Energetics of quasiequivalence: computational analysis of protein-protein interactions in icosahedral viruses

Elucidating the interactions between Kinesin-5/BimC and the microtubule: insights from TIRF microscopy and molecular dynamics simulations

Kinesin-5 s are bipolar motor proteins that contribute to cell division by crosslinking and sliding apart antiparallel microtubules inside the mitotic spindle. However, the mechanism underlying the interactions between kinesin-5 and the microtubule remains poorly understood. In this study, we investigated the binding of BimC, a kinesin-5 motor from Aspergillus nidulans, to the microtubule using a combination of total internal reflection fluorescence (TIRF) microscopy and molecular dynamics (MD) simulations. TIRF microscopy experiments revealed that increasing the concentration of KCl in the motility buffer from 0 mM to 150 mM completely abolishes the ability of BimC to bind to the microtubule. Consistent with this experimental finding, MD simulations demonstrated a significant reduction in the strength of electrostatic interactions between BimC and microtubules at 150 mM KCl compared to 0 mM KCl. Furthermore, we identified several salt bridges at the BimC-microtubule interface, with positively charged residues on BimC interacting with negatively charged residues on the tubulin heterodimer. These results provide mechanistic insights into the role of electrostatic interactions in kinesin-5-microtubule binding, advancing our understanding of the molecular underpinnings of kinesin-5 motility.

Modeling Viral Capsid Assembly: A Review of Computational Strategies and Applications

Viral capsid assembly is a complex and critical process, essential for understanding viral behavior, evolution, and the development of antiviral treatments, vaccines, and nanotechnology. Significant progress in studying viral capsid assembly has been achieved through various computational approaches, including molecular dynamics (MD) simulations, stochastic dynamics simulations, coarse-grained (CG) models, electrostatic analyses, lattice models, hybrid techniques, machine learning methods, and kinetic models. Each of these techniques offers unique advantages, and by integrating these diverse computational strategies, researchers can more accurately model the dynamic behaviors and structural features of viral capsids, deepening our understanding of the assembly process. This review provides a comprehensive overview of studies on viral capsid assembly, emphasizing their critical role in advancing our knowledge. It examines the contributions, strengths, and limitations of different computational methods, presents key computational works in the field, and analyzes milestone studies that have shaped current research.

Approach to Study pH-Dependent Protein Association Using Constant-pH Molecular Dynamics: Application to the Dimerization of β-Lactoglobulin

Protein-protein association is often mediated by electrostatic interactions and modulated by pH. However, experimental and computational studies have often overlooked the effect of association on the protonation state of the protein. In this work, we present a methodological approach based on constant-pH molecular dynamics (MD), which aims to provide a detailed description of a pH-dependent protein-protein association, and apply it to the dimerization of β-lactoglobulin (BLG). A selection of analyses is performed using the data generated by constant-pH MD simulations of monomeric and dimeric forms of bovine BLG, in the pH range 3-8. First, we estimate free energies of dimerization using a computationally inexpensive approach based on the Wyman-Tanford linkage theory, calculated in a new way through the use of thermodynamically based splines. The individual free energy contribution of each titratable site is also calculated, allowing for identification of relevant residues. Second, the correlations between the proton occupancies of pairs of sites are calculated (using the Pearson coefficient), and extensive networks of correlated sites are observed at acidic pH values, sometimes involving distant pairs. In general, strongly correlated sites are also slow proton exchangers and contribute significantly to the pH-dependency of the dimerization free energy. Third, we use ionic density as a fingerprint of protein charge distribution and observe electrostatic complementarity between the monomer faces that form the dimer interface, more markedly at the isoionic point (where maximum dimerization occurs) than at other pH values, which might contribute to guide the association. Finally, the pH-dependent dimerization modes are inspected using PCA, among other analyses, and two states are identified: a relaxed state at pH 4-8 (with the typical alignment of the crystallographic structure) and a compact state at pH 3-4 (with a tighter association and rotated alignment). This work shows that an approach based on constant-pH MD simulations can produce rich detailed pictures of pH-dependent protein associations, as illustrated for BLG dimerization.

Buckling transitions and soft-phase invasion of two-component icosahedral shells

What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.

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

Icosahedral viruses are under a micrometer in diameter, 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 types of 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 symmetry-related 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 all the way 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 @ 3.2 Ghz 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.

Osmotic stress and pore nucleation in charged biological nanoshells and capsids

A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.

Hot Spots and Their Contribution to the Self-Assembly of the Viral Capsid: In Silico Prediction and Analysis

The viral capsid is a macromolecular complex formed by a defined number of self-assembled proteins, which, in many cases, are biopolymers with an identical amino acid sequence. Specific protein-protein interactions (PPI) drive the capsid self-assembly process, leading to several distinct protein interfaces. Following the PPI hot spot hypothesis, we present a conservation-based methodology to identify those interface residues hypothesized to be crucial elements on the self-assembly and thermodynamic stability of the capsid. We validate the predictions through a rigorous physical framework which integrates molecular dynamics simulations and free energy calculations by Umbrella sampling and the potential of mean force using an all-atom molecular representation of the capsid proteins of an icosahedral virus in an explicit solvent. Our results show that a single mutation in any of the structure-conserved hot spots significantly perturbs the quaternary protein-protein interaction, decreasing the absolute value of the binding free energy, without altering the protein's secondary nor tertiary structure. Our conservation-based hot spot prediction methodology can lead to strategies to rationally modulate the capsid's thermodynamic properties.

