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Learning protein fitness models from evolutionary and assay-labeled data

Nature Biotechnology volume 40, pages 1114–1122 (2022)Cite this article

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Abstract

Machine learning-based models of protein fitness typically learn from either unlabeled, evolutionarily related sequences or variant sequences with experimentally measured labels. For regimes where only limited experimental data are available, recent work has suggested methods for combining both sources of information. Toward that goal, we propose a simple combination approach that is competitive with, and on average outperforms more sophisticated methods. Our approach uses ridge regression on site-specific amino acid features combined with one probability density feature from modeling the evolutionary data. Within this approach, we find that a variational autoencoder-based probability density model showed the best overall performance, although any evolutionary density model can be used. Moreover, our analysis highlights the importance of systematic evaluations and sufficient baselines.

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Fig. 1: Machine learning methods for protein fitness prediction.
Fig. 2: Performance of existing methods and the augmented Potts model.
Fig. 3: Augmented approach using different probability density models.
Fig. 4: Performance on individual data sets.
Fig. 5: Extrapolative performance from single mutants to higher-order mutants.
Fig. 6: Edit distance from wild-type sequence as a predictive model.

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Data availability

All protein fitness data were publicly available through citations available in the paper. A processed version of these data and our evaluation results are available on Dryad with https://doi.org/10.6078/D1K71B. All protein structures used in the study are available publicly with PDB IDs 2WUR, 6R5K and 2KR4.

Code availability

The code to reproduce the results is available at https://github.com/chloechsu/combining-evolutionary-and-assay-labelled-data.

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Acknowledgements

We thank A. Aghazadeh, P. Almhjell, F. Arnold, A. Busia, D. Brookes, M. Jagota, K. Johnston, L. Schaus, N. Thomas, Y. Wang and B. Wittmann for helpful discussions. We also thank P. Barrat-Charlaix, S. Biswas, J. Meier and Z. Shamsi for providing helpful details about their methods and implementations. Partial support was provided by the US Department of Energy, Office of Biological and Environmental Research, Genomic Science Program Lawrence Livermore National Laboratory’s Secure Biosystems Design Scientific Focus Area under grant award no. SCW1710 (J.L., C.H.), the Chan Zuckerberg Investigator program (J.L.) and C3.ai (J.L., H.N.). Research reported in this publication was supported by the National Library Of Medicine of the National Institutes of Health under grant award no. T32LM012417 (H.N.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. This material is based on work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE 2146752 (C.F.).

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of California, Berkeley, USA

    Chloe Hsu, Clara Fannjiang & Jennifer Listgarten

  2. Center for Computational Biology, University of California, Berkeley, USA

    Hunter Nisonoff & Jennifer Listgarten

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Contributions

C.H. and J.L. conceptualized the study and developed the methodology. C.H. implemented models and analyzed data, with contributions from H.N. and C.F. All authors wrote the paper.

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Correspondence to Chloe Hsu or Jennifer Listgarten.

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J.L. is on the Scientific Advisory Board of Patch Biosciences and Foresite Laboratories. The remaining authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Performance of existing methods and the augmented Potts model with NDCG.

Analog of Fig. 2, but using NDCG instead of Spearman correlation. (a) Average performance across all 19 data sets, as measured by NDCG. The horizontal axis shows the number of supervised training examples used. Error bars are centered at the mean and indicate bootstrapped 95% confidence intervals estimated from 20 random splits of training and test data. Asterisks (*) indicate that P < 0.01 among all two-sided Mann-Whitney U tests that the augmented Potts model has different performance from each other method, at a given sample size. In particular, the largest such p-value for each training set size was respectively, P = 3.9 × 10−2, 6.9 × 10−7, 2.2 × 10−7, 7.9 × 10−8, 7.7 × 10−4, 6.8 × 10−8, 6.8 × 10−8, 6.8 × 10−8 and P = 7.7 × 10−4 for the 80-20 split. (b) Average performance across all three data sets containing double mutant sequences (sequences that are two mutations away from the wild-type), and restricted to testing on only double mutants.

Extended Data Fig. 2 Performance on individual data sets when trained on limited labeled data.

A breakdown of averaged Spearman correlation results presented in Fig. 2a by individual data set. See Supplementary Fig. 1 for the analogous plot using NDCG. Error bands are centered at mean and indicate bootstrapped 95% confidence interval from 20 random data splits.

Extended Data Fig. 3 Performance on individual data sets when trained on 80% data.

