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.

Introduction

The evolution of microbes and viral pathogens is affected by a hierarchy of constraints on multiple levels of biological organization (Bershtein et al. 2017). Mutations and other genetics changes primarily affect the structure and function of macromolecules, and these consequently change the fitness of the organism. Whether these arising mutations survive or are purged is also determined by the population size and dynamics. The first layer of constraints is defined by the relationship between mutations in the viral genome and the fitness of the individual virions (de Visser and Krug 2014). This relationship is the fitness landscape, which is a complex, multidimensional function; however, this can rarely be quantitatively determined. Nevertheless, it is essential for predicting selection of the most probable mutants. Several works have tried to quantitatively map organismal fitness to molecular properties. For example, bacterial fitness can be mapped to biophysical properties of core metabolic enzymes using flux-balance theory (Flint et al. 1981; Dykhuizen et al. 1987; Bershtein et al. 2013; Bershtein et al. 2015; Rodrigues et al. 2016). Bloom and co-workers also demonstrated with Influenza that viral growth is strongly dependent on the folding stability of its nucleoprotein, which then constrains possible mutational pathways in its evolution (Gong et al. 2013). Recent experimental techniques that enable high-throughput and comprehensive interrogation of the fitness landscape, such as deep mutational scanning, confirm the pervasive role of folding stability in evolution (Fowler et al. 2010; Jacquier et al. 2013; Baier and Tokuriki 2014; Firnberg et al. 2014; Bank et al. 2015; Rodrigues et al. 2016; Sarkisyan et al. 2016; Wrenbeck et al. 2017).

The second layer of constraint refers to how the fitness landscape itself is explored. The survival or purging of mutations in an evolving population is a function of competition, which is proportional to population size (Kimura 1968). In particular, population size changes the balance between the impact of random mutations on fitness and that of selection (Lynch and Conery 2003), and is thought to affect both the rate and direction of evolution (Wright 1931). Recent studies have used microbial fitness landscapes (Sanjuan et al. 2004; Gong et al. 2013; Acevedo et al. 2014) or population structure (Lang et al. 2013; Nahum et al. 2015) to predict the course of evolution, but to date, none links these elements together. Without this quantitative link between the biophysical phenotypes of the viral fitness landscape and the viral population demography, further progress in determining the course of viral evolution is significantly hindered.

In this paper, we quantitatively determine a biophysical fitness landscape for an RNA virus subjected to the pressure of a neutralizing antibody, and use it to account for the evolution of the key biophysical traits of the viral antibody-binding epitope under conditions that constrain population size. The experimentally measured biophysical fitness landscape can be described by two biophysical parameters: the thermodynamics of folding of the capsid protein and its binding to the antibody. We probe the evolution of a model norovirus both in bulk, where population size is large, and in a microfluidic set-up that uses small drops to concurrently perform millions of evolution experiments (Guo et al. 2012; Fischer et al. 2015; Tao et al. 2015a, 2015b; Zhang et al. 2015) in very small population sizes. We show that the dynamics of viral adaptation is strongly dependent on population size. These results can be quantitatively described by a theoretical framework that combines protein biophysics and population genetics, providing the critical link between fitness landscape and population structure that enables exploring the quantitative interplay between the factors operating at different scales of biological organization—protein biophysics and viral population dynamics—in determining the course of viral evolution.

We focus in this work on Murine Norovirus (MNV), a model for human RNA viruses, which are a major cause of gastrointestinal disease epidemics in the world (Wobus et al. 2006; Jones et al. 2014; Ettayebi et al. 2016). MNV is a nonenveloped RNA virus that consists of 180 copies of the capsid protein assembled around a 7.5 kb long positive-strand RNA genome. It mutates at ∼1 base per genome per replication cycle and produces ∼10⁴ progenies in a single cell infection, of which ∼100 are infectious viral particles, or plaque forming units (pfu) (Fischer et al. 2015).

