  Membrane proteins and lipids can self-assemble into membrane protein
polyhedral nanoparticles (MPPNs). MPPNs have a closed spherical surface and a
polyhedral protein arrangement, and may offer a new route for structure
determination of membrane proteins and targeted drug delivery. We develop here
a general analytic model of how MPPN self-assembly depends on bilayer-protein
interactions and lipid bilayer mechanical properties. We find that the
bilayer-protein hydrophobic thickness mismatch is a key molecular control
parameter for MPPN shape that can be used to bias MPPN self-assembly towards
highly symmetric and uniform MPPN shapes. Our results suggest strategies for
optimizing MPPN shape for structural studies of membrane proteins and targeted
drug delivery.
