Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Deep generative models of genetic variation capture the effects of mutations

Nature Methods volume 15, pages 816–822 (2018)Cite this article

Subjects

Abstract

The functions of proteins and RNAs are defined by the collective interactions of many residues, and yet most statistical models of biological sequences consider sites nearly independently. Recent approaches have demonstrated benefits of including interactions to capture pairwise covariation, but leave higher-order dependencies out of reach. Here we show how it is possible to capture higher-order, context-dependent constraints in biological sequences via latent variable models with nonlinear dependencies. We found that DeepSequence (https://github.com/debbiemarkslab/DeepSequence), a probabilistic model for sequence families, predicted the effects of mutations across a variety of deep mutational scanning experiments substantially better than existing methods based on the same evolutionary data. The model, learned in an unsupervised manner solely on the basis of sequence information, is grounded with biologically motivated priors, reveals the latent organization of sequence families, and can be used to explore new parts of sequence space.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: A nonlinear latent-variable model captures higher-order dependencies in proteins and RNAs.
Fig. 2: Mutation effects can be quantified by likelihood ratios.
Fig. 3: A deep latent-variable model predicts the effects of mutations better than site-independent or pairwise models.
Fig. 4: Latent variables capture the organization of sequence space.
Fig. 5: Structured priors over weights capture biological assumptions.
Fig. 6: Interpretation of model and effect predictions.

Similar content being viewed by others

Data availability

The sequence data and code supporting this work are available at https://github.com/debbiemarkslab/DeepSequence. The mutation-effects data from all analyzed experiments, as well as all model predictions, are available in Supplementary Table 2.

References

  1. Fowler, D. M. & Fields, S. Deep mutational scanning: a new style of protein science. Nat. Methods 11, 801–807 (2014).

    Article  CAS  Google Scholar 

  2. Kosuri, S. & Church, G. M. Large-scale de novo DNA synthesis: technologies and applications. Nat. Methods 11, 499–507 (2014).

    Article  CAS  Google Scholar 

  3. Romero, P. A., Tran, T. M. & Abate, A. R. Dissecting enzyme function with microfluidic-based deep mutational scanning. Proc. Natl Acad. Sci. USA 112, 7159–7164 (2015).

    Article  CAS  Google Scholar 

  4. Roscoe, B. P. & Bolon, D. N. Systematic exploration of ubiquitin sequence, E1 activation efficiency, and experimental fitness in yeast. J. Mol. Biol. 426, 2854–2870 (2014).

    Article  CAS  Google Scholar 

  5. Roscoe, B. P., Thayer, K. M., Zeldovich, K. B., Fushman, D. & Bolon, D. N. Analyses of the effects of all ubiquitin point mutants on yeast growth rate. J. Mol. Biol. 425, 1363–1377 (2013).

    Article  CAS  Google Scholar 

  6. Melamed, D., Young, D. L., Gamble, C. E., Miller, C. R. & Fields, S. Deep mutational scanning of an RRM domain of the Saccharomyces cerevisiae poly(A)-binding protein. RNA 19, 1537–1551 (2013).

    Article  CAS  Google Scholar 

  7. Stiffler, M. A., Hekstra, D. R. & Ranganathan, R. Evolvability as a function of purifying selection in TEM-1 β-lactamase. Cell 160, 882–892 (2015).

    Article  CAS  Google Scholar 

  8. McLaughlin, R. N. Jr, Poelwijk, F. J., Raman, A., Gosal, W. S. & Ranganathan, R. The spatial architecture of protein function and adaptation. Nature 491, 138–142 (2012).

    Article  CAS  Google Scholar 

  9. Kitzman, J. O., Starita, L. M., Lo, R. S., Fields, S. & Shendure, J. Massively parallel single-amino-acid mutagenesis. Nat. Methods 12, 203–206 (2015).

    Article  CAS  Google Scholar 

  10. Melnikov, A., Rogov, P., Wang, L., Gnirke, A. & Mikkelsen, T. S. Comprehensive mutational scanning of a kinase in vivo reveals substrate-dependent fitness landscapes. Nucleic Acids Res. 42, e112 (2014).

