RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Single Particle Observation of SV40 VP1 Polyanion-Induced Assembly Shows That Substrate Size and Structure Modulate Capsid Geometry

Simian virus 40 capsid protein (VP1) is a unique system for studying substrate-dependent assembly of a nanoparticle. Here, we investigate a simplest case of this system where 12 VP1 pentamers and a single polyanion, e.g., RNA, form a T = 1 particle. To test the roles of polyanion substrate length and structure during assembly, we characterized the assembly products with size exclusion chromatography, transmission electron microscopy, and single-particle resistive-pulse sensing. We found that 500 and 600 nt RNAs had the optimal length and structure for assembly of uniform T = 1 particles. Longer 800 nt RNA, shorter 300 nt RNA, and a linear 600 unit poly(styrene sulfonate) (PSS) polyelectrolyte produced heterogeneous populations of products. This result was surprising as the 600mer PSS and 500-600 nt RNA have similar mass and charge. Like ssRNA, PSS also has a short 4 nm persistence length, but unlike RNA, PSS lacks a compact tertiary structure. These data indicate that even for flexible substrates, shape as well as size affect assembly and are consistent with the hypothesis that work, derived from protein-protein and protein-substrate interactions, is used to compact the substrate.

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.

Modeling Effects of RNA on Capsid Assembly Pathways via Coarse-Grained Stochastic Simulation

The environment of a living cell is vastly different from that of an in vitro reaction system, an issue that presents great challenges to the use of in vitro models, or computer simulations based on them, for understanding biochemistry in vivo. Virus capsids make an excellent model system for such questions because they typically have few distinct components, making them amenable to in vitro and modeling studies, yet their assembly can involve complex networks of possible reactions that cannot be resolved in detail by any current experimental technology. We previously fit kinetic simulation parameters to bulk in vitro assembly data to yield a close match between simulated and real data, and then used the simulations to study features of assembly that cannot be monitored experimentally. The present work seeks to project how assembly in these simulations fit to in vitro data would be altered by computationally adding features of the cellular environment to the system, specifically the presence of nucleic acid about which many capsids assemble. The major challenge of such work is computational: simulating fine-scale assembly pathways on the scale and in the parameter domains of real viruses is far too computationally costly to allow for explicit models of nucleic acid interaction. We bypass that limitation by applying analytical models of nucleic acid effects to adjust kinetic rate parameters learned from in vitro data to see how these adjustments, singly or in combination, might affect fine-scale assembly progress. The resulting simulations exhibit surprising behavioral complexity, with distinct effects often acting synergistically to drive efficient assembly and alter pathways relative to the in vitro model. The work demonstrates how computer simulations can help us understand how assembly might differ between the in vitro and in vivo environments and what features of the cellular environment account for these differences.

Allosteric Control of Icosahedral Capsid Assembly

During the life cycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article, we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly and thus should be taken into account in models that are used to estimate interaction parameters from experimental data.

A well-balanced preexisting equilibrium governs electron flux efficiency of a multidomain diflavin reductase

Diflavin reductases are bidomain electron transfer proteins in which structural reorientation is necessary to account for the various intramolecular and intermolecular electron transfer steps. Using small-angle x-ray scattering and nuclear magnetic resonance data, we describe the conformational free-energy landscape of the NADPH-cytochrome P450 reductase (CPR), a typical bidomain redox enzyme composed of two covalently-bound flavin domains, under various experimental conditions. The CPR enzyme exists in a salt- and pH-dependent rapid equilibrium between a previously described rigid, locked state and a newly characterized, highly flexible, unlocked state. We further establish that maximal electron flux through CPR is conditioned by adjustable stability of the locked-state domain interface under resting conditions. This is rationalized by a kinetic scheme coupling rapid conformational sampling and slow chemical reaction rates. Regulated domain interface stability associated with fast stochastic domain contacts during the catalytic cycle thus provides, to our knowledge, a new paradigm for improving our understanding of multidomain enzyme function.

Multiscale modeling of virus replication and spread

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.

Dynamic Viral Glycoprotein Machines: Approaches for Probing Transient States That Drive Membrane Fusion

The fusion glycoproteins that decorate the surface of enveloped viruses undergo dramatic conformational changes in the course of engaging with target cells through receptor interactions and during cell entry. These refolding events ultimately drive the fusion of viral and cellular membranes leading to delivery of the genetic cargo. While well-established methods for structure determination such as X-ray crystallography have provided detailed structures of fusion proteins in the pre- and post-fusion fusion states, to understand mechanistically how these fusion glycoproteins perform their structural calisthenics and drive membrane fusion requires new analytical approaches that enable dynamic intermediate states to be probed. Methods including structural mass spectrometry, small-angle X-ray scattering, and electron microscopy have begun to provide new insight into pathways of conformational change and fusion protein function. In combination, the approaches provide a significantly richer portrait of viral fusion glycoprotein structural variation and fusion activation as well as inhibition by neutralizing agents. Here recent studies that highlight the utility of these complementary approaches will be reviewed with a focus on the well-characterized influenza virus hemagglutinin fusion glycoprotein system.

