Mutation effects predicted from sequence co-variation


Many high-throughput experimental technologies have been developed to assess the effects of large numbers of mutations (variation) on phenotypes. However, designing functional assays for these methods is challenging, and systematic testing of all combinations is impossible, so robust methods to predict the effects of genetic variation are needed. Most prediction methods exploit evolutionary sequence conservation but do not consider the interdependencies of residues or bases. We present EVmutation, an unsupervised statistical method for predicting the effects of mutations that explicitly captures residue dependencies between positions. We validate EVmutation by comparing its predictions with outcomes of high-throughput mutagenesis experiments and measurements of human disease mutations and show that it outperforms methods that do not account for epistasis. EVmutation can be used to assess the quantitative effects of mutations in genes of any organism. We provide pre-computed predictions for 7,000 human proteins at

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Figure 1: Inferring context-dependent effects of mutations from sequences.
Figure 2: Saturation mutagenesis experiments provide a quantitative test of context-dependent predictions.
Figure 3: ΔE captures experimental fitness landscapes and identifies deleterious human variants.
Figure 4: Improvements of the epistatic model for functional sites.
Figure 5: Computational predictions complement experimental measurements.

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  • 30 January 2017

    In the version of this article initially published online, an equation in the Online Methods section “Inference of epistatic models of biological sequences section” was incorrect: the term “λJ/2” should have been “λJ/2”. Two sentences later, the sentence presenting the next equation was also incorrect: instead of ending with “and is 0 otherwise,” that should read “and is 1 otherwise.” Both errors have been corrected in the print, PDF and HTML versions of the article.


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The authors would like to thank A. Lapedes, B. Rost, and members of the Marks laboratory for scientific discussion, and J. Reeb for help with existing mutation prediction software. C.S. was funded by NIGMS (R01GM106303). D.S.M. and T.A.H. were funded by NIGMS (R01GM106303) and the Raymond and Beverley Sackler Foundation. J.B.I. was funded by an NSF Graduate Research Fellowship (DGE1144152).

Author information




D.S.M., T.A.H. and C.S. initiated the project. T.A.H. and J.B.I. developed algorithms and wrote software. T.A.H., J.B.I. and D.S.M. analyzed the data with contributions from M.S. F.J.P. advised on the interpretation of experiments. C.P.I.S. supplied processed human genetic variation data. T.A.H., J.B.I., C.S. and D.S.M. wrote the paper. D.S.M. supervised the project.

Corresponding author

Correspondence to Debora S Marks.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Computation of context-dependent mutation effects from the coevolutionary sequence record

Left: The evolutionary pressure to maintain functional biomolecules leaves a record of amino acid or nucleotide co-conservation in multiple alignments of a sequence family. Middle: A pairwise graphical model learned from the natural sequence variation reveals family-specific constraints between pairs of positions (Jij) as well as at single sites (hi). Each hi is a vector unique to each position in the family that describes the relative favorability of different amino acids or nucleotides at that position, while each Jij is a matrix unique to each pair of positions describing an interaction pattern for the relative favorability of different combinations of amino acids/nucleotides at those positions. The values of these parameters are inferred by maximizing the probability of observing the natural sequences, with additional penalties for model complexity. Right: The inferred probability model can be applied to compute the relative effect of both single and higher-order substitutions. The calculation evaluates how compatible substitutions in the context of the wild-type sequence are with the functional constraints on the family by summing over the changes of couplings to all other sites (Jij), as well as the changes of single-site constraint terms in the changed positions (hi).

Supplementary Figure 2 Evolutionary statistical energy landscapes capture mutational sensitivity of sites

Computed mutational sensitivities per position (average difference in evolutionary statistical energy ΔE across all possible substitutions for each site) based on the epistatic model agree with experimental mutational sensitivities on 20 analyzed single-substitution landscapes for 15 biomolecules as measured by Spearman's rank correlation coefficient ρ. For correlations with the effects of individual substitutions, see Fig. 3a.

