Early stages of the HIV-1 capsid protein lattice formation

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Understanding Virus Structure and Dynamics through Molecular Simulations

Viral outbreaks remain a serious threat to human and animal populations and motivate the continued development of antiviral drugs and vaccines, which in turn benefits from a detailed understanding of both viral structure and dynamics. While great strides have been made in characterizing these systems experimentally, molecular simulations have proven to be an essential, complementary approach. In this work, we review the contributions of molecular simulations to the understanding of viral structure, functional dynamics, and processes related to the viral life cycle. Approaches ranging from coarse-grained to all-atom representations are discussed, including current efforts at modeling complete viral systems. Overall, this review demonstrates that computational virology plays an essential role in understanding these systems.

Initiation of HIV-1 Gag lattice assembly is required for recognition of the viral genome packaging signal

The encapsidation of HIV-1 gRNA into virions is enabled by the binding of the nucleocapsid (NC) domain of the HIV-1 Gag polyprotein to the structured viral RNA packaging signal (Ψ) at the 5' end of the viral genome. However, the subcellular location and oligomeric status of Gag during the initial Gag-Ψ encounter remain uncertain. Domains other than NC, such as capsid (CA), may therefore indirectly affect RNA recognition. To investigate the contribution of Gag domains to Ψ recognition in a cellular environment, we performed protein-protein crosslinking and protein-RNA crosslinking immunoprecipitation coupled with sequencing (CLIP-seq) experiments. We demonstrate that NC alone does not bind specifically to Ψ in living cells, whereas full-length Gag and a CANC subdomain bind to Ψ with high specificity. Perturbation of the Ψ RNA structure or NC zinc fingers affected CANC:Ψ binding specificity. Notably, CANC variants with substitutions that disrupt CA:CA dimer, trimer, or hexamer interfaces in the immature Gag lattice also affected RNA binding, and mutants that were unable to assemble a nascent Gag lattice were unable to specifically bind to Ψ. Artificially multimerized NC domains did not specifically bind Ψ. CA variants with substitutions in inositol phosphate coordinating residues that prevent CA hexamerization were also deficient in Ψ binding and second-site revertant mutants that restored CA assembly also restored specific binding to Ψ. Overall, these data indicate that the correct assembly of a nascent immature CA lattice is required for the specific interaction between Gag and Ψ in cells.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Atomistic dynamics of a viral infection process: Release of membrane lytic peptides from a non-enveloped virus

Molecular simulations have played an instrumental role in uncovering the structural dynamics and physical properties of virus capsids. In this work, we move beyond equilibrium physicochemical characterization of a virus system to study a stage of the infection process that is required for viral proliferation. Despite many biochemical and functional studies, the molecular mechanism of host cell entry by non-enveloped viruses remains largely unresolved. Flock House virus (FHV) is a model system for non-enveloped viruses and is the subject of the current study. FHV infects through the acid-dependent endocytic pathway, where low pH triggers externalization of membrane-disrupting (γ) peptides from the capsid interior. Using all-atom equilibrium and enhanced sampling simulations, the mechanism and energetics of γ peptide liberation and the effect of pH on this process are investigated. Our computations agree with experimental findings and reveal nanoscopic details regarding the pH control mechanism, which are not readily accessible in experiments.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). II. Temperature transferability and structural properties at low temperature

A number of studies have constructed coarse-grained (CG) models of water to understand its anomalous properties. Most of these properties emerge at low temperatures, and an accurate CG model needs to be applicable to these low-temperature ranges. However, direct use of CG models parameterized from other temperatures, e.g., room temperature, encounters a problem known as transferability, as the CG potential essentially follows the form of the many-body CG free energy function. Therefore, temperature-dependent changes to CG interactions must be accounted for. The collective behavior of water at low temperature is generally a many-body process, which often motivates the use of expensive many-body terms in the CG interactions. To surmount the aforementioned problems, we apply the Bottom-Up Many-Body Projected Water (BUMPer) CG model constructed from Paper I to study the low-temperature behavior of water. We report for the first time that the embedded three-body interaction enables BUMPer, despite its pairwise form, to capture the growth of ice at the ice/water interface with corroborating many-body correlations during the crystal growth. Furthermore, we propose temperature transferable BUMPer models that are indirectly constructed from the free energy decomposition scheme. Changes in CG interactions and corresponding structures are faithfully recapitulated by this framework. We further extend BUMPer to examine its ability to predict the structure, density, and diffusion anomalies by employing an alternative analysis based on structural correlations and pairwise potential forms to predict such anomalies. The presented analysis highlights the existence of these anomalies in the low-temperature regime and overcomes potential transferability problems.