RNA-Mediated Virus Assembly: Mechanisms and Consequences for Viral Evolution and Therapy

Viruses, entities composed of nucleic acids, proteins, and in some cases lipids lack the ability to replicate outside their target cells. Their components self-assemble at the nanoscale with exquisite precision-a key to their biological success in infection. Recent advances in structure determination and the development of biophysical tools such as single-molecule spectroscopy and noncovalent mass spectrometry allow unprecedented access to the detailed assembly mechanisms of simple virions. Coupling these techniques with mathematical modeling and bioinformatics has uncovered a previously unsuspected role for genomic RNA in regulating formation of viral capsids, revealing multiple, dispersed RNA sequence/structure motifs [packaging signals (PSs)] that bind cognate coat proteins cooperatively. The PS ensemble controls assembly efficiency and accounts for the packaging specificity seen in vivo. The precise modes of action of the PSs vary between viral families, but this common principle applies across many viral families, including major human pathogens. These insights open up the opportunity to block or repurpose PS function in assembly for both novel antiviral therapy and gene/drug/vaccine applications.

Chemically Induced Morphogenesis of P22 Virus-like Particles by the Surfactant Sodium Dodecyl Sulfate

In the infectious P22 bacteriophage, the packaging of DNA into the initially formed procapsid triggers a remarkable morphological transformation where the capsid expands from 58 to 62 nm. Along with the increase in size, this maturation also provides greater stability to the capsid and initiates the release of the scaffolding protein (SP). (2,4) In the P22 virus-like particle (VLP), this transformation can be mimicked in vitro by heating the procapsid particles to 65 °C or by treatment with sodium dodecyl sulfate (SDS). (5,6) Heating the P22 particles at 65 °C for 20 min is well established to trigger the transformation of P22 to the expanded (EX) P22 VLP but does not always result in a fully expanded population. Incubation with SDS resulted in a >80% expanded population for all P22 variants used in this work. This study elucidates the importance of the stoichiometric ratio between P22 subunits and SDS, the charge of the headgroup, and length of the carbon chain for the transformation. We propose a mechanism by which the expansion takes place, where both the negatively charged sulfate group and hydrophobic tail interact with the coat protein (CP) monomers within the capsid shell in a process that is facilitated by an internal osmotic pressure generated by an encapsulated macromolecular cargo.

A modelling paradigm for RNA virus assembly

Virus assembly, a key stage in any viral life cycle, had long been considered to be primarily driven by protein-protein interactions and nonspecific interactions between genomic RNA and capsid protein. We review here a modelling paradigm for RNA virus assembly that illustrates the crucial roles of multiple dispersed, specific interactions between viral genomes and coat proteins in capsid assembly. The model reveals how multiple sequence-structure motifs in the genomic RNA, termed packaging signals, with a shared coat protein recognition motif enable viruses to overcome a viral assembly-equivalent of Levinthal's Paradox in protein folding. The fitness advantages conferred by this mechanism suggest that it should be widespread in viruses, opening up new perspectives on viral evolution and anti-viral therapy.

Viral nanomechanics with a virtual atomic force microscope

One of the most important components of a virus is the protein shell or capsid that encloses its genetic material. The main role of the capsid is to protect the viral genome against external aggressions, facilitating its safe and efficient encapsulation and delivery. As a consequence, viral capsids have developed astonishing mechanical properties that are crucial for viral function. These remarkable properties have started to be unveiled in single-virus nanoindentation experiments, and are opening the door to the use of viral-derived artificial nanocages for promising bio- and nano-technological applications. However, the interpretation of nanoindentation experiments is often difficult, requiring the support of theoretical and simulation analysis. Here we present a 'Virtual AFM' (VAFM), a Brownian Dynamics simulation of a coarse-grained model of virus aimed to mimic the standard setup of atomic force microscopy (AFM) nanoindentation experiments. Despite the heavy level of coarse-graining, these simulations provide valuable information which is not accessible in experiments. Rather than focusing on a specific virus, the VAFM will be used to analyze how the mechanical response and breaking of viruses depend on different parameters controlling the effective interactions between capsid's structural units. In particular, we will discuss the influence of adsorption, the tip radius, and the rigidity and shape of the shell on its mechanical response.

Characterization of AAV vector particle stability at the single-capsid level

Virus families have evolved different strategies for genome uncoating, which are also followed by recombinant vectors. Vectors derived from adeno-associated viruses (AAV) are considered as leading delivery tools for in vivo gene transfer, and in particular gene therapy. Using a combination of atomic force microscopy (AFM), biochemical experiments, and physical modeling, we investigated here the physical properties and stability of AAV vector particles. We first compared the morphological properties of AAV vectors derived from two different serotypes (AAV8 and AAV9). Furthermore, we triggered ssDNA uncoating by incubating vector particles to increasing controlled temperatures. Our analyses, performed at the single-particle level, indicate that genome release can occur in vitro via two alternative pathways: either the capsid remains intact and ejects linearly the ssDNA molecule, or the capsid is ruptured, leaving ssDNA in a compact entangled conformation. The analysis of the length distributions of ejected genomes further revealed a two-step ejection behavior. We propose a kinetic model aimed at quantitatively describing the evolution of capsids and genomes along the different pathways, as a function of time and temperature. This model allows quantifying the relative stability of AAV8 and AAV9 particles.

