Model-based analysis of assembly kinetics for virus capsids or other spherical polymers

The assembly of virus capsids or other spherical polymers--empty, closed structures composed of hundreds of protein subunits--is poorly understood. Assembly of a closed spherical polymer is unlike polymerization of a filament or crystal, examples of open-ended polymers. This must be considered to develop physically meaningful analyses. We have developed a model of capsid assembly, based on a cascade of low-order reactions, that allows us to calculate kinetic simulations. The behavior of this model resembles assembly kinetics observed in solution (Zlotnick, A., J. M. Johnson, P. W. Wingfield, S. J. Stahl, and D. Endres. 1999. Biochemistry. 38:14644-14652). We exhibit two examples of this general model describing assembly of dodecahedral and icosahedral capsids. Using simulations based on these examples, we demonstrate how to extract robust estimates of assembly parameters from accessible experimental data. These parameters, nucleus size, average nucleation rate, and average free energy of association can be determined from measurement of subunit and capsid as time and concentration vary. Mathematical derivations of the analyses, carried out for a general model, are provided in an Appendix. The understanding of capsid assembly developed in this paper is general; the examples provided can be readily modified to reflect different biological systems. This enhanced understanding of virus assembly will allow a more quantitative analysis of virus stability and biological or antiviral factors that affect assembly.     

Mechanisms of Capsid Assembly around a Polymer

Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; polymers that are significantly longer than optimal often lead to partial-capsids with unpackaged polymer “tails” or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.     

Structural transitions in Cowpea chlorotic mottle virus (CCMV)

Viral capsids act as molecular containers for the encapsulation of genomic nucleic acid. These protein cages can also be used as constrained reaction vessels for packaging and entrapment of synthetic cargos. The icosahedral Cowpea chlorotic mottle virus (CCMV) is an excellent model for understanding the encapsulation and packaging of both genomic and synthetic materials. High-resolution structural information of the CCMV capsid has been invaluable for evaluating structure-function relationships in the assembled capsid but does not allow insight into the capsid dynamics. The dynamic nature of the CCMV capsid might play an important role in the biological function of the virus. The CCMV capsid undergoes a pH and metal ion dependent reversible structural transition where 60 separate pores in the capsid open or close, exposing the interior of the protein cage to the bulk medium. In addition, the highly basic N-terminal domain of the capsid, which is disordered in the crystal structure, plays a significant role in packaging the viral cargo. Interestingly, in limited proteolysis and mass spectrometry experiments the N-terminal domain is the first part of the subunit to be cleaved, confirming its dynamic nature. Based on our fundamental understanding of the capsid dynamics in CCMV, we have utilized these aspects to direct packaging of a range of synthetic materials including drugs and inorganic nanoparticles.     

Dynamic pathways for viral capsid assembly

We develop a class of models with which we simulate the assembly of particles into T1 capsidlike objects using Newtonian dynamics. By simulating assembly for many different values of system parameters, we vary the forces that drive assembly. For some ranges of parameters, assembly is facile; for others, assembly is dynamically frustrated by kinetic traps corresponding to malformed or incompletely formed capsids. Our simulations sample many independent trajectories at various capsomer concentrations, allowing for statistically meaningful conclusions. Depending on subunit (i.e., capsomer) geometries, successful assembly proceeds by several mechanisms involving binding of intermediates of various sizes. We discuss the relationship between these mechanisms and experimental evaluations of capsid assembly processes.     

A theoretical model successfully identifies features of hepatitis B virus capsid assembly.

The capsids of most spherical viruses are icosahedral, an arrangement of multiples of 60 subunits. Though it is a salient point in the life cycle of any virus, the physical chemistry of virus capsid assembly is poorly understood. We have developed general models of capsid assembly that describe the process in terms of a cascade of low order association reactions. The models predict sigmoidal assembly kinetics, where intermediates approach a low steady state concentration for the greater part of the reaction. Features of the overall reaction can be identified on the basis of the concentration dependence of assembly. In simulations, and on the basis of our understanding of the models, we find that nucleus size and the order of subsequent "elongation" reactions are reflected in the concentration dependence of the extent of the reaction and the rate of the fast phase, respectively. The reaction kinetics deduced for our models of virus assembly can be related to the assembly of any "spherical" polymer. Using light scattering and size exclusion chromatography, we observed polymerization of assembly domain dimers of hepatitis B virus (HBV) capsid protein. Empty capsids assemble at a rate that is a function of protein concentration and ionic strength. The kinetics of capsid formation were sigmoidal, where the rate of the fast phase had second-power concentration dependence. The extent of assembly had third-power concentration dependence. Simulations based on the models recapitulated the concentration dependences observed for HBV capsid assembly. These results strongly suggest that in vitro HBV assembly is nucleated by a trimer of dimers and proceeds by the addition of individual dimeric subunits. On the basis of this mechanism, we suggest that HBV capsid assembly could be an important target for antiviral therapeutics.     