The impact of Gag non-cleavage site mutations on HIV-1 viral fitness from integrative modelling and simulations

The high mutation rate in retroviruses is one of the leading causes of drug resistance. In human immunodeficiency virus type-1 (HIV-1), synergistic mutations in its protease and the protease substrate - the Group-specific antigen (Gag) polyprotein - work together to confer drug resistance against protease inhibitors and compensate the mutations affecting viral fitness. Some Gag mutations can restore Gag-protease binding, yet most Gag-protease correlated mutations occur outside of the Gag cleavage site. To investigate the molecular basis for this, we now report multiscale modelling approaches to investigate various sequentially cleaved Gag products in the context of clinically relevant mutations that occur outside of the cleavage sites, including simulations of the largest Gag proteolytic product in its viral membrane-bound state. We found that some mutations, such as G123E and H219Q, involve direct interaction with cleavage site residues to influence their local environment, while certain mutations in the matrix domain lead to the enrichment of lipids important for Gag targeting and assembly. Collectively, our results reveal why non-cleavage site mutations have far-reaching implications outside of Gag proteolysis, with important consequences for drugging Gag maturation intermediates and tackling protease inhibitor resistance.

Visualization of Single Molecules Building a Viral Capsid Protein Lattice through Stochastic Pathways

Direct visualization of pathways followed by single molecules while they spontaneously self-assemble into supramolecular biological machines may provide fundamental knowledge to guide molecular therapeutics and the bottom-up design of nanomaterials and nanodevices. Here, high-speed atomic force microscopy is used to visualize self-assembly of the bidimensional lattice of protein molecules that constitutes the framework of the mature human immunodeficiency virus capsid. By real-time imaging of the assembly reaction, individual transient intermediates and reaction pathways followed by single molecules could be revealed. As when assembling a jigsaw puzzle, the capsid protein lattice is randomly built. Lattice patches grow independently from separate nucleation events whereby individual molecules follow different paths. Protein subunits can be added individually, while others form oligomers before joining a lattice or are occasionally removed from the latter. Direct real-time imaging of supramolecular self-assembly has revealed a complex, chaotic process involving multiple routes followed by individual molecules that are inaccessible to bulk (averaging) techniques.

Modular HIV-1 Capsid Assemblies Reveal Diverse Host-Capsid Recognition Mechanisms

The HIV-1 capsid is an ordered protein shell that houses the viral genome during early infection. Its expansive surface consists of an ordered and interfacing array of capsid protein hexamers and pentamers that are recognized by numerous cellular proteins. Many of these proteins recognize specific, assembled capsid interfaces not present in unassembled capsid subunits. We used protein-engineering tools to capture diverse capsid assembly intermediates. We built a repertoire of capsid assemblies (ranging from two to 42 capsid protein molecules) that recreate the various surfaces in infectious capsids. These assemblies reveal unique capsid-targeting mechanisms for each of the anti-HIV factors, TRIMCyp, MxB, and TRIM5α, linked to inhibition of virus uncoating and nuclear entry, as well as the HIV-1 cofactor FEZ1 that facilitates virus intracellular trafficking. This capsid assembly repertoire enables elucidation of capsid recognition modes by known capsid-interacting factors, identification of new capsid-interacting factors, and potentially, development of capsid-targeting therapeutics.