Results

Lab Evolution of Norovirus in Large and Small Population Sizes

To study viral evolution, we propagate a viral isolate (MNV-1, denoted as wt) in the presence of a neutralizing antibody (mAb6.2, Kolawole et al. 2014) that binds to the protruding domain (P-domain) of the capsid, and prevents viral entry into the host cell (Katpally et al. 2008; Taube et al. 2010). This set-up allows us to study the way the virus evolves to adapt to a new environment. To investigate the dynamics of this escape from the antibody, we sequence a 376 bp fragment of the genome encoding the epitope containing the outermost part of the P-domain (residues 281–412 of VP1) and follow the frequency of 37,244 unique haplotypes (see supplementary fig. S1, Supplementary Material online for a schema of the approach and supplementary tables S1 and S2, Supplementary Material online for data) observed over several passages, allowing us to follow the evolution over several generations. First, we propagate wt in standard bulk culture conditions, using ∼10⁸ virions per passage under Ab pressure (fig. 1A). The population is initially dominated by the wt (∼90% of the population) with the rest of the viral quasi-species consisting of single and double mutants (supplementary tables S1 and S2, Supplementary Material online). After two passages the total number of surviving viruses has decreased by two orders of magnitude due to the neutralizing effect of the Ab (supplementary fig. S2, Supplementary Material online); however, three single mutants E296K (A), D385G (B), T301I (C) as well as their double mutants (AB, AC, BC) occur at higher frequencies than the other haplotypes. By the fourth passage the triple mutant ABC, which first arises on passage 2, occurs at a frequency even higher than the other mutant haplotypes (86%); moreover, the total number of viruses increases to levels comparable to those observed after the first passage (supplementary fig. S2C, Supplementary Material online). This suggests that ABC is an escape variant. Additionally, we note that the escape variant in bulk ABC is not present in the starting stock (supplementary table S1, Supplementary Material online), although some of the single- and double-mutants occur in the starting stock at low frequency. Thus, the escape variants arise from de novo mutations and not from standing genetic variation.

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.

A central tenet of evolutionary theory is that the way organisms explore their fitness landscape depends on the size of their population, which controls the balance between random drift (i.e. direction of randomly arising mutations) in the population and positive selection (i.e. direction of beneficial mutations) (Kimura 1968; Lynch and Conery 2003). This balance determines the most likely evolutionary pathways on a given fitness landscape. Indeed, the population size may be particularly important for noroviruses where a single viral particle is sufficient to infect the host animal (Teunis et al. 2008); thus it is possible that viruses propagate in very small populations as they adapt to a new environment prior to the emergence of an epidemic. We can directly probe this hypothesis experimentally by drastically reducing population size compared with typical laboratory bulk cultures, which propagate ∼10⁶–10⁸ viruses (supplementary fig. S2C, Supplementary Material online). To evolve viruses in small population sizes, we use a novel microfluidics set-up, which propagates ∼10⁶ subpopulations of 1–10 infectious particles (pfu) in distinct and non-mixing compartments (fig. 2B and supplementary fig. S3, movies S1, and S2, Supplementary Material online). The microfluidics system allows us to drastically reduce the population size without reducing the total number of viruses sampled, thereby maintaining the statistics comparable to that of a bulk experiment.

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.

To ascertain that the effective population sizes between bulk and drops are indeed different, we measured the RNA titer (genomes/mL) in each passage, which fluctuates between 10⁶ and 10⁸ in bulk (supplementary fig. S2C and D, Supplementary Material online). Thus, a conservative estimate of the effective population size for the well-mixed bulk culture is N_e = 10⁶. On the other hand, the total number of viral genomes for all 10⁶ drops ranges from 10⁶ to 10⁸, thus the average number of MNV-1 genome in a drop is 1–100. The effective population size in drops is therefore at least N_e = 1 or at most N_e = 10². Thus, the effective population sizes in drops and bulk differ by 4–6 orders of magnitude, which we estimate to be strong enough to give rise to different population dynamics.

In stark contrast with the bulk experiments, amplification and hence growth of potential escape variants that sweep the population is precluded when each variant is confined in a single drop with just two host cells; as a result, the wt remains the dominant fraction of the observed viruses through all passages. Potential escape viruses are present, but are in complete isolation from each other, at population sizes of just a single infection event per generation. This partitioning of single variants in the microfluidic setup (figs. 1B and 5D;supplementary fig. S3, Supplementary Material online) weakens selection and increases genetic drift as subpopulations evolve without competition between drops.

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.

Next, we determine if the escapee is indeed more fit than the wild type. To address this question, we engineered the mutations ABC into the infectious clone and recovered mutant viruses. We then performed head-to-head competition of wt and variant ABC and show in figure 2, the frequency of each of the clones at the end of the competition. Indeed, ABC is a true escape variant since it outcompetes wt under neutralizing antibody. However, without antibody, wt is more fit than ABC, which explains the observation that ABC does not spontaneously arise in serial passaging without Ab.

