MMechanisms of Virus Assembly Mechanisms of Virus Assembly J ASON
D. P
ERLMUTTER , M
ICHAEL
F. H
AGAN
Martin Fisher School of Physics, Brandeis University, Waltham, MA, 02454; email:[email protected]
Key Words virus,capsid,self-assembly,RNA packaging,simulation,kinetics,thermodynamics,membrane
Abstract
Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell calleda capsid, and in some cases surrounded by a lipid bilayer membrane. This review summarizes the physicsthat govern the processes by which capsids assembles within their host cells and in vitro. We describethe thermodynamics and kinetics for assembly of protein subunits into icosahedral capsid shells, and howthese are modified in cases where the capsid assembles around a nucleic acid or on a lipid bilayer. Wepresent experimental and theoretical techniques that have been used to characterize capsid assembly, andwe highlight aspects of virus assembly which are likely to receive significant attention in the near future.
CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capsid architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental and theoretical methods to characterize capsid assembly . . . . . . . . . . . . . Empty capsid assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics of assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assembly driving forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empty capsid assembly mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empty capsid assembly kinetics and products . . . . . . . . . . . . . . . . . . . . . . . . . . Capsid assembly around nucleic acids and other polyelectrolytes . . . . . . . . . . . . . Thermodynamics of assembly around a cargo . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal genome length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assembly at non-optimal parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assembly mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a r X i v : . [ q - b i o . B M ] J u l . 2000 1056-8700/97/0610-00 Sequence-specific contributions to assembly and selective genome packaging . . . . . . . . . . Capsid assembly on membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics of membrane-associated assembly. . . . . . . . . . . . . . . . . . . . . . . Modeling of assembly and budding dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . Small molecule assembly effectors as antiviral agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The formation of a virus is a remarkable feat of natural engineering. A large number( ∼ − , ) of protein subunits and other components assemble from the crowdedcellular milieu to form ordered, complete, reproducible structures on biologically rele-vant time scales. Viruses are infectious agents responsible for a significant portion ofhuman diseases, as well as those of other animals, plants, and bacteria. Thus, it is ofbiomedical interest to understand their formation process, with the aim of designing an-tiviral therapies that block it, or alternatively reengineering viruses for use as targeteddelivery vehicles. More generally, the assembly of basic units into structures with in-creased size and complexity is ubiquitous in biology and is playing increasingly impor-tant roles in nanoscience. Understanding the mechanisms by which viral componentsco-assemble may elucidate diverse classes of assembly reactions.Viruses vary tremendously in size and complexity, ranging from the 16-nm satellite pan-icum mosaic virus (SPMV) (1), whose 826 nucleotide genome encodes for a singleprotein, to the µ m-sized pandoravirus, whose 2.5 megabase genome is larger than somebacterial genomes and encodes for 2556 putative proteins (2). However, viruses sharea common body plan, consisting of a genome, which can be single-stranded (ss) ordouble-stranded (ds) and can be RNA or DNA, surrounded by a protective container,which is usually a protein shell called a capsid. For ‘enveloped’ viruses (e.g. HIV or in-fluenza), the capsid is additionally surrounded by a lipid bilayer acquired from the hostcell. Formation of an infectious virion requires assembly of the capsid, envelopmentby a membrane (if enveloped), and packaging of the nucleic acid (NA) genome within.Many viruses with single-stranded genomes assemble spontaneously around their NA,as demonstrated in 1955 by the experiments of Fraenkel-Conrat and Williams in whichtobacco mosaic virus RNA and capsid proteins spontaneously assembled into infectiousvirions in vitro (3). In contrast, the stiffness and high charge density of dsDNA ordsRNA preclude spontaneous encapsidation (unless the genome is first complexed withNA-folding proteins). Therefore, many dsDNA viruses assemble an empty protein cap-sid (procapsid) and a molecular motor that hydrolyzes ATP to pump the DNA into the2 echanisms of Virus Assembly The viral genome length, and hence the number of unique proteins that it can encode, isconstrained by the requirement that it be enclosed by its capsid. Most capsids thereforecomprise one or a few protein sequences arranged with a high degree of symmetry. Themajority of viruses can be classified as rodlike or spherical, with the capsid proteins ofrodlike viruses arranged with helical symmetry around the nucleic acid, and the capsidsof most spherical viruses arranged with icosahedral symmetry. The number of units in ahelix is arbitrary, and thus a helical capsid can accommodate a nucleic acid of any length.In contrast, icosahedral capsids are constrained by the fact that at most 60 identical sub-units can form a regular polyhedron. Based on the observation that many capsids containinteger multiples of 60 proteins, Caspar and Klug (6) proposed geometrical argumentsthat describe how multiples of 60 proteins can be arranged with icosahedral symmetry,where individual proteins interact through the same interfaces but take slightly different,or quasi-equivalent, conformations (reviewed in (7, 8)). A complete capsid is comprisedof T subunits, where T is the ‘triangulation number’, which is equal to the numberof distinct subunit conformations (Fig. 1). An extensive collection of capsid structuresdetermined from x-ray crystallography and/or cryo-electron microscopy (cryo-EM) datacan be found at the VIPER website (http://viperdb.scripps.edu) (9). Bulk experiments.