A Multiscale Model for the Self-Assembly of Coat Proteins in Bacteriophage MS2

The self-assembly of viral capsids is an essential step to the formation of infectious viruses. Elucidating the kinetic mechanisms of how a capsid or virus-like particle assembles could advance our knowledge about the viral lifecycle, as well as the general principles in self-assembly of biomaterials. However, current understanding of capsid assembly remains incomplete for many viruses due to the fact that the transient intermediates along the assembling pathways are experimentally difficult to be detected. In this paper, we constructed a new multiscale computational framework to simulate the self-assembly of virus-like particles. We applied our method to the coat proteins of bacteriophage MS2 as a specific model system. This virus-like particle of bacteriophage MS2 has a unique feature that its 90 sequence-identical dimers can be classified into two structurally various groups: one is the symmetric CC dimer, and the other is the asymmetric AB dimer. The homotypic interactions between AB dimers result in a 5-fold symmetric contact, while the heterotypic interactions between AB and CC dimers result in 6-fold symmetric contact. We found that the assembly can be described as a physical process of phase transition that is regulated by various factors such as concentration and specific stoichiometry between AB and CC dimers. Our simulations also demonstrate that heterotypic and homotypic interfaces play distinctive roles in modulating the assembling kinetics. The interaction between AB and CC dimers is much more dynamic than that between two AB dimers. We therefore suggest that the alternate growth of viral capsid through the heterotypic dimer interactions dominates the assembling pathways. This is, to the best of our knowledge, the first multiscale model to simulate the assembling process of coat proteins in bacteriophage MS2. The generality of this approach opens the door to its further applications in assembly of other viral capsids, virus-like particles, and novel drug delivery systems.

Recent Advances in Coarse-Grained Models for Biomolecules and Their Applications

Molecular dynamics simulations have emerged as a powerful tool to study biological systems at varied length and timescales. The conventional all-atom molecular dynamics simulations are being used by the wider scientific community in routine to capture the conformational dynamics and local motions. In addition, recent developments in coarse-grained models have opened the way to study the macromolecular complexes for time scales up to milliseconds. In this review, we have discussed the principle, applicability and recent development in coarse-grained models for biological systems. The potential of coarse-grained simulation has been reviewed through state-of-the-art examples of protein folding and structure prediction, self-assembly of complexes, membrane systems and carbohydrates fiber models. The multiscale simulation approaches have also been discussed in the context of their emerging role in unravelling hierarchical level information of biosystems. We conclude this review with the future scope of coarse-grained simulations as a constantly evolving tool to capture the dynamics of biosystems.

Off-Pathway Assembly: A Broad-Spectrum Mechanism of Action for Drugs That Undermine Controlled HIV-1 Viral Capsid Formation

The early and late stages of human immunodeficiency virus (HIV) replication are orchestrated by the capsid (CA) protein, which self-assembles into a conical protein shell during viral maturation. Small molecule drugs known as capsid inhibitors (CIs) impede the highly regulated activity of CA. Intriguingly, a few CIs, such as PF-3450074 (PF74) and GS-CA1, exhibit effects at multiple stages of the viral lifecycle at effective concentrations in the pM to nM regimes, while the majority of CIs target a single stage of the viral lifecycle and are effective at nM to μM concentrations. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanisms that enable CIs to have such curious broad-spectrum activity. Our quantitatively analyzed findings show that CIs can have a profound impact on the hierarchical self-assembly of CA by perturbing populations of small CA oligomers. The self-assembly process is accelerated by the emergence of alternative assembly pathways that favor the rapid incorporation of CA pentamers, and leads to increased structural pleomorphism in mature capsids. Two relevant phenotypes are observed: (1) eccentric capsid formation that may fail to encase the viral genome and (2) rapid disassembly of the capsid, which express at late and early stages of infection, respectively. Finally, our study emphasizes the importance of adopting a dynamical perspective on inhibitory mechanisms and provides a basis for the design of future therapeutics that are effective at low stoichiometric ratios of drug to protein.

Integrative modeling of the HIV-1 ribonucleoprotein complex

A coarse-grain computational method integrates biophysical and structural data to generate models of HIV-1 genomic RNA, nucleocapsid and integrase condensed into a mature ribonucleoprotein complex. Several hypotheses for the initial structure of the genomic RNA and oligomeric state of integrase are tested. In these models, integrase interaction captures features of the relative distribution of gRNA in the immature virion and increases the size of the RNP globule, and exclusion of nucleocapsid from regions with RNA secondary structure drives an asymmetric placement of the dimerized 5’UTR at the surface of the RNP globule.

The genome of HIV-1 is composed of two strands of RNA that are packaged in the mature virion as a condensed ribonucleoprotein complex with nucleocapsid, integrase, and other proteins. We have generated models of the HIV-1 ribonucleoprotein that integrate experimental results from multiple structural and biophysical experiments, exploring several hypotheses about the state of the RNA before condensation, and the role of crosslinking by integrase. The models suggest that the 5’UTR, which shows extensive secondary structure, has a propensity to be placed on the surface of the condensed globule, due to reduced binding of nucleocapsid to double-stranded regions within the 5’UTR. This unexpected localization of the 5’UTR may have consequences for the subsequent structural transitions that occur during the process of reverse transcription.

