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

Coarse-grained models for self-assembling systems

In the last years, a considerable deal of work has so far been spent to understand and hence harness the physical principles that underpin the general properties of self-assembling systems. In particular, theoretical and computational modelling have been extensively used to obtain a detailed description of the actual process. This thesis reports on computational work, focusing on two different self-assembling systems and from two distinct perspectives. In the first part, a computational study of the self-assembly of string-like rigid templates in solution aims to explore to what extent it is possible to direct the assembly of the templates into knotted or linked structures by suitably tuning geometrical parameters of the system. The second part is devoted to some of the smallest instances of molecular self-assembly in nature, that is viral capsids. We report on the development of a physics-based algorithm to subdivide the structure of a capsid in quasi-rigid units, helping to elucidate the pathway of assembly from the identification of its building blocks with a top-down approach

Knowledge-based identification of functional domains in proteins

The characterization of proteins and enzymes is traditionally organised according to the sequence-structure-function paradigm. The investigation of the inter-relationships between these three properties has motivated the development of several experimental and computational techniques, that have made available an unprecedented amount of sequence and structural data. The interest in developing comparative methods for rationalizing such copious information has, of course, grown in parallel. Regarding the structure-function relationship, for instance, the availability of experimentally resolved protein structures and of computer simulations have improved our understanding of the role of proteins' internal dynamics in assisting their functional rearrangements and activity. Several approaches are currently available for elucidating and comparing proteins' internal dynamics. These can capture the relevant collective degrees of freedom that recapitulate the main conformational changes. These collective coordinates have the potential to unveil remote evolutionary relationships between proteins, that are otherwise not easily accessible from purely sequence- or structure-based investigations. Starting from this premise, in the first chapter of this thesis I will present a novel and general computational method that can detect large-scale dynamical correlations in proteins by comparing different representative conformers. This is accomplished by applying dimensionality-reduction techniques to inter-amino acid distance fluctuation matrices. As a result, an optimal quasi-rigid domain decomposition of the protein or macromolecular assembly of interest is identified, and this facilitates the functionally-oriented interpretation of their internal dynamics. Building on this approach, in the second chapter I will discuss its systematic application to a class of membrane proteins of paramount biochemical interest, namely the class A G protein-coupled receptors. The comparative analysis of their internal dynamics, as encoded by the quasi-rigid domains, allowed us to identify recurrent patterns in the large-scale dynamics of these receptors. This, in turn, allowed us to single out a number of key functional sites. These were, for the most part, previously known -- a fact that at the same time validates the method, and gives confidence for the viability of the other, novel sites. Finally, for the last part of the thesis, I focussed on the sequence-structure relationship. In particular, I considered the problem of inferring structural properties of proteins from the analysis of large multiple sequence alignments of homologous sequences. For this purpose, I recasted the strategies developed for the dynamical features extraction in order to identify compact groups of coevolving residues, based only on the knowledge of amino acid variability in aligned primary sequences. Throughout the thesis, many methodological techniques have been taken into considerations, mainly based on concepts from graph theory and statistical data analysis (clustering). All these topics are explained in the methodological sections of each chapter

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

Rapid prediction of crucial hotspot interactions for icosahedral viral capsid self-assembly by energy landscape atlasing validated by mutagenesis

Icosahedral viruses have their infectious genome encapsulated by a shell assembled by a multiscale process, starting from an integer multiple of 60 viral capsid or coat protein (VP) monomers. We predict and validate inter-atomic hotspot interactions between VP monomers that are important for the assembly of 3 icosahedral viral capsids: Adeno Associated Virus serotype 2 (AAV2) and Minute Virus of Mice (MVM), both T=1 single stranded DNA viruses, and Bromo Mosaic Virus (BMV), a T=3 single stranded RNA virus. Experimental validation is by in-vitro, site-directed mutagenesis data found in literature. We combine ab-initio predictions at two scales: at the interface-scale, we predict the importance (cruciality) of an interaction for successful subassembly across each interface between VP monomers; and at the capsid-scale, we predict the cruciality of an interface for successful capsid assembly. At the interface-scale, we measure cruciality by changes in the capsid free-energy landscape partition function when an interaction is removed. The partition function computation uses atlases of interface subassembly landscapes, rapidly generated by a novel geometric method and curated opensource software EASAL (efficient atlasing and search of assembly landscapes). At the capsid-scale, cruciality of an interface for successful assembly of the capsid is based on combinatorial entropy. Our study goes from resource-light, multiscale computational predictions of crucial hotspot inter-atomic interactions to validation using data on site-directed mutagenesis' effect on capsid assembly. By reliably and rapidly narrowing down target interactions, (no more than 1.5 hours per interface on a laptop with Intel Core i5-2500K 3.2Ghz CPU and 8GB of RAM) our predictions can inform and reduce time-consuming in-vitro and in-vivo experiments, or more computationally intensive in-silico analyses

Dynamical implications of Viral Tiling Theory

The Caspar–Klug classification of viruses whose protein shell, called viral capsid, exhibits icosahedral symmetry, has recently been extended to incorporate viruses whose capsid proteins are exclusively organised in pentamers. The approach, named ‘Viral Tiling Theory’, is inspired by the theory of quasicrystals, where aperiodic Penrose tilings enjoy 5-fold and 10-fold local symmetries. This paper analyses the extent to which this classification approach informs dynamical properties of the viral capsids, in particular the pattern of Raman active modes of vibrations, which can be observed experimentally