Capsid assembly kinetics have been measured in vitro with sizeexclusion chromatography (SEC), small angle X-ray scattering (SAXS), and light scat-tering (e.g. (10,11,12,13,14,15,16,17), Fig. 3A below). The SEC experiments show that
Perlmutter and Hagan hk (1,0) (1,1) T=1 T=3
Figure 1: The geometry of icosahedral lattices. Moving h and k steps along each ofthe ˆh and ˆk lattice vectors results in a triangle with area T / (for unit spacing betweenlattice points), where T is the triangulation number defined as T = h + hk + k .The blue and purple triangles correspond to T =1 and T =3 respectively. The resultingicosahedrons are shown in the center and right images, with triangular facets in distinct(quasi-equivalent) environments distinguished by color. The purple triangle from the leftimage is inscribed on the T =3 icosahedron.under optimal assembly conditions the only species present in detectable concentrationsare either complete capsids or small protein oligomers which we refer to as the basic as-sembly unit. The size of the basic assembly unit is virus dependent and ranges from 2-6proteins. Under certain conditions, the intensity of light scattering signal is proportionalto the mass-averaged molecular weight of species in solution, which closely tracks thefraction of subunits in capsids (provided that intermediate concentrations remain small). Single molecule techniques.
It is difficult to characterize assembly pathways with bulktechniques because most intermediates are transient. Techniques that monitor individ-ual capsids have begun to address this limitation. For example, a Coulter-counter-likeapparatus that uses resistive pulse sensing to identify the passage of individual capsidsthrough nanopores was able to distinguish between T =3 and T =4 HBV capsids (18).Mass spectrometry has been used to characterize key intermediates and assembly path-ways for several viruses (19, 20, 21, 22, 23). Fluorescent labeling of capsid proteinsor RNA has enabled tracking assembly and protein-RNA association of HIV capsidsin cells (24, 25). Borodavka et al. (26) used single molecule fluorescence correlationspectroscopy to monitor the hydrodynamic radii of assembling nucleocapsid complexes(section 3.5).
Theoretical models.
Zlotnick and coworkers (27, 11, 28) developed an approach to de-scribe capsid assembly kinetics with a system of rate equations for the time evolutionof concentrations of intermediates. Their equations are analogous to the classic Becker-D¨oring rate equations for cluster concentrations in a system undergoing crystallization(29), except that the capsids terminate at a finite size. The equations are made tractableby assuming one or a few structures for each intermediate size. Continuum-level de-scriptions of assembly dynamics (with further simplifications) have also been developed(30,31). The assumption of one structure per intermediate size can be relaxed by enumer- echanisms of Virus Assembly
Particle-based dynamics simulations.
The approaches described in the previous para-graph must pre-assume the state space (i.e. the possible structures of partial capsidintermediates). This limitation can be relaxed by performing simulations which ex-plicitly track the dynamics of subunit positions and orientations using molecular dy-namics, Brownian dynamics, or other equations of motion. Several groups have de-veloped coarse-grained models for subunits, which have excluded-volume geometry andorientation-dependent attractions designed such that the lowest energy structure is a shellwith icosahedral symmetry (e.g. (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51)). A recentapproach uses particle-based simulations to systematically derive Markov state models,which can then be simulated using methods from the previous paragraph (52).
We begin by analyzing the formation process of an empty capsid. While this process ismost relevant to viruses that first form empty procapsids during assembly, it also pro-vides a useful starting point to understand co-assembly with nucleic acids, lipid mem-branes, or scaffolding proteins. Although we focus on icosahedral capsids, we note thatmany viruses have non-icosahedral capsids, and that the capsid proteins of some icosa-hedral viruses can form other structures including sheets, tubes, and multi-layered shellsdepending on solution conditions (53).
We consider the thermodynamics for a system of identical protein subunits that canassemble into empty T =1 capsids. To simplify the presentation, we assume that there isone dominant intermediate species for each number of subunits n . Minimizing the totalfree energy under the constraint of fixed total subunit concentration c T = (cid:80) Nn =1 nc n results in the law of mass action for the equilibrium concentration of each species c n (27, 54, 55, 5): c n v = ( c v ) n exp ( − G cap n /k B T ) , (1)with with v the standard state volume and k B T the thermal energy. Here G cap n is the freeenergy due to subunit-subunit interactions for intermediate n . Zlotnick developed a classof models in which the interaction free energy is proportional to the number of subunit-subunit contacts: G cap n = g b C n − T S n with C n the number of subunit-subunit contactsin an intermediate, g b the subunit-subunit binding free energy, and S n a symmetry factor(27, 28). Perlmutter and Hagan