    Article  Google Scholar 

  11. Araya, C. L. et al. A fundamental protein property, thermodynamic stability, revealed solely from large-scale measurements of protein function. Proc. Natl Acad. Sci. USA 109, 16858–16863 (2012).

    Article  CAS  Google Scholar 

  12. Firnberg, E., Labonte, J. W., Gray, J. J. & Ostermeier, M. A comprehensive, high-resolution map of a gene’s fitness landscape. Mol. Biol. Evol. 31, 1581–1592 (2014).

    Article  CAS  Google Scholar 

  13. Starita, L. M. et al. Massively parallel functional analysis of BRCA1 RING domain variants. Genetics 200, 413–422 (2015).

    Article  CAS  Google Scholar 

  14. Rockah-Shmuel, L., Tóth-Petróczy, Á. & Tawfik, D. S. Systematic mapping of protein mutational space by prolonged drift reveals the deleterious effects of seemingly neutral mutations. PLoS Comput. Biol. 11, e1004421 (2015).

    Article  Google Scholar 

  15. Jacquier, H. et al. Capturing the mutational landscape of the beta-lactamase TEM-1. Proc. Natl Acad. Sci. USA 110, 13067–13072 (2013).

    Article  CAS  Google Scholar 

  16. Qi, H. et al. A quantitative high-resolution genetic profile rapidly identifies sequence determinants of hepatitis C viral fitness and drug sensitivity. PLoS Pathog. 10, e1004064 (2014).

    Article  Google Scholar 

  17. Wu, N. C. et al. Functional constraint profiling of a viral protein reveals discordance of evolutionary conservation and functionality. PLoS Genet. 11, e1005310 (2015).

    Article  Google Scholar 

  18. Mishra, P., Flynn, J. M., Starr, T. N. & Bolon, D. N. A. Systematic mutant analyses elucidate general and client-specific aspects of Hsp90 function. Cell Rep. 15, 588–598 (2016).

    Article  CAS  Google Scholar 

  19. Doud, M. B. & Bloom, J. D. Accurate measurement of the effects of all amino-acid mutations to influenza hemagglutinin. bioRxiv Preprint at https://www.biorxiv.org/content/early/2016/04/07/047571 (2016).

  20. Deng, Z. et al. Deep sequencing of systematic combinatorial libraries reveals β-lactamase sequence constraints at high resolution. J. Mol. Biol. 424, 150–167 (2012).

    Article  CAS  Google Scholar 

  21. Starita, L. M. et al. Activity-enhancing mutations in an E3 ubiquitin ligase identified by high-throughput mutagenesis. Proc. Natl Acad. Sci. USA 110, E1263–E1272 (2013).

    Article  CAS  Google Scholar 

  22. Aakre, C. D. et al. Evolving new protein-protein interaction specificity through promiscuous intermediates. Cell 163, 594–606 (2015).

    Article  CAS  Google Scholar 

  23. Julien, P., Miñana, B., Baeza-Centurion, P., Valcárcel, J. & Lehner, B. The complete local genotype-phenotype landscape for the alternative splicing of a human exon. Nat. Commun. 7, 11558 (2016).

    Article  CAS  Google Scholar 

  24. Li, C., Qian, W., Maclean, C. J. & Zhang, J. The fitness landscape of a tRNA gene. Science 352, 837–840 (2016).

    Article  CAS  Google Scholar 

  25. Mavor, D. et al. Determination of ubiquitin fitness landscapes under different chemical stresses in a classroom setting. eLife 5, e15802 (2016).

    Article  Google Scholar 

  26. Gasperini, M., Starita, L. & Shendure, J. The power of multiplexed functional analysis of genetic variants. Nat. Protoc. 11, 1782–1787 (2016).

    Article  CAS  Google Scholar 

  27. Starita, L. M. et al. Variant interpretation: functional assays to the rescue. Am. J. Hum. Genet. 101, 315–325 (2017).