Elucidating the structural mechanisms of capsid stability and assembly using a hyperthermophilic bacteriophage

Nearly all viruses encapsulate their genomes in protective protein shells known as capsids. Capsids self-assemble from repeating protein subunits, which surround the viral genome. Many viruses use a powerful biomotor to pump DNA into preformed capsid shells. Therefore, not only does the capsid protect the genome from environmental stress, it additionally stabilizes against high internal pressure caused by the tightly-packaged genome inside. To understand how capsids remain stable despite extreme conditions, I use thermophilic bacteriophage P74-26 as a model to probe the structural mechanisms that govern capsid assembly and stability. P74-26 capsids have a similar architecture to capsids of mesophilic tailed bacteriophages, allowing direct comparison to elucidate the structural basis of enhanced thermostability. Here I determine the structure of the P74-26 capsid decoration protein, which contains a core beta-barrel domain termed the ‘beta-tulip’ domain. The beta-tulip domain is conserved in structural proteins from both Herpesviruses and phage, as well as a broad-spectrum Cas9 inhibitor, providing evidence of shared evolutionary ancestry. Additionally, my high-resolution structure of the P74-26 virion capsid reveals unique interdigitated architectural features that contribute to enhanced stability in the thermophile. P74-26 has a significantly larger capsid than related mesophiles yet retains the same icosahedral geometry, demonstrating a novel mechanism for increasing capsid capacity. Furthermore, my thesis work explores capsid assembly and maturation mechanisms in vitro, establishing P74-26 as a platform for future development of novel nanoparticles and therapeutic delivery systems. Taken together, this work illuminates the incredible stability of a thermophilic virus and illustrates its utility as a powerful tool for studying viral maturation

Structural insights into HIV-1 capsid assembly, maturation and stability by cryo-electron tomography

Human immunodeficiency virus type 1 (HIV-1) is an enveloped lentivirus from the family Retroviridae which infects CD4+ T-lymphocytes in a human host, leading to Acquired Immunodeficiency Syndrome (AIDS) if untreated. A subset of retroviruses, most notably lentiviruses such as HIV-1, are unique in their ability to infect non-dividing cells. To do this, the reverse transcribed viral genome must be trafficked across an intact nuclear membrane and integrated into the host cell genome. The viral capsid plays a central role in this process. The first stage of capsid assembly is polymerisation of the viral polyprotein Gag via its CA (capsid) domain into a hexagonal immature lattice, forming a truncated sphere. The viral protease cleaves Gag and frees the CA domain, which rearranges to form a conical capsid around the viral genome, built from CA hexamers and pentamers. Despite advances in recent years, many open questions remain about immature Gag lattice assembly, maturation and modulation of capsid stability by host factors upon infection. One key question that has persisted in the field is how the remarkable structural transition between the immature Gag lattice and the mature CA lattice is achieved, which involves breaking almost all of the interactions stabilising the immature lattice. To address this, I applied cryo-electron tomography (cryo-ET) and subtomogram averaging to obtain high resolution structures of immature and mature CA in a panel of HIV-1 constructs containing different combinations of proteolytic cleavage sites inactivated by mutation. Unexpectedly, proteolytic processing directly on either side of CA was sufficient for mature lattice formation at low frequencies. I also show that a beta-hairpin domain at the CA N-terminus, previously proposed to be a structural switch, is dispensable for maturation. Instead, destabilisation of a six-helix bundle between the CA C-terminus and the adjacent SP1 peptide is the main structural determinant of maturation. Viral maturation is tightly linked to immature Gag lattice assembly, but many details such as the basic unit of lattice assembly remain unclear. The immature lattice is maintained by inter- and intra-hexamer interactions but is not a complete sphere, and the structure of Gag at discontinuous lattice edges is unknown. I implemented a new workflow to obtain Gag lattice structures by subtomogram classification of a cryo-ET data set of intact HIV-1 virions. These structures show that Gag forms novel, incomplete hexamers at lattice edges and that the CA-SP1 region forms ordered helical bun- dles in partial hexamers. Molecular dynamics simulations suggest that these partial bundles exhibit increased an tendency to unfold, suggesting a role of partial hexamer structures in initiation of maturation. Capsid stability after cell entry is important to prevent degradation of the viral RNA genome, and is modulated by small molecules such as inositol hexakisphosphate (IP6) and host proteins, including cleavage and polyadenylation specific factor 6 (CPSF6) and nucleoporin 153 (Nup153). A combination of CA pentamers and hexamers that flex to adopt different curvatures provides many different potential interfaces for cofactor binding. I developed a workflow to routinely obtain near-atomic resolution structures of CA hexamers and pentamers, by subtomogram averaging of conical, IP6-stabilised in vitro CA assemblies. These were used to investigate CPSF6 and Nup153 binding to pentamers and the effect of lattice curvature on the common binding pocket for these factors. The structures obtained show that CPSF6 and Nup153 do not bind to pentamers at the concentrations used, and that lattice flexibility can modulate Nup153 binding to hexamers

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science