Under most conditions at equilibrium, almost all of the subunits are found in completecapsids or as free subunits (27, 5). This prediction arises from virtually any model forassembly of finite-size structures (e.g. capsids or micelles) in which the interaction freeenergy G cap n is minimum for one structure ( n = N ) and the total subunit concentrationis conserved (54). Under these conditions Eq.(1) can be simplified by neglecting allintermediates except free subunits or complete capsids, so that c T = c + N c N with N the number of subunits in a complete capsid (i.e. a two-state approximation). Then, inthe limit N (cid:29) the fraction of subunits in capsids, f c = N c N /c T , is given by (30, 5) f c ≈ (cid:16) c T c ∗ (cid:17) N (cid:28) for c T (cid:28) c ∗ ≈ − c ∗ c T for c T (cid:29) c ∗ (2)with the ‘pseudo-critical’ subunit concentration c ∗ ≈ v − exp (cid:0) G cap N /N k B T (cid:1) belowwhich there is no assembly.Zlotnick and coworkers have shown that the assembly of HBV (56) can be captured byEq.(2) using the subunit-subunit binding free energy g b as a fit parameter. Their datashows that productive assembly requires weak binding free energies, on the order of g b = 4 kcal/mol ( . k B T ). The requirement for weak interactions appears to be quitegeneral, for reasons discussed in section 2.4 (see also Ref.(57) in this issue). Eq. (1) reflects the fact that formation of an ordered capsid reduces the translationalentropy of its constituent subunits, and thus must be driven by favorable interactions thatovercome this penalty. These interactions (and changes in subunit rotational entropy) aredescribed by the factor G cap . In many cases assembly is primarily driven by hydrophobicinteractions, attenuated by electrostatics (58, 59) with directional specificity imposed byelectrostatic, van de Waals, and hydrogen bonding interactions. These interactions areshort-ranged under assembly conditions, with scales ranging from a few angstroms (Vander Waals interactions and hydrogen bonds) to . − nm for hydrophobic interactions(60). Similarly, electrostatic interactions are screened on the scale of the Debye length λ D , which is about 1 nm at physiological ionic strength (150 mM) and decreases withionic strength I according to λ D ≈ . /I / with λ D in nm and I in molar units. As first suggested by Prevelige (10), empty capsids assemble by a ‘nucleation-and-growth’ mechanism, in which a critical nucleus forms followed by a growth phase inwhich one or a few subunits add sequentially until the capsid is completed (Fig. 2).The critical nucleus is defined as the smallest intermediate which has a greater than 50% echanisms of Virus Assembly τ nuc ∼ c n nuc with n nuc the nucleus size (28, 61). In contrast, intermediates in the growthphase are relatively stable; thus, successive additions of subunits or small oligomers areindependent and the timescale for a capsid to complete the growth phase has a low-orderdependence on the free subunit concentration (61, 5).Due to the geometry of an icosahedral shell, the first few intermediates have relativelyfew subunit-subunit contacts and are thus relatively unstable. The critical nucleus oftencorresponds to a small polygon (Fig. 2) whose geometry maximizes the number of inter-actions; furthermore, subunit conformation changes may provide additional stabilizationupon polygon formation . As the subunit-subunit binding free energy or the free subunitconcentration decreases, small intermediates become less stable and the critical nucleussize increases (62). Therefore, as subunit supersaturation decreases over the course ofan assembly reaction, the critical nucleus size increases, asymptotically approaching ahalf capsid (5). Disassembly.
Similar considerations apply to capsid disassembly. The first few subunitsto disassemble must break many contacts, leading to a large activation barrier. There istherefore a pronounced hysteresis between assembly and disassembly at a given set ofconditions (63,41). This condition allows capsids to be highly metastable even at infinitedilution (64), which is an important feature given that they must eventually leave theirhost cell to infect another. Some capsids undergo post-assembly maturation processeswhich further increase their stability.
Capsid assembly kinetics, whether measured by experiments (10,11,12,13,14,15,16,17)or calculated from theoretical or computational models (27,11,28,61,14,16,37), are sig-moidal (Fig. 3A). There is an initial lag phase during which capsid intermediates form,followed by rapid capsid production, and then an asymptotic approach to equilibriumduring which assembly slows as nucleation barriers rise due to depletion of free sub-units. Increasing the subunit concentration c T or the strength of inter-subunit interac-tions g b (typically by decreasing pH or increasing salt concentration) initially leads tomore rapid assembly. However, while thermodynamics (Eq. 2) indicates that the yield ofwell-formed capsids monotonically increases with g b and c T , the yield at long but finitetimes is nonmonotonic with variation of these parameters (see the highest ionic strengthin Fig. 3A) due to kinetic traps.These modeling and experimental studies show that there is a trade-off between interac-tion specificity and kinetic accessibility — more specific interactions increase selectivity In general there can be an ensemble of critical nuclei, whose members depend on solution conditionsand protein subunit concentration.
Perlmutter and Hagan
Complete CapsidGrowthCritical Nucleus
Pentamer of Dimers
Assembly Subunit
Dimer
Nucleation ...
Figure 2: Schematic of the assembly mechanism for cowpea chlorotic mottle virus(CCMV) (12). In the nucleation phase, addition of capsid protein dimers is unfavorableuntil reaching the critical nucleus. Subsequent additions (the growth phase) are relativelyfavorable, though still reversible, until the capsid is completed. Subunits must intercon-vert between different quasi-equivalent conformations to assemble the T =3 icosahedralgeometry (Fig. 1); different conformations are distinguished by color. The diameter ofthe complete CCMV capsid is 28 nm.of assembly for the target structure but decrease assembly rates due to decreased kineticcross-sections (65, 57). The outcome of this competition between thermodynamics andkinetics has been summarized by mapping ‘kinetic phase diagrams’ (Fig. 3B) whichdescribe the predominant assembly outcome at long but finite times as a function of sub-unit concentration, interaction strength, and degree of interaction specificity. For a giveninteraction specificity, the kinetic phase diagram can be classified into five regimes. (i) No assembly at equilibrium: For weak interactions or low subunit concentrations,such that c T < c ∗ (Eq.(2)), assembly is unfavorable at equilibrium. (ii) Prohibitive nu-cleation barriers: As interactions or subunit concentrations increase to c T (cid:38) c ∗ , assem-bly is favorable, but does not occur on experimentally relevant timescales due to largenucleation barriers. (iii) Productive assembly: Further increasing interactions or subunitconcentrations leads to moderate nucleation barriers and large yields of well-formedcapsids on relevant timescales (which can range from seconds to hours for empty cap-sids). Finally, stronger-than-optimal interactions lead to suppressed yields due to twoforms of kinetic traps. (iv) Free subunit starvation kinetic trap:
