Local rules for the self-assembly of a non-quasi-equivalent viral capsid.

The structures of many large bacteriophages, such as the P23-77 capsids, do not adhere strictly to the quasi-equivalence principle of viral architecture. Although the general architecture of the P23-77 capsids is classed as T=28d, it self-assembles from multiple copies of two types of coat protein subunits, and the resulting hexameric capsomers do not conform to the Caspar-Klug paradigm. There are two types of hexamers with distinct internal organization, that are located at specific positions in the capsid. It is an open problem which assembly mechanism can lead to such a complex capsid organization. Here we propose a simple set of local rules that can explain how such non-quasi-equivalent capsid structures can arise as a result of self-assembly.

Resting-state functional brain connectivity predicts cognitive performance: An exploratory study on a time-based prospective memory task.

Resting-state functional brain connectivity (rsFC) is in wide use for the investigation of a variety of cognitive neuroscience phenomena. In the first phase of this study, we explored the changes in EEG-reconstructed rsFC in young vs. older adults, in the both the open-eyes (OE) and the closed-eyes (CE) conditions. The results showed significant differences in several rsFC network metrics in the two age groups, confirming and detailing established knowledge that aging modulates brain functional organisation. In the study's second phase we investigated the role of rsFC architecture on cognitive performance through a time-based Prospective Memory task involving participants who monitored the passage of time to perform a specific action at an appropriate time in the future. Regression models revealed that the monitoring strategy (i.e. the number of clock checks) can be predicted by rsFC graph metric, specifically, eccentricity and betweenness in the OE condition, and assortativity in the CE condition. These results show for the first time how metrics qualifying functional brain connectivity at rest can account for the differences in the way individuals strategically handle cognitive loads in the Prospective Memory domain.

Surface stresses in complex viral capsids and non-quasi-equivalent 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 (CP), they code for multiple distinct structural proteins that either break the local symmetry of the CP building blocks (capsomers) in specific positions or exhibit auxiliary proteins that stabilize 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 CPs, that represents the basic features of protein organization 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, which 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 expansion of the human rhinovirus 2 capsid reveals insights in genome release.

Human rhinoviruses are causative agents of the common cold. In order to release their RNA genome into the host during a viral infection, these small viruses must undergo conformational changes in their capsids, whose detailed mechanism is strictly related to the process of RNA extrusion, which has been only partially elucidated. We study here a mathematical model for the structural transition between the native particle of human rhinovirus type 2 and its expanded form, viewing the process as an energy cascade, i.e. a sequence of metastable states with decreasing energy connected by minimum energy paths. We explore several transition pathways and discuss their implications for the RNA exit process.

Minimum energy paths for conformational changes of viral capsids.

In this work we study conformational changes of viral capsids 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 dodecahedral 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.

Principles Governing the Self-Assembly of Coiled-Coil Protein Nanoparticles.

Self-assembly refers to the spontaneous organization of individual building blocks into higher order structures. It occurs in biological systems such as spherical viruses, which utilize icosahedral symmetry as a guiding principle for the assembly of coat proteins into a capsid shell. In this study, we characterize the self-assembling protein nanoparticle (SAPN) system, which was inspired by such viruses. To facilitate self-assembly, monomeric building blocks have been designed to contain two oligomerization domains. An N-terminal pentameric coiled-coil domain is linked to a C-terminal coiled-coil trimer by two glycine residues. By combining monomers with inherent propensity to form five- and threefold symmetries in higher order agglomerates, the supposition is that nanoparticles will form that exhibit local and global symmetry axes of order 3 and 5. This article explores the principles that govern the assembly of such a system. Specifically, we show that the system predominantly forms according to a spherical core-shell morphology using a combination of scanning transmission electron microscopy and small angle neutron scattering. We introduce a mathematical toolkit to provide a specific description of the possible SAPN morphologies, and we apply it to characterize all particles with maximal symmetry. In particular, we present schematics that define the relative positions of all individual chains in the symmetric SAPN particles, and provide a guide of how this approach can be generalized to nonspherical morphologies, hence providing unprecedented insights into their geometries that can be exploited in future applications.

Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition.

Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV) for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available.

Nonicosahedral pathways for capsid expansion.

For a significant number of viruses a structural transition of the protein container that encapsulates the viral genome forms an important part of the life cycle and is a prerequisite for the particle becoming infectious. Despite many recent efforts the mechanism of this process is still not fully understood, and a complete characterization of the expansion pathways is still lacking. We present here a coarse-grained model that captures the essential features of the expansion process and allows us to investigate the conditions under which a viral capsid becomes unstable. Based on this model we demonstrate that the structural transitions in icosahedral viral capsids are likely to occur through a low-symmetry cascade of local expansion events spreading in a wavelike manner over the capsid surface.

An algorithm for the arithmetic classification of multilattices.

A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.

A crystallographic approach to structural transitions in icosahedral viruses.

Viruses with icosahedral capsids, which form the largest class of all viruses and contain a number of important human pathogens, can be modelled via suitable icosahedrally invariant finite subsets of icosahedral 3D quasicrystals. We combine concepts from the theory of 3D quasicrystals, and from the theory of structural phase transformations in crystalline solids, to give a framework for the study of the structural transitions occurring in icosahedral viral capsids during maturation or infection. As 3D quasicrystals are in a one-to-one correspondence with suitable subsets of 6D icosahedral Bravais lattices, we study systematically the 6D-analogs of the classical Bain deformations in 3D, characterized by minimal symmetry loss at intermediate configurations, and use this information to infer putative viral-capsid transition paths in 3D via the cut-and-project method used for the construction of quasicrystals. We apply our approach to the Cowpea Chlorotic Mottle virus (CCMV) and show that the putative transition path between the experimentally observed initial and final CCMV structures is most likely to preserve one threefold axis. Our procedure suggests a general method for the investigation and prediction of symmetry constraints on the capsids of icosahedral viruses during structural transitions, and thus provides insights into the mechanisms underlying structural transitions of these pathogens.