Limits to detecting epistasis in the fitness landscape of HIV

Avik Biswas; Allan Haldane; Ronald M Levy

doi:10.1371/journal.pone.0262314

. 2022 Jan 18;17(1):e0262314. doi: 10.1371/journal.pone.0262314

Limits to detecting epistasis in the fitness landscape of HIV

Avik Biswas ^1,², Allan Haldane ^1,², Ronald M Levy ^1,^2,^3,^*

Editor: Emilio Gallicchio⁴

PMCID: PMC8765623 PMID: 35041711

Abstract

The rapid evolution of HIV is constrained by interactions between mutations which affect viral fitness. In this work, we explore the role of epistasis in determining the mutational fitness landscape of HIV for multiple drug target proteins, including Protease, Reverse Transcriptase, and Integrase. Epistatic interactions between residues modulate the mutation patterns involved in drug resistance, with unambiguous signatures of epistasis best seen in the comparison of the Potts model predicted and experimental HIV sequence “prevalences” expressed as higher-order marginals (beyond triplets) of the sequence probability distribution. In contrast, experimental measures of fitness such as viral replicative capacities generally probe fitness effects of point mutations in a single background, providing weak evidence for epistasis in viral systems. The detectable effects of epistasis are obscured by higher evolutionary conservation at sites. While double mutant cycles in principle, provide one of the best ways to probe epistatic interactions experimentally without reference to a particular background, we show that the analysis is complicated by the small dynamic range of measurements. Overall, we show that global pairwise interaction Potts models are necessary for predicting the mutational landscape of viral proteins.

Introduction

A major challenge in biological research, clinical medicine, and biotechnology is how to decipher and exploit the effects of mutations [1]. In efforts ranging from the identification of genetic variations underlying disease-causing mutations, to the understanding of the genotype-phenotype mapping, to development of modified proteins with useful properties, there is a need to rapidly assess the functional effects of mutations. Experimental techniques to assess the effect of multiple mutations on phenotype have been effective [2–5], but functional assays to test all possible combinations are not possible due to the vast size of the mutational landscape. Recent advances in biotechnology have enabled deep mutational scans [6] and multiplexed assays [7] for a more complete description of the mutational landscapes of a few proteins, but remain resource intensive and limited in scalability. The measured phenotypes depend on the type of experiment and are susceptible to changes in experimental conditions making the comparison between measurements difficult [8]. These methodologies are also utilized under externally applied conditions, but how in vitro selection pressures can be extended to the interpretation of pressures in vivo is not always clear [9].

Potts sequence covariation models have been developed for the identification of spatial contacts in proteins from sequence data [10–19] by exploiting the wealth of information available in protein sequences observed in nature, and have also been successfully used to infer the fitness landscape and study mutational outcomes in a wide variety of protein families in viruses to humans [1, 20–29]. The Potts model is a generative, global pairwise interaction model that induces correlations between residues to all orders, such as triplet and quadruplet correlations. Given a multiple sequence alignment (MSA) of related protein sequences, the Potts probabilistic model of the network of interacting protein residues can be inferred from the pair correlations encoded in the MSA, and can be used to assign scores to individual protein sequences. The extent to which sequence scores correlate with experimental measures of fitness can then be analyzed. The context dependence of a mutation, termed “epistasis”, determines the favorability/disfavorability of the mutation in a given genomic sequence background, and the Potts model predictions can be used to predict the likelihoods of mutations in a variety of sequence backgrounds.

The HIV pandemic is the result of a large, genetically diverse, and dynamic viral population characterized by a highly mutable genome that renders efforts to design a universal vaccine a significant challenge [30] and drives the emergence of drug-resistant variants upon antiretroviral (ARV) therapy. Gaining a comprehensive understanding of the mutational tolerance, and the role of epistatic interactions in the fitness landscape of HIV is important for the identification and understanding of mutational routes of pathogen escape and resistance.

In this work, we explore the limits to detecting epistasis and the role of epistatic interactions between sites in modulating the fitness landscape of HIV with many mutations, focusing on the drug target proteins, protease (PR), reverse transcriptase (RT), and integrase (IN), as well as the emerging target protein of capsid (CA). We first show that the evidence for long-range epistasis is strong (in HIV) based on the analysis of the high-order marginals of the MSA distribution (up to subsequences of length 14). The observed effects of epistasis in determining the higher-order mutational patterns, however, differs significantly between drug-resistance-associated residues, and non-drug-resistance-associated sites due to the higher “evolutionary conservation” at sites not associated with drug resistance. In contrast to the effects of epistasis on higher-order marginals, we find, in accordance with the current literature [31], that the evidence for epistasis from experimental measures of HIV fitness, such as viral replicative capacities, is weak; as both a correlated Potts and a site-independent model (devoid of interactions between sites) can capture replicative capacities almost equally well. This is primarily because experimental fitness measurements are generally carried out for single-point (or few-point) mutations in specific laboratory molecular clones, that are close in sequence to the consensus sequence. Instead, in the comparison of higher-order marginals, unambiguous signatures of epistasis are observed. Although double mutant cycle experiments in principle provide the classic, biophysical way to examine epistasis, we demonstrate with numerical examples that accurate predictions of double mutant cycles are difficult due to the small dynamic range of the measurements making them much more susceptible to noise. While fitness measures such as thermostability, activity, or binding energetics, etc. of a protein generally do not all contribute to fitness in the same way, we further find that the Potts model provides a more general representation of the protein fitness landscape capturing contributions from different features of the landscape, replicative capacities and folding energetics, that are not fully captured by either measurement on their own.

Results and discussion

Protein sequence covariation models have been extensively used to study networks of interacting residues for inference of protein structure and function. The Potts model is a maximum-entropy model based on the observed mutational correlations in a multiple sequence alignment (MSA) and constrained to accurately capture the bivariate (pairwise) residue frequencies in the MSA. A central quantity known as the “statistical” energy of a sequence E(S) (Eq 2, Methods) is commonly interpreted to be proportional to fitness; the model predicts that sequences will appear in the dataset with probability P(S) ∝ e^−E(S), such that sequences with favorable statistical energies are more prevalent in the MSA. P(S) describes the “prevalence” landscape of a protein and the marginals of P(S) can be compared with observed frequencies in a multiple sequence alignment. Previous studies have indicated that the Potts model is an accurate predictor of “prevalence” in HIV proteins [20, 21, 23, 32–36]; “prevalence” is often used as a proxy for “fitness” with covariation models serving as a natural extension for measures of “fitness” based on experiments and model predictions have been compared to different experimental measures of “fitness” with varying degrees of success [1, 21, 23, 28, 32, 34, 36]. Site-independent models, devoid of interactions between sites have also been reported to capture experimentally measured fitness well, in particular for viral proteins [1, 31] with studies (on HIV Nef and protease) implying that the dominant contribution to the Potts model predicted sequence statistical energy comes from site-wise “field” parameters h_i (see Methods) in the model [28, 36]. In this study, we show that interaction between sites is necessary to capture the higher order (beyond pairwise) mutational landscape of HIV proteins for functionally relevant sites, such as those involved in engendering drug resistance, and cannot be predicted by a site-independent model. The correspondence between model predictions of fitness based on “prevalences” in natural sequences with experimentally measured “fitness” is however, confounded by a number of different factors. Here, we explore comparisons between model predictions and “fitness” experiments (Fig 1) focusing primarily on three HIV enzymes: Protease (PR), Reverse Transcriptase (RT), and Integrase (IN) that have been targets of antiretroviral therapy (ART) over the past several decades, as well as viral Capsid (CA), which is fast emerging as a promising new target for drug therapy.