    Article  CAS  Google Scholar 

  28. Adzhubei, I. A. et al. A method and server for predicting damaging missense mutations. Nat. Methods 7, 248–249 (2010).

    Article  CAS  Google Scholar 

  29. Hecht, M., Bromberg, Y. & Rost, B. Better prediction of functional effects for sequence variants. BMC Genomics 16, S1 (2015).

    Article  Google Scholar 

  30. Huang, Y.-F., Gulko, B. & Siepel, A. Fast, scalable prediction of deleterious noncoding variants from functional and population genomic data. Nat. Genet. 49, 618–624 (2017).

    Article  CAS  Google Scholar 

  31. Kircher, M. et al. A general framework for estimating the relative pathogenicity of human genetic variants. Nat. Genet. 46, 310–315 (2014).

    Article  CAS  Google Scholar 

  32. Ng, P. C. & Henikoff, S. SIFT: predicting amino acid changes that affect protein function. Nucleic Acids Res. 31, 3812–3814 (2003).

    Article  CAS  Google Scholar 

  33. Finn, R. D. et al. HMMER web server: 2015 update. Nucleic Acids Res. 43, W30–W38 (2015).

    Article  CAS  Google Scholar 

  34. Hopf, T. A. et al. Mutation effects predicted from sequence co-variation. Nat. Biotechnol. 35, 128–135 (2017).

    Article  CAS  Google Scholar 

  35. Mann, J. K. et al. The fitness landscape of HIV-1 gag: advanced modeling approaches and validation of model predictions by in vitro testing. PLoS Comput. Biol. 10, e1003776 (2014).

    Article  Google Scholar 

  36. Figliuzzi, M., Jacquier, H., Schug, A., Tenaillon, O. & Weigt, M. Coevolutionary landscape inference and the context-dependence of mutations in beta-lactamase TEM-1. Mol. Biol. Evol. 33, 268–280 (2016).

    Article  CAS  Google Scholar 

  37. Lapedes, A., Giraud, B. & Jarzynski, C. Using sequence alignments to predict protein structure and stability with high accuracy. arXiv Preprint at https://arxiv.org/abs/1207.2484 (2012).

  38. Weinreich, D. M., Lan, Y., Wylie, C. S. & Heckendorn, R. B. Should evolutionary geneticists worry about higher-order epistasis? Curr. Opin. Genet. Dev. 23, 700–707 (2013).

    Article  CAS  Google Scholar 

  39. Bendixsen, D. P., Østman, B. & Hayden, E. J. Negative epistasis in experimental RNA fitness landscapes. J. Mol. Evol. 85, 159–168 (2017).

    Article  CAS  Google Scholar 

  40. Rodrigues, J. V. et al. Biophysical principles predict fitness landscapes of drug resistance. Proc. Natl Acad. Sci. USA 113, E1470–E1478 (2016).

    Article  CAS  Google Scholar 

  41. Echave, J. & Wilke, C. O. Biophysical models of protein evolution: understanding the patterns of evolutionary sequence divergence. Annu. Rev. Biophys. 46, 85–103 (2017).

    Article  CAS  Google Scholar 

  42. Schmidt, M. & Hamacher, K. Three-body interactions improve contact prediction within direct-coupling analysis. Phys. Rev. E 96, 052405 (2017).

    Article  Google Scholar 

  43. Roweis, S. & Ghahramani, Z. A unifying review of linear gaussian models. Neural Comput. 11, 305–345 (1999).

    Article  CAS  Google Scholar 

  44. Pritchard, J. K., Stephens, M. & Donnelly, P. Inference of population structure using multilocus genotype data. Genetics 155, 945–959 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  45. Patterson, N., Price, A. L. & Reich, D. Population structure and eigenanalysis. PLoS Genet. 2, e190 (2006).

    Article  Google Scholar 

  46. Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. arXiv Preprint at https://arxiv.org/abs/1312.6114 (2013).

  47. Rezende, D. J., Mohamed, S. & Wierstra, D. Stochastic backpropagation and approximate inference in deep generative models. arXiv Preprint at https://arxiv.org/abs/1401.4082 (2014).

