Influence of length and flexibility of spacers on the binding affinity of divalent ligands

We present a quantitative model for the binding of divalent ligand-receptor systems. We study the influence of length and flexibility of the spacers on the overall binding affinity and derive general rules for the optimal ligand design. To this end, we first compare different polymeric models and determine the probability to simultaneously bind to two neighboring receptor binding pockets. In a second step the binding affinity of divalent ligands in terms of the IC50 value is derived. We find that a divalent ligand has the potential to bind more efficiently than its monovalent counterpart only, if the monovalent dissociation constant is lower than a critical value. This critical monovalent dissociation constant depends on the ligand-spacer length and flexibility as well as on the size of the receptor. Regarding the optimal ligand-spacer length and flexibility, we find that the average spacer length should be equal or slightly smaller than the distance between the receptor binding pockets and that the end-to-end spacer length fluctuations should be in the same range as the size of a receptor binding pocket.