When nucleation isfast compared to growth, too many capsids nucleate at early times and free subunits orsmall intermediates are depleted before a significant number of capsids finish assembling(11, 12, 28, 41, 43, 48). This condition occurs when the timescale required for capsids tocomplete the growth phase exceeds the typical nucleation timescale (61, 5). (v) Malformed capsids:
Under sufficiently strong interactions, subunits with imperfectorientations are trapped into growing clusters by subsequent subunit additions, leading echanisms of Virus Assembly partial/misassembled capsidspartial capsids m o n o m e r i c u n i t s m o n o m e r s / p a r t i a l c a p s i d s c a p s i d s / m o n o m e r s f u l l c a p s i d s p a r t i a l / f u l l c a p s i d s Capsomer concentration (ln[c]) R e d u c e d t e m p e r a t u r e , T * A B L i gh t S ca tt e r time, s Figure 3: (A)
Light scattering measured as a function of time for 5 µ M dimer of HBVcapsid protein at indicated ionic strengths. The image is reprinted with permission fromRef. (11) Copyright (1999) American Chemical Society. (B)
Assembly products at longtimes for a 20-subunit icosahedral shell as a function of temperature (i.e. inverse ofinteraction strength) and particle concentration. Representative structures for several re-gions are shown on the right. Figure adapted with permission from Ref. (43), Copyright(2007) American Chemical Society.to either defective closed shells that lack icosahedral symmetry or open, spiral structuresin simulations (40, 41, 42, 43, 45) and experiments (66, 67, 68). The presence of thesetwo forms of kinetic traps ( iv and v ) explain the experimental (56,69) and computational(41, 48) observation that weak interactions are required for productive capsid assembly.These kinetic traps lead to similar constraints on interactions in other forms of assemblysuch as crystallization (57). This section focuses on viruses for which the capsid assembles spontaneously around theviral genome during infection. This category includes most ssRNA viruses and the Hep-adnaviridae (e.g. HBV), and Spumaviridae, which assemble around ssRNA pregenomesthat then undergo reverse transcription to yield dsDNA within the virions.Electrostatic interactions between positive charges on capsid proteins and negative chargeson RNA provide an important thermodynamic driving force for this process. For ex-ample, the capsid proteins of many negative-stranded RNA viruses bind RNA via apositively-charged cleft (70). For many positive-stranded RNA viruses, the capsid pro-teins bind RNA via flexible terminal domains rich in basic amino acids, called argininerich motifs (ARMs)(71). Specific RNA sequences or chemistry are not essential for as-sembly, as demonstrated by early in vitro experiments in which ssRNA capsid proteinsassembled around heterologous nucleic acids and even polyvinylsulfate (72, 73), andmore recent experiments in which capsid proteins assembled around various negativelycharged substrates (e.g. (73, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85)). We begin0
Perlmutter and Hagan this section by describing what these experiments and theoretical models have revealedabout how assembly depends on the physical characteristics of RNA or other polyelec-trolytes, such as charge, size, and structure. Due to space limitations, we do not discussstudies on assembly around non-polymeric cores (see Refs. (5, 86)). We then discussmechanisms by which virus-specific interactions can enhance co-assembly and enableselective packaging of the viral genome.
We consider a solution of capsid protein subunits and cores (e.g. RNA molecules) withrespective total concentrations of c T and x T . We define a stoichiometric ratio as theratio of available cores to the maximum number of capsids which can be assembled, r = N x T /c T . Extending Eq. 1 to include interior cores results in two laws of massaction(87, 88, 5): c n v = ( c v ) n exp[ − G cap n /k B T ] (3) x n v = x v ( c v ) n exp[ − G core n /k B T ] (4)with x the concentration of empty cores. Eqs. 3 and 4 describe assembly of empty andcore-containing capsids with respective interaction free energies G cap and G core . Thecore interaction energy G core includes, for example in the case of an RNA core, attrac-tive protein-RNA interactions, intramolecular electrostatic repulsions, and base-pairinginteractions. Eq. 4 identifies a new critical subunit concentration, which for excess cap-sid protein is given by c ∗∗ = exp [ G core N /N k B T ] /v (87). If the net contribution of thecore to assembly is favorable ( G core N < G cap N ) core-assisted assembly can occur at con-centrations below the threshold concentration for empty capsid assembly ( c ∗∗ < c ∗ ).This capability is exploited by many ssRNA viruses, whose capsids assemble only in thepresence of RNA or other polyanions at physiological conditions, thus ensuring that thegenome is packaged during assembly. On the other hand, unfavorable core contributions,such as would arise from the stiffness and electrostatic repulsions of dsDNA molecules,can direct assembly away from the capsid structure to other morphologies (89). It has been proposed that viral genomes face a selective pressure to maintain a lengthwhich maximizes the stability of the nucleocapsid complex (i.e., minimizes G core N ). Insupport of the importance of nonspecific electrostatics to driving RNA encapsidation, thetotal positive charge on the capsid inner surface correlates to the length of the genomicRNA for a diverse group of ssRNA viruses (90, 91) (Fig. 4). Furthermore, changing thecapsid charge alters the amount of cargo encapsidated in cells and in vitro (92, 93,94, 95,96), although the effect of mutations on the amounts and sequences of packaged RNA echanisms of Virus Assembly C ha r ge R a t i o ( G eno m e C ha r ge / A R M C ha r ge ) Total ARM Charge A PaV BMV CCMV PC2 STNV BBT STMVSPMV C ha r ge R a t i o ( G eno m e C ha r ge / A R M C ha r ge ) Viral Species B GenomeLinearBase-Paired
