Abstract

In particular, the protein containers encapsulating viral genomes have been determined to high resolution using symmetry averaging techniques that exploit the icosahedral architecture seen in many viruses. By contrast, structure determination of asymmetric components remains a challenge, and novel analysis methods are required to reveal such features and characterize their functional roles during infection. Motivated by the important, cooperative roles of viral genomes in the assembly of single-stranded RNA viruses, we have developed a new analysis method that reveals the asymmetric structural organization of viral genomes in proximity to the capsid in such viruses. The method uses geometric constraints on genome organization, formulated based on knowledge of icosahedralIy-averaged reconstructions and the roles of the RNA-capsid protein contacts, to analyse cryo-electron tomographic data. We apply this method to the low-resolution tomographic data of a model virus and infer the unique asymmetric organization of its genome in contact with the protein shell of the capsid. This opens unprecedented opportunities to analyse viral genomes, revealing conserved structural features and mechanisms that can be targeted in antiviral drug design.

Author Summary

Their genetic material is transported into their host organisms Via protein containers, called Viral capsids, that act as Trojan horses: they release their cargo into the cells of their hosts, hijacking their molecular machinery for the production of progeny Viruses. Imaging techniques exploiting the symmetric structures of Viral capsids have been used to determine details of their organization to atomic resolution, opening up the possibility to design antiViral agents against specific surface structures. In many Viruses the genomes take on specific organizations as a consequence of their roles in capsid formation. In order to design an additional class of antiviral drugs that interfere with this process, it is important to understand the asymmetric organization of the genome inside viral capsids. This is currently a challenge, as the averaging techniques used to achieve high resolution structures of the protein containers cannot be used. We present a new approach and demonstrate its predictive power here for a test virus. This paves the way for a better understanding of the functional roles of viral RNAs in virus assembly and their exploitation in antiviral drug design.

Introduction

The protein containers that encapsulate most viral genomes are formed from just a few different protein building blocks that self-assemble into particles with icosahedral symmetry, and can be described in terms of icosahedral surface lattices [1]. This geometry minimizes the amount of the genome fragment needed to code for the viral capsid, while maximizing its volume/ surface area ratio; the principle of genetic economy [2]. Symmetry therefore plays a pivotal role in understanding virus structure. Symmetry averaging techniques have been used to determine viral capsid structures at atomic resolution by X-ray crystallography, and by reconstruction of such structures at medium resolution by cryo-electron microscopy (cryo-EM). However, not all viral components are organized with icosahedral symmetry. Cryo-EM can be used to refine such asymmetric structures provided that they are large enough in mass terms to contribute significantly to the image [3, 4].

Note, in crystals of viral particles, the asymmetric features of the individual viruses usually do not dictate crystal packing contacts, and are therefore averaged out by the lattice. The important functional roles of such viral components in the viral life cycle are therefore difficult to characterize. An example is the single-copy of maturation protein (MP, also called A-protein) in bacteriophage MSZ that is hypothesized to replace a protein dimer in the capsid [6]. It attaches to the bacterial receptor during the infection to facilitate genome extraction. The asymmetric organization of the viral genome inside a capsid is also difficult to reconstruct. Indeed, M82 is typical in that the high resolution crystal structure lacks density for the ~ 3.7kb genome [7, 8], but cryo-EM reconstructions from both our group and others show extensive density for the RNA [6, 9—12]. This difference arises because of technical aspects of the ways the EM and X-ray data are collected.

Recently we have shown that a number of positive-sense single-stranded (ss)RNA viruses encode dispersed, degenerate sequence/ structure elements within their genomes that bind their cognate coat proteins specifically during assembly, facilitating capsid assembly efficiency [13—17]. These packaging signals (PSs) can have dramatic effects on the kinetics and fidelity of virion assembly [18]. There are widespread contacts between genomic RNA and capsid protein in picornaviruses, e.g. rhinovirus [19] , and preliminary in vivo experiments for human parecho-virus 1 suggest that they function as PSs (ongoing work with collaborators). The requirement for the PSs to contact the coat proteins of the viral capsid at specific positions in the capsid imposes a constraint on the conformation of the genome within each viral particle, that we are exploiting here to analyse tomograms of the packaged genomes.

