangements increases in a highly nonlinear way with receptor coverage. Somewhat counterintuitively, our study shows that selectivity can be improved by making the individual ligand-receptor bonds weaker. 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.ne of the key challenges in nano-medicine is to acquire the ability to design supramolecular constructs that can target surfaces that display a motif or receptor above a threshold concentration while leaving surfaces with lower coverage of such receptors unaffected (1-4). Experiments indicate that such selective behavior can be obtained using multivalency (5-8). During multivalent interactions a type of particle (henceforth referred to as the "guest") uses multiple ligands to bind simultaneously to several of the receptors displayed by another type of particle or surface (the "host") (9, 10). Mammen et al. (9) recognized the importance of this type of system more than ten years ago. Since then, the concept of multivalency has found numerous applications in cell biology (7, 11), supramolecular chemistry (10), nano-medicine (4, 6), immunology (12, 13), and cancer treatment (2,3,5,14), to name but a few examples. The work of Davis et al. There is a substantial body of theoretical work that aims to explain the pronounced enhancement in binding strength that certain multivalent systems can present in comparison with their monovalent counterparts (15-17). In particular, Kitov and Bundle (18) have pointed out that the strength of multivalent binding can be enhanced if there are many possible permutations in the binding pattern of receptors and ligands. The role of steric repulsion and conformational entropy in multivalent systems have been studied using molecular theories (19) and Monte Carlo (MC) simulations (20, 21). However, a unified picture that explains why high selectivity is observed in some experimental realizations of multivalent systems but not in others is still lacki...

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Optimal multivalent targeting of membranes with many distinct receptors

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