Fig 1 — The correspondence between either covariation models, or “prevalences” in multiple sequence alignments, with other experimental measures of “fitness” is less clear and often inconsistent between different statistics and measures of fitness.

“Prevalence” landscape of HIV proteins and the role of correlations between residues

An important statistic of the multiple sequence alignment is the sequence diversity and the level of conservation in the protein or protein family which is represented in the distribution of the number of mutations in the constituent sequences. Fig 2 shows the distribution of the number of mutations (hamming distances) from the HIV-1 subtype B wild-type consensus sequence in MSAs containing drug-experienced HIV-1 sequences, and distributions predicted by the Potts and independent models. The Potts model predicts a distribution of mutations that closely represents the dataset distribution, whereas the independent model predicts a distribution that differs especially near the the ends of the distribution where the number of mutations is either very low or very high. This provides support for the importance of epistasis in these datasets. However, in Fig 9 of S1 File we also show that for some datasets the difference between the Potts and Independent distributions is small, and so may be a less reliable test of the importance of epistasis. The importance of pairwise interactions is also apparent through the fact that the Potts model also accurately predicts the likelihoods and “entrenchment” of mutations based on the sequence background, as has been verified using aggregate sequence statistics from the MSA [35].

Fig 2 — Probabilities of observing sequences with any k number of mutations relative to the HIV-1 subtype B wild-type consensus sequence as observed in original MSA (black) and predicted by the Potts (blue) and independent (gray) models are shown for HIV-1 protease (PR) in (A), and reverse transcriptase (RT) in (B), respectively. The independent model predicted distribution does not accurately capture the distribution of hamming distances in the dataset MSA, especially near the ends of the distribution with either very low or very high number of mutations, where the epistatic effects can be more significant.

But the most direct and strongest evidence of the ability of the Potts model to capture epistatic interactions is seen in its ability to reproduce the higher-order marginals of the MSA, upto order 14 in Fig 3, much beyond the pairwise marginals which the model is parameterized to capture. While the prevalence of sequence marginals (subsequence frequencies) can be compared directly with Potts model predictions, this is not possible for predictions for complete sequence probabilities because most sequences in an unbiased MSA are observed only once due to the minuscule sample size in comparison to the vast size of sequence space. Only sequence marginals up to sizes ∼14 residues, depending upon protein family, are observed with sufficient frequencies such that their marginal counts are a good proxy for the marginal probabilities predicted by the Potts model. Fig 3 shows the rank-correlation between model predicted marginal probabilities and marginal frequencies in the MSA for subsequences of lengths 2–14, with a subsequence being the concatenation of amino acid characters from an often nonconsecutive subset of residue positions. With further increase in the subsequence length, data limitations due to finite sampling become more prominent and the observed and model predicted marginals become dominated by noise. The Potts model’s ability to predict higher-order marginals, much beyond the pairwise, for drug-resistance associated sites, while the independent model cannot, provides the most direct evidence of the ability of the Potts model to accurately capture the long-range epistatic interactions that modulate the “prevalence” of amino acid residues at connected sites in the protein. The Potts model is able to accurately predict the higher-order marginal frequencies (which have not been directly fit) at drug-associated sites with a Spearman ρ² ≈ 0.95 for the longest subsequence (of length 14) in PR, whereas, the correlation for the independent model deteriorates sharply with subsequence length (Fig 3A, 3C and 3E) with a Spearman ρ² ≈ 0.34 for the longest subsequence in PR.

The strongly interacting nature of the sites in HIV that are involved in engendering drug resistance, is also evident from Fig 3A, 3C and 3E, where the role of epistatic interactions between residues is more pronounced and the site-independent model is not able to capture the higher-order marginals. In contrast, for residue positions that are not associated with drug resistance, the site-independent model can sufficiently recover the higher order marginals in the MSA. Sites in the protein associated with drug resistance, also however, exhibit considerably more variability contributing to their higher site-entropies (Fig 2A of S1 File). The lack of variability at sites can obscure the effect of correlations. To test for this, we selected protease-inhibitor associated and non-associated sites with site-entropy distributions similar to that of the drug-resistance associated sites (Fig 2B of S1 File) and compared their higher order marginals as predicted by the Potts and site-independent models (Fig 2C and 2D of S1 File, respectively). When marginals are chosen from non-drug associated positions with site entropies more similar to those of the drug-associated positions, the role of correlations is more apparent. This is suggestive of strong couplings between sites that are likely to co-mutate, allow for mutations at lesser costs to fitness than the individual mutations alone, resulting in mutational pathways selected for pathogen escape. Such sets of sites are more likely to be associated with resistance, as resistance cannot be achieved through selectively neutral mutations at single sites, in which case drug treatment would likely be ineffective [37].

In contrast to Fig 3A for HIV PR, Fig 3E shows the somewhat improved predictive capacity of a site-independent model in capturing the higher order sequence statistics for drug-resistance associated positions in HIV IN. This is indicative that correlations between drug-resistance-associated sites appear to play a stronger role in protease than in IN. This is also in line with the fact that the IN enzyme is more conserved than PR (Fig 1 of S1 File). Amongst the three drug-target proteins, PR, RT, and IN, the degree of “evolutionary conservation” is considerably higher in IN than in the others. The lack of variability at sites or considerably smaller site-entropies in IN plays a role in obscuring the effect of correlations, as discussed. Furthermore, the MSA depth for IN is also considerably lower than in PR or RT, which adversely affects the quality of the Potts model fit, further making the correlated model less distinguishable from a site-independent one [38].

The majority of the literature on HIV discusses drug resistance in relation to correlated mutations limited to primary/accessory pairs. Fig 3 depicts the effect of correlated mutations on the “prevalence” landscape of HIV well beyond pairwise interactions, upto the 14^th order, that is captured accurately by the Potts model. This illustrates the existence of correlated networks of long-range interactions between sites in HIV, which play an important role in determining its evolutionary fitness landscape. The entrenchment of primary resistance mutations in HIV was shown to be contingent on the presence of specific patterns of background mutations beyond the well studied primary/accessory compensatory pairs, and could not be predicted on the basis of the number of background mutations alone [35], also indicating that long-range correlations involving many sites can potentially shape the evolutionary trajectory of the virus.

From sequence covariation to “fitness”

The Potts model predicted statistical energies E(S) have been established to be a good indicator of the likelihoods (P(S) ∝ e^−E(S)) or “prevalence” of natural sequences in multiple sequence alignments; prevalence has often been characterized as a proxy for fitness with sequences more prevalent in the MSA likely to have a fitness advantage over others. But depending on context, the notion of fitness can entail a variety of experimental measures from replicative capacity (RC), to protein stability, catalytic efficiency, molecular recognition, drug-resistance values, etc., each of which may capture different features of the fitness landscape, and can have varying degrees of correspondence to observed likelihoods in MSAs of natural sequences. In this section, we explore the correspondence between measures of fitness based on experimental replicative capacities of HIV mutants and the Potts model predicted likelihoods in an MSA. The correspondence is confounded by a number of factors such as the reproducibility of experiments, the quality of inferred Potts models, the degree of evolutionary conservation in the proteins amongst others.

Fig 4 shows the correlation between model predicted likelihoods of HIV mutant proteins and measures of fitness based on/related to replicative capacities for four HIV proteins, PR, RT, IN, and p24 CA. The independent model generally performs on par or marginally worse than the Potts model in capturing experimental replicative capacity measurements. Although the difference is somewhat larger for measurements focusing on only drug-resistance-associated mutations indicated with “D” in Fig 4 rather than random mutations or mutations at non-resistance-associated positions indicated with “R”, along the lines of Fig 3 for marginal statistics, the difference is not as clear as for marginal statistics. It has been suggested that the independent model performs on par with correlated Potts or advanced machine learning models in capturing experimental fitness measurements for viral proteins, possibly as a consequence of limited diversity of the sequence alignments or, due to a discrepancy between the proxy for viral fitness in the laboratory and the in vivo fitness of the virus [1, 9]. Overall, we find that the evidence for epistasis from measures of fitness based on experimental replicative capacities is much weaker compared to that available from the higher-order marginal statistics.