Multiconfigurational Coarse-Grained Molecular Dynamics

Standard low resolution coarse-grained modeling techniques have difficulty capturing multiple configurations of protein systems. Here, we present a method for creating accurate coarse-grained (CG) models with multiple configurations using a linear combination of functions or “states”. Individual CG models are created to capture the individual states, and the approximate coupling between the two states is determined from an all-atom potential of mean force. We show that the resulting multiconfiguration coarse-graining (MCCG) method accurately captures the transition state as well as the free energy between the two states. We have tested this method on the folding of dodecaalanine, as well as the amphipathic helix of endophilin.

Advances in coarse-grained modeling of macromolecular complexes

Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.

Modeling the Self-Assembly of Protein Complexes through a Rigid-Body Rotational Reaction-Diffusion Algorithm

The reaction-diffusion equations provide a powerful framework for modeling nonequilibrium, cell-scale dynamics over the long time scales that are inaccessible by traditional molecular modeling approaches. Single-particle reaction-diffusion offers the highest resolution technique for tracking such dynamics, but it has not been applied to the study of protein self-assembly due to its treatment of reactive species as single-point particles. Here, we develop a relatively simple but accurate approach for building rigid structure and rotation into single-particle reaction-diffusion methods, providing a rate-based method for studying protein self-assembly. Our simplifying assumption is that reactive collisions can be evaluated purely on the basis of the separations between the sites, and not their orientations. The challenge of evaluating reaction probabilities can then be performed using well-known equations based on translational diffusion in both 3D and 2D, by employing an effective diffusion constant we derive here. We show how our approach reproduces both the kinetics of association, which is altered by rotational diffusion, and the equilibrium of reversible association, which is not. Importantly, the macroscopic kinetics of association can be predicted on the basis of the microscopic parameters of our structurally resolved model, allowing for critical comparisons with theory and other rate-based simulations. We demonstrate this method for efficient, rate-based simulations of self-assembly of clathrin trimers, highlighting how formation of regular lattices impacts the kinetics of association.

Single-molecule studies of flavivirus envelope dynamics: Experiment and computation

Flaviviruses are simple enveloped viruses exhibiting complex structural and functional heterogeneities. Decades of research have provided crucial basic insights, antiviral medication and moderately successful gene therapy trials. The most infectious particle is, however, not always the most abundant one in a population, questioning the utility of classic ensemble-averaging virology approaches. Indeed, viral replication is often not particularly efficient, prone to errors or containing parallel routes. Here, we review different single-molecule sensitive fluorescence methods that are employed to investigate flaviviruses. In particular, we review how (i) time-resolved Förster resonance energy transfer (trFRET) was applied to probe dengue envelope conformations; (ii) FRET-fluorescence correlation spectroscopy to investigate dengue envelope intrinsic dynamics and (iii) single particle tracking to follow the path of dengue viruses in cells. We also discuss how such methods may be supported by molecular dynamics (MD) simulations over a range of spatio-temporal scales, to provide complementary data on the structure and dynamics of flaviviral systems. We describe recent improvements in multiscale MD approaches that allowed the simulation of dengue particle envelopes in near-atomic resolution. We hope this review is an incentive for setting up and applying similar single-molecule studies and combine them with MD simulations to investigate structural dynamics of entire flavivirus particles over the nanosecond-to-millisecond time-scale and follow viruses during infection in cells over milliseconds to minutes.

All-atom molecular dynamics of the HBV capsid reveals insights into biological function and cryo-EM resolution limits

The hepatitis B virus capsid represents a promising therapeutic target. Experiments suggest the capsid must be flexible to function; however, capsid structure and dynamics have not been thoroughly characterized in the absence of icosahedral symmetry constraints. Here, all-atom molecular dynamics simulations are leveraged to investigate the capsid without symmetry bias, enabling study of capsid flexibility and its implications for biological function and cryo-EM resolution limits. Simulation results confirm flexibility and reveal a propensity for asymmetric distortion. The capsid’s influence on ionic species suggests a mechanism for modulating the display of cellular signals and implicates the capsid’s triangular pores as the location of signal exposure. A theoretical image reconstruction performed using simulated conformations indicates how capsid flexibility may limit the resolution of cryo-EM. Overall, the present work provides functional insight beyond what is accessible to experimental methods and raises important considerations regarding asymmetry in structural studies of icosahedral virus capsids.

