Minimum energy paths for conformational changes of viral capsids

In this work we study how a viral capsid can change conformation using techniques of Large Deviations Theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units - the proteins forming the capsomers - interact by weak forces to form a structure with exceptional mechanical resistance. The destabilization of such a structure is interesting both per se, since it is related either to infection or maturation processes, and because it yields insights into the stability of complex structures in which the constitutive elements interact by weak attractive forces. We focus here on a simplified model of a dodecahederal viral capsid, and assume that the capsomers are rigid plaquettes with one degree of freedom each. We compute the most probable transition path from the closed capsid to the final configuration using minimum energy paths, and discuss the stability of intermediate states.Comment: 27 pages, 4 figures. New version, to appear in Physical Review

Classification of self-assembling protein nanoparticle architectures for applications in vaccine design

We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response

Classification of self-assembling protein nanoparticle architectures for applications in vaccine design

We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response

Surface stresses in complex viral capsids and non-quasiequivalent viral architectures

Many larger and more complex viruses deviate from the capsid layouts predicted in the seminal Caspar-Klug theory of icosahedral viruses. Instead of being built from one type of capsid protein, they code for multiple distinct structural proteins that either break the local symmetry of the capsid protein building blocks (capsomers) in specific positions, or exhibit auxiliary proteins that stabilise the capsid shell. We investigate here the hypothesis that this occurs as a response to mechanical stress. For this, we construct a coarse-grained model of a viral capsid, derived from the experimentally determined atomistic positions of the capsid proteins, that represents the basic features of protein organisation in the viral capsid as described in Caspar-Klug theory. We focus here on viruses in the PRD1-adenovirus lineage. For T=28 viruses in this lineage, that have capsids formed from two distinct structural proteins, we show that the tangential shear stress in the viral capsid concentrates at the sites of local symmetry breaking. In the T=21,25 and 27 capsids, we show that stabilizing proteins decrease the tangential stress. These results suggest that mechanical properties can act as selective pressures on the evolution of capsid components, offsetting the coding cost imposed by the need for such additional protein components

A coarse-grained model of the expansionof the human rhinovirus 2 capsid revealsinsights in genome release

Human rhinoviruses are causative agents of the common cold. In order torelease their RNA genome into the host during a viral infection, these smallviruses must undergo conformational changes in their capsids, whosedetailed mechanism is strictly related to the process of RNA extrusion,which has been only partially elucidated. We study here a mathematicalmodel for the structural transition between the native particle of human rhi-novirus type 2 and its expanded form, viewing the process as an energycascade, i.e. a sequence of metastable states with decreasing energy connectedby minimum energy paths. We explore several transition pathways anddiscuss their implications for the RNA exit proces