The Potts model is affected by the degree of conservation in the respective proteins which can, not only affect the quality of the model as reflected in the signal-to-noise ratio or SNR (see Methods), but also obscure the effect of correlations between sites. To check how the Potts model predictions may be affected by the quality and sample sizes of the underlying multiple sequence alignments, we look at the effect of using Potts models built on MSAs that all have the same depth but contain different sequences (randomly subsampled from a larger dataset) on the correspondence between experimental and model predictions of fitness (Fig 5). The correlation also decreases slightly because MSAs of depth half that of the original (reference Potts) are used for mutational fitness predictions. Overall, this gives an estimate that the statistical error associated with Potts model predictions of fitness is low. The correspondence between the predicted fitness based on Potts prevalence and on experiment also depends in part on which experimental assays are chosen as a proxy for fitness and the extent to which they can capture phenotypes that are under direct, long-term selection [42], as illustrated in Figs 3 and 4 of S1 File. Fig 3 of S1 File shows little correlation between two closely related experimental measures of fitness for HIV PR; one based on replicative capacity [5] and the other based on selection coefficients [40]. Interestingly, the Potts model predictions correlate well with one of the datasets. More careful analysis is needed to improve our understanding of which experimental measures contribute most to the “prevalence” landscape captured by Potts models.

Figure shows replicative capacity based experimental fitness measurements (from [21]) compared to Potts model predicted likelihoods of mutations in HIV-1 CA. The Potts model predicted values shown in “blue circles” correspond to the mean of 3 predictions based on jackknife tests with error bars indicating the standard deviations. Random values are then picked from within each standard deviation to represent each Potts model prediction (shown as “orange triangles”) and the corresponding effect on the correlation coefficient is observed. Spearman rank-order correlation ρ = 0.8 for mean of 3 predictions, and ρ = 0.78 for random selection of data from within the margin of error. For jackknife tests, three sets of ≈1024 weighted patient sequences are subsampled at random from the original MSA of ≈2200 weighted sequences, and new Potts models are then inferred based on each set. For comparison, the Spearman rank-order correlation is ρ = 0.85 for the original Potts model (based on an MSA of 2200 sequences) predictions compared to experimental values (Fig 5A of S1 File). Figure shows an estimate of the error associated with Potts model predictions of likelihoods of mutants stemming from sampling of sequences in the MSA and its effect on the correspondence with experimental measures of fitness.

Effect of epistasis on measurements of fitness and double mutant cycles in HIV

Double mutant cycles provide a biophysical means to interrogate epistatis without reference to a specific sequence background [43]. For a pair of mutations α, β at positions i, j in the protein respectively, the strength of epistatic interactions can be quantified using the difference between the sum of the independent mutational effects, $Δ E_{α}^{i} + Δ E_{β}^{j}$ , and the effect of the corresponding double mutation, $Δ E_{α β}^{i j}$ .

\begin{matrix} Δ Δ E_{α β}^{i j} = Δ E_{α β}^{i j} - (Δ E_{α}^{i} + Δ E_{β}^{j}) \end{matrix}

(1)

If ΔΔE ≠ 0, then the two mutations are epistatically coupled, whereas if ΔΔE = 0, then the mutations are mutually independent. As fitness is inversely proportional to the Potts energy, ΔΔE > 0 implies that the mutations are beneficial/co-operative to each other and vice versa. The dynamic range of double mutant cycles is an order-of-magnitude smaller than the predictions/measurements of likelihoods/fitness effects of mutations (ΔEs), shown in Fig 6A. Double mutant cycle measurements/predictions (ΔΔEs) are therefore, much more susceptible to noise, and strongly affected by both the quality of the experimental measurements, as well as finite sampling errors that affect the Potts model fit, making accurate numerical predictions very difficult. The MSA depth also plays a role in degrading the quality of the Potts model double mutant cycle predictions, ΔΔEs much faster than the fitness effect of point mutations, ΔEs (Fig 6 of S1 File). The sensitivity and possible interpretation of experimental measurements for very detrimental mutational changes is crucial for accurate prediction of double mutant cycles. When experimental replicative capacities for example, of a single and a double mutant(s) are both zero (the virus is dead), there is no comparative experimental data to inform if and which mutation(s) are more deleterious. In contrast, the calculated likelihoods from the Potts model are quantifiable for both.

Fig 6 — (A) The dynamic range of the measurements (experimental) or predictions (model) of the epistatic effects through the use of double mutant cycles is an order of magnitude smaller than the range of measurements/predictions of the fitness/likelihoods of point mutations. This makes predictions for double mutant cycles more susceptible to noise. (B) Simulation of the expected correlation of the Potts model prediction to experimental values for ΔE and ΔΔE as a function of simulated experimental noise η, showing that the the correlation for ΔΔE drops much more quickly. The dotted section of the curves show where the p-value for the ΔΔE correlation is >0.05, or insignificant, showing that noise can make it impossible to verify ΔΔE values even when ΔE values are well predicted. The level of noise corresponding to ΔE correlation of ρ ≈ 0.8, as in Fig 4 column 6 for Capsid, is shown in dashed black.

The correspondence between the ΔΔE values predicted by the Potts model and the equivalent experimental values would provide a strong confirmation of epistasis that can be directly experimentally measured; but in practice, such a comparison is often statistically not possible due to experimental and statistical uncertainties(s). In Fig 6B, we illustrate how error in individual fitness measurements can cause the double mutant cycle predictions to be unverifiable even when there exists good correspondence between Potts model and experimental fitness predictions. In this simulated test, the Potts model ΔE predictions for capsid (for mutation datapoints shown in Fig 4 (column 6) are rescaled to have the same range and scale as experimental replicative capacity values, and are used as simulated replicative capacity values. Varying amounts of random noise representing experimental error(s) and modelled as Gaussian white noise with mean 0 and standard deviation η are added to each ΔE value, which are then interpreted as simulated experimental RC values. The simulated RC values are taken to be the “ground truth” which are used to evaluate double mutant cycles, to compare to the Potts predictions. The Spearman rank-order correlation coefficients between the Potts model predicted and simulated experimental RC values, as well as double mutant cycle values, are then computed for the mutation residue-identities as available in our experimental dataset, and the process is repeated for varying degrees of noise strength (specified by varying η), representing varying degrees of experimental uncertainty. The correlation between model predicted and simulated experimental RC values are shown in Fig 6B. We see that even when the ΔE correlation with the simulated RC is as high as ∼0.8 (as is observed for capsid), the corresponding ΔΔE correlation with differences in Replicative Capacity between double mutants and the corresponding sum of single mutants is very low, ∼0.1 and is typically not statistically significant. For a correlation between model and experimental RC values ∼0.6 as observed for HIV protease (Fig 4 column 3), the same result is obtained, namely double mutant cycle analysis can not be used to verify epistatic interactions for HIV protease (Fig 7A of S1 File). Indeed, the correlation with double mutant cycles computed from the experimental values in Fig 4 is very low and statistically insignificant (Fig 7B of S1 File) in agreement with this test. Nevertheless, many of the strongest predicted (by the Potts model) double mutant cycles in HIV proteins, indeed qualitatively agree with the effects studied in the literature, especially amongst those involving compensatory pairs of drug-resistance mutations in HIV drug-target proteins (S2A and S2B Fig, S2A and S2B of S2 File).

Contribution of the changes in structural stability due to a mutation to the predicted likelihoods of mutant sequences

In this section, we explore the contribution from changes in structural stability due to a mutation to its Potts model predicted likelihood(s). To explore the impact of a mutation on structural stability, we employ a well-known protein design algorithm called FoldX [44, 45], which uses an empirical force field to determine the energetic effects of a point mutation. FoldX mutates protein side chains using a probability-based rotamer library while exploring alternative conformations of the surrounding side chains, in order to model the energetic effects of a mutation. We observe good correspondence between Potts model predicted likelihoods and FoldX predicted changes in structural stabilities of mutations in Fig 7B, and Fig 8B of S1 File for a set of multiple inhibitor-associated mutations (from [28]) in PR. There also exists statistically significant correlation between experimentally measured replicative capacities of these mutations and their Potts model predicted likelihoods (Fig 7A, and Fig 8A of S1 File), but the FoldX predicted changes in structural stabilities do not correlate so well with experimentally measured replicative capacities (Fig 7C, Fig 8C of S1 File). This is indicative that different measures of fitness such as thermostability, activity, or folding energetics of a protein do not generally contribute to fitness in the same way [1]. While some measures or properties being tested may only have an indirect context-dependent impact on fitness, “prevalence” in multiple sequence alignments of thousands of protein sequences may be more reflective of the overall survival fitness. Fig 7 and Fig 8 of S1 File show that the Potts model can capture contributions to fitness from both structural stabilities measured by FoldX, and from other aspects of the viral replicative life-cycle measured by replicative capacity experiments, which are not captured completely by either measurement on its own.

Fig 7 — Figure shows that the Potts model predicted ΔEs can capture different features of the fitness landscape that may be orthogonal, and may not correlate well with each other. (A) Relative fitness (replicative capacity) measurements obtained from deep mutational scanning of HIV-1 variants [28] involving combinations (of three or lesser) of mutations in protease associated with resistance to (particularly second-generation) inhibitors in clinic, are compared to changes in Potts statistical energies, ΔEs with a Spearman rank-order correlation, ρ = 0.66 (p ≪ 0.001). [28] also report statistically significant correlation (|ρ| = 0.46) with a Potts model inferred using the Adaptive Cluster Expansion (ACE) algorithm. (B) FoldX predicted changes in folding energies, ΔΔGs (PDB: 3S85) of the mutations also correlate well with Potts predicted changes in statistical energies, ΔEs for the same (Spearman ρ = −0.57). The HIV-1 protease structure (PDB: 3S85) is used as reference, repaired using the RepairPDB function in the FoldX suite, and the free energy of mutants is calculated with the BuildModel function under default parameters. Changes in structural stability due to mutations correlate well with their predicted likelihoods (estimated by the Potts model ΔEs) as seen here with a Spearman rank-order correlation, ρ = −0.57 (p < 0.001) between the two. However, FoldX calculations are susceptible to small changes in structure that can be caused by the presence of small-molecule ligands, etc. For another PDB:4LL3, we still find statistically significant correlation between the two (ρ = −0.64). (C) Experimental relative fitness measurements however, do not correlate as well with FoldX predicted changes in folding energies due to the mutations (ρ = −0.36).

Conclusion

Fitness is a complex concept at the foundation of ecology and evolution. The measures of fitness range from those such as replicative capacity, protein stability, catalytic efficiency, that can be determined experimentally in the lab to measures stemming from the “prevalence” in collections of sequences obtained from nature, that can be quantified and compared using predictions of coevolutionary models which encode mutational patterns in multiple sequence alignments. For viral fitness measurements, the large majority of studies focus on measures like selection coefficients or replicative fitness within hosts or cells in culture. Potts models of sequence co-variation provide a measure of fitness tied to the frequency of sequences appearing after longer in vivo evolutionary times in the virus’ natural environment.

The functions of proteins are defined by the collective interactions of many residues, and yet many statistical models of biological sequences consider sites nearly independently [31]. While studies [1] have demonstrated the benefits of including interactions to capture pairwise covariation in successfully predicting the effects of mutations across a variety of protein families and high-throughput experiments, for viral proteins, the predictions of mutational fitness by pairwise or latent-space models often fall short of predictions by site-independent models. It has been suggested that this could be a consequence of the limited diversity of the sequence alignments [1] or due to a discrepancy between the proxy for viral fitness in the laboratory and the in vivo fitness of the virus [9]. Here, we show that the signatures of epistasis are best manifested for viruses like HIV in the comparison of the Potts model predicted and experimental HIV sequence “prevalences” when expressed as higher-order marginals of the sequence probability distribution. Gupta and Adami have shown that epistasis in HIV can also be detected using a different metric, the pairwise mutual information [46]. The approach presented here goes further and accurately describes the higher order mutational landscape of the virus in response to external selection pressures such as drug exposure.

The model, which is parameterized to reproduce the bivariate marginals in the MSA, also accurately captures the higher order marginal probabilities (seen in Fig 3A, 3C and 3E, upto the 14^th order) in the MSA for sets of drug-resistance associated positions; whereas, the fidelity of a site-independent model decreases much more rapidly with the size of the marginal. We further show that epistatic interactions are particularly important in determining the higher order mutation patterns of drug-resistance-associated sites in HIV; in clear contrast with non-drug-resistance-associated positions, as the virus evolves under drug pressure employing the most strongly interacting positions in mutational pathways.

It has been suggested that the success of models based on sequence covariation at recapitulating high-throughput mutation experiments depends in part on the extent to which experimental assays can capture phenotypes that are under direct, long-term selection [1]. For some proteins, such as nonessential peripheral enzymes or signaling proteins, the property being tested in the laboratory may only have an indirect, context-dependent impact on the organism. We observe higher correlation between Potts model and experiment for the structural protein Capsid than other enzymatic proteins like PR, RT, or IN. A similar correlation has been observed for Capsids of other types of viruses [47]. This indicates that changes in CA perhaps have a more direct effect on the viral lifecycle than enzymatic proteins. However, the evidence for epistasis from fitness measurements based on replicative capacity experiments remains weak as both the Potts and independent models often show comparable degrees of correlation with experiment, and the distinction may not be statistically significant. While double mutant cycles provide a well established biophysical way to probe epistatic effects without reference to a particular sequence background, the order-of-magnitude smaller dynamic range makes accurate quantitative predictions very difficult and we only see weak evidence for epistasis through double mutant cycles.

Different measures may also contribute to fitness in different ways. In this study, we employ FoldX to probe the contribution of structural changes and folding energetics due to mutations to their predicted/observed likelihoods, finding that the Potts model predicted likelihoods of mutations in HIV correlate well with FoldX predicted changes in free energies. FoldX predictions, however, do not correlate well with experimental replicative capacity measurements. This is suggestive that the overall fitness landscape predicted by the Potts model includes contributions from many different features, some may even be orthogonal and thus, may not necessarily correlate well with each other.

The evolution of viruses like HIV under drug and immune selection pressures induces correlated mutations due to constraints on the structural stability and fitness (ability to assemble, replicate, and propagate infection) of the virus [48]. This is a manifestation of the epistatic interactions in the viral genome. The analysis presented here provides a framework based on sequence prevalence to examine the role of correlated mutations in determining the structural and functional fitness landscape of HIV proteins, especially under drug-selection pressure. Epistatic effects are vital in shaping the higher order (well beyond pairwise) “prevalence” landscape of HIV proteins involved in engendering drug resistance. Identifying/elucidating the epistatic effects for key resistance mutations can help in designing better experiments to probe epistasis and has the potential to impact future HIV drug therapies.

Materials and methods

The Potts Hamiltonian model of protein sequence covariation is a probabilistic model built from the single and pairwise site amino-acid frequencies in a protein multiple sequence alignment, and aimed at describing the probabilities of observing different sequences in the MSA. To approximate the unknown empirical probability distribution P(S) that best describes a sequence S of length L with each residue encoded in a Q-letter alphabet using a model probability distribution P^m(S), we choose the maximum entropy or least biased distribution as the model distribution. Similar distributions that maximize the entropy, with the constraint that the empirical univariate and bivariate marginal distributions are preserved, have been derived in [10, 11, 22, 32, 49]. We follow a derivation of the maximum entropy model in [32, 50], which takes the form of an exponential distribution:

\begin{matrix} E (S) = \sum_{i}^{L} h_{S_{i}}^{i} + \sum_{i = 1}^{L} \sum_{j = 1}^{i - 1} J_{S_{i} S_{j}}^{i j} \end{matrix}

(2)

\begin{matrix} P^{m} (S) \propto e^{- E (S)} \end{matrix}

(3)

where the quantity E(S) is the Potts statistical energy of a sequence S of length L; the model parameters $h_{S_{i}}^{i}$ called “fields” represent the contribution to statistical energy from a residue S_i at position i in S, and $J_{S_{i} S_{j}}^{i j}$ called “couplings” represent the energy contribution from a pair of residues at positions i, j. In this form, the Potts Hamiltonian consists of LQ “field” terms and $(\begin{matrix} L \\ 2 \end{matrix}) Q^{2}$ “coupling” terms. For the distribution P^m ∝ e^−E, negative fields and couplings indicate favored amino acids. The change in Potts energy for a mutation α → β at position i in S is given by:

\begin{matrix} Δ E (S_{α \to β}^{i}) = E (S_{α}^{i}) - E (S_{β}^{i}) = h_{α}^{i} - h_{β}^{i} + \sum_{j \neq i}^{L} J_{α S_{j}}^{i j} - J_{β S_{j}}^{i j} \end{matrix}

(4)

In this form, $Δ E (S_{α \to β}^{i}) > 0$ implies that residue β is more favorable than residue α at the given position and vice versa.

While the original model developed by Potts et al. only included nearest neighbor interactions and spin state vectors distributed across a hypersphere [51–53], in contrast, the “spin” models used in biological physics which correspond to global models of protein sequence-covariation, are generalizations of the Potts model with each “spin” state representing the amino-acid character at a given position in the protein, and able to interact with every other “spin” (“infinite range”). Such spin-models have been well established in the maximum entropy protein sequence-covariation literature and are often referred to simply as the Potts or Ising (in case of just two spins or amino-acid residues, wildtype and mutant) model [17, 20–23, 25, 33–35, 37, 38, 54]. In accordance with the literature, we refer to this model concisely as simply the Potts model.

Data processing

HIV protein multiple sequence alignments for protease, reverse transcriptase, and integrase are obtained from the Stanford University HIV Drug Resistance Database (HIVDB, https://hivdb.stanford.edu) [55, 56] using the genotype-rx search (https://hivdb.stanford.edu/pages/genotype-rx.html) (alternatively, downloadable datasets are also available at https://hivdb.stanford.edu/pages/geno-rx-datasets.html) and filtered using the criteria HIV-1 subtype B and nonCRF, drug-experienced (# of protease inhibitors or PIs = 1–9 for PR, # of nucleoside analog reverse transcriptase inhibitors or NRTIs = 1–9 and # of non-nucleoside analog reverse transcriptase inhibitors or NNRTIs = 1–4 for RT, and # of integrase strand-transfer inhibitors or INSTIs = 1–3 for IN); and we remove sequences with mixtures or ambiguous amino acids. Complete sequences with any insertions (’#’) or deletions (’∼’) are removed. Such sequences form a small (<1%) fraction of the MSA and removing them doesn’t significantly affect the MSA statistics. MSA columns with more than 1% “dots” (’.’) which represent unsequenced positions in the sequences are removed to avoid spurious correlations in the subsequent Potts model built on the MSA. Remaining sequences with any “dots” or unsequenced positions are then removed. This resulted in a final MSA size of N = 5710 sequences of length L = 99 for PR, N = 19194 sequences of length L = 188 for RT, and N = 1220 sequences of length L = 263 for IN. For RT, sequences with exposure to both NRTIs and NNRTIs were selected due to much lesser number of sequences exposed to only NRTIs or only NNRTIs being available. Multiple sequence alignments for the p24 Capsid protein are obtained from the the Los Alamos HIV Sequence Database [57] using the customizable advanced search interface https://www.hiv.lanl.gov/components/sequence/HIV/asearch/map_db.comp and selecting for subtype B and nonCRF, etc. Sequences with inserts/deletions are filtered out. For capsid, drug exposure data and a comprehensive list of drug-resistance mutations are not yet available; drug-naive sequences are used. The subtype B consensus sequence is obtained from the Los Alamos HIV sequence database [57] consensus and ancestral sequence alignments (https://www.hiv.lanl.gov/content/sequence/HIV/CONSENSUS/Consensus.html, last updated August 2004). The subtype B consensus sequence is referred to as the ‘consensus/wild-type’ throughout the text.

It has been previously established that phylogenetic corrections are not required for HIV patient protein sequences [23, 32] as they exhibit star-like phylogenies [46, 58]. For model inference, HIV patient sequences, are given sequence weights such that the effective number of sequences obtained from any single patient is 1. Sequences obtained from different patients are considered to be independent.

Mutation information

Drug resistance information, including a list of drug-resistance associated mutations are obtained from the Stanford HIVDB (https://hivdb.stanford.edu/dr-summary/resistance-notes) and from [59]. Mutations in HIV are generally classified into three categories: primary, accessory, and polymorphic. Mutations occurring as natural variants in drug-naive individuals are referred to as polymorphic mutations. Mutations affecting in vitro drug-susceptibility, occurring commonly in patients experiencing virological failure, and with fairly low extent of polymorphism are classified as major or primary drug-resistance mutations. In contrast, mutations with little or no effect on drug susceptibility directly but reducing drug susceptibility or increasing fitness in combination with primary mutations are classified as accessory. For this work, mutations classified as both primary/accessory are considered as drug-resistance associated mutations.

Alphabet reduction

A reduced grouping of alphabets based on statistical properties can capture most of the information in the full 20 letter amino acid alphabet while decreasing the dimensionality of the parameter space leading to more efficient model inference [17, 19, 22]. All possible alphabet reductions from a Q-letter alphabet to a Q − 1 letter alphabet at a site i are enumerated for all pairs of positions i, j (j ≠ i) by summing the bivariate marginals for each of the Q2 possible combinations and selecting the alphabet grouping that minimizes the root mean square difference (RMSD) in the mutual information (MI):

\begin{matrix} M I_{R M S D} = \sqrt{\frac{1}{N} \sum_{i j} {(M I_{Q}^{i j} - M I_{Q - 1}^{i j})}^{2}} \end{matrix}

(5)

The process is then iteratively carried out until the desired reduction in amino acid characters is achieved. Using the reduced alphabet, the original MSA is then re-encoded and the bivariate marginals are recalculated. Small pseudocounts are added to the bivariate marginals, as described in [17, 23, 35] to make up for sampling biases, or to limit divergences in the inference procedure.

Due to residue conservation at many sites in HIV-1, several studies have used a binary alphabet to extract meaningful information from sequences ([32, 60, 61]). A binary alphabet however, marginalizes the information at a site to only the wild-type and mutant residues with the loss of some informative distinctions between residues at sites acquiring multiple mutations. To strike a balance between loss of information and the reduction of the number of degrees of freedom, we choose a reduced alphabet of 4 letters. Our 4 letter alphabet reduction gives a Pearson’s R² coefficient of 0.995, 0.984, 0.980, and 0.992, for protease, reverse transcriptase, integrase, and p24 capsid protein, respectively between the MI of bivariate marginal distributions with the full 21 letter alphabet and the reduced 4 letter alphabet, representing minimal loss of information due to the reduction.

Due to reduction in alphabet, some mutations may not be amenable to our analysis when comparing to experimental fitness measurements such as replicative capacities, etc. We choose mutations corresponding to marginals with higher values in the MSA to be more representative of the model predictions.

Model inference

The goal of the Potts model inference is to find a suitable set of fields and couplings {h, J} parameters that fully determine the Potts Hamiltonian E(S), and best reproduce the empirical bivariate marginals.

A number of techniques have been developed for inferring the model parameters previously [10, 11, 22, 32, 49, 62–66]. The methodology followed here is similar to the one in [32], where, the bivariate marginals are estimated by generating sequences through a Markov Chain Monte Carlo (MCMC) sampling procedure, given a set of fields and couplings. The Metropolis criterion for the generated sequence(s) is proportional to their Potts energies. This is followed by a gradient descent step using a multidimensional Newton search, to determine the optimal set of Potts parameters that minimizes the difference between the empirical bivariate marginal distribution and the bivariate marginal estimates from the MCMC sample. The scheme for choosing the Newton update step is important. A quasi-Newton parameter update approach determining the updates to $J_{S_{i} S_{j}}^{i j}$ and $h_{S_{i}}^{i}$ by inverting the system’s Jacobian was developed in [32], which we follow here. Although the methodology involves approximations during the computation of the Newton steps, the advantage of the methodology is that it avoids making explicit approximations to the model probability distribution at the cost of being heavily computationally intensive. We have employed a GPU implementation of the MCMC methodology, which makes it computationally tractable without resorting to more approximate inverse inference methods. The MCMC algorithm implemented on GPUs has been previously used to infer accurate Potts models in [17, 23, 35, 38, 54, 67].

The computational cost of fitting $(\binom{L}{2}) * {(4 - 1)}^{2} + L * (4 - 1)$ model parameters for the smallest protein in our analysis, PR, on 2 NVIDIA K80 or 4 NVIDIA TitanX GPUs is ≈20h. For a more detailed description of data preprocessing, model inference, and comparison with other methods, we refer the reader to [19] and [17, 23, 38, 54]. A repository containing the final MSAs is available at https://github.com/ComputationalBiophysicsCollaborative/HIV_MSAs.

The site-independent model is inferred based on the univariate marginals, or the residue frequencies, $f_{α}^{i}$ (for a residue α at position i) in the MSA alone, giving the “field” parameters as:

\begin{matrix} h_{α}^{i} = - ln f_{α}^{i} \end{matrix}

(6)

A small pseudo-count is added to the $f_{α}^{i}$ to avoid indeterminate logarithms. The independent model energies of a sequence S are given as $E (S) = \sum_{i}^{L} h_{S_{i}}^{i}$ , where i is a position in the sequence, and L is the length of the sequence.

Prediction of higher order marginals

The Potts model inferred using the methodology described above is generative, allowing for generation of new synthetic sequences which very closely represent the sequences in the MSA of protein sequences obtained from HIV patients. For prediction and comparison of the higher-order marginals, both the Potts and independent models are used to generate new sequences, and subsequence frequencies (marginals) are compared between the dataset MSA and the Potts/independent model generated MSAs. For each subsequence of length 2–14, the process is repeated for 500 randomly picked subsequences and the Spearman correlation coefficient is calculated for all subsequences which appear with a frequency greater than the threshold (to avoid noise).

Statistical robustness of HIV Potts models

Finite sampling and overfitting can affect all inference problems, and the inverse Ising inference is no exception. In case of the Potts model, the number of model parameters can vastly outsize the number of sequences in the MSA, yet it is possible to fit accurate Potts models [54] to those MSAs, as the model is not directly fit to the sequences but to the bivariate marginals of the MSA. However, finite sampling can affect the estimation of the marginal distributions, which, in turn, affects model inference. In fact, overfitting in the inverse Ising inference arises due to the finite-sampling error in the bivariate marginals estimated from a finite-sized MSA. The degree of overfitting can be quantified using the “signal-to-noise ratio” (SNR), which is a function of the sequence length L, alphabet size q, number of sequences in the MSA N, and the degree of evolutionary conservation in the protein. The SNR for Potts models fit to protein sequences is discussed in more detail in [54]. If the SNR is small, the Potts model is unable to reliably distinguish high scoring sequences in the data set from low-scoring sequences. If SNR is close to or greater than 1, then overfitting is minimal and the Potts model is more reliable. In the analysis presented here, IN has the lowest SNR (0.14 compared to 43.7 for RT, and 21.6 for PR) on account of being one of the more conserved proteins with the lowest number of sequences in the MSA, and may be more affected by overfitting. Different predictions of the Potts model, however are differently affected by finite sampling errors with predictions of ΔEs which form the basis of Potts model “fitness” predictions among the more robust [54]. The Potts model is also able to accurately capture the higher-order marginals in the MSA. Thus, we conclude that the MSA sample sizes used in this study are sufficiently large to construct Potts models for these HIV proteins that adequately reflect the effect of the sequence background on mutations.

Protein stability analysis

The changes in folding free energies due to mutations are analyzed using FoldX [44, 45], which uses an empirical force field to determine the energetic effects of point mutations. The HIV-1 protease structure (PDB: 3S85) is used as reference, repaired using the RepairPDB function in the FoldX suite, and the free energy of mutants is calculated with the BuildModel function under default parameters. For each mutation, the mean of 10 FoldX calculations is used as the ΔΔG value.

Supporting information

S1 File. Supplementary methods, details and figures.

Details of the evolutionary conservation in different HIV enzymatic proteins and its effect on the observable evidence for epistasis is given in Section 1. Details on comparison with different experimental measures of fitness and Potts and independent models, along with comparisons with FoldX predicted changes in folding energetics due to mutations are given in Section 2, as well as details of why comparisons for double mutant cycles are difficult. Details of the weak evidence for epistasis that can be drawn from hamming distance distributions are given in Section 3.

(PDF)

Click here for additional data file.^{(1.3MB, pdf)}

S2 File. Supplementary figures and tables for double mutant cycles.

Figures and tables showing the distribution of Potts model predicted double mutant cycle effects for all double mutations indicating the strongest, predicted double mutant cycle effects involving mutations (at least one amongst the pair) at drug-resistance-associated sites and corresponding literature references in HIV-1 protease and integrase are given.

(PDF)

Click here for additional data file.^{(347.3KB, pdf)}

Data Availability

The code used for model inference and associated utilities is publicly available through Haldane et al., 2020 (https://doi.org/10.1016/j.cpc.2020.107312). HIV protein sequences, including sequence alignments, consensus sequences, etc. are obtained from the Stanford HIV drug resistance database (HIVDB, https://hivdb.stanford.edu) and the Los Alamos HIV sequence database (https://www.hiv.lanl.gov/content/sequence/HIV/mainpage.html). The details, filtering criteria (if any) are mentioned in the Materials and Methods section. The protein sequences for the molecular clones NL4-3 and HXB2 are obtained from GenBank (Clar et al., 2015, https://doi.org/10.1093/nar/gkv1276) with accession number AF324493.2 and K03455.1, respectively. A repository containing the final MSAs used in the study is available at https://github.com/ComputationalBiophysicsCollaborative/HIV_MSAs. Drug resistance information, including list of drug-resistance-associated mutations are obtained from the Stanford HIVDB and from Wensing et al., 2019 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6892618/). Any additional information can be obtained on request to the corresponding author.

