Evolution on the Biophysical Fitness Landscape of an RNA Virus

Abstract

Viral evolutionary pathways are determined by the fitness landscape, which maps viral genotype to fitness. However, a quantitative description of the landscape and the evolutionary forces on it remain elusive. Here, we apply a biophysical fitness model based on capsid folding stability and antibody binding affinity to predict the evolutionary pathway of norovirus escaping a neutralizing antibody. The model is validated by experimental evolution in bulk culture and in a drop-based microfluidics that propagates millions of independent small viral subpopulations. We demonstrate that along the axis of binding affinity, selection for escape variants and drift due to random mutations have the same direction, an atypical case in evolution. However, along folding stability, selection and drift are opposing forces whose balance is tuned by viral population size. Our results demonstrate that predictable epistatic tradeoffs between molecular traits of viral proteins shape viral evolution.

Fig. 1.

Viral evolution in large and small population sizes. (A) Viral evolution in large populations. Top: 10⁸ viruses evolving against a neutralizing antibody by serial propagation in bulk. Bottom: The allele frequencies of 1,364 distinct P-domain haplotype sequences are plotted per passage (supplementary fig. S2A and B, Supplementary Material online). (B) Viral evolution in small populations. Approximately 10⁶ pico-liter drops are loaded with on average 1–10 infectious viral particles (pfu) and two host cells per drop and the viruses evolve in drops for five passages (see also supplementary fig. S3 and movies S1 and S2, Supplementary Material online). (C) The ruggedness of the fitness landscape as perceived by the virus depends on the population size. Haplotype legend: A: E296K, B: D385G, C: T301I, D: A382V.

Fig. 2.

Head-to-head competition between wildtype and escapee. To perform pairwise competition of the clones, we mixed equal titers of the clone, propagate them for three passages, and then perform deep sequencing. Averages over three biological replicates are shown for each measurement. See also supplementary table S3, Supplementary Material online.

Fig. 3.

Fitness landscape of norovirus escaping a neutralizing antibody. (A) The structure of P-domain in complex with Antibody. The SNPs of all dominant P-domain variants (red circles) are located on the docking site of the P-domain-antibody complex (PDB ID: 3LQE). (B) A high correlation exists between Ab dissociation constant K_d that was experimentally measured using surface plasmon resonance (SPR) and the one from force field calculations. (C) The anti-correlation between the experimentally measured P-Domain melting temperature (T_m) and the folding stability from force field calculations. (D) A 3D plot of the probability of infection F averaged over 2,076 distinct haplotypes binned according to their dissociation constant K_d and folding stability ΔG_fold (blue points) overlaid with the theoretical fit according to equation (1) (gray surface). Cross sections (black frames) demark the regions used for the projections in E and F. (E) The probability of infection for all haplotypes with ΔG_fold < 4.5 Kcal/mol (cross section parallel to K_d axis in A) is projected on the K_d-F plane, binned according to their K_d (blue points) and overlaid with the theoretical fit to equation (1) (dashed line). F) The probability of infection for all haplotypes with K_d > 10³ nM (cross section parallel to ΔG_fold axis in A is projected on the ΔG_fold-F plane, binned according to their ΔG_fold (blue points) and overlaid with the theoretical fit to equation (1) (dashed line). F is determined from the deep sequencing of lysates of in vitro experiments in the presence of neutralizing antibody. K_d and ΔG_fold are estimated from mapping the haplotype mutations to the 3D structure of the capsid P-domain in complex with the neutralizing antibody. Error bars in panels D, E, and F denote Standard Error.

Fig. 4.

MNV-1 neutralization versus binding affinity of the P-domain to neutralizing antibody. (A) In vitro neutralization of dominant haplotypes correlates to their K_d and the average ratio between them is ∼120, in good agreement with the modeled value of m ≈ 70 (see fig. 3E and eq. 1) (supplementary Methods, Supplementary Material online: in vitro neutralization measurements). (B) In vivo neutralization of dominant haplotypes in mice correlates to their K_d. Viral strains were neutralized in STAT−/− mice injected with 500 µg mAb A6.2 and compared with their infection in mice injected with an isotype as described in (Firnberg et al. 2014). The decrease in viral titers was first standardized for each tissue across viral strains, before the average over all tissues within each strain was taken as its final neutralization score.

Fig. 5.

Dominant haplotypes from bulk and droplet experiments. (A and B) Average stringency of selection on the viral fitness landscape depend on population size (see Text and Equations 2–4). For large population sizes, the increase in K_d is strongly coupled to the increase in T_m. However, for small population sizes, the selection for K_d is decoupled from the selection for folding stability. The white lines are the predicted trajectories from forward evolutionary simulations of an MNV population escaping an Ab, and with a P-domain that is initially unstable. Each trajectory is the average of 1,000 independent simulations. The direction of selection (black arrows) is towards greater folding stability and weaker affinity to the antibody. Selection is strong when the P-domain is unstable and/or is tightly bound to the Ab. Selection pressure is approximately zero when the fitness landscape is flat (neutral). Along the direction of folding stability, most random mutations are destabilizing which lead to a random drift (white arrows) towards protein destabilization. Along binding affinity axis, most random mutations perturb the protein–protein interaction that leads to a random drift towards weaker binding. (C and D) Density plots of all experimentally measured dominant haplotypes grouped according to passages. Each dominant variant is represented as a circle with a center determined by the measured biophysical properties and size proportional to its allele frequency, see also legend inset. (E and F) Histograms of K_d and T_min passage 5 of all serial passaging in either bulk or drops. The positions of the escape variants are shown in the projection of the fitness landscape (green line, see also fig. 3E and F). The variants ABC and E are bona fide escapees from the neutralizing antibody with K_d values that lead to the peak of the fitness landscape. Although the T_m values of the two bulk escapees ABC and E are different, they have comparable fitness because of the “mesa”-like nature of the landscape. To ascertain that the population dynamics on the landscape under bulk and droplet conditions are distinct, we considered the ∼10⁶ independent serial passages of the droplet experiment as the null model. We estimate the likelihood of escape variants with T_m ≥ T_m ∼ 39°C. This stability value is the threshold for the high fitness plateau of the landscape (shown in panel E). Specifically, to estimate the probability of observing an escapee with T_m ≥ 39°C, we repeatedly draw 10⁶ random variants from the null distribution, and then calculate this probability as the number of occurrences for variants with T_m ≥ 39°C divided by 10⁶. The resulting value of ∼3 × 10⁻⁴ reflects the probability of observing a bulk escapee with T_m ≥ 39°C in one experiment. The overall probability of observing variants with T_m ≥ 39°C in five independent experiments is ∼2 × 10⁻¹⁸.