Fitness Landscape of Norovirus Escaping an Antibody Is Projected onto the Biophysical Properties of Its Capsid Domain

In general, fitness is expected to be a complex function of multiple traits. Instead we focus on the dependence of viral fitness in the presence of a neutralizing antibody on two biophysical properties of the epitope containing P-domain: the folding energy, which is a measure of stability, and the binding affinity to the antibody, which is a measure of neutralization. While the importance of binding affinity to antibody is apparent, the universal importance of protein folding stability for bacterial and viral fitness was also shown (Gong et al. 2013; Rodrigues et al. 2016). This choice of variables is further supported by the fact that all the mutations of the dominant escape variants we observe in our experiments are located within the binding site between the P-domain and the Ab, as shown by mapping the mutations on the 3D structure of the wt P-domain in figure 3A.

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.

First, we calculate the folding energy of the P-domain and its binding affinity to the antibody for several dominant haplotype sequences, using force field calculations based on the structural mapping in figure 3A (Yin et al. 2007).

We calculate the change in folding energy ΔΔG_fold between the mutant and the wt; from this we determine ΔG_fold of the mutant by adding the folding energy of the wt, ΔG_wt. We also computationally determine the change in binding energy, ΔΔG_bind, between the mutated P-domain-Ab complex and the wt; from this we determine the dissociation constant $K_d=K_0\hspace{0.17em}\text{exp}\hspace{0.17em}\left(\beta \Delta \Delta G_{\text{bind}}\right)$ where K₀ is the dissociation constant of the wt. We test the accuracy of our calculations by comparing the calculated biophysical properties of the escape haplotypes to experimentally measured properties. To accomplish this, we express and purify the P-domain of each haplotype and measure its binding to the Ab to extract K_d; we also measure the melting temperature of the P-domain, T_m, which correlates inversely to ΔG_fold (supplementary table S4, Supplementary Material online; Privalov 1979). The measured values of the biophysical properties of the dominant escape haplotypes correlate strongly with the calculated values as shown in figure 3B and C. Importantly, we reverse engineer the escape viruses with their haplotype sequences on the background of the wt for the rest of the virus and confirm that the observed mutations in the P-domain are directly responsible for their increase in fitness both in vitro (fig. 4A and supplementary fig. S6A, Supplementary Material online) and in vivo in mice (fig. 4B and supplementary fig. S6B, Supplementary Material online); thus, our biophysical variables are relevant for viral fitness inside the real animal host.

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.

The biophysical fitness landscape describes the dependence of viral fitness in the presence of a neutralizing antibody on ΔG_fold and 1/(mK_d), where the parameter m accounts for the multiple binding sites of the capsid. To arrive at a biophysical description of the viral fitness, we assume that the wt P-domain occurs in three specific states: folded and unbound, folded and bound, and unfolded (which is always unbound). The virus infects only when the P-domain is folded and unbound, hence, we can express the viral infectivity F at a given concentration of antibody [Ab] as (Cheron et al. 2016):

$$F=b_0\frac{e^{-\beta \Delta G_{\text{fold}}}}{1+e^{-\beta \Delta G_{\text{fold}}}+\frac{\left[Ab\right]}{m{K}_d}{e}^{-\beta \Delta G_{\text{fold}}}}$$ (1)

where the numerator is the Boltzmann factor describing the relative probability of being folded and unbound and the denominator is the partition function that sums over the probability of all three states, and β = 1/k_BT where k_B is the Boltzmann constant and T is the temperature. The function F has two regimes as shown by the surface in figure 3D. For low binding affinities and stable P-domain structures, viruses are expected to infect host cells at some fixed probability, 0 < b₀ < 1, determined by the average effect of all remaining viral properties on the infection process, and F = b₀. By contrast, when the binding to the Ab is strong or when the P-domain is unstable, the virus cannot infect its host and F = 0.