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.

Reconstruction of the Disassembly Pathway of an Icosahedral Viral Capsid and Shape Determination of Two Successive Intermediates

Viral capsids derived from an icosahedral plant virus widely used in physical and nanotechnological investigations were fully dissociated into dimers by a rapid change of pH. The process was probed in vitro at high spatiotemporal resolution by time-resolved small-angle X-ray scattering using a high brilliance synchrotron source. A powerful custom-made global fitting algorithm allowed us to reconstruct the most likely pathway parametrized by a set of stoichiometric coefficients and to determine the shape of two successive intermediates by ab initio calculations. None of these two unexpected intermediates was previously identified in self-assembly experiments, which suggests that the disassembly pathway is not a mirror image of the assembly pathway. These findings shed new light on the mechanisms and the reversibility of the assembly/disassembly of natural and synthetic virus-based systems. They also demonstrate that both the structure and dynamics of an increasing number of intermediate species become accessible to experiments.

The Role of Packaging Sites in Efficient and Specific Virus Assembly

During the life cycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, short sequences (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work, we develop a coarse-grained particle-based computational model for capsid proteins and RNA that represents protein-RNA interactions arising both from nonspecific electrostatics and from specific packaging site interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) and the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs compete against non-cognate RNAs for assembly by capsid proteins.

Mechanisms of virus assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.

Modeling Viral Capsid Assembly

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.

Pathways for virus assembly around nucleic acids

Understanding the pathways by which viral capsid proteins assemble around their genomes could identify key intermediates as potential drug targets. In this work, we use computer simulations to characterize assembly over a wide range of capsid protein-protein interaction strengths and solution ionic strengths. We find that assembly pathways can be categorized into two classes, in which intermediates are either predominantly ordered or disordered. Our results suggest that estimating the protein-protein and the protein-genome binding affinities may be sufficient to predict which pathway occurs. Furthermore, the calculated phase diagrams suggest that knowledge of the dominant assembly pathway and its relationship to control parameters could identify optimal strategies to thwart or redirect assembly to block infection. Finally, analysis of simulation trajectories suggests that the two classes of assembly pathways can be distinguished in single-molecule fluorescence correlation spectroscopy or bulk time-resolved small-angle X-ray scattering experiments.

Using Markov state models to study self-assembly

Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.

Weak protein-ligand interactions studied by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is a powerful technique for studying weak interactions between proteins and their ligands (other proteins, DNA/RNA or small molecules) in solution. SAXS provides knowledge about the equilibrium state, the stoichiometry of binding and association-dissociation processes. The measurements are conducted in a solution environment that allows easy monitoring of modifications in protein-ligand association state upon environmental changes. Model-free parameters such as the molecular mass of a system and the radius of gyration can be obtained directly from the SAXS data and give indications about the association state. SAXS is also widely employed to build models of biological assemblies at a resolution of approximately 10-20 Å. Low-resolution shapes can be generated ab initio, although more detailed and biologically interpretable information can be obtained by hybrid modelling. In the latter approach, composite structures of protein-ligand complexes are constructed using atomic models of individual molecules. These may be predicted homology models or experimental structures from X-ray crystallography or NMR. This review focuses on using SAXS data to model structures of protein-ligand complexes and to study their dynamics. The combination of SAXS with other methods such as size exclusion chromatography and dynamic light scattering is discussed.

Pathogens use structural mimicry of native host ligands as a mechanism for host receptor engagement

A pathogen's ability to engage host receptors is a critical determinant of its host range and interspecies transmissibility, key issues for understanding emerging diseases. However, the identification of host receptors, which are also attractive drug targets, remains a major challenge. Our structural bioinformatics studies reveal that both bacterial and viral pathogens have evolved to structurally mimic native host ligands (ligand mimicry), thus enabling engagement of their cognate host receptors. In contrast to the structural homology, amino acid sequence similarity between pathogen molecules and the mimicked host ligands was low. We illustrate the utility of this concept to identify pathogen receptors by delineating receptor tyrosine kinase Axl as a candidate receptor for the polyomavirus SV40. The SV40-Axl interaction was validated, and its participation in the infection process was verified. Our results suggest that ligand mimicry is widespread, and we present a quick tool to screen for pathogen-host receptor interactions.

