Building a viral capsid in the presence of genomic RNA

Eric C. Dykeman, Peter G. Stockley, and Reidun Twarock

Phys. Rev. E 87, 022717 – Published 25 February 2013

Abstract

Virus capsid assembly has traditionally been considered as a process that can be described primarily via self-assembly of the capsid proteins, neglecting interactions with other viral or cellular components. Our recent work on several ssRNA viruses, a major class of viral pathogens containing important human, animal, and plant viruses, has shown that this protein-centric view is too simplistic. Capsid assembly for these viruses relies strongly on a number of cooperative roles played by the genomic RNA. This realization requires a new theoretical framework for the modeling and prediction of the assembly behavior of these viruses. In a seminal paper Zlotnick [J. Mol. Biol. 241, 59 (1994)] laid the foundations for the modeling of capsid assembly as a protein-only self-assembly process, illustrating his approach using the example of a dodecahedral study system. We describe here a generalized framework for modeling assembly that incorporates the regulatory functions provided by cognate protein–nucleic-acid interactions between capsid proteins and segments of the genomic RNA, called packaging signals, into the model. Using the same dodecahedron system we demonstrate, using a Gillespie-type algorithm to deal with the enhanced complexity of the problem instead of a master equation approach, that assembly kinetics and yield strongly depend on the distribution and nature of the packaging signals, highlighting the importance of the crucial roles of the RNA in this process.

Received 19 September 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022717

Authors & Affiliations

Eric C. Dykeman^1,2, Peter G. Stockley³, and Reidun Twarock^1,2

¹Department of Biology, York Centre for Complex Systems Analysis, University of York, York, YO10 5DD United Kingdom
²Department of Mathematics, York Centre for Complex Systems Analysis, University of York, York, YO10 5DD United Kingdom
³Astbury Centre for Structural Molecular Biology, University of Leeds, Leeds, LS2 9JT United Kingdom

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Vol. 87, Iss. 2 — February 2013

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Figure 1
Geometry of the dodecahedron study system. (a) Dodecahedron as a coarse-grained model for a viral capsid formed from 12 pentamers. (b) The RNA-protein contacts at the centers of the pentagonal faces inscribe an icosahedron, here shown in red. (c) Example of a Hamiltonian path on the icosahedron. (d) Example of a protein intermediate that cannot occur during coassembly with RNA. Dashed lines illustrate how this intermediate would violate the local-rule-assembly model by jumping to another part of the shell instead of moving to one of the four neighboring pentamer sites that are vacant. (e) and (f) Two assembly intermediates with identical protein configurations but different RNA organizations. These are considered as different intermediates in the case of assembly in the presence of RNA.Reuse & Permissions
Figure 2
Possible assembly reactions in the model. (a) The RNA is modeled as containing 12 packaging signals of varying affinity, numbered from $-$ 6 to 6. Binding can occur at any of the unoccupied sites at any time in the simulation. (b) Protein pentamers and RNAs react via two different types of events: the second-order reaction of a protein-RNA association (vertical arrows) where coat proteins bind and unbind to RNA or a first-order reaction where protein-protein interactions (horizontal arrows) are formed or broken.Reuse & Permissions
Figure 3
Comparison of the effects of protein association energies on assembly yield with and without RNA interactions. (a) Percentage of capsid assembled from available pentamers (solid black curve) and time to reach 90 $%$ of the maximum amount of capsid assembled (dashed red line) at thermodynamic equilibrium for a protein-only assembly scenario. Vertical lines indicate an optimal window of $Δ G_{P}$ values that result in efficient assembly, i.e., high yield and speedy assembly reaction. (b) Percentage of capsid assembled in the presence of RNA for $κ_{P}^{1} = 100$ s $^{- 1}$ shows that weaker protein-protein association energies can increase the yield at the expense of overall capsid stability. Data points (dots) in (a) and (b) are averaged over 100 assembly simulations. Data for the percentage of capsid assembled are taken at $t = 1000$ s, which is thermal equilibrium for all points except those lower than $| Δ G_{P} | = 2.5$ kcal M $^{- 1}$ in (b), where the slow annealing occurs.Reuse & Permissions
Figure 4
Assembly efficiency depends on the location of the high-affinity packaging signal. The percentage of capsid assembled for $κ_{P}^{1} = 100$ s $^{- 1}$ from available RNA and pentamers is illustrated for different locations of the strong packaging signal, i.e., the assembly initiation point, in the RNA. The highest yield of completed capsid is achieved when the strong packaging signal is placed at positions $-$ 4 and $-$ 5 (or the symmetric positions 4 and 5). Data points (dots) are averaged over 100 simulations and splined to produce the curve shown.Reuse & Permissions
Figure 5
Exploring the effect of $κ_{P}^{1}$ and packaging signal distribution on capsid assembly. (a) Distribution of capsid yields for an ensemble of 300 RNAs with a random distribution of packaging signals. The distribution shows the probability of finding an RNA in the ensemble of 300 that achieves a given yield of capsid. The leftmost peak is computed for $κ_{P}^{1} = 100$ s $^{- 1}$ , while the rightmost peak is for $κ_{P}^{1} = 10^{6}$ s $^{- 1}$ , illustrating the effect of the parameter on capsid assembly. (b) Capsid yield for the case of a homogeneous RNA containing 12 PSs with identical affinities. For $κ_{P}^{1} = 100$ s $^{- 1}$ , the yield of the capsid is roughly independent of the PS affinities, while for $κ_{P}^{1} = 10^{6}$ s $^{- 1}$ there exists an optimal value of PS affinity at $- 3.0$ kcal M $^{- 1}$ in which capsid yield achieves a maximum of about 92 $%$ . (c) Percentage of capsid assembled for four RNAs at values of $κ_{P}^{1} = 10^{6}$ s $^{- 1}$ and $Δ G_{P} = - 2.5$ kcal M $^{- 1}$ . The RNA1 is a high-yield RNA chosen from the ensemble of 300 RNAs, while RNA2–RNA4 contain a uniform distribution of PS affinities. Although RNA1 and RNA2 have similar yields, RNA1 is more efficient at the coassembly scenario when compared to the homogeneous RNAs. Statistical data for the assembly curves were collected over 100 assembly simulations.Reuse & Permissions
Figure 6
Examining the Hamiltonian path organizations of different RNAs. (a) Probability that an RNA in a capsid will be observed in one of the 1264 Hamiltonian paths. The probabilities are calculated using roughly 300 000 assembled capsids containing RNA1, a high-yield scenario with an inhomogeneous PS affinity distribution, and 300 000 assembled capsids containing RNA2, a high-yield scenario with a homogeneous PS affinity distribution. For both RNAs, there is a clear bias towards a subset of paths. Roughly 250 paths account for 75 $%$ of particles containing RNA1, while about 300 paths account for 75 $%$ of particles containing RNA2. The geometric origin of this bias is shown below the plot where 94 $%$ of RNAs pass through the two most stable intermediates with four pentamers. (b) Probability that an assembled capsid containing the low-yield homogeneous RNA3 or RNA4 will be observed in one of the 1264 Hamiltonian paths. The probability for each path is roughly 1 in a 1000, illustrating that each path is roughly equally likely. In contrast to (a) only 80 $%$ of the RNAs will pass through the two most stable intermediates with four pentamers, showing a propensity for the higher-yield RNA1 and RNA2 to bias assembly along these more stable intermediates.Reuse & Permissions

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