  48. Gómez-Bombarelli, R. et al. Automatic chemical design using a data-driven continuous representation of molecules. arXiv Preprint at https://arxiv.org/abs/1610.02415 (2016).

  49. Wainwright, M. J. & Jordan, M. I. Graphical Models, Exponential Families, and Variational Inference (Now Publishers, Hanover, MA, 2008).

    Article  Google Scholar 

  50. Ingraham, J. & Marks, D. in Proceedings of the 34th International Conference on Machine Learning Vol. 70 (eds Precup, D. & Teh, Y. W.) 1607–1616 (PMLR/Microtome Publishing, Brookline, MA, 2017).

  51. Kingma, D. P. et al. in Advances in Neural Information Processing Systems 29 (eds Lee, D. D. et al.) 4743–4751 (Curran Associates, Red Hook, NY, 2016).

  52. Murphy, K. P. Machine Learning: A Probabilistic Perspective (MIT Press, Cambridge, MA, 2012).

  53. Srivastava, N., Hinton, G. E., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014).

    Google Scholar 

  54. Hopf, T. A. et al. Three-dimensional structures of membrane proteins from genomic sequencing. Cell 149, 1607–1621 (2012).

    Article  CAS  Google Scholar 

  55. Marks, D. S. et al. Protein 3D structure computed from evolutionary sequence variation. PLoS One 6, e28766 (2011).

    Article  CAS  Google Scholar 

  56. Morcos, F. et al. Direct-coupling analysis of residue coevolution captures native contacts across many protein families. Proc. Natl Acad. Sci. USA 108, E1293–E1301 (2011).

    Article  CAS  Google Scholar 

  57. Jones, D. T., Singh, T., Kosciolek, T. & Tetchner, S. MetaPSICOV: combining coevolution methods for accurate prediction of contacts and long range hydrogen bonding in proteins. Bioinformatics 31, 999–1006 (2015).

    Article  CAS  Google Scholar 

  58. Sim, N. L. et al. SIFT web server: predicting effects of amino acid substitutions on proteins. Nucleic Acids Res. 40, W452–W457 (2012).

    Article  CAS  Google Scholar 

  59. Adzhubei, I., Jordan, D. M. & Sunyaev, S. R. Predicting functional effect of human missense mutations using PolyPhen-2. Curr. Protoc. Hum. Genet. 76, 7.20.1–7.20.41 (2013).

    Article  Google Scholar 

  60. Tubiana, J., Cocco, S. & Monasson, R. Learning protein constitutive motifs from sequence data. arXiv Preprint at https://arxiv.org/abs/1803.08718 (2018).

  61. Sinai, S., Kelsic, E., Church, G. M. & Nowak, M. A. Variational auto-encoding of protein sequences. arXiv Preprint at https://arxiv.org/abs/1712.03346 (2017).

  62. Rezende, D. J. & Mohamed, S. Variational inference with normalizing flows. arXiv Preprint at https://arxiv.org/abs/1505.05770 (2015).

  63. Burda, Y., Grosse, R. & Salakhutdinov, R. Importance weighted autoencoders. arXiv Preprint at https://arxiv.org/abs/1509.00519 (2015).

  64. Johnson, M., Duvenaud, D. K., Wiltschko, A., Adams, R. P. & Datta, S. R. in Advances in Neural Information Processing Systems 29 (eds Lee, D. D. et al.) 2946–2954 (Curran Associates, Red Hook, NY, 2016).

  65. Ovchinnikov, S. et al. Large-scale determination of previously unsolved protein structures using evolutionary information. eLife 4, e09248 (2015).

    Article  Google Scholar 

  66. Weinreb, C. et al. 3D RNA and functional interactions from evolutionary couplings. Cell 165, 963–975 (2016).

    Article  CAS  Google Scholar 

  67. Toth-Petroczy, A. et al. Structured states of disordered proteins from genomic sequences. Cell 167, 158–170 (2016).

    Article  CAS  Google Scholar 

  68. Boucher, J. I., Bolon, D. N. & Tawfik, D. S. Quantifying and understanding the fitness effects of protein mutations: laboratory versus nature. Protein Sci. 25, 1219–1226 (2016).

