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Electrostatic interaction is the driving force for the encapsulation by viruscoat proteins of nanoparticles such as quantum dots, gold particles andmagnetic beads for, e.g., imaging and therapeutic purposes. In recentexperimental work, Daniel et al. [ACS Nano 4 (2010), 3853-3860] found theencapsulation efficiency to sensitively depend on the interplay between thesurface charge density of negatively charged gold nanoparticles and the numberof positive charges on the RNA binding domains of the proteins. Surprisingly,these experiments reveal that despite the highly cooperative nature of theco-assembly at low pH, the efficiency of encapsulation is a gradual function oftheir surface charge density. We present a simple all-or-nothing mass actionlaw combined with an electrostatic interaction model to explain theexperiments. We find quantitative agreement with experimental observations,supporting the existence of a natural statistical charge distribution betweennanoparticles.

Impact of Charge Variation on the Encapsulation of Nanoparticles by Virus Coat Proteins