Changes in the stability and biomechanics of P22 bacteriophage capsid during maturation

The capsid of P22 bacteriophage undergoes a series of structural transitions during maturation that guide it from spherical to icosahedral morphology. The transitions include the release of scaffold proteins and capsid expansion. Although P22 maturation has been investigated for decades, a unified model that incorporates thermodynamic and biophysical analyses is not available. A general and specific model of icosahedral capsid maturation is of significant interest to theoreticians searching for fundamental principles as well as virologists and material scientists seeking to alter maturation to their advantage. To address this challenge, we have combined the results from orthogonal biophysical techniques including differential scanning fluorimetry, atomic force microscopy, circular dichroism, and hydrogen-deuterium exchange mass spectrometry. By integrating these results from single particle and population measurements, an energy landscape of P22 maturation from procapsid through expanded shell to wiffle ball emerged, highlighting the role of metastable structures and the thermodynamics guiding maturation. The propagation of weak quaternary interactions across symmetric elements of the capsid is a key component for stability in P22. A surprising finding is that the progression to wiffle ball, which lacks pentamers, shows that chemical and thermal stability can be uncoupled from mechanical rigidity, elegantly demonstrating the complexity inherent in capsid protein interactions and the emergent properties that can arise from icosahedral symmetry. On a broader scale, this work demonstrates the power of applying orthogonal biophysical techniques to elucidate assembly mechanisms for supramolecular complexes and provides a framework within which other viral systems can be compared.

Structure-based assessment of protein-protein interactions and accessibility of protein IX in adenoviruses with implications for antigen display

The exterior minor protein IX of adenoviruses (AdVs) is a frequent target of attachment of antigens and the modified AdVs are being used as potent vaccine platforms. The organization of protein IX is disticntly different between human adenoviruses (HAdVs) and non-HAdVs. The analysis of solvent accessibility, based on the near atomic resolution structures, suggests that the C-terminal residues of IX are more accessible in non-HAdVs (e.g., bovine adenovirus) than in HAdVs. Although the C-terminal fusions of IX are displayed on the capsid surface, they could disrupt the formation of tetrameric coiled-coils (4-HLXB) in HAdVs due to steric hinderance, thereby potentially affecting the capsid stability. Importantly, the parallel-antiparallel arrangement of helices seen in the 4-HLXB is not condusive for IX C-terminal fusions in HAdVs. In contrast, the parallel trimeric C-terminal coiled-coils in non-HAdVs are unlikely to be affected by the attachment of antigens and more efficiently displayed on the AdV surface.

Photosynthetic fuel for heterologous enzymes: the role of electron carrier proteins

Plants, cyanobacteria, and algae generate a surplus of redox power through photosynthesis, which makes them attractive for biotechnological exploitations. While central metabolism consumes most of the energy, pathways introduced through metabolic engineering can also tap into this source of reducing power. Recent work on the metabolic engineering of photosynthetic organisms has shown that the electron carriers such as ferredoxin and flavodoxin can be used to couple heterologous enzymes to photosynthetic reducing power. Because these proteins have a plethora of interaction partners and rely on electrostatically steered complex formation, they form productive electron transfer complexes with non-native enzymes. A handful of examples demonstrate channeling of photosynthetic electrons to drive the activity of heterologous enzymes, and these focus mainly on hydrogenases and cytochrome P450s. However, competition from native pathways and inefficient electron transfer rates present major obstacles, which limit the productivity of heterologous reactions coupled to photosynthesis. We discuss specific approaches to address these bottlenecks and ensure high productivity of such enzymes in a photosynthetic context.

Interacting motif networks located in hotspots associated with RNA release are conserved in Enterovirus capsids

Enteroviruses are responsible for a multitude of human diseases. Expansion of the virus capsid is associated with a cascade of conformational changes that allow the subsequent release of RNA. For the first time, this study presents a comprehensive bioinformatic screen for the prediction of interacting motifs within intraprotomer interfaces and across respective interfaces surrounding the fivefold and twofold axes. The results identify a network of conserved motif residues involved in interactions in enteroviruses that may be critical to capsid stabilisation, providing guidelines towards developing antivirals that interfere with viral expansion during RNA release.

Imaging and Quantitation of a Succession of Transient Intermediates Reveal the Reversible Self-Assembly Pathway of a Simple Icosahedral Virus Capsid

Understanding the fundamental principles underlying supramolecular self-assembly may facilitate many developments, from novel antivirals to self-organized nanodevices. Icosahedral virus particles constitute paradigms to study self-assembly using a combination of theory and experiment. Unfortunately, assembly pathways of the structurally simplest virus capsids, those more accessible to detailed theoretical studies, have been difficult to study experimentally. We have enabled the in vitro self-assembly under close to physiological conditions of one of the simplest virus particles known, the minute virus of mice (MVM) capsid, and experimentally analyzed its pathways of assembly and disassembly. A combination of electron microscopy and high-resolution atomic force microscopy was used to structurally characterize and quantify a succession of transient assembly and disassembly intermediates. The results provided an experiment-based model for the reversible self-assembly pathway of a most simple (T = 1) icosahedral protein shell. During assembly, trimeric capsid building blocks are sequentially added to the growing capsid, with pentamers of building blocks and incomplete capsids missing one building block as conspicuous intermediates. This study provided experimental verification of many features of self-assembly of a simple T = 1 capsid predicted by molecular dynamics simulations. It also demonstrated atomic force microscopy imaging and automated analysis, in combination with electron microscopy, as a powerful single-particle approach to characterize at high resolution and quantify transient intermediates during supramolecular self-assembly/disassembly reactions. Finally, the efficient in vitro self-assembly achieved for the oncotropic, cell nucleus-targeted MVM capsid may facilitate its development as a drug-encapsidating nanoparticle for anticancer targeted drug delivery.

Identification of a major intermediate along the self-assembly pathway of an icosahedral viral capsid by using an analytical model of a spherical patch

Viruses are astonishing edifices in which hundreds of molecular building blocks fit into the final structure with pinpoint accuracy. We established a robust kinetic model accounting for the in vitro self-assembly of a capsid shell derived from an icosahedral plant virus by using time-resolved small-angle X-ray scattering (TR-SAXS) data at high spatiotemporal resolution. By implementing an analytical model of a spherical patch into a global fitting algorithm, we managed to identify a major intermediate species along the self-assembly pathway. With a series of data collected at different protein concentrations, we showed that free dimers self-assembled into a capsid through an intermediate resembling a half-capsid. The typical lifetime of the intermediate was a few seconds and yet the presence of so large an oligomer was not reported before. The progress in instrumental detection along with the development of powerful algorithms for data processing contribute to shedding light on nonequilibrium processes in highly complex systems such as viruses.

Physical Ingredients Controlling Stability and Structural Selection of Empty Viral Capsids

One of the crucial steps in the viral replication cycle is the self-assembly of its protein shell. Typically, each native virus adopts a unique architecture, but the coat proteins of many viruses have the capability to self-assemble in vitro into different structures by changing the assembly conditions. However, the mechanisms determining which of the possible capsid shapes and structures is selected by a virus are still not well-known. We present a coarse-grained model to analyze and understand the physical mechanisms controlling the size and structure selection in the assembly of empty viral capsids. Using this model and Monte Carlo simulations, we have characterized the phase diagram and stability of T = 1,3,4,7 and snub cube shells. In addition, we have studied the tolerance of different shells to changes in physical parameters related to ambient conditions, identifying possible strategies to induce misassembly or failure. Finally, we discuss the factors that select the shape of a capsid as spherical, faceted, elongated, or decapsidated. Our model sheds important light on the ingredients that control the assembly and stability of viral shells. This knowledge is essential to get capsids with well-defined size and structure that could be used for promising applications in medicine or bionanotechnology.

Monitoring Assembly of Virus Capsids with Nanofluidic Devices

Virus assembly is a coordinated process in which typically hundreds of subunits react to form complex, symmetric particles. We use resistive-pulse sensing to characterize the assembly of hepatitis B virus core protein dimers into T = 3 and T = 4 icosahedral capsids. This technique counts and sizes intermediates and capsids in real time, with single-particle sensitivity, and at biologically relevant concentrations. Other methods are not able to produce comparable real-time, single-particle observations of assembly reactions below, near, and above the pseudocritical dimer concentration, at which the dimer and capsid concentrations are approximately equal. Assembly reactions across a range of dimer concentrations reveal three distinct patterns. At dimer concentrations as low as 50 nM, well below the pseudocritical dimer concentration of 0.5 μM, we observe a switch in the ratio of T = 3 to T = 4 capsids, which increases with decreasing dimer concentration. Far above the pseudocritical dimer concentration, kinetically trapped, incomplete T = 4 particles assemble rapidly, then slowly anneal into T = 4 capsids. At all dimer concentrations tested, T = 3 capsids form more rapidly than T = 4 capsids, suggesting distinct pathways for the two forms.

Mechanism of polymorphism and curvature of HIV capsid assemblies probed by 3D simulations with a novel coarse grain model

BACKGROUND

During the maturation process, HIV capsid proteins self-assemble into polymorphic capsids. The strong polymorphism precludes high resolution structural characterization under in vivo conditions. In spite of the determination of structural models for various in vitro assemblies of HIV capsid proteins, the assembly mechanism is still not well-understood.

METHODS

We report 3D simulations of HIV capsid proteins by a novel coarse grain model that captures the backbone of the rigid segments in the protein accurately. The effects of protein dynamics on assembly are emulated by a static ensemble of subunits in conformations derived from molecular dynamics simulation.

RESULTS

We show that HIV capsid proteins robustly assemble into hexameric lattices in a range of conditions where trimers of dimeric subunits are the dominant oligomeric intermediates. Variations of hexameric lattice curvatures are observed in simulations with subunits of variable inter-domain orientations mimicking the conformation distribution in solution. Simulations with subunits based on pentameric structural models lead to assembly of sharp curved structures resembling the tips of authentic HIV capsids, along a distinct pathway populated by tetramers and pentamers with the characteristic quasi-equivalency of viral capsids.

CONCLUSIONS

Our results suggest that the polymorphism assembly is triggered by the inter-domain dynamics of HIV capsid proteins in solution. The assembly of highly curved structures arises from proteins in conformation with a highly specific inter-domain orientation.

SIGNIFICANCE

Our work proposes a mechanism of HIV capsid assembly based on available structural data, which can be readily verified. Our model can be applied to other large biomolecular assemblies.

A minimal representation of the self-assembly of virus capsids

Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer interaction in icosahedral capsids and the requirement of low frustration fix the form of the shortest and universal truncated multipolar expansion of the two-body interaction between capsomers. The structures of many of the icosahedral and related virus capsids are located as single lowest energy states of a potential energy surface built from this interaction. Our minimalist representation is consistent with other models known to produce a controllable and efficient self-assembly, and unveils relevant features of the natural design of the capsids. It promises to be very useful in physical virology and may also be of interest in fields of nanoscience and nanotechnology where similar hollow convex structures are relevant.

Structure-based design and experimental engineering of a plant virus nanoparticle for the presentation of immunogenic epitopes and as a drug carrier

Biomaterials research for the discovery of new generation nanoparticles is one of the most active areas of nanotechnology. In the search of nature-made nanometer-sized objects, plant virus particles appear as symmetrically defined entities that can be formed by protein self-assembly. In particular, in the field of plant virology, there is plenty of literature available describing the exploitation of plant viral cages to produce safe vaccine vehicles and nanoparticles for drug delivery. In this context, we have investigated on the use of the artichoke mottled crinkle virus (AMCV) capsid both as a carrier of immunogenic epitopes and for the delivery of anticancer molecules. A dual approach that combines both in silico tools and experimental virology was applied for the rational design of immunologically active chimeric virus-like particles (VLPs) carrying immunogenic peptides. The atomic structures of wild type (wt) and chimeric VLPs were obtained by homology modeling. The effects of insertion of the HIV-1 2F5 neutralizing epitope on the structural stability of chimeric VLPs were predicted and assessed by detailed inspection of the nanoparticle intersubunit interactions at atomic level. Wt and chimeric VLPs, exposing on their surface the 2F5 epitope, were successfully produced in plants. In addition, we demonstrated that AMCV capsids could also function as drug delivery vehicles able to load the chemotherapeutic drug doxorubicin. To our knowledge, this is the first systematic predictive and empirical research addressing the question of how this icosahedral virus can be used for the production of both VLPs and viral nanoparticles for biomedical applications.

Assembly, stability and dynamics of virus capsids

Most viruses use a hollow protein shell, the capsid, to enclose the viral genome. Virus capsids are large, symmetric oligomers made of many copies of one or a few types of protein subunits. Self-assembly of a viral capsid is a complex oligomerization process that proceeds along a pathway regulated by ordered interactions between the participating protein subunits, and that involves a series of (usually transient) assembly intermediates. Assembly of many virus capsids requires the assistance of scaffolding proteins or the viral nucleic acid, which interact with the capsid subunits to promote and direct the process. Once assembled, many capsids undergo a maturation reaction that involves covalent modification and/or conformational rearrangements, which may increase the stability of the particle. The final, mature capsid is a relatively robust protein complex able to protect the viral genome from physicochemical aggressions; however, it is also a metastable, dynamic structure poised to undergo controlled conformational transitions required to perform biologically critical functions during virus entry into cells, intracellular trafficking, and viral genome uncoating. This article provides an updated general overview on structural, biophysical and biochemical aspects of the assembly, stability and dynamics of virus capsids.

Surveying capsid assembly pathways through simulation-based data fitting

Virus capsid assembly has attracted considerable interest from the biophysical modeling community as a model system for complicated self-assembly processes. Simulation methods have proven valuable for characterizing the space of possible kinetics and mechanisms of capsid assembly, but they have so far been able to say little about the assembly kinetics or pathways of any specific virus. It is not possible to directly measure the detailed interaction rates needed to parameterize a model, and there is only a limited amount of experimental evidence available to constrain possible pathways, with almost all of it gathered from in vitro studies of purified coat proteins. In prior work, we developed methods to address this problem by using simulation-based data-fitting to learn rate parameters consistent with both structure-based rule sets and experimental light-scattering data on bulk assembly progress in vitro. We have since improved these methods and extended them to fit simulation parameters to one or more experimental light-scattering curves. Here, we apply the improved data-fitting approach to three capsid systems-human papillomavirus (HPV), hepatitis B virus (HBV), and cowpea chlorotic mottle virus (CCMV)-to assess both the range of pathway types the methods can learn and the diversity of assembly strategies in use between these viruses. The resulting fits suggest three different in vitro assembly mechanisms for the three systems, with HPV capsids fitting a model of assembly via a nonnucleation-limited pathway of accumulation of individual capsomers while HBV and CCMV capsids fit similar but subtly different models of nucleation-limited assembly through ensembles of pathways involving trimer-of-dimer intermediates. The results demonstrate the ability of such data fitting to learn very different pathway types and show some of the versatility of pathways that may exist across real viruses.

Mechanical disassembly of single virus particles reveals kinetic intermediates predicted by theory

New experimental approaches are required to detect the elusive transient intermediates predicted by simulations of virus assembly or disassembly. Here, an atomic force microscope (AFM) was used to mechanically induce partial disassembly of single icosahedral T=1 capsids and virions of the minute virus of mice. The kinetic intermediates formed were imaged by AFM. The results revealed that induced disassembly of single minute-virus-of-mice particles is frequently initiated by loss of one of the 20 equivalent capsomers (trimers of capsid protein subunits) leading to a stable, nearly complete particle that does not readily lose further capsomers. With lower frequency, a fairly stable, three-fourths-complete capsid lacking one pentamer of capsomers and a free, stable pentamer were obtained. The intermediates most frequently identified (capsids missing one capsomer, capsids missing one pentamer of capsomers, and free pentamers of capsomers) had been predicted in theoretical studies of reversible capsid assembly based on thermodynamic-kinetic models, molecular dynamics, or oligomerization energies. We conclude that mechanical manipulation and imaging of simple virus particles by AFM can be used to experimentally identify kinetic intermediates predicted by simulations of assembly or disassembly.