Figure 4: Relationship between genome length and capsid charge. (A)
Survey of thecharge ratio, or number of nucleotides in the genome divided by total positive charge onthe inner capsid surface, for ssRNA viruses. (B)
The thermodynamic optimum chargeratio predicted from simulations (99) ( (cid:78) symbols) is compared to actual charge ratios( (cid:68) symbols ) for several viruses. Predicted optimal charge ratios in the absence ofbase-pairing are also shown ( • symbols). The thermodynamic optimum charge ratio isdefined as the NA length which minimizes the free energy for encapsidating the genomedivided by the positive capsid charge.can depend on factors other than charge(97, 95). Importantly, ssRNA viruses are consis-tently overcharged, with typical charge ratios of r charge = | NA charge | / | protein charge | in the range . ≤ r charge ≤ (Fig. 4). In vitro competition assays in which differ-ent species of RNAs competed for packaging demonstrated that longer RNAs (up tothe viral genome length) are preferentially packaged over shorter RNAs (98), indicatingthat overcharged genomes are optimal for packaging even in the absence of cell-specificfactors.Motivated by these observations, researchers theoretically and computationally calcu-lated how the free energy F encap ( L ) to encapsulate a linear polyelectrolyte varies withits length L (reviewed in (86, 5)). Several works performed self-consistent field the-ory calculations in which F ( L ) is calculated from a continuum description of polymerconformational statistics coupled to the Poisson-Boltzmann equation. While Ref. (100)predicted an optimal charge ratio of r charge = 2 , most subsequent calculations predicted r charge (cid:46) (101, 86, 95, 90, 102). Ref. (90) noted that if the charge on the RNA andthe peptide tails were renormalized according to counterion condensation theory (103)overcharging would be predicted; however, the condensed counterions are released byRNA-peptide association and thus the charge cannot simply be renormalized (99). Tinget al. (102) found that the optimal charge ratio varies with capsid volume and the chargedensity on capsid protein ARMs (i.e., there is no single optimal charge ratio). Since inall cases the model predicted r charge < , they suggested that a Donnan potential arisingfrom negatively charged macromolecules within cells drives overcharging. However, the2 Perlmutter and Hagan subsequent in vitro competition assays (98) demonstrated that overcharging is optimalfor assembly in the absence of a Donnan potential.Perlmutter et al. (99) used a coarse-grained particle-based computational model, inwhich ARMs were represented as flexible polyelectrolytes affixed to capsid subunits,to determine the optimal lengths of encapsulated polyelectrolytes and NAs as functionsof capsid size, ARM charge, and ionic strength. The model predicted overcharging( r charge > ) in all cases. Optimal lengths predicted by the model for several specificviruses closely matched genome lengths for those viruses (Fig. 4B). Overcharging wasfound to arise because only a fraction of encapsulated polymer segments can closelyinteract with positive capsid charges (i.e. within a Debye length). Consequently, pack-aging of multiple short polyelectrolytes will lead to reduced or no overcharging. Thethermodynamic optimal lengths closely matched the lengths which optimized the yieldof long but finite-time dynamical simulations, indicating a connection between the ther-mostability and optimal assembly of a viral particle. Effect of RNA base-pairing.
About 50-60% of nucleotides undergo intramolecularbase-pairing in ssRNA molecules, leading to compact, branched structures, as recentlyvisualized using cryo-EM (104). Although a self-consistent field theory predicted nodifference between the optimal lengths for linear polyelectrolytes and compact star ar-chitectures(102), subsequent theory (105) and simulations (99) found that branchingconsistent with the structures of base-paired RNA increases the optimal genome lengthas compared to a linear polyelectrolyte, by compensating for intramolecular charge re-pulsions and by favoring compact conformations (Fig. 4B). Based on secondary struc-ture predictions, Yoffe et al. (106) suggested that viral RNAs tend to have more compacttertiary structures than cellular RNAs with equal numbers of nucleotides, which couldfavor assembly around the viral RNA.
The previous section showed that, for a given capsid protein and solution conditions,there is a length of RNA for which assembly is optimal. To understand the effectof perturbing parameters from these optimal values, in vitro assembly products werecharacterized by electron microscopy (e.g. (76, 108, 98, 109, 78)) or SAXS (16, 17) asfunctions of subunit and RNA concentrations, subunit-subunit interactions (controlledby pH, ionic strength, and protein sequence), and subunit-polymer interactions (con-trolled by ionic strength and protein-RNA binding domains). In addition, several groupshave performed Brownian dynamics simulations in which coarse-grained triangular orpentameric subunits assemble around flexible polyelectrolytes (49, 50, 99, 110, 111, 112),semiflexible polyelectrolytes (112), or model NAs (99). In both experiments and simula-tions, parameters must be carefully tuned to achieve high yields of well-formed capsids.An example simulation phase diagram illustrating some of the alternative products that echanisms of Virus Assembly SV40 Capsid SubunitModel CapsidSubunit Positivelycharged ARMs
Success DisorderedOn Pathway UnnucleatedMalformed
BA DC E S ubun i t - S ubun i t A tt r a c t i on ( k B T ) Ionic Strength (mM)
Figure 5: (A)
Crystal structure of the SV40 basic assembly unit (107), which is a ho-mopentamer of the capsid protein capsid subunit, and a coarse-grained model pentamericsubunit. The locations of the positively charged ARMs are shown in yellow (most of theARM residues are not resolved in the crystal structure). (B)