Modeling the dynamics and kinetics of HIV-1 Gag during viral assembly

We report a computational model for the assembly of HIV-1 Gag into immature viral particles at the plasma membrane. To reproduce experimental structural and kinetic properties of assembly, a process occurring on the order of minutes, a coarse-grained representation consisting of a single particle per Gag molecule is developed. The model uses information relating the functional interfaces implicated in Gag assembly, results from cryo electron-tomography, and biophysical measurements from fluorescence microscopy, such as the dynamics of Gag assembly at single virions. These experimental constraints eliminated many classes of potential interactions, and narrowed the model to a single interaction scheme with two non-equivalent interfaces acting to form Gags into a hexamer, and a third interface acting to link hexamers together. This model was able to form into a hexameric structure with correct lattice spacing and reproduced biologically relevant growth rates. We explored the effect of genomic RNA seeding punctum growth, finding that RNA may be a factor in locally concentrating Gags to initiate assembly. The simulation results infer that completion of assembly cannot be governed simply by Gag binding kinetics. However the addition of membrane curvature suggests that budding of the virion from the plasma membrane could factor into slowing incorporation of Gag at an assembly site resulting in virions of the same size and number of Gag molecules independent of Gag concentration or the time taken to complete assembly. To corroborate the results of our simulation model, we developed an analytic model for Gag assembly finding good agreement with the simulation results.

Immature HIV-1 lattice assembly dynamics are regulated by scaffolding from nucleic acid and the plasma membrane

The packaging and budding of Gag polyprotein and viral RNA is a critical step in the HIV-1 life cycle. High-resolution structures of the Gag polyprotein have revealed that the capsid (CA) and spacer peptide 1 (SP1) domains contain important interfaces for Gag self-assembly. However, the molecular details of the multimerization process, especially in the presence of RNA and the cell membrane, have remained unclear. In this work, we investigate the mechanisms that work in concert between the polyproteins, RNA, and membrane to promote immature lattice growth. We develop a coarse-grained (CG) computational model that is derived from subnanometer resolution structural data. Our simulations recapitulate contiguous and hexameric lattice assembly driven only by weak anisotropic attractions at the helical CA-SP1 junction. Importantly, analysis from CG and single-particle tracking photoactivated localization (spt-PALM) trajectories indicates that viral RNA and the membrane are critical constituents that actively promote Gag multimerization through scaffolding, while overexpression of short competitor RNA can suppress assembly. We also find that the CA amino-terminal domain imparts intrinsic curvature to the Gag lattice. As a consequence, immature lattice growth appears to be coupled to the dynamics of spontaneous membrane deformation. Our findings elucidate a simple network of interactions that regulate the early stages of HIV-1 assembly and budding.

Molecular simulations of self-assembly processes in metal-organic frameworks: Model dependence

Molecular simulation is a powerful tool for investigating microscopic behavior in various chemical systems, where the use of suitable models is critical to successfully reproduce the structural and dynamic properties of the real systems of interest. In this context, molecular dynamics simulation studies of self-assembly processes in metal-organic frameworks (MOFs), a well-known class of porous materials with interesting chemical and physical properties, are relatively challenging, where a reasonably accurate representation of metal-ligand interactions is anticipated to play an important role. In the current study, we both investigate the performance of some existing models and introduce and test new models to help explore the self-assembly in an archetypal Zn-carboxylate MOF system. To this end, the behavior of six different Zn-ion models, three solvent models, and two ligand models was examined and validated against key experimental structural parameters. To explore longer time scale ordering events during MOF self-assembly via explicit solvent simulations, it is necessary to identify a suitable combination of simplified model components representing metal ions, organic ligands, and solvent molecules. It was observed that an extended cationic dummy atom (ECDA) Zn-ion model combined with an all-atom carboxylate ligand model and a simple dipolar solvent model can reproduce characteristic experimental structures for the archetypal MOF system. The successful use of these models in extensive sets of molecular simulations, which provide key insights into the self-assembly mechanism of this archetypal MOF system occurring during the early stages of this process, has been very recently reported.