On the effect of thermodynamic equilibrium on the assembly efficiency of complex multi-layered virus-like particles (VLP): the case of rotavirus VLP

Previous studies have reported the production of malformed virus-like-particles (VLP) in recombinant host systems. Here we computationally investigate the case of a large triple-layered rotavirus VLP (RLP). In vitro assembly, disassembly and reassembly data provides strong evidence of microscopic reversibility of RLP assembly. Light scattering experimental data also evidences a slow and reversible assembly untypical of kinetic traps, thus further strengthening the fidelity of a thermodynamically controlled assembly. In silico analysis further reveals that under favourable conditions particles distribution is dominated by structural subunits and completely built icosahedra, while other intermediates are present only at residual concentrations. Except for harshly unfavourable conditions, assembly yield is maximised when proteins are provided in the same VLP protein mass composition. The assembly yield decreases abruptly due to thermodynamic equilibrium when the VLP protein mass composition is not obeyed. The latter effect is more pronounced the higher the Gibbs free energy of subunit association is and the more complex the particle is. Overall this study shows that the correct formation of complex multi-layered VLPs is restricted to a narrow range of association energies and protein concentrations, thus the choice of the host system is critical for successful assembly. Likewise, the dynamic control of intracellular protein expression rates becomes very important to minimize wasted proteins.

Simulated self-assembly of the HIV-1 capsid: protein shape and native contacts are sufficient for two-dimensional lattice formation

We report Monte Carlo simulations of the initial stages of self-assembly of the HIV-1 capsid protein (CA), using a coarse-grained representation that mimics the CA backbone structure and intermolecular contacts observed experimentally. A simple representation of N-terminal domain/N-terminal domain and N-terminal domain/C-terminal domain interactions, coupled with the correct protein shape, is sufficient to drive formation of an ordered lattice with the correct hexagonal symmetry in two dimensions. We derive an approximate concentration/temperature phase diagram for lattice formation, and we investigate the pathway by which the lattice develops from initially separated CA dimers. Within this model, lattice formation occurs in two stages: 1), condensation of CA dimers into disordered clusters; and 2), nucleation of the lattice by the appearance of one hexamer unit within a cluster. Trimers of CA dimers are important early intermediates, and pentamers are metastable within clusters. Introduction of a preformed hexamer at the beginning of a Monte Carlo run does not directly seed lattice formation, but does facilitate the formation of large clusters. We discuss possible connections between these simulations and experimental observations concerning CA assembly within HIV-1 and in vitro.

On the origin of order in the genome organization of ssRNA viruses

Single-stranded RNA (ssRNA) viruses form a major class that includes important human, animal, and plant pathogens. While the principles underlying the structures of their protein capsids are generally well understood, much less is known about the organization of their encapsulated genomic RNAs. Cryo-electron microscopy and x-ray crystallography have revealed striking evidence of order in the packaged genomes of a number of ssRNA viruses. The physical determinants of such order, however, are largely unknown. We study here the relative effect of different energetic contributions, as well as the role of confinement, on the genome packaging of a representative ssRNA virus, the bacteriophage MS2, via a series of biomolecular simulations in which different energy terms are systematically switched off. We show that the bimodal radial density profile of the packaged genome is a consequence of RNA self-repulsion in confinement, suggesting that it should be similar for all ssRNA viruses with a comparable ratio of capsid size/genome length. In contrast, the detailed structure of the outer shell of the RNA density depends crucially on steric contributions from the capsid inner surface topography, implying that the various different polyhedral RNA cages observed in experiment are largely due to differences in the inner surface topography of the capsid.

First-step mutations for adaptation at elevated temperature increase capsid stability in a virus

The relationship between mutation, protein stability and protein function plays a central role in molecular evolution. Mutations tend to be destabilizing, including those that would confer novel functions such as host-switching or antibiotic resistance. Elevated temperature may play an important role in preadapting a protein for such novel functions by selecting for stabilizing mutations. In this study, we test the stability change conferred by single mutations that arise in a G4-like bacteriophage adapting to elevated temperature. The vast majority of these mutations map to interfaces between viral coat proteins, suggesting they affect protein-protein interactions. We assess their effects by estimating thermodynamic stability using molecular dynamic simulations and measuring kinetic stability using experimental decay assays. The results indicate that most, though not all, of the observed mutations are stabilizing.

Discrete fracture patterns of virus shells reveal mechanical building blocks

Viral shells are self-assembled protein nanocontainers with remarkable material properties. They combine simplicity of construction with toughness and complex functionality. These properties make them interesting for bionanotechnology. To date we know little about how virus structure determines assembly pathways and shell mechanics. We have here used atomic force microscopy to study structural failure of the shells of the bacteriophage Φ29. We observed rigidity patterns following the symmetry of the capsid proteins. Under prolonged force exertion, we observed fracture along well-defined lines of the 2D crystal lattice. The mechanically most stable building block of the shells was a trimer. Our approach of "reverse engineering" the virus shells thus made it possible to identify stable structural intermediates. Such stable intermediates point to a hierarchy of interactions among equal building blocks correlated with distinct next-neighbor interactions. The results also demonstrate that concepts from macroscopic materials science, such as fracture, can be usefully employed in molecular engineering.