The dominant products of as-sembly around a linear polyelectrolyte as a function of ionic strength and subunit-subunitinteraction strength at thermodynamically optimal polyelectrolyte lengths, which varyfrom 350-575 depending on the ionic strength. (C)
Simulation snapshots which exem-plify the dominant assembly outcomes. (D)
A doublet formed in simulations around apolyelectrolyte with 1200 segments (twice the optimal length). (E)
A doublet assembledfrom CCMV capsid proteins around RNA with 6400 nucleotides (about twice the num-ber of nucleotides encapsidated in native CCMV virions) (108). Image provided by R.Garmann, C. Knobler and W. Gelbart.form at non-optimal parameters is shown in Fig. 5.Assembly around polymers with non-optimal lengths leads to several outcomes. Thefirst is polymorphism, or formation of capsids with different T -numbers (Fig. 1). CCMVcapsid proteins (which form native T =3 capsids) formed T =3 capsids around genomic-length RNA and pseudo- T =2 -sized capsids around shorter RNAs (108,98). The favoredpolymorph depends on RNA length, the preferred curvature of capsid protein-proteininteractions (i.e. spontaneous curvature, section 4.1) and stoichiometry (76, 87). ForRNA significantly below optimal length, multiple RNAs were packaged in each capsid(108, 113), as seen in coarse-grained dynamics simulations with short linear polyelec-trolytes(111). In the experiments, capsid formation required equilibrium between multi-ple disordered protein-RNA complexes, leading to highly cooperative assembly (113).While longer-than-optimal polymers sometimes led to T =4 -sized capsids, the morecommon outcome was the assembly of multiplets, or multiple distinct capsids assembledaround one RNA (108) or conjugated polyelectrolyte (78). RNAs which were 2, 3, or 4times the genome length lead respectively to predominantly doublets (Fig. 5D), triplets,and quadruplets. An early study likely also observed doublets, although the structurescould not be confirmed (72) and recently doublet dodedecadron capsids were observedfor assembly of SV40 capsid proteins around certain lengths of RNA (17). Simulations4 Perlmutter and Hagan ε =3.0k T, I=100mM
En masse
Nucleation-and-Growth ss ss ε =6.0k T, I=300mM
B B
Figure 6: Two mechanisms for assembly around a polyelectrolyte (110). (A)
Low ionicstrength (strong subunit-polyelectrolyte interactions) and weak subunit-subunit interac-tions lead to the en masse mechanism typified by disordered intermediates. (B)
Highionic strength (weak subunit-polymer interactions) and strong subunit-subunit interac-tions lead to the nucleation-and-growth mechanism in which an ordered nucleus formson the polymer followed by sequential addition of subunits.independently predicted the formation of doublets around polyelectrolytes with abouttwice the optimal length (114, 49, 99) (Fig. 5C). At lengths only slightly greater thanoptimal, simulations predict malformed but single capsids (49, 99, 50). However, thesemalformations may be difficult to resolve experimentally.
Simulations (49,110) show that two classes of assembly mechanisms occur around RNAor a linear polymer (Fig. 6). One closely resembles the nucleation-and-growth mecha-nism found for empty capsid assembly, except that the polymer stabilizes protein-proteininteractions and can enhance the flux of proteins to the assembling capsid (115). A smallpartial capsid first nucleates on the polymer, followed by a growth phase in which oneor a few subunits sequentially and reversibly add to the partial capsid. In the alternativemechanism, first proposed by McPherson (116) and then Refs (117, 118, 49), subunitsadsorb onto the polymer en masse in a disordered fashion and then cooperatively re-arrange to form an ordered capsid. Simulations predict that the assembly mechanismcan be tuned by solution conditions and capsid protein-protein interactions(110). Thenucleation-and-growth mechanism is favored by weak protein-polymer association (highsalt concentration) and strong protein-protein interactions (typically low pH (89)), whilethe en masse mechanism arises for lower salt and weaker protein-protein interactions.Observations in vitro suggest that both mechanisms are viable. Time-resolved SAXSexperiments monitoring assembly of SV40 capsid proteins assembling around ssRNAproduced scattering profiles which could be decomposed into profiles corresponding to echanisms of Virus Assembly en masse pathways lead to measurably different SAXSprofiles, whereas profiles from nucleation-and-growth trajectories are consistent withthe experimental observations. Other observations suggest that virus-like particles canassemble through the en masse mechanism. Refs. (108, 109, 119) found that in vitro assembly CCMV assembly was most productive when performed in two steps. First, atlow salt (strong protein-RNA interactions) and neutral pH (weak protein-protein interac-tions) the proteins undergo extensive but disordered adsorption onto RNA. Subsequently,pH is reduced to enhance protein-protein binding, leading to the formation of orderedcapsids (109). Similarly, a recent observation of capsid protein assembly around charge-functionalized nanoparticles found that assembly initially proceeded through nonspecificaggregation of proteins and nanoparticles, followed by the gradual extrusion of completecapsids formed around nanoparticles (84).The CCMV experiments (108, 109, 119) found that complete encapsidation of all RNApresent in solution requires a significant excess of capsid protein, such that the positivecharges in protein ARMs balance the negative RNA charge (recall that in the completecapsid the negative RNA charge significantly exceeds the positive ARM charge, sec-tion 3.2). This criteria occurs because the disordered protein-RNA complexes occurringduring the first step of assembly are charge-balanced. During capsid formation (thesecond step), excess proteins are displaced to the exterior, where their positive ARMcharges interact with negative residues on the outer surface of the capsid (119).