To compare the model to experiment, we use sequencing data to determine the growth rate of all observed viral haplotypes from their change in frequency between successive generations (Acevedo et al. 2014). The growth rates distribute into two distinct groups with 87% of haplotypes exhibiting little or no growth and the rest exhibiting considerably larger growth. We take the first group to be noninfective, and take the second group to be infective (supplementary fig. S4A, Supplementary Material online). For each haplotype sequence, we map the mutations to the 3D structure of the wt P-domain (Yin et al. 2007) and use force field calculations to determine the change in folding energy ΔΔG_fold between the mutant and the wt; from this we determine stability of the mutant ΔG_fold = ΔG_fold,wt + ΔΔG_fold, where ΔG_wt is the folding energy of the wt. We also determine the change in binding energy, ΔΔG_bind, between the mutated P-domain-Ab complex and the wt; from this we determine the dissociation constant K_d = K₀e^βΔΔGbind where K₀ is the dissociation constant of the wt. We bin the haplotypes using ΔΔG_fold and K_d and calculate F for each bin from the fraction of infective haplotypes. This binning exploits the large number of unique haplotypes to reduce the effects of errors in the calculations and of contributions from other biophysical properties. We fit the model by varying the three unknown parameters, b₀, ΔG_wt and the multiplier m.

We obtain excellent agreement between the model and the data, as shown by the dashed line in figure 3E and F. The infectivity of haplotypes is zero at low K_d or high ΔG_fold, while at high K_d and low ΔG_fold, the landscape plateaus at F ∼ 0.25 independent of either of the biophysical coordinates. The value of 1/m ≈ 1.4% obtained from the fit reflects the fact that only about three of the 180 P-domains on the capsid have to be blocked by the Ab to prevent infection (fig. 3E and Fischer et al. (2015)). The value of F ∼ 0.25 at the plateau is less than the expected value of b₀ = 1; this points to the role of factors not included in the model, such as biophysical requirements for successful virus assembly or the interaction of the capsid with the host-cell receptor, in successful infection. In the absence of the neutralizing antibody, we do not expect the fitness landscape to depend on K_d, which is indeed the case (supplementary fig. S5, Supplementary Material online). Altogether, these results demonstrate that binding and folding energies are very good predictors of viral extinction; however they are less successful in predicting infectivity. This suggests that antibody escape and folding stability of the capsid protein are necessary but not sufficient for viral infection.

We note that the parameter b₀, being the height of the sigmoidal function, reflects the optimal fitness when the viral capsid is both stable (negative ΔG) and free from the antibody (high K_d). That is, b₀ is the fitness when the virus is on the plateau of the landscape. The ∼10⁴ new virions in a single burst are, however, not uniformly distributed on the binding-stability plane (supplementary fig. S4B, Supplementary Material online). In fact, most new virions fall in the unstable rather than stable regime in a ratio of approximately 100:1 (supplementary fig. S4, Supplementary Material online), which recapitulates previous estimate that of the ∼10⁴ progenies in a single cell infection, ∼100 are infectious viral particles, or plaque forming units (pfu) (Fischer et al. 2015).

Population Dynamics on the Viral Fitness Landscape

We plot the position of viral haplotypes evolving on the landscape as a function of K_dand T_m and denote their allele frequencies by the size of the circles for each passage (see fig. 5C and D and supplementary table S4, Supplementary Material online). In the five independent bulk experiments, four evolved towards the fixation of variant ABC (represented also in fig. 1A) that has T_m∼39.4°C and K_d∼ 23,300 nM and one lead to the fixation of variant E (L386F) that has T_m∼ 45.0°C and K_d∼ 1,080 nM (supplementary table S4, Supplementary Material online). These two dominant variants that fixed in independent evolutionary runs manifest as two large circles in figure 5B. Altogether, there is a clear trajectory as the intermediate variants evolve, having increasingly weaker affinities and higher T_m, with the escape variants at passage 5 ultimately having the weakest affinity, with an overall average of K_d∼3,000 nM and the highest P-domain stability with an average of T_m∼ 43.5°C, as shown in figure 5B (blue line).