BAY 41-4109 has multiple effects on Hepatitis B virus capsid assembly

Here we report the effect of a heteroaryldihydropyrimidine (HAP) antiviral compound, BAY 41-4109, on Hepatitis B virus (HBV) capsid assembly and on preformed HBV capsids. The HBV capsid is an icosahedral complex of 120 capsid protein dimers. BAY41-4109 inhibits virus production in vivo by a mechanism that targets the viral capsid. We found that BAY 41-4109 was able to both accelerate and misdirect capsid assembly in vitro. As little as one HAP molecule for every five HBV dimers was sufficient to induce formation of non-capsid polymers. Unlike the related molecule HAP-1 (Stray et al., Proc. Natl. Acad. Sci. USA 102:8138-43, 2005), no stable assembly intermediates were observed in assembly reactions with BAY 41-4109, indicating that accelerated assembly by BAY 41-4109 was still kinetically regulated by the nucleation rate. Preformed capsids were stabilized by BAY 41-4109, up to a ratio of one inhibitor molecule per two dimers. However, at BAY 41-4109:dimer ratios of 1:1 and greater, capsids were destabilized to yield very large non-capsid polymers. These data suggest the existence of two functionally distinguishable classes of drug-binding sites on HBV capsids. Occupation of the first class of site stabilizes capsid, while binding at the second class requires or induces structural changes that cannot be tolerated without destabilizing the capsid. Our data suggest that HAP compounds may inhibit virus replication by inducing assembly inappropriately and, when in excess, by misdirecting assembly decreasing the stability of normal capsids.     

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

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

A micromolar pool of antigenically distinct precursors is required to initiate cooperative assembly of hepatitis B virus capsids in Xenopus oocytes.

Assembly of hepatitis B virus capsid-like (core) particles occurs efficiently in a variety of heterologous systems via aggregation of approximately 180 molecules of a single 21.5-kDa core protein (p21.5), resulting in an icosahedral capsid structure with T = 3 symmetry. Recent studies on the assembly of hepatitis B virus core particles in Xenopus oocytes suggested that dimers of p21.5 represent the major building block from which capsids are generated. Here we determined the concentration dependence of this assembly process. By injecting serially diluted synthetic p21.5 mRNA into Xenopus oocytes, we expressed different levels of intracellular p21.5 and monitored the production of p21.5 dimers and capsids by radiolabeling and immunoprecipitation, by radioimmunoassay, or by quantitative enzyme-linked immunosorbent assay analysis. The data revealed that (i) p21.5 dimers and capsids are antigenically distinct, (ii) capsid assembly is a highly cooperative and concentration-dependent process, and (iii) p21.5 must accumulate to a signature concentration of approximately 0.7 to 0.8 microM before capsid assembly initiates. This assembly process is strikingly similar to the assembly of RNA bacteriophage R17 as defined by in vitro studies.     

The Trimeric Major Capsid Protein of Mavirus is stabilized by its Interlocked N-termini Enabling Core Flexibility for Capsid Assembly