Enumeration of viral capsid assembly pathways: tree orbits under permutation group action

This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the capsid is modeled by a polyhedron whose facets represent the monomers. The assembly process is modeled by a rooted tree, the leaves representing the facets of the polyhedron, the root representing the assembled polyhedron, and the internal vertices representing intermediate stages of assembly (subsets of facets). Besides its virological motivation, the enumeration of orbits of trees under the action of a finite group is of independent mathematical interest. If G is a finite group acting on a finite set X, then there is a natural induced action of G on the set T(x) of trees whose leaves are bijectively labeled by the elements of X. If G acts simply on X, then |X|:=|X(n)|=n·|G|, where n is the number of G-orbits in X. The basic combinatorial results in this paper are (1) a formula for the number of orbits of each size in the action of G on T(x)(n), for every n, and (2) a simple algorithm to find the stabilizer of a tree τ ∈T(x) in G that runs in linear time and does not need memory in addition to its input tree. These results help to clarify the effect of symmetry on the probability and number of assembly pathways for icosahedral viral capsids, and more generally for any finite, symmetric macromolecular assembly.

Exploring the paths of (virus) assembly

Assembly of viruses that have hundreds of subunits or folding of proteins that have hundreds of amino acids-complex biological reactions-are often spontaneous and rapid. Here, we examine the complete set of intermediates available for the assembly of a hypothetical viruslike particle and the connectivity between these intermediates in a graph-theory-inspired study. Using a build-up procedure, assuming ideal geometry, we enumerated the complete set of 2,423,313 species for formation of an icosahedron from 30 dimeric subunits. Stability of each n-subunit intermediate was defined by the number of contacts between subunits. The probability of forming an intermediate was based on the number of paths to it from its precedecessors. When defining population subsets predicted to have the greatest impact on assembly, both stability- and probability-based criteria select a small group of compact and degenerate species; ergo, only a few hundred intermediates make a measurable contribution to assembly. Though the number of possible intermediates grows combinatorially with the number of subunits in the capsid, the number of intermediates that make a significant contribution to the reaction grows by a much smaller function, a result that may contribute to our understanding of assembly and folding reactions.

A parameter estimation technique for stochastic self-assembly systems and its application to human papillomavirus self-assembly

Virus capsid assembly has been a key model system for studies of complex self-assembly but it does pose some significant challenges for modeling studies. One important limitation is the difficulty of determining accurate rate parameters. The large size and rapid assembly of typical viruses make it infeasible to directly measure coat protein binding rates or deduce them from the relatively indirect experimental measures available. In this work, we develop a computational strategy to deduce coat-coat binding rate parameters for viral capsid assembly systems by fitting stochastic simulation trajectories to experimental measures of assembly progress. Our method combines quadratic response surface and quasi-gradient descent approximations to deal with the high computational cost of simulations, stochastic noise in simulation trajectories and limitations of the available experimental data. The approach is demonstrated on a light scattering trajectory for a human papillomavirus (HPV) in vitro assembly system, showing that the method can provide rate parameters that produce accurate curve fits and are in good concordance with prior analysis of the data. These fits provide an insight into potential assembly mechanisms of the in vitro system and give a basis for exploring how these mechanisms might vary between in vitro and in vivo assembly conditions.

In vitro assembly of the T=13 procapsid of bacteriophage T5 with its scaffolding domain

The Siphoviridae coliphage T5 differs from other members of this family by the size of its genome (121 kbp) and by its large icosahedral capsid (90 nm), which is organized with T=13 geometry. T5 does not encode a separate scaffolding protein, but its head protein, pb8, contains a 159-residue aminoterminal scaffolding domain (Delta domain) that is the mature capsid. We have deciphered the early events of T5 shell assembly starting from purified pb8 with its Delta domain (pb8p). The self assembly of pb8p is regulated by salt conditions and leads to structures with distinct morphologies. Expanded tubes are formed in the presence of NaCl, whereas Ca(2+) promotes the association of pb8p into contracted tubes and procapsids. Procapsids display an angular organization and 20-nm-long internal radial structures identified as the Delta domain. The T5 head maturation protease pb11 specifically cleaves the Delta domain of contracted and expanded tubes. Ca(2+) is not required for proteolytic activity but for the organization of the Delta domain. Taken together, these data indicate that pb8p carries all of the information in its primary sequence to assemble in vitro without the requirement of the portal and accessory proteins. Furthermore, Ca(2+) plays a key role in introducing the conformational diversity that permits the formation of a stable procapsid. Phage T5 is the first example of a viral capsid consisting of quasi-equivalent hexamers and pentamers whose assembly can be carried out in vitro, starting from the major head protein with its scaffolding domain, and whose endpoint is an icosahedral T=13 particle.

