Irreversible growth model for virus capsid assembly

Controlling viral capsid assembly with templating

We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can dramatically enhance rates and robustness of assembly, as compared to the spontaneous assembly of subunits into empty capsids. For large core-subunit interactions, subunits adsorb onto core surfaces en masse in a disordered manner, and then undergo a cooperative rearrangement into an ordered capsid structure. These assembly pathways are unlike any identified for empty capsid formation. Our models can be directly applied to recent experiments in which viral capsid proteins assemble around functionalized inorganic nanoparticles [Sun, Proc. Natl. Acad. Sci. U.S.A. 104, 1354 (2007)]. In addition, we discuss broader implications for understanding the dynamic encapsidation of single-stranded genomic molecules during viral replication and for developing multicomponent nanostructured materials.

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.

Soft modes near the buckling transition of icosahedral shells

Icosahedral shells undergo a buckling transition as the ratio of Young's modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transition. We define elastic susceptibilities as the response to forces applied at vertices, edges, and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order, and other shell-like structures with icosahedral symmetry.

Distinguishing reversible from irreversible virus capsid assembly

Capsids of spherical viruses may be constructed from hundreds or thousands of copies of the major capsid protein(s). These assembly reactions are poorly understood. Here we consider the predicted behavior for assembly where the component reactions have weak association energy and are reversible and compare them to essentially irreversible reactions. The comparisons are based on mass action calculations and the behavior predicted from kinetic simulations where assembly is described as a cascade of low order reactions. Reversible reactions are characterized by a pseudo-critical concentration, whereas irreversible reactions consume all free subunits. Irreversible reactions are more susceptible to kinetic traps comprised of numerous small intermediates. In the case where only the ultimate step is irreversible, very low concentrations of intermediates slow the completion of the reaction so that overall it closely matches the predictions for the reversible reactions that make up the majority of the cascade. Data in the literature strongly support the hypothesis that most viruses are held together by many weak interactions.