A breakdown of averaged Spearman correlation results presented in the right-side mini-panel in Fig. 2a, on 80-20 splits, by individual data set. See Supplementary Fig. 2 for the analogous plot using NDCG. Error bars indicate bootstrapped 95% confidence interval from 20 random data splits. Box-and-whisker plots show the first and third quartiles as well as median values. The upper and lower whiskers extend from the hinge to the largest or smallest value no further than 1.5 x interquartile range from the hinge.

Extended Data Fig. 4 Augmented approach using different probability density models, with NDCG.

Analogous to Fig. 3, but using NDCG. Methods are compared with their augmented counterpart, using matching colors on each pair. Flat, horizontal lines represent evolutionary density models that do not have access to assay-labeled data. Dashed lines indicate existing methods. Error bars are centered at the mean and indicate bootstrapped 95% confidence interval from 20 random data splits.

Extended Data Fig. 5 Performance on individual data sets with NDCG.

Analogous to Fig. 4, but using NDCG. (a) Other than the EVmutation Potts model, the DeepSequence VAE, and Profile HMM, none of which use supervised data, all other methods here used 240 labeled training sequences. Each colored dot is the average NDCG from 20 random train-test splits. Random horizontal jitter was added for display purposes. The bottom row of black dots indicates the effective MSA size determined by accounting for sequence similarity with sample reweighting at 80% identity cutoff. (b) Summary of how often each modeling strategy had maximal NDCG. Such modelling strategies were determined by first identifying the top-performing strategy for any given scenario, and then also identifying any other strategy that came within the 95% confidence interval of the top performer.

Extended Data Fig. 6 The distribution of best model(s) on each data set.

Analogous to Fig. 4b, but varying the number of assay-labeled training examples. (a) Summary of how often each modelling strategy had maximal Spearman correlation. Such modelling strategies were determined by first identifying the top-performing strategy for any given scenario, and then also identifying any other strategy that came within the 95% confidence interval of the top performer. Four settings are used: with no assay-labeled data, when training on 48 or 240 assay-labeled single-mutant examples, and in the 80-20 train-test split setting. (b) Summary of how often each modelling strategy had maximal NDCG.

Extended Data Fig. 7 Extrapolation performance from single and double mutants to higher-order mutants.

Analogous to Fig. 5, but training on a random sample from both single and double mutants. Each column shows the performance when training on randomly sampled single mutants and then separately testing on single, double, or triple mutants, none of which were in the training data. The total size (TS) indicates the total number of mutants of a particular order in all of the data. For example, ‘TS=613’ for single mutants means there were 613 total single mutants in the data set that we sampled from. Error bars are centered at the mean and indicate bootstrapped 95% confidence interval from 20 random data splits. See Supplementary Fig. 6 for analogous plot using NDCG.

Extended Data Fig. 8 Edit distance from wild-type sequence as a predictive model (UBE4B U-box domain).

Analogous to Fig. 6, but on the UBE4B U-box domain data set. We compared the performance of non-augmented evolutionary density models to two predictive models that use only the edit distance of a sequence to the wild type. In one version, the edit distance is defined as the number of mutations away from the wild type. In the other version, we used BLOSUM62 to compute the distance from wild type, which thus accounts not only for the number of mutations, but also the type of mutation. Each dot represents a UBE4B U-box domain sequence, with darker colors indicating larger distances from the wild-type.

Extended Data Fig. 9 FoldX predictions as additional features in augmented models.

Each column shows the performance of augmented models with a single FoldX-derived stability feature added, when training on randomly sampled single mutants and then separately testing on single, double, or triple mutants. It also shows augmentation of two density models at the same time, without FoldX, as in "Augmented VAE + Potts". Error bars are centered at the mean and indicate bootstrapped 95% confidence interval from 20 random data splits. See Supplementary Fig. 7 for analogous evaluation with NDCG.

Extended Data Fig. 10 Performance of linear model using only one feature per site (not per amino acid at each site).

In addition to the linear model with one-hot encoded, site-specific amino acid features, we also evaluated a simpler linear model with position-only features that encode which sites are mutated. The evaluation uses Spearman correlation. Each column shows the performance when training on randomly sampled single mutants and then separately testing on single, double, or triple mutants, none of which were in the training data. Error bars are centered at the mean and indicate bootstrapped 95% confidence interval from 20 random data splits.

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Hsu, C., Nisonoff, H., Fannjiang, C. et al. Learning protein fitness models from evolutionary and assay-labeled data. Nat Biotechnol 40, 1114–1122 (2022). https://doi.org/10.1038/s41587-021-01146-5

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