For example, if PSs are located at the vertices of these cages, as in the model system we are considering here, then the RNA organization in proximity to capsid can be modelled as connected paths along the edges of the RNA cage [15, 20]. If the majority of the potential binding sites are occupied by a PS in every particle, as is expected, for example, if such contacts are vital in triggering a conformational change in the protein building block with which they are in complex, then this path has the mathematical properties of a Hamiltonian path. In this paper, we will discuss explicitly an example for which the constraint set is given by Hamiltonian paths.

For example, if PSs are stem-loops positioned along the edges of the polyhedral RNA cage, such as in Satellite Tobacco Mosaic Virus (STMV) [21] , then constraints have to be formulated in terms of paths that permit edges to be transversed twice in opposite directions. The library of all possible paths with that property would then replace the library of Hamiltonian paths we are using for our model system here. Moreover, it is possible that only a fraction of the potential binding sites are occupied by PSs. For example, this might happen if PSs facilitate CP-CP interactions rather than CP quasi-conformer switching, as is the case for STNV [16, 22]. In this case, the constraint set corresponds to all paths on the polyhedral cage that connect subsets of the potential binding sites corresponding to the number of the PSs: these are therefore also not Hamiltonian paths. The overall strategy, however, would remain the same: deducing information from tomographic data using an appropriate constraint set formulated in terms of paths that encode information on the specifics of the RNA-CP contacts (PSs) and their positions relative to the ordered genome segments in the averaged structures.

Importantly, this asymmetric distribution of viral genomes within a virion may also be an essential factor in the extrusion/uncoating of these genomes as the first step in subsequent infection [6, 32—37]. The analysis presented here provides a novel way of deriving information on such asymmetric genome organizations, thus contributing to the understanding of such events.

In pursuit of this goal we recently used the association of M82 phage particles to its natural receptor, a bacterial pilus, to create highly asymmetric complexes that could be subjected to asymmetric structure determination. This led to completion of a reconstruction using reduced (fivefold vs. icosahedral) symmetry averaging [12] and subsequently to a tomographic reconstruction of the whole virion using alignment and averaging of thousands of single particle tomograms [6]. The former result confirmed the presence of extensive RNA density, and the latter revealed its asymmetric structure; a first for any ssRNA virus. This suggests that the MP occupies a twofold position in the otherwise icosahedral coat protein lattice, presumably replacing the normal CP dimer at that site. Unfortunately, the resolution of the asymmetric tomographic reconstruction is very low (39A) and the molecular details are still unclear. It is therefore important to develop new analysis techniques that are able to reveal such genome organizations based on a range of data from different techniques, including the low resolution information contained in tomographic data. We introduce here a new method that uses information from icosahedrally-averaged maps, as well as knowledge of the contact sites between genomic RNA and CP to analyse the low resolution, tomographic density maps via a constraint optimization technique revealing the putative asymmetric genome organization of bacteriophage MS2. As we describe in detail here, the constraint set for the analysis of MS2 is derived from circular Hamiltonian paths connecting the PS contact sites, and similar constraints are likely to apply also to other Leviviridae [9]. For other viruses, in which occupation of the majority of the PS binding sites is likely due to their function in assembly, and for which the PSs are positioned at the vertices of the RNA cage corresponding to the icosahedrally-aver-aged map of the genome in proximity to capsid, the constraint set is also given by Hamiltonian paths. However, the set of Hamiltonian paths would be distinct from the one used for our model system if the numbers of binding sites and the connectivity between them differ. We are providing detailed instructions on how to modify our code (freely available at http://hprna. github.io/) to accommodate such alterations. If there is evidence that the 5’ and 3’ ends are in proximity in the packaged genome as in our model system, then the set of constraints can be reduced to only the circular Hamiltonian paths; otherwise, the full set of Hamiltonian paths has to be taken into account. Our code includes a setting that allows switching between these options, to compute either circular or non-circular Hamiltonian path constraint sets as required. Note that this method also applies if some of the potential binding sites remain unoccupied in random positions across the ensemble of particles used to generate the tomographic data, as such random mistakes would not be reinforced during averaging over different particles: hence it is sufficient that the majority of PS binding sites are occupied. Note that in the case of insufficient information being available to decide a priori between multiple constraint sets (stemming from different assumptions on the specifics of the PS-mediated assembly scenario), the tomogram could also be interrogated against the different possible options. This could give an indication, perhaps in combination with additional experimental insights, as to which of the proposed mechanisms is most likely to occur.