We also plot the position of viral haplotypes evolving in ∼1 million independent drop passaging experiments (fig. 5C), which shows that the predominant fraction of the population is wild type. The lack of clonal sweep is due to the fact that each lineage in the droplets is confined. For more quantitative comparison, shown in figure 5E and F are the histograms of K_d and T_min passage 5 of serial passaging only in bulk and in passage 5 of serial passaging only in drops. 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. This large number of independent biological repeats achieved using the microfluidic setup provides statistical power. We estimate the likelihood of escape variants with T_m ≥39°C. This stability value is the threshold for the high fitness plateau of the landscape (fig. 5E). Specifically, to estimate the probability of observing 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 an escape variant with T_m ≥ 39°C in one experiment. Considering that the bulk escapee ABC (T_m = 39.4°C) was observed in four out of five experiments and the escapee E (T_m = 45.0°C) was observed in the remaining experiment, the overall probability of observing variants with T_m ≥ 39°C in five independent experiments is ∼2 × 10⁻¹⁸.This analysis clearly indicates that higher folding stability of bulk escapee is the result of evolutionary selection rather than a random occurrence.

Balance between Selection and Random Drift on the Viral Fitness Landscape: Theory and Simulation

In general, the trajectories on the fitness landscape depend on the strength and direction of two evolutionary forces, drift, and selection. To quantify the balance of these forces on the landscape, we use population genetics theory and calculate the ratio dN/dS, where dN is the rate of nonsynonymous evolutionary rate and dS is the synonymous evolutionary rate (Yang and Nielsen 2002) (For greater details, see section on Balance between selection and mutational drift on the fitness landscape in the Materials and Methods). Assuming that synonymous mutations are neutral, dN/dS = 1 implies that nonsynonymous mutations are also neutral because they are fixed at the same rate as synonymous mutations. Deviation from this expectation implies selection. Specifically, dN/dS > 1, implies positive selection for nonsynonymous mutations, while dN/dS < 1 implies purifying selection.

We first limit ourselves to the simple case where a single mutation occurs on a monoclonal population, where the chance that the mutant eventually dominates is determined by its probability of fixation. To that end, we compare the probability of fixation of a nonsynonymous mutation that changes folding stability and binding with the probability of fixation of a synonymous mutation, which we assume is neutral. We denote this ratio as ω. The underlying motivation for this ratio is that when ω = 1, mutations are neutral at the level of fitness, and random drift dominates. Specifically, (Nielsen and Yang 2003)

$$\omega =\frac{dN}{dS}=N_e{P}_{\text{fix}}\left(s,N_e\right)=N_e\left[\frac{1-e^{-2s}}{1-e^{-2N_{e}s}}\right]$$ (2)

Where $P_{\text{fix}}\left(s,N_e\right)$ is the probability of fixation (Kimura 1968) and N_e is the effective population size and s is the selection coefficient. The selection coefficient defines the fitness advantage of an arising mutation relative to wildtype, $s=\left(F_{\text{mut}}-F_{wt}\right)/F_{wt}$. Because we have a quantitative description of the fitness landscape (eq. 1), when a random mutation arises that changes the folding stability, ΔG_fold = ΔG_fold,wt+ ΔΔG_fold, and the binding affinity K_d = K₀e^βΔΔGbind, the selection coefficient can be calculated explicitly (Methods for details):

$$s\approx \beta \Delta \Delta G_{\text{bind}}\left(\frac{\left[Ab\right]}{m{K}_{d,\text{wt}}}\right)-\beta \Delta \Delta G_{\text{fold}}\left(e^{-\beta \Delta G_{\text{fold},\text{wt}}}\right)$$ (3)

The fitness (dis)advantage s is a function of the wildtype folding stability $\Delta G_{wt}$ and binding affinity K₀ and the changes induced by the mutation to folding stability and binding ΔΔG_bind and ΔΔG_fold. This also implies that the dN/dS ratio is a function of the biophysical properties of the wildtype ($\Delta G_{wt}$ and binding affinity K₀), the changes induced by the mutation on folding and binding (ΔΔG_fold and ΔΔG_bind, respectively), and effective population size.

The effect of random mutations on folding stability, denoted by the normalized probability density distribution P(ΔΔG_fold), and on binding affinity, denoted by the normalized probability density distribution P(ΔΔG_bind), are both well-characterized (Tokuriki et al. 2007; Zeldovich et al. 2007; Moal and Fernandez-Recio 2012). Thus, we can derive the rate of protein evolution averaged over all possible effect of random mutations on folding and binding, that is,

$$\overline{\omega }\left(\Delta G_{\text{fold}};K_{d,\text{wt}};N_e\right)=\int \int \omega P\left(\Delta \Delta G_{\text{fold}}\right)P\left(\Delta \Delta G_{\text{bind}}\right)d\left(\Delta \Delta G_{\text{fold}}\right)d\left(\Delta \Delta G_{\text{bind}}\right)$$ (4)

Equation (4) defines the average stringency of selection as a function of background, and hence the strength of epistatic interaction on the fitness landscape defined by protein folding and binding. We show in figure 5A (color map) the value of the integral over the range of K_d,wt and ΔG_fold,wt values.