Comparison of Biochemical Properties of HIV-1 and HIV-2 Capsid Proteins

Timely disassembly of viral core composed of self-assembled capsid (CA) in infected host cells is crucial for retroviral replication. Extensive in vitro studies to date on the self-assembly/disassembly mechanism of human immunodeficiency virus type 1 (HIV-1) CA have revealed its core structure and amino acid residues essential for CA–CA intermolecular interaction. However, little is known about in vitro properties of HIV-2 CA. In this study, we comparatively analyzed the polymerization properties of bacterially expressed HIV-1 and HIV-2 CA proteins. Interestingly, a much higher concentration of NaCl was required for HIV-2 CA to self-assemble than that for HIV-1 CA, but once the polymerization started, the reaction proceeded more rapidly than that observed for HIV-1 CA. Analysis of a chimeric protein revealed that N-terminal domain (NTD) is responsible for this unique property of HIV-2 CA. To further study the molecular basis for different in vitro properties of HIV-1 and HIV-2 CA proteins, we determined thermal stabilities of HIV-1 and HIV-2 CA NTD proteins at several NaCl concentrations by fluorescent-based thermal shift assays. Experimental data obtained showed that HIV-2 CA NTD was structurally more stable than HIV-1 CA NTD. Taken together, our results imply that distinct in vitro polymerization abilities of the two CA proteins are related to their structural instability/stability, which is one of the decisive factors for viral replication potential. In addition, our assay system described here may be potentially useful for searching for anti-CA antivirals against HIV-1 and HIV-2.

Parameter Optimization for Interaction between C-Terminal Domains of HIV-1 Capsid Protein

HIV-1 capsid proteins (CAs) assemble into a capsid that encloses the viral RNA. The binding between a pair of C-terminal domains (CTDs) constitutes a major interface in both the CA dimers and the large CA assemblies. Here, we attempt to use a general residue-level coarse-grained model to describe the interaction between two isolated CTDs in Monte Carlo simulations. With the standard parameters that depend only on the residue types, the model predicts a much weaker binding in comparison to the experiments. Detailed analysis reveals that some Lennard-Jones parameters are not compatible with the experimental CTD dimer structure, thus resulting in an unfavorable interaction energy. To improve the model for the CTD binding, we introduce ad hoc modifications to a small number of Lennard-Jones parameters for some specific pairs of residues at the binding interface. Through a series of extensive Monte Carlo simulations, we identify the optimal parameters for the CTD-CTD interactions. With the refined model parameters, both the binding affinity (with a dissociation constant of 13 ± 2 μM) and the binding mode are in good agreement with the experimental data. This study demonstrates that the general interaction model based on the Lennard-Jones potential, with some modest adjustment of the parameters for key residues, could correctly reproduce the reversible protein binding, thus potentially applicable for simulating the thermodynamics of the CA assemblies.

In vitro protease cleavage and computer simulations reveal the HIV-1 capsid maturation pathway

HIV-1 virions assemble as immature particles containing Gag polyproteins that are processed by the viral protease into individual components, resulting in the formation of mature infectious particles. There are two competing models for the process of forming the mature HIV-1 core: the disassembly and de novo reassembly model and the non-diffusional displacive model. To study the maturation pathway, we simulate HIV-1 maturation in vitro by digesting immature particles and assembled virus-like particles with recombinant HIV-1 protease and monitor the process with biochemical assays and cryoEM structural analysis in parallel. Processing of Gag in vitro is accurate and efficient and results in both soluble capsid protein and conical or tubular capsid assemblies, seemingly converted from immature Gag particles. Computer simulations further reveal probable assembly pathways of HIV-1 capsid formation. Combining the experimental data and computer simulations, our results suggest a sequential combination of both displacive and disassembly/reassembly processes for HIV-1 maturation.

Two competing models—disassembly/reassembly and displacive—have been proposed for how immature spherical HIV virions transform into mature particles with conical cores. Here the authors provide evidence that both disassembly/reassembly and displacive processes occur sequentially during the maturation process.

Reaction-diffusion basis of retroviral infectivity

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env₃) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env₃ molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env₃ diffuses comparably to Gag-absent Env₃ Initial immobility of Env₃ is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env₃ diffusion, and permits Env₃ clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Molecular dynamics simulations of membrane proteins and their interactions: from nanoscale to mesoscale

Molecular dynamics simulations provide a computational tool to probe membrane proteins and systems at length scales ranging from nanometers to close to a micrometer, and on microsecond timescales. All atom and coarse-grained simulations may be used to explore in detail the interactions of membrane proteins and specific lipids, yielding predictions of lipid binding sites in good agreement with available structural data. Building on the success of protein-lipid interaction simulations, larger scale simulations reveal crowding and clustering of proteins, resulting in slow and anomalous diffusional dynamics, within realistic models of cell membranes. Current methods allow near atomic resolution simulations of small membrane organelles, and of enveloped viruses to be performed, revealing key aspects of their structure and functionally important dynamics.