In order to demonstrate this for a model system, the specifics of that system must be built into the formulation of the constraint set. However, as we argue above, the method of interrogating tomographic data via constraint sets inspired by PS-mediat-ed assembly mechanisms is more generally applicable to wider classes of viruses.

Results

Geometric constraints on genome organization

M82 has a quasi-equivalent T = 3 capsid formed from 89 non-covalent CP dimers, comprising 29 symmetric ones (C/ C) located at the particle twofold axes, and 60 asymmetric ones (A/ B) organized in groups of five around the capsid fivefold axes, and one MP that replaces a C/ C dimer, see Fig. 1A. RNA PSs in the genome have been shown to act as allosteric regulators of the CP-dimer conformation, PS binding favouring formation of the A/B dimer [38, 39]. Thus, in an ideal case, we would expect to find 60 PSs within the genome. PSs are highly degenerate in nucleotide sequence. We have identified all the PSs in both M82 and the related phage GA Via a new analysis method based on biochemical RNA-CP binding and SELEX data [15]. In the icosahedrally-averaged MS2 cryo-EM map [11] the ~ 3.7 kb long RNA genome appears inside the capsid as two concentric shells with density connections at the particle fivefold axes. This arrangement reflects the contacts that the genomic RNA makes between PSs and the CP layer, which appear as the outer shell, Whilst the inner shell is the consequence of RNA segments that do not bind to CPs but extend into the interior of the capsid. The start and end points of these segments are located at the same fivefold vertex in the capsid [11]. Therefore, every PS is connected to two other PSs in the outer RNA shell, and hence the RNA in the outer shell, i.e. disregarding fragments extended into the interior, forms a connected path. If the path were disconnected, PSs at different fivefold vertices would have to be connected directly via RNA in the capsid interior, which is not consistent with the cryo-EM analysis in Toropova et al. [11]. The averaged outer shell density (Fig. 1A) is in the form of a polyhedral cage (Fig. 1B), positioned such that its vertices are in contact with the 60 asymmetric dimers (see yellow circles in the contact map in Fig. 1D). The RNA outer shell is intimately associated with the inside surface of the CP shell, as is also seen in the asymmetric reconstruction (Fig. 1C). The positions of the PSs in the genome determined earlier [15] suggest that the connections between PSs are single-stranded. The connected path described by the RNA in the outer shell is therefore a Hamiltonian path on that polyhedral RNA shell, i.e. a path that meets all vertices (aka PS positions). In particular, we determined all possible ways in which the RNA can be positioned in the icosahedrally-averaged density of the outer shell by computing all possible Hamiltonian paths on the polyhedron in Fig. 1B. Note that for viruses with different polyhedral RNA organizations the same method can be applied by computation of the Hamiltonian paths on the corresponding polyhedral density. Moreover, since Hamiltonian path computations only depend on the topology of the polyhedron, i.e. the network of connections between vertices irrespective of the lengths and orientations of the edges, the same library of Hamiltonian paths can be used for wider classes of viruses, such as those studied by van den Worm et al. [9] or bacteriophage GA [15].

This circularization reduces the number of possible Hamiltonian paths for the RNA. In particular, filtering out all those Hamiltonian paths with end points at the same fivefold axis, reduced the number to only 66 [20]. Since abstract paths have no directionality to them, each could potentially be realized by the RNA in two different ways by interchanging the positions of 5’ and 3’ ends, resulting in 132 path solutions. Since the resolution of the averaged tomogram, obtained via alignment and averaging of individual tomograms, was not sufficient to unambiguously identify the location of the MP, and the binding sites of the RNA were difficult to identify, we bookmarked all paths which started and finished within the eight fivefold axes closest to MP. This was a very conservative overestimate, which ensured that no possible path was missed in our analysis. Each of these (Hamiltonian) paths could potentially start at any of the fivefold vertices. In total, we therefore obtained a library of 8*5* 132 = 5280 possible paths for the genomic RNA in the outer RNA shell. As mentioned above, this library can be applied to a wide range of RNA viruses, covering all those with a polyhedral RNA organization topologically equivalent to that of M82.