Indeed, positive selection is strongest when the wt P-domain is unstable (low ΔG) or tightly bound to the antibody. At large population sizes, purifying selection and positive selection dominates in the regime of low folding stability and tight binding affinity (red colors in fig. 5A). The prediction is that if the population starts in the unstable regime, it would migrate away from the regime where selection is strong and towards the regime where it is more neutral. In large population sizes, dN/dS exhibits a strong gradient towards high K_d and high folding stability (fig. 5A). Consequently, a wt population that is initially unstable and neutralized by Ab is expected to evolve resistance by increasing both K_d and stability. However, in small population sizes the gradient of dN/dS is directed only towards high K_d and the same initially unstable population will evolve resistance to Ab without increasing folding stability (fig. 5B).

The effect of population size on the course of evolution can be explained by analyzing the balance between selection and mutational drift, the two forces driving evolution. The direction of drift and selection along the trait of folding stability and binding affinity to the antibody can be inferred from protein engineering and systematic studies on effects of random mutations on proteins. Along the axis of folding stability ΔG_fold, beneficial mutations increase folding stability, but random de novo mutations in proteins tend to decrease stability(Kumar et al. 2006; Tokuriki et al. 2007; Zeldovich et al. 2007; Moal and Fernandez-Recio 2012). Thus, selection and drift act in opposite directions (fig. 5A and B, arrows), leading to mutation-selection balance. Along the axis of binding affinity K_d, beneficial mutations for the virus lead to escape from Ab (towards high K_d), and random mutations on protein interfaces perturb binding (also towards high K_d). Thus, selection and drift act along the same direction (fig. 5A and B, arrows). We note that in general, and at the level of sequence space, the random genetic drift is indeed nondirectional by definition. However, at the level of biophysical properties of proteins, there is directionality. Random mutations are predominantly destabilizing, thus drift points towards lower stability (fig. 5A and B). Random mutations are also predominantly perturbing the interfaces of PPI, thus drift points towards lower affinity (higher K_d).

For tractabilty, the theoretical analysis is done in the monoclonal regime, which holds only in the limit of weak mutation and strong selection(Kryazhimskiy and Plotkin 2008), where mutations arise rarely and fix rapidly. This is not strictly applicable for an RNA virus like norovirus, which is polyclonal. Thus, to complement our theoretical analyses, we also simulate using a polyclonal viral population the trajectory for four sequential fixations of a single mutation starting from the position of the wt virus population on the viral fitness landscape (supplementary fig. S7, Supplementary Material online; see also Cheron et al. 2016 for details). For large N, the simulations show that the norovirus population increases both its folding stability and dissociation constant, K_d, as it escapes the neutralizing antibody, following the trajectory shown by the solid points in figure 5A and B (see also supplementary fig. S7, Supplementary Material online for simulations in the polyclonal regime). After four sequential single mutations the model shows a rise of five orders of magnitude in K_d and an increase of 3 kcal/mol in ΔG_fold towards stabilization corresponding to a change of 9°C in T_m. On the other hand, for small N the simulations show that the norovirus population increases its K_d to escape the antibody but exhibits only a small change in folding stability of <1 kcal/mol, corresponding to an increase in T_mof about 2°C, as shown by the trajectory in figure 5B (see also fig. 5A).

Most Likely Pathways on the Viral Fitness Landscape Agree with Predictions by Protein Biophysics and Population Genetics

We compare the theoretical prediction to the direction of evolution on the landscape in a bulk passaging that lead to ABC (fig. 5C). Indeed, the increase in K_d of the escapee in bulk ABC is accompanied by an increase in folding stability T_m = 39.4°C (fig. 5C, passage 5, red circle). The other bulk escapee E has an even more dramatic increase in folding stability T_m = 45.0°C (shown in fig. 5C, passage 5, blue circle). 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 (fig. 5E). This result is supported by the head-to-head competition assays between WT and these variants in the presence and absence of antibody (fig. 2). Additionally, while the T_m values of the two bulk escapees ABC and E are different, they have comparable fitness because of the “plateau”-like or sigmoidal shape of the landscape.