Scaffold properties are a key determinant of the size and shape of self-assembled virus-derived particles

Controlling the geometry of self-assembly will enable a greater diversity of nanoparticles than now available. Viral capsid proteins, one starting point for investigating self-assembly, have evolved to form regular particles. The polyomavirus SV40 assembles from pentameric subunits and can encapsidate anionic cargos. On short ssRNA (≤814 nt), SV40 pentamers form 22 nm diameter capsids. On RNA too long to fit a T = 1 particle, pentamers forms strings of 22 nm particles and heterogeneous particles of 29-40 nm diameter. However, on dsDNA SV40 forms 50 nm particles composed of 72 pentamers. A 7.2-Å resolution cryo-EM image reconstruction of 22 nm particles shows that they are built of 12 pentamers arranged with T = 1 icosahedral symmetry. At 3-fold vertices, pentamers each contribute to a three-helix triangle. This geometry of interaction is not seen in crystal structures of T = 7 viruses and provides a structural basis for the smaller capsids. We propose that the heterogeneous particles are actually mosaics formed by combining different geometries of interaction from T = 1 capsids and virions. Assembly can be trapped in novel conformations because SV40 interpentamer contacts are relatively strong. The implication is that by virtue of their large catalog of interactions, SV40 pentamers have the ability to self-assemble on and conform to a broad range of shapes.

Intracellular nucleic acid delivery by the supercharged dengue virus capsid protein

Supercharged proteins are a recently identified class of proteins that have the ability to efficiently deliver functional macromolecules into mammalian cells. They were first developed as bioengineering products, but were later found in the human proteome. In this work, we show that this class of proteins with unusually high net positive charge is frequently found among viral structural proteins, more specifically among capsid proteins. In particular, the capsid proteins of viruses from the Flaviviridae family have all a very high net charge to molecular weight ratio (> +1.07/kDa), thus qualifying as supercharged proteins. This ubiquity raises the hypothesis that supercharged viral capsid proteins may have biological roles that arise from an intrinsic ability to penetrate cells. Dengue virus capsid protein was selected for a detailed experimental analysis. We showed that this protein is able to deliver functional nucleic acids into mammalian cells. The same result was obtained with two isolated domains of this protein, one of them being able to translocate lipid bilayers independently of endocytic routes. Nucleic acids such as siRNA and plasmids were delivered fully functional into cells. The results raise the possibility that the ability to penetrate cells is part of the native biological functions of some viral capsid proteins.

To build a virus on a nucleic acid substrate

Many viruses package their genomes concomitant with assembly. Here, we show that this reaction can be described by three coefficients: association of capsid protein (CP) to nucleic acid (NA), KNA; CP-CP interaction, ω; and α, proportional to the work required to package NA. The value of α can vary as NA is packaged. A phase diagram of average lnα versus lnω identifies conditions where assembly is likely to fail or succeed. NA morphology can favor (lnα > 0) or impede (lnα < 0) assembly. As lnω becomes larger, capsids become more stable and assembly becomes more cooperative. Where (lnα + lnω) < 0, the CP is unable to contain the NA, so that assembly results in aberrant particles. This phase diagram is consistent with quantitative studies of cowpea chlorotic mottle virus, hepatitis B virus, and simian virus 40 assembling on ssRNA and dsDNA substrates. Thus, the formalism we develop is suitable for describing and predicting behavior of experimental studies of CP assembly on NA.

Budding pathway in the templated assembly of viruslike particles

A new pathway for the assembly of viral capsid protein around inorganic nanoparticle cores was observed by time-course light scattering and cryo-electron tomography. Gold nanoparticles with an average diameter of 11.3 nm have been used as a template for the assembly of Brome mosaic virus (BMV) capsid protein at different concentrations. At least at low protein concentrations the kinetic features of the scattering and extinction measurements are consistent with the initial rapid formation of large nanoparticle-protein clusters, which subsequently separate into individual viruslike particles (VLPs). The occurrence of multiparticle clusters at short times after mixing nanoparticles and proteins was confirmed by cryo-EM. Cryo-electron tomography of the multiparticle clusters yielded an average surface-to-surface interparticle distance of ∼7.5 nm, equivalent to ∼1.5 times the thickness of a protein shell. We propose a scenario in which VLP generation may take place through monomer exchange between aggregated particles with defect-ridden or incomplete shells, leading to the formation of stable icosahedral shells, which eventually bud off the aggregate. Together with results from previous works, the findings highlight the astonishing versatility of plant virus capsid protein assembly. This previously unknown mechanism for VLP formation has features that may have relevance for the crowded environment characterizing virus factories in the cell.