To be infectious, a virion must assemble specifically around the viral genome amidst apanoply of cellular RNA molecules. Many viruses achieve high specificity; for example,a recent quantitative analysis found that flock house virus particles are 99% selectivefor the viral RNA (120). Structure- and sequence-specific RNA-protein interactionsmay be a widespread mechanism of achieving specificity by promoting assembly aroundthe viral genome (although not all viruses are selective for their genomic RNA in vitro(96, 98)) , suggesting the importance of cell-specific factors).Several studies suggest that the specific folded structure of the genomic RNA may en-hance assembly. Based on the crystal structure of STMV, which shows 30 ds helicalsegments interacting with the capsid inner surface (121,122), McPherson and coworkers(123) proposed that during assembly the STMV genome forms a conformation com-prising linearly connected stem loops which sequentially bind capsid proteins. Usingthe crystal structure as constraints, Schroeder et al. (124) combined chemical probing6
Perlmutter and Hagan and computational methods to predict an RNA secondary structure containing 30 stem-loops. Simulation of the complete STMV capsid with atomic resolution demonstratedthat this secondary structure is consistent with the crystal structure (125). More recently,two studies (126, 127) used the chemical probe method SHAPE to characterize unen-capsidated STMV RNA. These analyses were not restricted to stem-loops, and foundsecondary structures that differed significantly from the encapsidated, stem-loop struc-ture. Interestingly though, the primary probing data is similar for the encapsidated andunencapsidated RNAs, suggesting that the same nucleic acids are base-paired in bothcases.Extensive evidence shows that packaging signals, or short RNA sequences that arespecifically bound by capsid proteins, play significant roles in controlling assembly path-ways for some viruses (reviewed in (128, 129)). Packaging signals have been identifiedfor several viruses including HIV (130, 131, 132), MS2, and STNV (133, 134, 135), anda number of plant viruses (128). Combining identified packaging signals with geometricconstraints derived from electron density maps of MS2 capsids led to a structure of theencapsidated genome (134). Earlier work using mass spectrometry (19), coarse-grainedsimulations (136), and kinetic models (137) suggested that RNA binding drives a con-formational switch in the MS2 capsid protein and identified two dominant pathways forMS2 assembly. Using Gillespie algorithm simulations (section 1.2), Dykeman et al.showed that packaging signals could enhance yields of capsids assembling around RNAin comparison to a polymer cargo with uniform interactions (36) and that specificity forthe genomic RNA can be enhanced by time-dependent capsid protein production ratesin bacteria (138).A striking observation supporting an active, sequence-specific role of the genome wasmade by Borodavka et al. (26), who used single molecule fluorescence correlation spec-troscopy (smFCS) to monitor the hydrodynamic radii R H of nucleocapsid complexes.Assembly around genomic RNAs was characterized by either constant R H or, in sometrajectories, a collapsed complex followed by gradual increase to the size of an assem-bled capsid. In contrast, assembly around heterologous RNA led to an increase in R H before eventually decreasing to the size of the capsid. The different assembly pathwayswere attributed to the presence of packaging signals in the genomic RNAs. The col-lapsed structures are reminiscent of a previous observation (139), in which incubationof CCMV RNA with sub-stoichiometric concentrations of capsid proteins led to a com-pact nucleocapsid complex that triggered rapid assembly upon introduction of additionalcapsid proteins.Finally, we emphasize that sequence-specific protein-RNA interactions are not the onlymechanism that drives selective genome packaging in vivo; other factors include, e.g.coordination of assembly with RNA replication (140, 128). As evidence for this, in (invitro) competition assays HBV capsid proteins show no preference for genomic RNAover heterologous RNA with equal length (96) and CCMV capsid proteins preferentially echanisms of Virus Assembly In this section we consider mechanisms by which the proteins of enveloped viruses as-semble on lipid bilayers to drive budding. The passage of nanoscale particles throughmembranes is an extremely broad topic; we focus on viral budding driven by proteinassembly.Enveloped viruses can be divided into two groups based on how they acquire their lipidmembrane envelope. For the first group, which includes influenza and type C retro-viruses (e.g. HIV), the nucleocapsid core assembles on the membrane concomitantwith budding (Fig. 7A). Capsid protein (CP) binding to membranes is driven by elec-trostatic interactions between positive residues on capsid proteins (e.g. the MA domainof HIV GAG) and negative charges in lipid head groups, and/or insertion of CP hy-drophobic moieties (e.g. the myristoyl domain on GAG) into the bilayer (141, 142). Inthe second group, a core assembles in the cytoplasm prior to envelopment (reviewed in(142, 143, 141)). In many families from this group envelopment of the core is driven byassembly of viral transmembrane glycoproteins (GPs) which form an outer shell aroundthe core (Fig. 7B), as shown by the fact that expression of GPs alone can drive bud-ding (144). Thus, in both groups membrane deformation is driven at least in part byreversible protein-protein and protein-lipid interactions. However, some viruses are as-sisted by cellular factors that create or support membrane curvature (145, 146, 141) orcytoskeletal machinery that actively drives budding (e.g. (147, 148, 143, 149)). Further-more, separation of budded viral particles from the host membrane (scission) is drivenby cell membrane remodeling machinery (150).Enveloped viruses have been the subject of extensive structural studies and in vivo inves-tigations (142, 143, 141), with budding of individual capsids from cells monitored usingfluorescently labeled CPs and RNA (24, 25). However, there are currently no in vitrosystems in which enveloped viruses assemble and bud, and information about assemblymechanisms and budding kinetics is limited in comparison to assembly in solution.