Icosahedral viral capsids assemble with high fidelity from a large number of identical buildings blocks. The mechanisms that enable individual capsid proteins to form stable oligomeric units (capsomers) while affording structural adaptability required for further assembly into capsids are mostly unknown.Understanding these mechanisms requires knowledge of the capsomers’ dynamics, especially for viruses where no additional helper proteins are needed during capsid assembly like for the Mavirus virophage that despite its complexity (triangulation number T = 27) can assemble from its major capsid protein (MCP) alone. This protein forms the basic building block of the capsid namely a trimer (MCP₃) of double-jelly roll protomers with highly intertwined N-terminal arms of each protomer wrapping around the other two at the base of the capsomer, secured by a clasp that is formed by part of the C-terminus.Probing the dynamics of the capsomer with HDX mass spectrometry we observed differences in conformational flexibility between functional elements of the MCP trimer. While the N-terminal arm and clasp regions show above average deuterium incorporation, the two jelly-roll units in each protomer also differ in their structural plasticity, which might be needed for efficient assembly. Assessing the role of the N-terminal arm in maintaining capsomer stability showed that its detachment is required for capsomer dissociation, constituting a barrier towards capsomer monomerisation. Surprisingly, capsomer dissociation was irreversible since it was followed by a global structural rearrangement of the protomers as indicated by computational studies showing a rearrangement of the N-terminus blocking part of the capsomer forming interface.     

Observed hysteresis of virus capsid disassembly is implicit in kinetic models of assembly

For many protein multimers, association and dissociation reactions fail to reach the same end point; there is hysteresis preventing one and/or the other reaction from equilibrating. We have studied in vitro assembly of dimeric hepatitis B virus (HBV) capsid protein and dissociation of the resulting T = 4 icosahedral capsids. Empty HBV capsids composed of 120 capsid protein dimers were more resistant to dissociation by dilution or denaturants than anticipated from assembly experiments. Using intrinsic fluorescence, circular dichroism, and size exclusion chromatography, we showed that denaturants dissociate the HBV capsids without unfolding the capsid protein; unfolding of dimer only occurred at higher denaturant concentrations. The apparent energy of interaction between dimers measured in dissociation experiments was much stronger than when measured in assembly studies. Unlike assembly, capsid dissociation did not have the concentration dependence expected for a 120-subunit complex; consequently the apparent association energy systematically varied with reactant concentration. These data are evidence of hysteresis for HBV capsid dissociation. Simulations of capsid assembly and dissociation reactions recapitulate and provide an explanation for the observed behavior; these results are also applicable to oligomeric and multidomain proteins. In our calculations, we find that dissociation is impeded by temporally elevated concentrations of intermediates; this has the paradoxical effect of favoring re-assembly of those intermediates despite the global trend toward dissociation. Hysteresis masks all but the most dramatic decreases in contact energy. In contrast, assembly reactions rapidly approach equilibrium. These results provide the first rigorous explanation of how virus capsids can remain intact under extreme conditions but are still capable of "breathing." A biological implication of enhanced stability is that a triggering event may be required to initiate virus uncoating.     

Small capsid protein pORF65 is essential for assembly of Kaposi's sarcoma-associated herpesvirus capsids

Kaposi's sarcoma-associated herpesvirus (KSHV) is the etiologic agent for KS tumors, multicentric Castleman's disease, and primary effusion lymphomas. Like other herpesvirus capsids, the KSHV capsid is an icosahedral structure composed of six proteins. The capsid shell is made up of the major capsid protein, two triplex proteins, and the small capsid protein. The scaffold protein and the protease occupy the internal space. The assembly of KSHV capsids is thought to occur in a manner similar to that determined for herpes simplex virus type 1 (HSV-1). Our goal was to assemble KSHV capsids in insect cells using the baculovirus expression vector system. Six KSHV capsid open reading frames were cloned and the proteins expressed in Sf9 cells: pORF25 (major capsid protein), pORF62 (triplex 1), pORF26 (triplex 2), pORF17 (protease), pORF17.5 (scaffold protein), and also pORF65 (small capsid protein). When insect cells were coinfected with these baculoviruses, angular capsids that contained internal core structures were readily observed by conventional electron microscopy of the infected cells. Capsids were also readily isolated from infected cells by using rate velocity sedimentation. With immuno-electron microscopy methods, these capsids were seen to be reactive to antisera to pORF65 as well as to KSHV-positive human sera, indicating the correct conformation of pORF65 in these capsids. When either virus expressing the triplex proteins was omitted from the coinfection, capsids did not assemble; similar to observations made in HSV-1-infected cells. If the virus expressing the scaffold protein was excluded, large open shells that did not attain icosahedral structure were seen in the nuclei of infected cells. The presence of pORF65 was required for capsid assembly, in that capsids did not form if this protein was absent as judged by both by ultrastructural analysis of infected cells and rate velocity sedimentation experiments. Thus, a novel outcome of this study is the finding that the small capsid protein of KSHV, like the major capsid and triplex proteins, is essential for capsid shell assembly.     