Optimal architectures of elongated viruses

Many viruses protect their genetic material by a closed elongated protein shell. Unlike spherical viruses, the structure of these prolates is not yet well understood, and only a few of them have been fully characterized. We present the results of a simple phenomenological model, which describes the remarkable structures of prolate or bacilliform viral shells. Surprisingly, we find that the special well-defined geometry of these elongated viruses arises just as a consequence of free-energy minimization of a generic interaction between the structural units of the capsid. Hemispherical T-number caps centered along the 5-, 3-, and 2-fold axes with hexagonally ordered cylindrical bodies are found to be local energy minima, thus justifying their occurrence as optimal viral structures. Moreover, closed elongated viruses show a sequence of magic numbers for the end-caps, leading to strict selection rules for the length and structure of the body as well as for the number of capsomers and proteins of the capsid. The model reproduces the architecture of spherical and bacilliform viruses, both in vivo and in vitro, and constitutes an important step towards understanding viral assembly and its potential control for biological and nanotechnological applications.

Vibrational energy funneling in viruses-simulations of impulsive stimulated Raman scattering in M13 bacteriophage

The vibrational excitation of a tubular M13 bacteriophage capsid is simulated using classical molecular dynamics. The excitation occurs through impulsive stimulated Raman scattering by ultra-short laser pulses which ping the vibrational modes of the capsid. Tuning the laser pulse temporal width determines the frequency region of the capsid that is excited. The simulations reveal that electromagnetic energy transferred to the high frequency modes by ultra-short pulses is funneled via anharmonicity to just five low frequency modes which receive approximately 80% of the funneled energy. A single mode receives most of the funneled energy (3-4% of the total energy delivered) involves swelling and is effective in damaging the capsid. However, the laser intensity necessary to produce damage to the capsid from a single laser pulse is found to be extremely high for this mechanism to be effective.

Structural and electrostatic characterization of pariacoto virus: implications for viral assembly

We present the first all-atom model for the structure of a T = 3 virus, pariacoto virus (PaV), which is a nonenveloped, icosahedral RNA virus and a member of the Nodaviridae family. The model is an extension of the crystal structure, which reveals about 88% of the protein structure but only about 35% of the RNA structure. New modeling methods, combining coarse-grained and all-atom approaches, were required for developing the model. Evaluation of alternative models confirms our earlier observation that the polycationic N- and C-terminal tails of the capsid proteins must penetrate deeply into the core of the virus, where they stabilize the structure by neutralizing a substantial fraction of the RNA charge. This leads us to propose a model for the assembly of small icosahedral RNA viruses: nonspecific binding of the protein tails to the RNA leads to a collapse of the complex, in a fashion reminiscent of DNA condensation. The globular protein domains are excluded from the condensed phase but are tethered to it, so they accumulate in a shell around the condensed phase, where their concentration is high enough to trigger oligomerization and formation of the mature virus.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Mechanical properties of the icosahedral shell of southern bean mosaic virus: a molecular dynamics study

The mechanical properties of viral shells are crucial for viral assembly and infection. To study their distribution and heterogeneity on the viral surface, we performed atomistic force-probe molecular dynamics simulations of the complete shell of southern bean mosaic virus, a prototypical T = 3 virus, in explicit solvent. The simulation system comprised more than 4,500,000 atoms. To facilitate direct comparison with atomic-force microscopy (AFM) measurements, a Lennard-Jones sphere was used as a model of the AFM tip, and was pushed with different velocities toward the capsid protein at 19 different positions on the viral surface. A detailed picture of the spatial distribution of elastic constants and yielding forces was obtained that can explain corresponding heterogeneities observed in previous AFM experiments. Our simulations reveal three different deformation regimes: a prelinear regime of outer surface atom rearrangements, a linear regime of elastic capsid deformation, and a rearrangement regime that describes irreversible structural changes and the transition from elastic to plastic deformation. For both yielding forces and elastic constants, a logarithmic velocity dependency is evident over nearly two decades, the explanation for which requires including nonequilibrium effects within the established theory of enforced barrier crossing.

A novel method to map and compare protein-protein interactions in spherical viral capsids

Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein-protein interactions. There have been efforts to identify and analyze these protein-protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein-protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein-protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6-0.3 for capsids from different families with the same T-number and similar subunit fold; and <0.3 for comparisons of the dissimilar capsids that display different quaternary architectures (T-numbers). Finally, the sequence conserved interface residues within a virus family, whose spatial locations were also conserved have been hypothesized as the essential residues for self-assembly of the member virus capsids.

Protein–protein interaction and quaternary structure

Protein–protein recognition plays an essential role in structure and function. Specific non-covalent interactions stabilize the structure of macromolecular assemblies, exemplified in this review by oligomeric proteins and the capsids of icosahedral viruses. They also allow proteins to form complexes that have a very wide range of stability and lifetimes and are involved in all cellular processes. We present some of the structure-based computational methods that have been developed to characterize the quaternary structure of oligomeric proteins and other molecular assemblies and analyze the properties of the interfaces between the subunits. We compare the size, the chemical and amino acid compositions and the atomic packing of the subunit interfaces of protein–protein complexes, oligomeric proteins, viral capsids and protein–nucleic acid complexes. These biologically significant interfaces are generally close-packed, whereas the non-specific interfaces between molecules in protein crystals are loosely packed, an observation that gives a structural basis to specific recognition. A distinction is made within each interface between a core that contains buried atoms and a solvent accessible rim. The core and the rim differ in their amino acid composition and their conservation in evolution, and the distinction helps correlating the structural data with the results of site-directed mutagenesis and in vitro studies of self-assembly.