The thermodynamics of assembly on a membrane can be obtained by extending theanalysis in section 2.1 to include membrane bending energy and subunit-membrane in-teractions. The free energy associated with membrane deformations on scales large incomparison to the 5 nm width of a lipid bilayer can be analyzed according to continuum8
Perlmutter and Hagan (A) (B)glycoproteinscapsid proteins nucleocapsid
Figure 7: Viral budding pathways. (A),(B)
Schematic of the two classes of buddingpathways for enveloped viruses. (A)
Assembly of capsid proteins (CPs, red) drivesbudding and recruitment of glycoproteins (e.g. type C retroviruses). (B)
Glycoproteins(GPs, black) drive budding of a pre-assembled nucleocapsid core (e.g. alphaviruses). (C)
Snapshots from simulations in which patchy sphere icosahedrons assemble on and budfrom a triangulated membrane. The top image is reprinted with permission from Ref.(151) Copyright (2012) American Institute of Physics. The bottom image is reprintedfrom Ref. (152). (D)
Model subunits assembling in and budding from a membranemicrodomain (153).elasticity (the Helfrich free energy) (154, 54): E bend = (cid:90) dA (cid:104) κ H − H ) + κ G K (cid:105) + (cid:90) γdA (5)with H = (1 /R + 1 /R ) as the mean curvature, K = 1 / ( R R ) as the Gaussian cur-vature, and R and R as the principal radii of curvature at each point on the membraneneutral surface. The remaining parameters are material properties: H is the membranespontaneous curvature, κ and κ G are respectively the bending modulus and Gaussianmodulus, H is the membrane spontaneous curvature, and γ is the surface tension.Because scission is actively driven by cell machinery, it is instructive to calculate themembrane bending energy for a completely budded viral particle just before scission(i.e., the bending energy of a vesicle). Since the total Gaussian curvature is constantfor fixed topology, the corresponding term in Eq.(5) can be neglected (for uniform κ G ).Assuming a tensionless membrane, that the membrane envelope is roughly spherical, andthat H = 0 (spontaneous curvature induced by protein binding will be considered next),Eq.(5) gives a fixed cost for any radius E bend ( sphere ) = 8 πκ . Lipid bilayer bendingmoduli are typically in the range < κ < k B T , giving a membrane bending energycost of 250-750 k B T for any size virus.This bending energy must be compensated by CP-membrane, GP-GP, GP-CP, and/or echanisms of Virus Assembly c ∗ v ≈ exp ( G N /N k B T ) G N /N = G cap N /N + g sm + 8 πκ/N (6)with g sm accounting for the subunit-membrane interactions (per subunit) in a completelyassembled and enveloped capsid. The second line of Eq.(6) emphasizes that, becausethe membrane bending energy is independent of capsid size, its effect is inversely pro-portional to the number of subunits. Thus, larger capsids are favored; perhaps relatedly,the smallest enveloped viruses have 240 proteins ( T =4 ). If | g sm | > πκ/N , assemblycan proceed on the membrane for subunit concentrations at which no assembly occursin bulk solution.Going beyond this simple thermodynamic analysis, the statistical mechanics of buddingof a preassembled nucleocapsid driven by interactions with membrane-associated GPs(Fig. 7B) was considered in continuum models by Refs. (155, 156). Tzlil et al. (155)identified a critical GP-capsid adhesion energy above which complete budding occurs,and that when complete budding occurs capsids are nearly saturated with GPs. Numer-ous other experimental, theoretical, and computational studies have analyzed the exit(exocytosis) or entry (endocytosis) of viruses and other nanoscale particles (reviewed in(157)). The first analysis of the dynamics of assembly and budding by membrane-adsorbed cap-sid proteins was performed by Zhang and Nguyen (158). They developed a continuummodel description, in which membrane-associated partial-capsid intermediates are rep-resented by hemispherical shells and the membrane deformation energy is modeled bythe Helfrich free energy, Eq.(5). The model predicted, depending on subunit supersat-uration, complete assembly and budding, or stalled partially assembled and partiallywrapped states.More recently, Matthews and Likos performed particle-based simulations of patchyspheres assembling into icosahedrons on a triangulated representation of a membrane(Fig. 7C) (151, 152). They found that subunit adsorption onto the membrane could driveassembly for parameters where no assembly occurred in bulk (see Eq. 6). Interestingly,the ability of the membrane to promote assembly depended non-monotonically on thebending modulus κ , with budding suppressed by membrane bending energy at high κ or entropic membrane fluctuations at low κ (151). Ruiz-Herrero and Hagan (153)0 Perlmutter and Hagan considered an implicit solvent lipid bilayer membrane model and pentameric subunitsthat adsorb onto the membrane and assemble to form a dodecahedron (Fig. 7D). Theyfound that, while adsorption onto the membrane promoted the formation of small partialcapsids, the geometry of adsorbed subunits could introduce new barriers to assembly.Based on the observation that many enveloped viruses preferentially bud from lipid rafts(159,143,160), assembly was also simulated on a phase separated membrane. Assemblyand budding were significantly enhanced for certain domain sizes.
In this section, we briefly consider small molecule ‘assembly effectors’ which modulateassembly by perturbing capsid protein-protein interactions, altering protein conforma-tions, or crosslinking protein-NA binding domains (for reviews see (161, 162)). Thesemolecules have been proposed as a new class of antiviral agents that interfere with cap-sid assembly, genome packaging, or disassembly. This strategy has significant promise,since relatively few existing treatments target these steps of the viral life cycle.It has been demonstrated that small molecules can stabilize the capsids of picornaviruses,inhibiting disassembly and preventing viral propagation (163, 164). Directly interferingwith assembly may also be a viable strategy; for HIV, peptides and small molecules havebeen developed which interfere with subunit-subunit interaction and prevent assemblyin vitro, as well as trigger premature disassembly and inhibit capsid maturation (161).Interestingly, two classes of small molecules have been found to interfere with HBVcapsid assembly by strengthening the interaction between capsid subunits (165, 166).The heteroaryldihydropyrimidine (HAP) compounds both strengthen and subtly alter thegeometry of the HBV capsid protein subunit-subunit interaction, leading to malformedcapsids (see section 2.4). The phenylpropenamides compounds do not alter the capsidgeometry, but by strengthening subunit-subunit interactions they enable the assembly inthe absence of the genome (see section 3.1), leading to empty capsids, which are (likely)a dead end for the HBV viral life cycle.
We have presented a summary of capsid assembly mechanisms, how they are influ-enced by non-protein components such as nucleic acids and lipid bilayers, and somevirus-specific interactions that facilitate selective genome packaging. Because most in-termediates on assembly pathways remain challenging to characterize, complementaryexperimental and theoretical investigations will play important roles in further elucidat-ing assembly mechanisms. As computer power and the sophistication of computationalmethods increase, models with increased resolution and complexity will become feasi-ble. At the same time, new experimental capabilities to monitor the assembly of indi- echanisms of Virus Assembly
Acknowledgement.
This work was supported by the NIH through Award NumberR01GM108021 from the National Institute Of General Medical Sciences and the NSFthrough award number NSF-MRSEC-0820492. We thank Chuck Knobler for a criticalread of the manuscript.L
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