Thermodynamics of nanospheres encapsulated in virus capsids

We investigate the thermodynamics of complexation of functionalized charged nanospheres with viral proteins. The physics of this problem is governed not only by electrostatic interaction between the proteins and the nanosphere cores (screened by salt ions), but also by configurational degrees of freedom of the charged protein N tails. We approach the problem by constructing an appropriate complexation free-energy functional. On the basis of both numerical and analytical studies of this functional we construct the phase diagram for the assembly which contains the information on the assembled structures that appear in the thermodynamical equilibrium, depending on the size and surface charge density of the nanosphere cores. We show that both the nanosphere core charge and its radius determine the size of the capsid that forms around the core.