    Article  CAS  Google Scholar 

  69. Doud, M. B. & Bloom, J. D. Accurate measurement of the effects of all amino-acid mutations on influenza hemagglutinin. Viruses 8, 155 (2016).

    Article  Google Scholar 

  70. Wrenbeck, E. E., Azouz, L. R. & Whitehead, T. A. Single-mutation fitness landscapes for an enzyme on multiple substrates reveal specificity is globally encoded. Nat. Commun. 8, 15695 (2017).

    Article  CAS  Google Scholar 

  71. Chan, Y. H., Venev, S. V., Zeldovich, K. B. & Matthews, C. R. Correlation of fitness landscapes from three orthologous TIM barrels originates from sequence and structure constraints. Nat. Commun. 8, 14614 (2017).

    Article  Google Scholar 

  72. Kelsic, E. D. et al. RNA structural determinants of optimal codons revealed by MAGE-Seq. Cell Syst. 3, 563–571 (2016).

    Article  CAS  Google Scholar 

  73. Brenan, L. et al. Phenotypic characterization of a comprehensive set of MAPK1/ERK2 missense mutants. Cell Rep. 17, 1171–1183 (2016).

    Article  CAS  Google Scholar 

  74. Bandaru, P. et al. Deconstruction of the Ras switching cycle through saturation mutagenesis. eLife 6, e27810 (2017).

    Article  Google Scholar 

  75. Findlay, G. M. et al. Accurate functional classification of thousands of BRCA1 variants with saturation genome editing. bioRxiv Preprint at https://www.biorxiv.org/content/early/2018/04/05/294520 (2018).

  76. Matreyek, K. A. et al. Multiplex assessment of protein variant abundance by massively parallel sequencing. bioRxiv Preprint at https://www.biorxiv.org/content/early/2018/01/16/211011 (2018).

  77. Klesmith, J. R., Bacik, J.-P., Michalczyk, R. & Whitehead, T. A. Comprehensive sequence-flux mapping of a levoglucosan utilization pathway in E. coli. ACS Synth. Biol. 4, 1235–1243 (2015).

    Article  CAS  Google Scholar 

  78. Haddox, H. K., Dingens, A. S., Hilton, S. K., Overbaugh, J. & Bloom, J. D. Mapping mutational effects along the evolutionary landscape of HIV envelope. eLife 7, e34420 (2018).

    Article  Google Scholar 

  79. Pokusaeva, V. et al. Experimental assay of a fitness landscape on a macroevolutionary scale. bioRxiv Preprint at https://www.biorxiv.org/content/early/2018/04/06/222778 (2018).

  80. Weile, J. et al. A framework for exhaustively mapping functional missense variants. Mol. Syst. Biol. 13, 957 (2017).

    Article  Google Scholar 

  81. Eddy, S. R. Accelerated profile HMM searches. PLoS Comput. Biol. 7, e1002195 (2011).

    Article  CAS  Google Scholar 

  82. Suzek, B. E., Wang, Y., Huang, H., McGarvey, P. B. & Wu, C. H. UniRef clusters: a comprehensive and scalable alternative for improving sequence similarity searches. Bioinformatics 31, 926–932 (2015).

    Article  CAS  Google Scholar 

  83. Ekeberg, M., Lövkvist, C., Lan, Y., Weigt, M. & Aurell, E. Improved contact prediction in proteins: using pseudolikelihoods to infer Potts models. Phys. Rev. E 87, 012707 (2013).

    Article  Google Scholar 

  84. Tipping, M. E. & Bishop, C. M. Probabilistic principal component analysis. J. R. Stat. Soc. Series B Stat. Methodol. 61, 611–622 (1999).

    Article  Google Scholar 

  85. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. arXiv Preprint at https://arxiv.org/abs/1412.6980 (2014).