Computational virology: From the inside out

Viruses typically pack their genetic material within a protein capsid. Enveloped viruses also have an outer membrane made up of a lipid bilayer and membrane-spanning glycoproteins. X-ray diffraction and cryoelectron microscopy provide high resolution static views of viral structure. Molecular dynamics (MD) simulations may be used to provide dynamic insights into the structures of viruses and their components. There have been a number of simulations of viral capsids and (in some cases) of the inner core of RNA or DNA packaged within them. These simulations have generally focussed on the structural integrity and stability of the capsid and/or on the influence of the nucleic acid core on capsid stability. More recently there have been a number of simulation studies of enveloped viruses, including HIV-1, influenza A, and dengue virus. These have addressed the dynamic behaviour of the capsid, the matrix, and/or of the outer envelope. Analysis of the dynamics of the lipid bilayer components of the envelopes of influenza A and of dengue virus reveals a degree of biophysical robustness, which may contribute to the stability of virus particles in different environments. Significant computational challenges need to be addressed to aid simulation of complex viruses and their membranes, including the need to integrate structural data from a range of sources to enable us to move towards simulations of intact virions. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

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.

Coarse-grained simulation reveals key features of HIV-1 capsid self-assembly

The maturation of HIV-1 viral particles is essential for viral infectivity. During maturation, many copies of the capsid protein (CA) self-assemble into a capsid shell to enclose the viral RNA. The mechanistic details of the initiation and early stages of capsid assembly remain to be delineated. We present coarse-grained simulations of capsid assembly under various conditions, considering not only capsid lattice self-assembly but also the potential disassembly of capsid upon delivery to the cytoplasm of a target cell. The effects of CA concentration, molecular crowding, and the conformational variability of CA are described, with results indicating that capsid nucleation and growth is a multi-stage process requiring well-defined metastable intermediates. Generation of the mature capsid lattice is sensitive to local conditions, with relatively subtle changes in CA concentration and molecular crowding influencing self-assembly and the ensemble of structural morphologies.

Significant morphological changes occur during the conversion of the immature HIV virion into a mature infectious form. Here the authors use coarse-grained molecular dynamics simulations to model HIV-1 capsid self-assembly and disassembly events that suggests several metastable capsid intermediates sensitive to local conditions.

HIV Capsid Assembly, Mechanism, and Structure

The HIV genome materials are encaged by a proteinaceous shell called the capsid, constructed from ∼1000-1500 copies of the capsid proteins. Because its stability and integrity are critical to the normal life cycle and infectivity of the virus, the HIV capsid is a promising antiviral drug target. In this paper, we review the studies shaping our understanding of the structure and dynamics of the capsid proteins and various forms of their assemblies, as well as the assembly mechanism.

Major Variations in HIV-1 Capsid Assembly Morphologies Involve Minor Variations in Molecular Structures of Structurally Ordered Protein Segments

We present the results of solid state nuclear magnetic resonance (NMR) experiments on HIV-1 capsid protein (CA) assemblies with three different morphologies, namely wild-type CA (WT-CA) tubes with 35-60 nm diameters, planar sheets formed by the Arg(18)-Leu mutant (R18L-CA), and R18L-CA spheres with 20-100 nm diameters. The experiments are intended to elucidate molecular structural variations that underlie these variations in CA assembly morphology. We find that multidimensional solid state NMR spectra of (15)N,(13)C-labeled CA assemblies are remarkably similar for the three morphologies, with only small differences in (15)N and (13)C chemical shifts, no significant differences in NMR line widths, and few differences in the number of detectable NMR cross-peaks. Thus, the pronounced differences in morphology do not involve major differences in the conformations and identities of structurally ordered protein segments. Instead, morphological variations are attributable to variations in conformational distributions within disordered segments, which do not contribute to the solid state NMR spectra. Variations in solid state NMR signals from certain amino acid side chains are also observed, suggesting differences in the intermolecular dimerization interface between curved and planar CA lattices, as well as possible differences in intramolecular helix-helix packing.