Production and biomedical applications of virus-like particles derived from polyomaviruses

Virus-like particles (VLPs), aggregates of capsid proteins devoid of viral genetic material, show great promise in the fields of vaccine development and gene therapy. These particles spontaneously self-assemble after heterologous expression of viral structural proteins. This review will focus on the use of virus-like particles derived from polyomavirus capsid proteins. Since their first recombinant production 27 years ago these particles have been investigated for a myriad of biomedical applications. These virus-like particles are safe, easy to produce, can be loaded with a broad range of diverse cargoes and can be tailored for specific delivery or epitope presentation. We will highlight the structural characteristics of polyomavirus-derived VLPs and give an overview of their applications in diagnostics, vaccine development and gene delivery.

Norovirus capsid proteins self-assemble through biphasic kinetics via long-lived stave-like intermediates

The self-assembly kinetics for a norovirus capsid protein were probed by time-resolved small-angle X-ray scattering and then analyzed by singular value decomposition and global fitting. Only three species contribute to the total scattering intensities: dimers, intermediates comprising some 11 dimers, and icosahedral T = 3 capsids made up of 90 dimers. Three-dimensional reconstructions of the intermediate robustly show a stave-like shape consistent with an arrangement of two pentameric units connected by an interstitial dimer. Upon triggering of self-assembly, the biphasic kinetics consist of a fast step in which dimers are assembled into intermediates, followed by a slow step in which intermediates interlock into capsids. This simple kinetic model reproduces experimental data with an excellent agreement over 6 decades in time and with nanometer resolution. The extracted form factors are robust against changes in experimental conditions. These findings challenge and complement currently accepted models for the assembly of norovirus capsids.

Viral genome structures are optimal for capsid assembly

Understanding how virus capsids assemble around their nucleic acid (NA) genomes could promote efforts to block viral propagation or to reengineer capsids for gene therapy applications. We develop a coarse-grained model of capsid proteins and NAs with which we investigate assembly dynamics and thermodynamics. In contrast to recent theoretical models, we find that capsids spontaneously ‘overcharge’; that is, the negative charge of the NA exceeds the positive charge on capsid. When applied to specific viruses, the optimal NA lengths closely correspond to the natural genome lengths. Calculations based on linear polyelectrolytes rather than base-paired NAs underpredict the optimal length, demonstrating the importance of NA structure to capsid assembly. These results suggest that electrostatics, excluded volume, and NA tertiary structure are sufficient to predict assembly thermodynamics and that the ability of viruses to selectively encapsidate their genomic NAs can be explained, at least in part, on a thermodynamic basis.

DOI:http://dx.doi.org/10.7554/eLife.00632.001

Viruses are infectious agents made up of proteins and a genome made of DNA or RNA. Upon infecting a host cell, viruses hijack the cell’s gene expression machinery and force it to produce copies of the viral genome and proteins, which then assemble into new viruses that can eventually infect other host cells. Because assembly is an essential step in the viral life cycle, understanding how this process occurs could significantly advance the fight against viral diseases.

In many viral families, a protein shell called a capsid forms around the viral genome during the assembly process. However, capsids can also assemble around nucleic acids in solution, indicating that a host cell is not required for their formation. Since capsid proteins are positively charged, and nucleic acids are negatively charged, electrostatic interactions between the two are thought to have an important role in capsid assembly. However, it is unclear how structural features of the viral genome affect assembly, and why the negative charge on viral genomes is actually far greater than the positive charge on capsids. These questions are difficult to address experimentally because most of the intermediates that form during virus assembly are too short-lived to be imaged.

Here, Perlmutter et al. have used state of the art computational methods and advances in graphical processing units (GPUs) to produce the most realistic model of capsid assembly to date. They showed that the stability of the complex formed between the nucleic acid and the capsid depends on the length of the viral genome. Yield was highest for genomes within a certain range of lengths, and capsids that assembled around longer or shorter genomes tended to be malformed.

Perlmutter et al. also explored how structural features of the virus—including base-pairing between viral nucleic acids, and the size and charge of the capsid—determine the optimal length of the viral genome. When they included structural data from real viruses in their simulations and predicted the optimal lengths for the viral genome, the results were very similar to those seen in existing viruses. This indicates that the structure of the viral genome has been optimized to promote packaging into capsids. Understanding this relationship between structure and packaging will make it easier to develop antiviral agents that thwart or misdirect virus assembly, and could aid the redesign of viruses for use in gene therapy and drug delivery.

DOI:http://dx.doi.org/10.7554/eLife.00632.002