  86. Berman, H. M. et al. The protein data bank. Nucleic Acids Res. 28, 235–242 (2000).

    Article  CAS  Google Scholar 

  87. Kyte, J. & Doolittle, R. F. A simple method for displaying the hydropathic character of a protein. J. Mol. Biol. 157, 105–132 (1982).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank C. Sander, F. Poelwijk, D. Duvenaud, S. Sinai, E. Kelsic, the Cold Spring Harbor Laboratory Sequence-Function Relationship Journal Club and members of the Marks lab for helpful comments and discussions. A.J.R. is supported by DOE CSGF fellowship DE-FG02-97ER25308. D.S.M. and J.B.I. were funded by NIGMS (R01GM106303).

Author information

Author notes

  1. These authors contributed equally: Adam J. Riesselman, John B. Ingraham.

Authors and Affiliations

  1. Department of Systems Biology, Harvard Medical School, Boston, MA, USA

    Adam J. Riesselman, John B. Ingraham & Debora S. Marks

  2. Program in Biomedical Informatics, Harvard Medical School, Boston, MA, USA

    Adam J. Riesselman

  3. Program in Systems Biology, Harvard University, Cambridge, MA, USA

    John B. Ingraham

Authors
  1. Adam J. Riesselman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John B. Ingraham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Debora S. Marks
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.J.R., J.B.I., and D.S.M. designed the study. A.J.R. and J.B.I. performed the computations. All authors wrote the paper.

Corresponding author

Correspondence to Debora S. Marks.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Integrated supplementary information

Supplementary Figure 1

Distribution of experimental mutation effects and predictions made by DeepSequence.

Supplementary Figure 2 Mutation-effect predictions from generative models can be generalized to unseen sequences.

(above) Spearman ρ of mutation effect prediction of β-lactamase7 of each of the three generative models (N = 4788). Sequences with a normalized hamming distance greater than 0.53, 0.6, 0.8, and 0.95 with respect to the reference sequence are removed from the alignment before model fitting and inference. The distribution of hamming distances of the alignment and the cutoff of inclusion into each alignment is shown below.

Supplementary Figure 3 Predictions from all generative models for sequence families exhibited biases when compared to experimental data.

By transforming all model predictions and mutations to normalized ranks, we can compare effect predictions to experimental data across all biological datasets and models. The site-independent, pairwise, and latent variable models systematically over and under predict the effects of mutations according to amino acid identity. These biases vary in magnitude and direction depending on the amino acid identity before mutation (wildtype) or the residue identity it is mutated to (mutant).

Supplementary Figure 4 Supervised calibration of mutation-effect predictions improves predictive performance.

Amino acid bias was corrected with linear regression for all generative models, leaving one protein out for test and training a model on the rest (Methods). The bottom of the bar is Spearman ρ before correction, while the top is Spearman ρ after correction. Predictions without any evolutionary information (Supervised) performed considerably worse than other predictors.

Supplementary Figure 5 Differential improvement was strongest for deleterious effects.

Top five positions with largest reduction in rank error from independent model to DeepSequence for eight proteins are shown on the crystal structure of the protein.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–5

Reporting Summary

Supplementary Table 1

Identification of sequences and datasets analyzed

Supplementary Table 2

Experimental and computed mutation effects

Supplementary Table 3

Correlation of DeepSequence and other evolutionary models to mutation effects

Supplementary Table 4

Statistical comparison to other mutation-effect prediction algorithms

Supplementary Table 5

Biologically motivated priors and Bayesian learning improve model performance

Supplementary Table 6

Dictionary parameters from all protein models

Supplementary Table 7

Group sparsity prior log enrichment statistics

Supplementary Table 8

PDB files used for scale parameter analysis

Supplementary Table 9

Residual analysis of effect predictions

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Riesselman, A.J., Ingraham, J.B. & Marks, D.S. Deep generative models of genetic variation capture the effects of mutations. Nat Methods 15, 816–822 (2018). https://doi.org/10.1038/s41592-018-0138-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41592-018-0138-4

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing