Elasticity theory of the maturation of viral capsids

• A new thin shell elasticity theory explains local conformational changes and global shape changes during virus maturation.
• Phase diagrams are used to determine the most effective conformational changes and uncover a broad range of capsid shapes
• A unifying stretching mechanism is proposed to describe local conformational changes and analyze capsid symmetry.
• The viral shell buckling transition is delayed by hexamers pre-shear (or pre-stretch).
• Hexamer conformational changes lower the viral capsid elastic energy and give rise to pre-shear/pre-stretch patterns.

Many viral capsids undergo a series of significant structural changes following assembly, a process known as maturation. The driving mechanisms for maturation usually are chemical reactions taking place inside the proteins that constitute the capsid (“subunits”) that produce structural changes of the subunits. The resulting alterations of the subunits may be directly visible from the capsid structures, as observed by electron microscopy, in the form of a shear shape change and/or a rotation of groups of subunits. The existing thin shell elasticity theory for viral shells does not take account of the internal structure of the subunits and hence cannot describe displacement patterns of the capsid during maturation. Recently, it was proposed for the case of a particular virus (HK97) that thin shell elasticity theory could in fact be generalized to include transformations of the constituent proteins by including such a transformations as a change of the stress-free reference state for the deformation free energy. In this study, we adopt that approach and illustrate its validity in more generality by describing shape changes occurring during maturation across different T-numbers in terms of subunit shearing. Using phase diagrams, we determine the shear directions of the subunits that are most effective to produce capsid shape changes, such as transitions from spherical to facetted capsid shape. We further propose an equivalent stretching mechanism offering a unifying view under which capsid symmetry can be analyzed. We conclude by showing that hexamer shearing not only drives the shape change of the viral capsid during maturation but also is capable of lowering the capsid elastic energy in particular for chiral   capsids (e.g., T=7T=7) and give rise to pre-shear patterns. These additional mechanisms may provide a driving force and an organizational principle for virus assembly.