Modeling HIV-1 viral capsid nucleation by dynamical systems

There are two stages generally recognized in the viral capsid assembly: nucleation and elongation. This paper focuses on the nucleation stage and develops mathematical models for HIV-1 viral capsid nucleation based on six-species dynamical systems. The Particle Swarm Optimization (PSO) algorithm is used for parameter fitting to estimate the association and dissociation rates from biological experiment data. Numerical simulations of capsid protein (CA) multimer concentrations demonstrate a good agreement with experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and dissociation rates further reveals the importance of CA trimer-of- dimers in the nucleation stage of viral capsid self- assembly.

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.

Molecular dynamics simulations of large macromolecular complexes

Connecting dynamics to structural data from diverse experimental sources, molecular dynamics simulations permit the exploration of biological phenomena in unparalleled detail. Advances in simulations are moving the atomic resolution descriptions of biological systems into the million-to-billion atom regime, in which numerous cell functions reside. In this opinion, we review the progress, driven by large-scale molecular dynamics simulations, in the study of viruses, ribosomes, bioenergetic systems, and other diverse applications. These examples highlight the utility of molecular dynamics simulations in the critical task of relating atomic detail to the function of supramolecular complexes, a task that cannot be achieved by smaller-scale simulations or existing experimental approaches alone.

Biomolecular engineering of virus-like particles aided by computational chemistry methods

Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.

Lipid directed assembly of the HIV capsid protein

Experimental evidence for in vivo capsid assembly suggests that capsid formation initiates from interactions between capsid (CA) proteins and lipids in the viral envelope. Various in vitro studies aiming to elucidate the detailed mechanisms of capsid self-assembly products have been carried out in conditions far removed from those, which would be encountered in a physiological environment. In this work we used lipid bilayers as a platform for studying the assembly of the CA protein with the rationale that the lipid-CA interactions play an important role in the nucleation of these structures. Observations using atomic force microscopy (AFM) have allowed a 'curling tadpole' mechanism to be suggested for the capsid self-assembly process. Stable dimeric CA proteins are able to move across the lipid bilayer to associate into trimers-of-dimers. These trimers form distinctly curved chains, which coil up to form larger features. As the feature grows additional trimers associate with the feature, giving a tadpole-like appearance. By comparing capsid assembly on mica, on single component lipid bilayers, and phase separated lipid bilayers, it was possible to determine the effect of lipid-protein interactions on capsid assembly.

3D molecular models of whole HIV-1 virions generated with cellPACK

As knowledge of individual biological processes grows, it becomes increasingly useful to frame new findings within their larger biological contexts in order to generate new systems-scale hypotheses. This report highlights two major iterations of a whole virus model of HIV-1, generated with the cellPACK software. cellPACK integrates structural and systems biology data with packing algorithms to assemble comprehensive 3D models of cell-scale structures in molecular detail. This report describes the biological data, modeling parameters and cellPACK methods used to specify and construct editable models for HIV-1. Anticipating that cellPACK interfaces under development will enable researchers from diverse backgrounds to critique and improve the biological models, we discuss how cellPACK can be used as a framework to unify different types of data across all scales of biology.

Applying molecular crowding models to simulations of virus capsid assembly in vitro

Virus capsid assembly has been widely studied as a biophysical system, both for its biological and medical significance and as an important model for complex self-assembly processes. No current technology can monitor assembly in detail and what information we have on assembly kinetics comes exclusively from in vitro studies. There are many differences between the intracellular environment and that of an in vitro assembly assay, however, that might be expected to alter assembly pathways. Here, we explore one specific feature characteristic of the intracellular environment and known to have large effects on macromolecular assembly processes: molecular crowding. We combine prior particle simulation methods for estimating crowding effects with coarse-grained stochastic models of capsid assembly, using the crowding models to adjust kinetics of capsid simulations to examine possible effects of crowding on assembly pathways. Simulations suggest a striking difference depending on whether or not a system uses nucleation-limited assembly, with crowding tending to promote off-pathway growth in a nonnucleation-limited model but often enhancing assembly efficiency at high crowding levels even while impeding it at lower crowding levels in a nucleation-limited model. These models may help us understand how complicated assembly systems may have evolved to function with high efficiency and fidelity in the densely crowded environment of the cell.