Funding Statement

This work has been supported by the National Institutes of Health through grants awarded to RML (U54-AI150472, R35-GM132090, S10OD020095). The National Science Foundation also provided funding through a grant awarded to to RML and AH (1934848). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS One. 2022 Jan 18;17(1):e0262314. doi: 10.1371/journal.pone.0262314.r001

Author response to previous submission

Transfer Alert

This paper was transferred from another journal. As a result, its full editorial history (including decision letters, peer reviews and author responses) may not be present.

15 Oct 2021

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PLoS One. doi: 10.1371/journal.pone.0262314.r002

Decision Letter 0

Emilio Gallicchio

29 Nov 2021

PONE-D-21-33103Limits to detecting epistasis in the fitness landscape of HIVPLOS ONE

Dear Dr. Levy,

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Reviewer #1: Yes

**********

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Reviewer #1: Yes

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Reviewer #1: Yes

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5. Review Comments to the Author

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Reviewer #1: The work of Biswas et al. focuses on the use of data-driven models of protein sequence composition to characterize the fitness landscape of proteins, particularly HIV proteins that are commonly targeted by antiretroviral drugs. This work deals with a common and relevant problem in the field of amino acid coevolution where both sequence data (or its diversity) is scarce, and where experimental measures of fitness are limited by experimental constraints. This extensive study has two important results: 1) higher order marginals can be recovered with a pairwise model and that such higher order marginals indeed play a role in the fitness landscape of viral proteins. 2) It sheds light on why existent experimental data trying to capture epistatic effects of mutations is hard to model due to the limited dynamic range of these experiments.

Being this a revision of an initial submission, I was able to review previous reviewers comments and the accompanying responses and changes. My assessment is that the responses to the reviewer comments were appropriate and the changes did in fact improve the clarify of the presentation. My general assessment from the previous reviewers was that they did not have enough background in the recent developments in the field of amino acid coevolution and were focused on challenging the model development itself which has been already established and refined in the literature. This revision is technically sound but also does a good job presenting the biological implications of their results. In conclusion, I think this study is relevant for the field and explains several open questions concerning the application of sequence Potts models to viral proteins. I find this study relevant and of use, especially in these times where understanding the fitness landscapes of proteins related to infectious diseases in a matter of pressing public health.

Given the extensive changes toward this revision, I only have a few questions and comments that if responded could make this manuscript more clear.

General

1. The finding that the Capsid shows a higher correlation with he Potts model is interesting. A similar correlation has been observed for Capsids on other types of viruses (AAV) providing further evidence of the relevance of Potts models in these types of studies. I suggest citing this additional study too (https://doi.org/10.1016/j.bpj.2020.12.018).

2. Data Processing. It is stated that positions with more than 1% gaps of gaps were removed. This seems to me like a very stringent cutoff, can the authors provide an explanation of why more than 1% is too much?

3. Data processing. The statement “Sequences with insertions and deletions are removed” is not clear to me. Do you mean the positions with insertions and deletions? Or are you removing any complete sequence that has an insertion or deletion? Somehow this does not makes sense to me.

4. Alphabet reduction. I wonder if Equation 5 could be improved by including an index instead of the explicit realizations like Q=20, my understanding is that after each iteractive step, Q will be reduced with respect to the previous step right? If this is true then it should be noted that this is not only valid for a change from 21 to 20. If I misinterpretted it, then it is possible that the equation needs some further clarification.

5.Alphabet reduction. The authors compared the model with alphabet reduction with the model using full parameters. If the model with the full parameters was inferred, then what was the motivation to reduce the alphabet?

6. In the section statistical robustness of HIV Potts models, the concept of Signal-to-noise ratio is introduced and scores for the different protein systems are presented. Although it is mentioned that SNR depends on several factors, it would be good to have a more concrete definition or point out to previous work where it is defined.

7. The quality of some images is quite low, I assume this is due to the system that converts the manuscript for review. Please make sure to have high quality images. Figure 3 axes could have larger fonts for readability.

Minor

1. The use of the term favorability/ disfavorability is a bit awkward, I would consider another term.

2. Conventions, should “Fig 1” be spelled “Fig. 1” ?

3. Page 5, line 149. Change “.. higher entropies in Supplementary File 1 Fig 2 A” to “.. higher entropies (Supplementary File 1 Fig 2 A).”

4. Page 5, line 157. Change “This is suggestive that strong couplings ..” to “This is suggestive of strong couplings”

5. Page 11, line 364. correct “changes in CA perhaps has a ..” to “changes in CA perhaps have a ..”

6. NRTIs is only defined in a figure caption, I suggest to define it also in the main text.

7. Data processing. The concept of “deletes” is used instead of “deletion”, I would simply use deletions.

8. Page 13, line 444. Add a period after “filtered out.”

9. Page 13, correct “drug resistance mutations is not yet” with “drug resistance mutations are not yet”

10. Mutation information section. Replace “including list of ..” with “ including a list of ..”

11. Subsection title. Use lower case across titles, e.g. Change “Statistical Robustness of HIV” with “Statistical robustness of HIV ..”

12. Change title in the SI to be compatible with the manuscript

13. What is the need of having two distinct Supplementary files? It seems to me that the two files can be combined into a single document

**********

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Reviewer #1: No

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PLoS One. 2022 Jan 18;17(1):e0262314. doi: 10.1371/journal.pone.0262314.r003

Author response to Decision Letter 0

18 Dec 2021

In response to the specific editor comments, we have provided a rebuttal letter that responds to each point raised by the academic editor and reviewer(s), a marked-up copy of the manuscript highlighting changes made to the original version, as well as an unmarked version of the revised paper without tracked changes.

In response to the specific comments raised by the reviewer, we provide a detailed response (in the rebuttal letter) as below:

The work of Biswas et al. focuses on the use of data-driven models of protein sequence composition to characterize the fitness landscape of proteins, particularly HIV proteins that are commonly targeted by antiretroviral drugs. This work deals with a common and relevant problem in the field of amino acid coevolution where both sequence data (or its diversity) is scarce, and where experimental measures of fitness are limited by experimental constraints. This extensive study has two important results: 1) higher order marginals can be recovered with a pairwise model and that such higher order marginals indeed play a role in the fitness landscape of viral proteins. 2)It sheds light on why existent experimental data trying to capture epistatic effects of mutations is hard to model due to the limited dynamic range of these experiments.

Given the extensive changes toward this revision, I only have a few questions and comments that if responded could make this manuscript more clear.

We thank the reviewer for the thoughtful commentary and for highlighting the main points of the manuscript. The reviewer finds the study "relevant and of use". Below we provide a point-by-point response to the questions and comments raised by the reviewer. We have also updated the manuscript with changes made in response to the current reviewer comments highlighted in "cyan", while changes made to the previous reviewers' comments are highlighted in "yellow".

General:

1. The finding that the Capsid shows a higher correlation with the Potts model is interesting. A similar correlation has been observed for Capsids on other types of viruses (AAV) providing further evidence of the relevance of Potts models in these types of studies. I suggest citing this additional study too (https://doi.org/10.1016/j.bpj.2020.12.018).

We thank the reviewer for the suggestion and have added the citation in the updated manuscript.

2. Data Processing. It is stated that positions with more than 1% gaps were removed. This seems to me like a very stringent cutoff, can the authors provide an explanation of why more than1% is too much?