Prediction of stability changes upon mutation in an icosahedral capsid

Identifying the contributions to thermodynamic stability of capsids is of fundamental and practical importance. Here we use simulation to assess how mutations affect the stability of lumazine synthase from the hyperthermophile Aquifex aeolicus, a T = 1 icosahedral capsid; in the simulations the icosahedral symmetry of the capsid is preserved by simulating a single pentamer and imposing crystal symmetry, in effect simulating an infinite cubic lattice of icosahedral capsids. The stability is assessed by estimating the free energy of association using an empirical method previously proposed to identify biological units in crystal structures. We investigate the effect on capsid formation of seven mutations, for which it has been experimentally assessed whether they disrupt capsid formation or not. With one exception, our approach predicts the effect of the mutations on the capsid stability. The method allows the identification of interaction networks, which drive capsid assembly, and highlights the plasticity of the interfaces between subunits in the capsid. Proteins 2015; 83:1733–1741. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc     

How does your virus grow? Understanding and interfering with virus assembly

Viruses have a coat to protect their genome. For about half of the known virus families, the coat is a ‘spherical’ or icosahedral capsid. The capsid can also play a role in binding to a host cell and in movement of the virus within it. Capsids are composed of hundreds of copies of individual components that must assemble rapidly and reproducibly on a biological timescale. Assembly implies stability, but many viruses also require a ‘switch’ that renders the capsid unstable so that the viral genome can be released. Although interfering with capsid assembly and stability could be an important target for antiviral therapeutics, no such therapeutics are currently available. We are just beginning to understand how to analyze the stability and the assembly kinetics of capsids.     

Genome packaging within icosahedral capsids and large-scale segmentation in viral genomic sequences

The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat proteins that should be reflected in quasi-regular segmentation of viral genomic sequences. Combining discrete direct and double Fourier transforms, we studied the quasi-regular large-scale segmentation in genomic sequences of different ssRNA, ssDNA, and dsDNA viruses. The particular representatives included satellite tobacco mosaic virus (STMV) and the strains of satellite tobacco necrosis virus (STNV), STNV-C, STNV-1, STNV-2, Escherichia phages MS2, ?X174, α3, and HK97, and Simian virus 40. In all their genomes, we found the significant quasi-regular segmentation of genomic sequences related to the virion assembly and the genome packaging within icosahedral capsid. We also found good correspondence between our results and available cryo-electron microscopy data on capsid structures and genome packaging in these viruses. Fourier analysis of genomic sequences provides the additional insight into mechanisms of hierarchical genome packaging and may be used for verification of the concepts of 3-fold or 5-fold intermediates in virion assembly. The results of sequence analysis should be taken into account at the choice of models and data interpretation. They also may be helpful for the development of antiviral drugs.     

Global structural changes in hepatitis B virus capsids induced by the assembly effector HAP1

Hepatitis B virus (HBV) is a leading cause of liver disease and hepatocellular carcinoma; over 400 million people are chronically infected with HBV. Specific anti-HBV treatments, like most antivirals, target enzymes that are similar to host proteins. Virus capsid protein has no human homolog, making its assembly a promising but undeveloped therapeutic target. HAP1 [methyl 4-(2-chloro-4-fluorophenyl)-6-methyl-2-(pyridin-2-yl)-1,4-dihydropyrimidine-5-carboxylate], a heteroaryldihydropyrimidine, is a potent HBV capsid assembly activator and misdirector. Knowledge of the structural basis for this activity would directly benefit the development of capsid-targeting therapeutic strategies. This report details the crystal structures of icosahedral HBV capsids with and without HAP1. We show that HAP1 leads to global structural changes by movements of subunits as connected rigid bodies. The observed movements cause the fivefold vertices to protrude from the liganded capsid, the threefold vertices to open, and the quasi-sixfold vertices to flatten, explaining the effects of HAP1 on assembled capsids and on the assembly process. We have identified a likely HAP1-binding site that bridges elements of secondary structure within a capsid-bound monomer, offering explanation for assembly activation. This site also interferes with interactions between capsid proteins, leading to quaternary changes and presumably assembly misdirection. These results demonstrate the plasticity of HBV capsids and the molecular basis for a tenable antiviral strategy.     

