Solving a Levinthal's paradox for virus assembly identifies a unique antiviral strategy

Abstract

One of the important puzzles in virology is how viruses assemble the protein containers that package their genomes rapidly and efficiently in vivo while avoiding triggering their hosts' antiviral defenses. Viral assembly appears directed toward a relatively small subset of the vast number of all possible assembly intermediates and pathways, akin to Levinthal's paradox for the folding of polypeptide chains. Using an in silico assembly model, we demonstrate that this reduction in complexity can be understood if aspects of in vivo assembly, which have mostly been neglected in in vitro experimental and theoretical modeling assembly studies, are included in the analysis. In particular, we show that the increasing viral coat protein concentration that occurs in infected cells plays unexpected and vital roles in avoiding potential kinetic assembly traps, significantly reducing the number of assembly pathways and assembly initiation sites, and resulting in enhanced assembly efficiency and genome packaging specificity. Because capsid assembly is a vital determinant of the overall fitness of a virus in the infection process, these insights have important consequences for our understanding of how selection impacts on the evolution of viral quasispecies. These results moreover suggest strategies for optimizing the production of protein nanocontainers for drug delivery and of virus-like particles for vaccination. We demonstrate here in silico that drugs targeting the specific RNA-capsid protein contacts can delay assembly, reduce viral load, and lead to an increase of misencapsidation of cellular RNAs, hence opening up unique avenues for antiviral therapy.

Fig. 1.

The dodecahedral model of virus assembly. (A) The building blocks of the system are: pentagons as proxies for capsid protein (CP) and viral RNA sequences, each with 12 CP binding sites modeled as RNA stem loops (PSs), with positions labeled −6 to 6 from the 5′ to the 3′ end. Each PS can interact with CP with a different affinity. The distribution of PS affinities, here and throughout is indicated as binding free energies as a string of color-coded beads. ΔG_b values (K_d values) of −9.5 > ΔG_b > −12.0 kcal/M (100 nM > K_d > 1.5 nM) are shown as green, −5.4 > ΔG_b > −9.5 kcal/M (100 μM > K_d > 100 nM) as blue, and −3.0 > ΔG_b > −5.4 kcal/M (6.2 mM > K_d > 100 μM) as red, respectively. (B) The two basic reactions of the assembly model: CP binding to RNA and subsequent formation of CP–CP contacts.

Fig. 2.

The impact of the protein ramp. (A) A population of 3000 RNAs, each containing a random selection of PS affinities was constructed, each RNA copied 3000 times, and the percentage of RNA packaged at a CP:RNA ratio (12:1) after 1000 s calculated. The histogram shows the frequency of occurrence of RNA sequences resulting in a particular yield of capsids. The highest (99%, RNA1) and lowest (75%, RNA2) yielding RNAs in the sample were used in further simulations. A representative cellular RNA was constructed by assigning a low affinity (−3 kcal/M) to all 12 PSs. (B) Assembly kinetics of RNA1 determined from the average of 100 assembly simulations with 3000 RNAs at the ratio of CP:RNA (12:1). The graph shows time-dependent assembly of (i) assembly intermediates (protein arrangements shown as cartoons) that are on pathway and complete to capsid; (ii) correctly assembled capsids; and (iii) kinetically trapped malformed species (Left). In the presence of the protein ramp (CP concentration shown as a dashed line, here and throughout) all of the RNAs are successfully encapsidated. The percentage of successfully packaged RNAs that nucleate at each pair of PSs is shown below each graph. In the presence of a ramp, nucleation is confined to the two highest affinity PSs.

Fig. 3.

Impact of the ramp on assembly pathway selection and intermediate stability. (A) In assembled capsids the PSs contact the midpoint of every pentagonal face of the dodecahedron and hence the RNA describes a connected path on the inscribed icosahedron (red). One such Hamiltonian path is shown on the Right; the icosahedron is the superposition of all possible Hamiltonian paths. (B) The frequency of occurrence of different Hamiltonian paths across a sample of 150,000 RNA1s determined by tracking the addition of CP on individual RNAs. The distribution in the presence of the ramp (red) shows a bias toward a small number of different paths, whereas in its absence, all possible paths occur (black). Dashed lines indicate the number of paths used by ∼90% of the 150,000 capsids. (C) Assembly intermediates contain more or less stable species depending on the number of CP–CP contacts. (D) For each assembly pathway taken the number of deviations in protein configurations from the most stable structure during assembly are shown. In the absence of the ramp (Left), up to six deviations can occur and their frequencies are relatively similar. In its presence (Right) assembly is strongly biased toward the most stable assembly intermediates.

Fig. 4.

Impact of the protein ramp on packaging selectivity. An in silico competition experiment between 2000 copies of RNA1 and 600,000 copies of RNA3 at a CP:RNA1 ratio (8:1) just sufficient to assemble 2000 capsids. (A) In the absence of the ramp, a significant fraction of RNA3 is encapsulated and the assembly yield of RNA1 is much lower due to the production of malformed species. The circular Inset indicates the percentages of encapsulated RNA1 (green), RNA3 (red), and malformed species (white) at the end of the simulation. (B) With the ramp assembly of RNA1 occurs almost to 100% with no encapsidation of RNA3, i.e., there is high packaging specificity.

Fig. 5.

Impact of PS-binding drugs on assembly efficiency. (A) Amounts of encapsidated viral RNAs (RNA1) in the absence of RNA3 (shown as percentages of RNA1 (green) and malformed species (white) in the presence of the ramp at differing drug concentrations. (B) As in A in the presence of cellular RNAs (RNA3, red) at a ratio RNA1:RNA3 of 1:300.