Fig. 1B&D), 60 short and 30 long ones, and it had 60 vertices (cf. yellow circles in Fig. 1D). Each path in the library was therefore given as a sequence of 60 edges on the polyhedral shell, which were a mixture of short and long edges depending on the path. Each path provided information on which edges are simultaneously occupied or unoccupied, and hence correlated occupancy information on different edges.

Analysis of the tomogram via graph theory

Note that any path in the library provided information on which edges were likely to be occupied, given that occupation of some of the edges—or the lack thereof—could be confirmed based on the tomogram. The first step was therefore to determine a subset of the 90 edges of the averaged map (with reference to the polyhedron in Fig. 1B) that were likely occupied or unoccupied given the density distribution of the tomogram. We excluded all short edges as they were too short to distinguish unambiguously whether density represented the RNA-CP contact (i.e. PS) positioned at the vertex, or a connection between two PSs along a short edge. We moreover disregarded the five long edges (see 81 Fig) around the MP, as it was not possible to ascertain whether density in these regions arose from the MP, genomic RNA, or a combination of both.

A ranking of the level of density associated with these edges was achieved using the mean of the fitted normal distribution. This method was used because outliers in the noisy, sparse dataset had less influence on the mean of the fitted distribution than they did with a simple arithmetic mean. Using the fitted mean, four connections stood apart from the others, with mean densities of 2.6—2.9, see Fig. 2, suggesting that these four edge connections were likely occupied by RNA in the virion. These were denoted as “occu-pied” connections, and were used as constraints in the analysis of the asymmetric structure.

Skewness characterizes the balance of a distribution to either side of the peak density. As expected, the group of connections classed “occupied” above had a skew between 0.1—0.3. Negatively skewed connections were disregarded from the analysis, because a negative skew meant that there were only a very limited number of high-density points, which made up the cumulative density. Because of their low copy numbers, small fluctuations in sampling made a big difference to the overall density, and we therefore did not want to make a judgement of occupancy based upon these data. Using the skew parameter, the remaining data were therefore separated into distinct groups. The five data points shown in the red circle in Fig. 2, with mean values between 1.5—1.8, were adjudged “non-occupied”, i.e. characterized by an absence of density corresponding to RNA. There were thus nine constraints on RNA organization that were used to compare the asymmetric structure with the library of all possible Hamiltonian path organizations: four long edges were deemed occupied, and five non-occupied.

Constraint optimization yields RNA organization in proximity to capsid

In Fig. 3 we display the occupation of long edges with reference to the two f1ve-fold vertices they connect, following the numbering scheme of vertices given in Fig. 1D. Note that the paths match for 13 of the 30 long edges, suggesting that the structure common to all paths is likely to be a prevalent feature in different viral particles.

In order to decide if any of these putative RNA organizations was more likely to occur than another, we used the following criterion: We associated with each option a density distribution by ascribing density to occupied edges in proportion to their lengths and computed the density obtained by averaging around the fivefold aXis adjacent to MP. We used this as a characteristic to benchmark against the f1ve-fold averaged density determined experimentally [12] (Fig. 4H, adapted from [20]). Path 4 (Fig. 5A) closely matched (Fig. 4F) this distribution, whereas the other paths did not. This strongly suggested that Path 4 was indeed the correct model for the organization of the RNA in M82. Remarkably, Path 4 is also consistent with results of two independent studies: the assembly pathways determined via kinetic modelling of capsid self-assembly [20], and the PS positions identified via a bioinformatics analysis of RNA SELEX data [15]. Our analysis here represents a completely independent reconfirmation that the organization of the viral genome in proximity to capsid is highly constrained and likely identical in every viral particle.

