Effective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valence

Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective interparticle potentials. Here we show that developing an effective potential for particles interacting with a limited number of 'lock-and-key' selective bonds (due to the specificity of biomolecular interactions) requires-in addition to the nonsphericity of the potential-a (many body) constraint that prevents multiple bonding on the same site. We show the importance of retaining both valence and bond selectivity by developing, as a case study, a simple effective potential describing the interaction between colloidal particles coated by four single-strand DNA chains.