In contrast, the viral mutants that propagate in drops increase in K_d while maintaining original T_m. In passage 5 of the droplet experiment (fig. 5D), excluding the dominant wt, the other segregating variants have an average of K_d∼ 1,000 nM and T_m ∼ 38.3°C.

Strong Epistasis and Compensation among Mutations That Eventually Lead to Viral Escape

There is epistasis on the fitness landscape as shown from the nonadditive effect of the single mutations compared with the double- or triple-mutants. For example, the double mutants AC, BC, and AB have less than additive K_d showing negative epistasis (supplementary table S4, Supplementary Material online). This also holds for the folding stability. Based on simple biophysics, we can develop expectations on the (non)additive effect of mutations on K_d. The binding constant K_d∼ exp(βΔΔG_binding), hence if two mutations A and B are noninteracting in the 3D structure (that is, nonepistatic), we can assume that they will have additive effect in the free energy of binding. Hence, for the ratio of the binding affinity of the double mutant to the binding affinity of the wildtype, K_{d, AB}/K_{d, wt} = exp(βΔΔG_{binding, mutantA} + βΔΔG_{binding, mutantB}) =(K_{d, A}/K_{d, wt})(K_{d, B}/K_{d, wt}). Thus, under no epistasis, the increase in K_d of a double mutant is equal to the product of the increases on K_d of single mutants. The mathematical analog in evolutionary biology is the relationship Wright–Fisher fitness w and the Malthusian fitness b, which is w ∼ exp(b). The absence of epistasis implied additive Malthusian fitness of multiplicative Wright–Fisher fitness. Indeed, the double- and triple-mutants have less than additive effect on K_d, which implies strong epistatic interactions among them (supplementary table S4, Supplementary Material online). These epistatic interactions have a structural basis because they are all found at the interface of the viral capsid-domain and the Fab domain of the neutralizing antibody. Notwithstanding the epistatic interactions among the mutations, in bulk, all single and double-mutants of the eventual escapee have all higher T_m and K_d compared with wildtype (fig. 5).

Discussion

A key requirement in determining, and perhaps in our future ability in predicting, the evolutionary dynamics of viral and microbial pathogens is a quantitative description of their fitness landscape. This landscape, which is a mapping of the full genotype–phenotype relationship, is complex. However, recent works have shown that in some biological and already very clinically relevant systems, such as evolution of bacterial resistance against antimicrobials (Rodrigues et al. 2016) and evolution of viral resistance against antiviral treatments (Gong et al. 2013; Cheron et al. 2016), the fitness landscape may be quantitatively and systematically defined. Here, we have shown that the fitness landscape of a norovirus evolving against a neutralizing antibody is systematically described by the biophysical properties of its capsid domain, in particular, folding stability and binding affinity to the neutralizing antibody. These biophysical parameters are relevant to other viruses; for example, both binding (Fonville et al. 2014) and folding stability (Gong et al. 2013) are relevant traits for the evolution of an influenza virus in the presence of a neutralizing antibody. Moreover, in this work, the dependence of fitness (viral infectivity) on these two traits is quantitatively predicted by theory based on the thermodynamics of protein folding and binding.

The geometry of the fitness landscape is strongly affected by population size (fig. 1). In general, competition for limited resources (media or mammalian cells to infect) is function to the number of individuals; hence the strength of purifying selection and adaptive evolution is also proportional to population size. Specifically, we find that the fitness landscape is flatter when the viral population is evolved in deep-bottlenecked population size of ∼100 virions in microfluidics. The flat landscape did not result in clonal sweeps. In contrast, standard bulk cultures where there were ∼10⁸ virions competing and the landscape is not flat, we observed multiple clonal sweep events. The escape variants showed the coupling between folding stability and binding—an increase in K_d to escape the neutralizing antibody is accompanied by an increase in folding stability. This coupling is not manifested in the flat landscape under low population size, as predicted by our simple biophysical model.