Discussion

Previously, a model of the asymmetric genome organization in the plant satellite virus STMV has been built [41]. That work relied on the icosahedrally-av-eraged crystal structure which revealed ~ 70% of the viral genome to be in contact with the protein shell via a series of dsRNA segments ~ 9 bp long [30, 42, 43]. The X-ray structure provided the first definition of RNA PSs [21]. In addition to the X-ray density the modelling used predictions of the most likely secondary structure elements within the genome to identify the sequences forming the double-stranded segments [44]. Ours is the first direct analysis of an asymmetric map containing RNA density. The method introduced here can be used to analyse any asymmetric dataset of a viral genome organization, provided that a distinct shell of density is seen in proximity to capsid in the averaged cryo-EM density, the contact sites between genomic RNA and capsid protein are known, and information regarding their positions and function can be used to formulate a constraint set on the connectivity between the PSs. Insights into PSs are becoming available for a number of ssRNA viruses via the use of CLIP-SEQ techniques [45]. In addition, there is a growing body of work directed at obtaining asymmetric structures for this class of viruses in order to understand how their genomes are released during infection. Our approach is therefore likely to provide important insights into genome organization in wider groups of RNA viruses. In particular, many RNA viruses show order in the organizations of their genomes in icosahedrally-averaged cryo-EM and X-ray structures [46], for example Bean Pod Mottle Virus [47], STMV [30] and Pariacoto virus [48]. In such cases, constraint sets in terms of paths with appropriate combinatorial properties can be used to map the putative asymmetric organization of their genomes into the corresponding symmetrically averaged densities and hence provide information on connectivity between the RNA-CP contact sites.

Recent research has revealed that far from being a passenger in the assembly of the viral particle, genomes critically enhance the efficiency of virus assembly via multiple dispersed, sequence-specific contacts with capsid protein [14]. These PSs act collectively in a cooperative manner [18, 49], and their relative placement in the tertiary structure of the genome is important for their function. In particular, it is the relative affinities of the PSs for CP at defined positions in the packaged genome that impact on the geometries of the assembly intermediates, i.e. on the structures of the partially assembled protein shells on pathway to capsid. For the virus discussed here, it had previously been shown that this interplay of PS affinities and capsid geometry results in a highly ordered genome organization in proximity to capsid. It has moreover been established that the same overall organization of the packaged genome occurs in an evolutionarily related virus, GA [9, 15] , suggesting that there is a selective advantage for a specific genome organization in this family of viruses. This advantage can be explained in terms of assembly pathways: since PSs are instrumental in recruiting CF to the growing nucleus during PS-mediated self-assem-bly, the positions of the PS-CP contacts impact on the geometry of the assembly intermediates and hence on the assembly pathways. For the conserved genome organization identified in MS2 and GA earlier [15], this corresponds to an assembly pathway through the most stable intermediates, i.e. those forming a maximal number of CP-CP bonds [20].

More broadly, the method applies to any virus for which RNA-protein contacts are important for virus assembly, i.e. all viruses that follow a PS-mediated assembly process [14]. PSs are known to exist in a number of viral families including those infecting humans, e.g. alphaviruses [50], and plants [51], so this method is applicable to wider groups of RNA viruses. We note that the exact mechanism by which PSs act to enhance virus assembly can vary. For example, for MS2 the PS-CP contacts trigger an allosteric switch between the two types of protein building blocks required for productive capsid formation, while for STNV PSs promote formation of the coat protein capsomere [22], a trimer, by overcoming electrostatic repulsions between protein building blocks allowing increased ordering of the N-terminal RNA-binding domain. In both those cases the PSs form stem-loops in contrast to the dsRNA regions of STMV. In each case, however, PS-RNA interactions bias assembly towards a subset of the possible assembly pathways due to differential PS-CP affinities [18]. Specific PS binding moreover enhances assembly efficiency by triggering a collapse in the hydrodynamic radius of the genome below the inner radius of the virus protein shell [52] , enabling the assembly of the protein shell around the compacted genome.

This, in turn, is a prerequisite for the development of novel antiviral strategies that target virus assembly. As demonstrated in [18] , drugs interrupting PS-CP interactions can slow down the assembly process and decrease viral yield via misencapsidation of cellular RNAs. Moreover, a better understanding of conserved features in the genome organization within a viral family provides novel insights into the selective pressures on viral evolution. The method described here enables the identification of such features, and therefore also has profound implications for our understanding of Viral evolution.

Methods

Asymmetrically averaged structure

1C) [6] , obtained by imaging mature MS2 bound to its natural receptor, the F-pilus of E. coli. A total of 22 tomograms were taken with 2374 bound viral particles. The 1500 best correlating Virion subtomo-grams (63% of the total) were normalized, low-pass Fourier filtered to 30A, and then averaged to produce a structure at 39A resolution. The data was presented as a density map of 643 pixels, sampled to 9.1224 per pixel (EMD-2365).

Difference map between tomogram and X-ray protein structure

Radial plots compared the distribution of density in the protein map and the tomogram, with the pilus/MP complex masked away for the calculation. The radial distributions were, as expected, similar in the radial ranges corresponding to CF, but different elsewhere at radial levels corresponding to viral RNA (which is organized as a two-shell architecture, see [11]) and the 44kDa single-copy MP. Note that the radial distributions were not identical in the area overlapping with CP—this was due to the low resolution of the map, as CP density could not easily be accounted for in the asymmetric map. Therefore, a contour mask of the tomogram with the protein map was used to sample the low-resolution map, and used to eliminate the protein density via the UCSF Chimera mask routine [53], rather than a direct subtraction of the normalized maps. A mask of 0.50 best isolated the RNA whilst excluding protein. Finally, two icosahedral masks were applied: the inner core of RNA was masked away under radius 80A, and an outside mask of radius 120A removed noise resulting from masking artifacts and the pilus/MP complex. The resultant pruned density contained information about (i) the outer RNA shell in contact with CP, (ii) MP, and (iii) potential traces of CP lying within the shell that were not captured by the masking process.

Difference map between icosahedraIIy-averaged EM density and the asymmetric structure

We based our analysis on density map EMD- 1431 of mature M82, which was calculated using single particle analysis of 9,335 separate images, equating to ~ 560,000 sample points with icosahedral averaging [11]. We used a procedure analogous to the one described above for the tomogram to isolate the RNA. The protein structure was filtered to 9.5A resolution, with a grid spacing of 1.26A, to match the symmetric map, and normalization of the resultant protein map to the CP area of the symmetric map was performed. The resampled filtered protein was then subtracted from the symmetric map, yielding a symmetric cage of RNA with a polyhedral shape as in Fig. 1B. The outer shell of RNA was isolated by icosahedral masking with vertex radii of 80A and 120A. The resulting map for the outer RNA shell in the icosahed-rally-averaged map was aligned with that for the asymmetric RNA organization in the tomogram by reference to the X-ray protein structure used to create each difference map, via UCSF Chimera [53]. After normalization, the aligned maps had similar average, standard deviation and maximum density values.

Mapping data onto the geometric model

Each long edge of the cage in Fig. 1B was represented by three segments as shown in 82 Fig. The same watershed segmentation was applied to the asymmetric RNA outer shell map. Hence pixels from the asymmetric RNA map were associated with defined segments on the polyhedral shell, and each connection thus had a density profile associated with it.

This was because the short segments close to the polyhedral vertices, as well as the short edges themselves, might have contained density corresponding to the RNA-CP contact (i.e. PS) located at a polyhedral vertex bordering the edge, which could have distorted the analysis. Moreover, connections between PS positions adjacent to the MP/pilus (see 81 Fig) were discarded as they may have contained unmasked MP density.

The density profiles of the long edges

We computed fitted normal distributions using the normfit function from the scipy.stats python library, since for a sparse dataset the mean of a fitted normal distribution is less affected by outliers than the raw data. The normal fitting function automatically calculated the best positioning of a unimodal normal distribution for the dataset. Connections occupied in the RNA density were expected to have a substantially higher mean density than unoccupied connections.

If a distribution representing density for a connection was negatively skewed, it could not be unambiguously classified as occupied or non-occupied, as this suggested smearing of density. We therefore did not place any constraints on edges with negatively skewed distributions.

Supporting Information

Five long edge connections, shown as solid lines between fivefold vertices, are omitted as their proximity to MP makes association of a corresponding RNA density distribution ambiguous.

Each long edge of the polyhedral density (corresponding to the icosahedrally-averaged map) is partitioned into three segments via the UCSF Chimera SegmentMap tool [53, 54]. Only tomographic density overlapping the middle segment (pink) is retained for analysis, as density overlapping with the outer segments (red) may potentially also sample density associated with short edges and RNA-CP connections (i.e. PSs). The segments shown in this figure are from a representative single connection (coloured cyan), not an average of all the connections, and are shown viewed from inside the virion along a particle twofold axis. CP in the background is shown in beige. (TIFF)

Author Contributions

Performed the experiments: JAG ECD. Analyzed the data: JAG NAR RT. Contributed reagents/ materials/ analysis tools: NAR. Wrote the paper: JAG RT ECD PGS NAR.