A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid

Hepatitis B virus (HBV) core protein is a model system for studying assembly and disassembly of icosahedral structures. Controlling disassembly will allow re‐engineering the 120 subunit HBV capsid, making it a molecular breadboard. We examined removal of subunits from partially crosslinked capsids to form stable incomplete particles. To characterize incomplete capsids, we used two single molecule techniques, resistive‐pulse sensing and charge detection mass spectrometry. We expected to find a binomial distribution of capsid fragments. Instead, we found a preponderance of 3 MDa complexes (90 subunits) and no fragments smaller than 3 MDa. We also found 90‐mers in the disassembly of uncrosslinked HBV capsids. 90‐mers seem to be a common pause point in disassembly reactions. Partly explaining this result, graph theory simulations have showed a threshold for capsid stability between 80 and 90 subunits. To test a molecular breadboard concept, we showed that missing subunits could be refilled resulting in chimeric, 120 subunit particles. This result may be a means of assembling unique capsids with functional decorations.     

Exploring the parameter space of complex self-assembly through virus capsid models

We use discrete event stochastic simulations to characterize the parameter space of a model of icosahedral viral capsid assembly as functions of monomer-monomer binding rates. The simulations reveal a parameter space characterized by three major assembly mechanisms, a standard nucleation-limited monomer-accretion pathway and two distinct hierarchical assembly pathways, as well as unproductive regions characterized by kinetically trapped species. Much of the productive parameter space also consists of border regions between these domains where hybrid pathways are likely to operate. A simpler octamer system studied for comparison reveals three analogous pathways, but is characterized by much lesser sensitivity to parameter variations in contrast to the sharp changes visible in the icosahedral model. The model suggests that modest changes in assembly conditions, consistent with expected differences between in vitro and in vivo assembly environments, could produce substantial shifts in assembly pathways. These results suggest that we must be cautious in drawing conclusions about in vivo capsid self-assembly dynamics from theoretical or in vitro models, as the nature of the basic assembly mechanisms accessible to a system can substantially differ between simple and complex model systems, between theoretical models and simulation results, and between in vitro and in vivo assembly conditions.     

Theoretical studies of viral capsid proteins

Recent results in structural biology and increases in computer power have prompted initial theoretical studies on capsids of nonenveloped icosahedral viruses. The macromolecular assembly of 60 to 180 protein copies into a protein shell results in a structure of considerable size for molecular dynamics simulations. Nonetheless, progress has been made in examining these capsid assemblies from molecular dynamics calculations and kinetic models. The goals of these studies are to understand capsid function and structural properties, including quarternary structural stability, effects of antiviral compounds that bind the capsid and the self-assembly process. The insight that can be gained from the detailed information provided by simulations is demonstrated in studies of human rhinovirus; an entropic basis for the antiviral activity of hydrophobic compounds, predicted from calculated compressibility values, has been corroborated by experimental measurements on poliovirus.     

Allosteric signaling and a nuclear exit strategy: binding of UL25/UL17 heterodimers to DNA-Filled HSV-1 capsids

UL25 and UL17 are two essential minor capsid proteins of HSV-1, implicated in DNA packaging and capsid maturation. We used cryo-electron microscopy to examine their binding to capsids, whose architecture observes T = 16 icosahedral geometry. C-capsids (mature DNA-filled capsids) have an elongated two-domain molecule present at a unique, vertex-adjacent site that is not seen at other quasiequivalent sites or on unfilled capsids. Using SDS-PAGE and mass spectrometry to analyze wild-type capsids, UL25 null capsids, and denaturant-extracted capsids, we conclude that (1) the C-capsid-specific component is a heterodimer of UL25 and UL17, and (2) capsids have additional populations of UL25 and UL17 that are invisible in reconstructions because of sparsity and/or disorder. We infer that binding of the ordered population reflects structural changes induced on the outer surface as pressure builds up inside the capsid during DNA packaging. Its binding may signal that the C-capsid is ready to exit the nucleus.