Supplementary Figure 3 Effect distributions of experimental mutation scans

The analyzed experimental datasets show considerable differences in the overall shape of their effect distributions. Many of the experiments are biased towards large fractions of neutral or deleterious variants, or have bimodal effect distributions biased towards either end of the effect scale but with little resolution of intermediate effects (here measured by the skewness and normality of the distributions (Online Methods); plots are ordered from negative to positive skew). Summary statistics can also be found in Supplementary Table 4.

Supplementary Figure 4 Agreement between evolutionary statistical energies and all features tested in experimental mutation scans

Full set of Spearman's rank correlation coefficients ρ between evolutionary statistical energies ΔE and experimental effects across all tested functional features and conditions in the analyzed mutation scans (e.g. different antibiotic concentrations or number of rounds of selection). Correlation coefficients are provided in Supplementary Table 3.

Supplementary Figure 5 Agreement of ΔE with bacterial fitness depends on strength of antibiotic selection

(a) Many mutations to TEM-1 β-lactamase which are deleterious according to ΔE are only revealed as deleterious in vivo by increasing selective pressure through higher ampicillin concentrations (mutational sensitivity per position (average ΔE); left to right, shades of blue additionally indicate concentration of first significant effect determined by fitting a two-component Gaussian mixture model at 2500 μg/ml). (b) Agreement between ΔE and experimental effects for kanamycin kinase decreases as the concentration of antibiotic is increased to a point where most variants are completely depleted and intermediate fitness effects cannot be resolved anymore (mixture model fitted at 1:8 WT MIC in log space).

Supplementary Figure 6 Prediction of human disease variants

(a) Evolutionary statistical energies ΔE computed using the independent model separate human disease-associated variants from frequent alleles in the population, but not as strongly as the epistatic model (Fig. 3b). The separation increases with the minimum allele frequency (AF) of the variants assumed to be neutral (area under the ROC curve (AUC)=0.88 for AF≥0.1, AUC=0.90 for AF≥0.25, AUC=0.92 for AF≥0.5). (b) The epistatic model outperforms all other tested methods on the HumVar dataset without any training on disease variants, as measured by the area under the ROC curve (colored lines for individual methods; grey line: expectation for random classifier; inset: AUC across the full range of specificities (left) and up to a false positive rate of 20% (right); AUCs of SIFT are < 0.5). Since PolyPhen-2 was trained on HumVar, the results here may overestimate its performance (see Online Methods for explanation). (c) On the subset of "difficult" variants that are predicted differently by SIFT and PolyPhen-2, the epistatic model is more accurate than all other methods but overall AUCs are lower than on the full dataset (figure elements as in b).

Supplementary Figure 7 Epistatic interactions critical for accurate prediction of functional residues

Across the proteins with high-throughput datasets where epistatic interactions lead to better agreement with the experimental data (first column), certain subgroups of substitutions contribute to the overall reduction in error, while others are predicted with comparable or slightly better accuracy by the independent model (for definitions of subgroups, see Online Methods).

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–7 and Supplementary Tables 1 and 6 (PDF 1504 kb)

Supplementary Table 2

Computed and experimental mutational landscapes. (XLSX 7104 kb)

Supplementary Table 3

Correlations between evolutionary statistical energy differences and experimental data. (XLSX 34 kb)

Supplementary Table 4

Skew and normality of effect distributions of experimental mutation scans. (XLSX 10 kb)

Supplementary Table 5

Comparison of epistatic model to established methods. (XLSX 20 kb)

Supplementary Table 7

Correlations with experiments across varying alignments depths. (XLSX 102 kb)

Supplementary Table 8

Error analysis for individual substitutions. (XLSX 2626 kb)

Supplementary Table 9

Evolutionary couplings for all analyzed biomolecules. (XLSX 17114 kb)

Supplementary Code

Source code for inferring pairwise graphical models from sequence alignments and predicting the effects of mutations. (ZIP 14051 kb)

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Hopf, T., Ingraham, J., Poelwijk, F. et al. Mutation effects predicted from sequence co-variation. Nat Biotechnol 35, 128–135 (2017).

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