Multishell structures of virus coat proteins.

Under conditions of low ionic strength and a pH ranging between about 3.7 and 5.0, solutions of purified coat proteins of cowpea chlorotic mottle virus (CCMV) form spherical multishell structures in the absence of viral RNA. The outer surfaces of the shells in these structures are negatively charged, whereas the inner surfaces are positively charged due to a disordered cationic N-terminal domain of the capsid protein, the arginine-rich RNA-binding motif that protrudes into the interior. We show that the main forces stabilizing these multishells are counterion release combined with a lower charge density in the RNA-binding motif region of the outer shells due to their larger radii of curvature, arguing that these compensate for the outer shells not being able to adopt the smaller, optimal, radius of curvature of the inner shell. This explains why the structures are only stable at low ionic strengths at pHs for which the outer surface is negatively charged and why the larger outer shells are not observed separately in solution. We show how to calculate the free energy of shells of nonoptimal radius of curvature from the elastic properties of the native shell. The spacing between shells is determined mainly by the entropic elasticity of the RNA-binding motifs. Although we focus on CCMV multishells, we also predict the solution conditions under which multishells formed by CCMV coat protein mutants with a lower RNA-binding motif charge are stable, and we examine other viruses as well. We conclude that at a given surface charge density, the boundaries separating regions of stable multishells with different numbers of shells shift to lower ionic strengths upon either increasing the length of the RNA-binding motif, increasing the stiffness of the shells, or decreasing the charge per RNA-binding motif.