Projection of the fitness landscape on well-defined biophysical properties also enabled the quantification of the evolutionary forces on the landscape. As found by several groups, including ours (Bloom et al. 2005; Zeldovich et al. 2007; Bloom et al. 2007; Serohijos and Shakhnovich 2014), the evolution of the folding stability as an evolutionary trait is determined by the balance between selection for greater stability and mutational drift, which is predominantly destabilizing among random mutations (fig. 5). This balance is tunable by population size because the magnitude of selection itself varies with population size (Wylie and Shakhnovich 2011; Serohijos et al. 2013). The biophysical fitness landscape also allowed for the quantification of the evolutionary forces along the trait of binding affinity to the antibody. Unlike folding stability, the direction of selection (beneficial mutations) is in the same direction as random mutational drift (fig. 5)—the supply of random mutations is predominantly biased towards perturbing the interface between the capsid and the antibody, and these same mutations are the most beneficial to viral escape. Thus, contrary to the classic notion that for a given trait, beneficial mutations are rare and evolution is the process of selection for these rare beneficial mutations, along the trait of binding affinity, beneficial mutations are in abundant supply. In essence, the evolutionary goal of the virus to escape against a neutralizing antibody is the opposite to the goals of enzyme design, which is to promote, instead of perturb, protein–protein interaction. To the best of our knowledge, this is the first definitive example in evolutionary biology, where selection and drift are in the same direction. However, we hypothesize that this may be ubiquitous and may also be found in evolution of antimicrobial resistance, where bacteria also want to escape an inhibitor. We note however, that in our experiments antibody itself did not evolve. The evolutionary force opposing pathogen escape—evolution of antibodies toward higher affinity to the antigen follow a more traditional intuitive scenario when selection and drift act in different directions (Zhang and Shakhnovich 2010).

Although binding affinity and folding stability of the MNV-1 capsid protein quantitatively map to infectivity, these two biophysical traits account for only ∼30% of infectivity (fig. 3). What might be the next most relevant axes of the viral fitness landscape? Protein dynamics and conformational flexibility is a strong candidate. For example, in MNV-1, it has been shown from structural studies of viral isolates that loop regions of their capsid sample multiple conformations, only some of which could bind to neutralizing antibodies (Kolawole et al. 2014).

We also found that the escape variant resistant to the neutralizing antibody is less fit in the absence of the antibody (fig. 2). This suggests that there is a fitness cost to the evolution of resistance against the neutralizing antibody. The increase in frequency of intermediate escapees B and AC relative to the final escapee ABC in the absence of antibody (fig. 2, Passage 3, -Ab) suggest that ABC might have higher fitness cost than either B or AC. More broadly, fitness cost is well documented in the evolution of resistance against antibiotics(Andersson and Hughes 2010; Sousa et al. 2012; Rodrigues et al. 2016). Although most resistant strains have a selective advantage in the presence of the antibiotic, they are often less fit in the absence of the drug. There is fitness cost associated with antimicrobial resistance because antibiotics target essential functions in the cell. Indeed, such is the case in our system—the neutralizing antibody targets the MNV-1 capsid’s P-domain which is crucial for viral entry into the host cell (Wobus et al. 2006).

Beyond the biophysical properties of the capsid proteins, viral fitness is also a function of replicative capacity inside the infected mammalian cell, the immune response of the host, and the fluctuations in effective concentration of neutralizing antibody. Altogether, combining our biophysical description of viral fitness landscape, together with these other factors, could lead to an integrative model of viral evolution.

Materials and Methods

The materials and methods are described in detail within supplementary Materials and Methods, Supplementary Material online. Briefly, to perform the lab evolution, we propagated a viral isolate (MNV-1) in the presence of a neutralizing antibody (mAb6.2; Kolawole et al. 2014) that binds to the protruding domain (P-domain) of the capsid, and prevents virus entry into the host cell (Katpally et al. 2008; Taube et al. 2010). And then, we deep sequenced using Illumina Miseq the 376 bp fragment of the genome encoding the outermost part of the P-domain (residues 281–412 of the VP1). We estimated the fitness (P_infect) of each haplotype based on its frequency throughout the passaging. We also estimated how the mutations in the haplotype change the folding stability of the P-domain of capsid and its binding affinity to the neutralizing antibody. These computational estimations of the biophysical properties were performed using the crystal structure of the proteins and a physical force field. We also purified the dominant clones, and then assayed their folding stability using thermal unfolding and binding affinity using surface plasmon resonance (SPR). The construction of the microfluidics devices for the serial passaging of the viruses in picoliter emulsions is described in the supplementary Materials and Methods, Supplementary Material online.