We had not used the correct wording, "gap"; whiIe referring to the "dot" character in HIV protein sequence alignments available from the Stanford HIV drug resistance database, which represents an unsequenced position in the sequence. Such positions (columns in the multiple sequence alignment) with more than 1% "dots" or missing amino characters were removed from the MSA, so that the subsequent Potts model built on the MSA would not have spurious correlations between missing amino acids/unsequenced positions and amino acid residues at other positions. Similarly remaining sequences (rows in the MSA) with "dots" (a small fraction of the MSA) after the first filtration step, were then removed to preserve the quality of sequences. We have made this clear by revising the previous statement in the Materials and Methods section:

" MSA columns with more than 1% ``dots" ('.') which represent unsequenced positions in the sequences are removed to avoid spurious correlations in the subsequent Potts model built on the MSA. Remaining sequences with any "dots" or unsequenced positions are then removed."

Complete sequences with insertions or deletions are removed. There are only few such sequences and removing them doesn't affect the multiple sequence alignment (MSA) statistics much; for example, less than 1% (~0.3%) of the sequences in the Reverse Transcriptase MSA contain insertions or deletions. On the other hand, keeping these sequences in the MSA would have complicated the subsequent model building, without improving the statistics. We have now made this clear in the revised text:

" Complete sequences with any insertions ('#') or deletions ('~') are removed. Such sequences form a small fraction (<1%) of the MSA and removing them doesn't significantly affect the MSA statistics. "

4. Alphabet reduction. I wonder if Equation 5 could be improved by including an index instead of the explicit realizations like Q=20, my understanding is that after each iterative step, Q will be reduced with respect to the previous step right? If this is true then it should be noted that this is not only valid for a change from 21 to 20. If I misinterpreted it, then it is possible that the equation needs some further clarification.

The reviewer is right. In each iterative step, the alphabet is reduced by 1 from a Q-letter alphabet in the previous step to a Q-1 letter alphabet. To make this clear, we have modified Equation 5 with an index instead of explicit realizations as below:

〖MI〗_RMSD= √(1/N ∑_ij▒(〖MI〗_Q^ij-〖MI〗_(Q-1)^ij )^2 )

We apologize for the confusion. We only compared the Mutual Information (MI) of the MSA encoded in the full 21-letter (20 amino acids + 1 gap character) alphabet to the MI of the MSA in a reduced alphabet. The Potts model is only inferred based on the MSA in the reduced alphabet for computational efficiency and not inferred based on the MSA encoded in the full 21-letter alphabet. In the most recent work in our group, we are using the full alphabet. The project described in this manuscript was carried out using a reduced alphabet. We do not believe the alphabet reduction affects any of the results presented in this manuscript.

We have now included a reference to previous work from the group which gives a more elaborate definition of the SNR and the several factors it depends on:

" The SNR for Potts models fit to protein sequences is discussed in more detail in [54]. "

Minor:

1. The use of the term favorability/ disfavorability is a bit awkward, I would consider another term.

We have used the terms "favorability/disfavorability" for a mutation in its specific sequence background, in keeping with previous published work (Biswas et al., eLife, 2019). The Potts model describes the prevalence landscapes of the protein sequences, and the model �Es best describe the favorability/disfavorability of mutations in a given sequence background. Alternatively, using terms like stabilizing/destabilizing (Flynn et al., MBE, 2017) can lead to further confusion as they can be interpreted to be pertaining specifically to protein stabilities.

2. Conventions, should “Fig 1” be spelled “Fig. 1” ?

We have now renamed all figures in the manuscript according to the convention, for example Fig 1 as Fig. 1.

3. Page 5, line 149. Change “.. higher entropies in Supplementary File 1 Fig 2 A” to “.. higher entropies (Supplementary File 1 Fig 2 A).”

We have modified the sentence in the Main text.

4. Page 5, line 157. Change “This is suggestive that strong couplings ..” to “This is suggestive of strong couplings”

We thank the reviewer for pointing out the typo and have corrected it in the revised text.

5. Page 11, line 364. correct “changes in CA perhaps has a ..” to “changes in CA perhaps have a ..”

We have corrected the typo in the revised text.

6. NRTIs is only defined in a figure caption, I suggest to define it also in the main text.

We thank the reviewer for pointing this out and have now defined all the major drug-classes used in antiretroviral therapy including NRTIs in the Main text lines 432-436.

7. Data processing. The concept of “deletes” is used instead of “deletion”, I would simply use deletions.

We have changed the word "deletes" to "deletions".

8. Page 13, line 444. Add a period after “filtered out.”

Added a period.

9. Page 13, correct “drug resistance mutations is not yet” with “drug resistance mutations are not yet”

Corrected.

10. Mutation information section. Replace “including list of ..” with “ including a list of ..”

We have modified the main text replacing "including list of .." with "including a list of .." as pointed out by the reviewer.

11. Subsection title. Use lower case across titles, e.g. Change “Statistical Robustness of HIV” with “Statistical robustness of HIV ..”

We have now modified the font for the subsection titles accordingly.

12. Change title in the SI to be compatible with the manuscript.

We have now changed the title of the SI to be compatible with the manuscript.

13. What is the need of having two distinct Supplementary files? It seems to me that the two files can be combined into a single document.

The supplementary files are kept separate for ease of readability. Supplementary file 1 contains the details of many methods, supplementary data, and figures. Supplementary file 2 on the other hand contains only supplementary tables and figures pertaining to double mutant cycles showing that most strongly coupled pairs of mutations predicted by the Potts model contain drug-resistance associated mutations studied in the literature.

Note that there was a slight error in Figure S2A in Supplementary File 2, in marking the standard deviations, which we have now corrected and modified in the revised version. This does not affect any of the results.

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PLoS One. doi: 10.1371/journal.pone.0262314.r004

Decision Letter 1

Emilio Gallicchio

21 Dec 2021

Limits to detecting epistasis in the fitness landscape of HIV

PONE-D-21-33103R1

Dear Dr. Levy,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Emilio Gallicchio, Ph.D.

Academic Editor

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Additional Editor Comments (optional):

Reviewers' comments:

PLoS One. doi: 10.1371/journal.pone.0262314.r005

Acceptance letter

Emilio Gallicchio

6 Jan 2022

PONE-D-21-33103R1

Limits to detecting epistasis in the fitness landscape of HIV

Dear Dr. Levy:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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on behalf of

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 File. Supplementary methods, details and figures.

(PDF)

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S2 File. Supplementary figures and tables for double mutant cycles.

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Data Availability Statement

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PERMALINK

Limits to detecting epistasis in the fitness landscape of HIV

Avik Biswas

Allan Haldane

Ronald M Levy

Roles

Abstract

Introduction

Results and discussion

Fig 1. The correspondence between sequence covariation models and sequence statistics in multiple sequence alignments is very strong across different HIV proteins.

“Prevalence” landscape of HIV proteins and the role of correlations between residues

Fig 2. Distribution of the number of mutations (hamming distances) in drug-experienced HIV-1 sequences as captured by the Potts and independent models.

Fig 3. Potts model is predictive of higher-order marginals in the sequence MSA.

From sequence covariation to “fitness”

Fig 4. Survey of correlation between sequence-based predictions and experimental measures of “fitness” based on replicative capacity.

Fig 5. Error estimate in Potts model predictions of fitness.

Effect of epistasis on measurements of fitness and double mutant cycles in HIV

Fig 6.

Contribution of the changes in structural stability due to a mutation to the predicted likelihoods of mutant sequences

Fig 7. Potts model captures different features of the fitness landscape.

Conclusion

Materials and methods

Data processing

Mutation information

Alphabet reduction

Model inference

Prediction of higher order marginals

Statistical robustness of HIV Potts models

Protein stability analysis

Supporting information

Data Availability

Funding Statement

References

Author response to previous submission

Transfer Alert

Decision Letter 0

Emilio Gallicchio

Roles

Author response to Decision Letter 0

Decision Letter 1

Emilio Gallicchio

Roles

Acceptance letter

Emilio Gallicchio

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

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