Why large icosahedral viruses need scaffolding proteins

Abstract

While small single-stranded viral shells encapsidate their genome spontaneously, many large viruses, such as the herpes simplex virus or infectious bursal disease virus (IBDV), typically require a template, consisting of either scaffolding proteins or an inner core. Despite the proliferation of large viruses in nature, the mechanisms by which hundreds or thousands of proteins assemble to form structures with icosahedral order (IO) is completely unknown. Using continuum elasticity theory, we study the growth of large viral shells (capsids) and show that a nonspecific template not only selects the radius of the capsid, but also leads to the error-free assembly of protein subunits into capsids with universal IO. We prove that as a spherical cap grows, there is a deep potential well at the locations of disclinations that later in the assembly process will become the vertices of an icosahedron. Furthermore, we introduce a minimal model and simulate the assembly of a viral shell around a template under nonequilibrium conditions and find a perfect match between the results of continuum elasticity theory and the numerical simulations. Besides explaining available experimental results, we provide a number of predictions. Implications for other problems in spherical crystals are also discussed.

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

“…The fact that most spherical viruses adopt structures with icosahedral symmetry reveals the important role of elasticity in the energetics of viral shells [44,53,54]. Nevertheless, it has remained a mystery how an error-free shell formed out of 90 dimers or 60 trimers grows with perfect icosahedral symmetry under many different in vitro assembly conditions.…”

“…Following the results of Ref. [52,53], we assume that pentamers grow linearly with the capsid area, so the pentameric For ks = 400kBT , it takes 78 steps for a pentamer to move and "correct" its location such that the cap has only 25 trimers when the pentamer formed in the "wrong" position dissociates. We note that each MC move involves any attempt to move any trimer or vertex through diffusion, growth or detachment.…”

Ground States of Crystalline Caps: Generalized Jellium on Curved Space

“…[47] We point out that in Ref. [22], the appearance of the first defect was found to be at θ 0.66 instead of 0.795 due to numerical error arising from summing over not enough modes in the multipole expansion of self-energy. A discussion is provided in SI.…”

Endocytic Clathrin Coats Develop Curvature at Early Stages of Their Formation

“…One of the major observables that distinguish the two models is the change in the projected area (i.e., footprint) of the clathrin coat as it gains curvature: While the constant curvature model predicts a steady rise in the projected area of the coat, the flat-to-curve transition requires an abrupt ~3-4 fold reduction in the same measure (see Figure 6 of 4 and Figure 1 of 19 ). To demonstrate this, we adapted a previously described self-assembly model to simulate growth of clathrin polyhedra with different triangulation (T) numbers (Figure 1B-F; Movies S1 & S2) 24 . We chose to work with these specific geometries as their sizes are in good agreement with our experimental findings ( Figure 3), and the previously reported clathrin-coated pits 4,18,19,25,26 .…”