Viral self-assembly pathway and mechanical stress relaxation.

The final shape of a virus is dictated by the self-assembly pathway of its constituents. Using standard thin-shell elasticity, we highlight the prominent role of the viral shell's spontaneous curvature in determining the assembly pathway. In particular, we demonstrate that the mechanical stress inherent to the growth of a curved surface can be relaxed in two different ways in the early steps of assembly, depending on the value of the spontaneous curvature of the surface. This important result explains why most viral shells have either a compact shape with icosahedral symmetry or an elongated shape lacking this symmetry.