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Bayesian estimation of gene constraint from an evolutionary model with gene features

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Abstract

Measures of selective constraint on genes have been used for many applications, including clinical interpretation of rare coding variants, disease gene discovery and studies of genome evolution. However, widely used metrics are severely underpowered at detecting constraints for the shortest ~25% of genes, potentially causing important pathogenic mutations to be overlooked. Here we developed a framework combining a population genetics model with machine learning on gene features to enable accurate inference of an interpretable constraint metric, shet. Our estimates outperform existing metrics for prioritizing genes important for cell essentiality, human disease and other phenotypes, especially for short genes. Our estimates of selective constraint should have wide utility for characterizing genes relevant to human disease. Finally, our inference framework, GeneBayes, provides a flexible platform that can improve the estimation of many gene-level properties, such as rare variant burden or gene expression differences.

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Fig. 1: Limitations of LOEUF and schematic representation for inferring shet using GeneBayes.
Fig. 2: Factors that contribute to our estimates of shet.
Fig. 3: GeneBayes estimates of shet perform well at identifying constrained and unconstrained genes.
Fig. 4: Breakdown of the gene features that are important for shet prediction.
Fig. 5: Comparing selection on LOFs (shet) between genes and shet to selection on other variant types.
Fig. 6: GeneBayes is a flexible framework for estimating gene-level properties.

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Data availability

Posterior means and 95% credible intervals for shet are available in Supplementary Table 1. Data sources for pLOF annotations, CpG methylation levels, exome sequencing coverage, variant frequencies and mappability/segmental duplication annotations are available in Supplementary Table 5. A description of the gene features is available in Supplementary Table 8. Posterior densities for shet, likelihoods for shet, LOF variants with misannotation probabilities and gene feature tables are available in ref. 83. Additional publicly available datasets used in this study are described in Methods and Supplementary Information and are accessible at IMPC essential genes (https://www.ebi.ac.uk/mi/impc/essential-genes-search/); pLOF annotations (gs://gnomad-public/papers/2019-tx-annotation/pre_computed/all.possible.snvs.tx_annotated.GTEx.v7.021520.tsv); mean methylation for CpG sites (gs://gcp-public-data–gnomad/resources/methylation); exome sequencing coverage (gs://gcp-public-data–gnomad/release/2.1/coverage/exomes/gnomad.exomes.coverage.summary.tsv.bgz); variant frequencies (gs://gcp-public-data–gnomad/release/2.1.1/vcf/exomes/gnomad.exomes.r2.1.1.sites.vcf.bgz); low mappability and segmental duplications (https://ftp-trace.ncbi.nlm.nih.gov/ReferenceSamples/giab/release/genome-stratifications/v3.1/GRCh37/Union/GRCh37_alllowmapandsegdupregions.bed.gz); ClinVar variants (https://ftp.ncbi.nlm.nih.gov/pub/clinvar/vcf_GRCh38/); DepMap 22Q2 release (https://depmap.org/portal/download/all/); DDD annotations (https://www.deciphergenomics.org/ddd/ddgenes); HPO phenotype-to-gene annotations (http://purl.obolibrary.org/obo/hp/hpoa/phenotype_to_genes.txt); DNMs from developmental disorder patients5; UK Biobank summary statistics (https://nealelab.github.io/UKBB_ldsc); RNA-seq from chimpanzee/human cortical models28; GTEx v8 release29.

Code availability

GeneBayes and code for estimating shet are available at https://github.com/tkzeng/GeneBayes and in ref. 84. Analysis code is available in ref. 85. All analyses were performed using Python v3.8, Python v3.9 or R v4.2. To train models, we used a modified version of NGBoost (v0.3.12)16,86 (https://github.com/tkzeng/ngboost), XGBoost (v2.0.2)87 and PyTorch (v1.12.1)88. Likelihoods were computed with fastDTWF (v.0.0.3)15 (https://github.com/jeffspence/fastDTWF). For hyperparameter tuning, we used shap-hypetune v0.2 (https://github.com/cerlymarco/shap-hypetune). For heritability enrichment analyses, we used ldsc (v1.0.1)89. For additional analyses, we used NumPy (v1.26.0)90, SciPy (v1.8.1)91, Pandas (v2.1.3)92, Scikit-learn (1.3.0)93 and Statsmodels (v0.14.0)94.

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Acknowledgements

We would like to thank I. Agarwal, M. Przeworski, J. Engreitz and members of the Pritchard Lab for valuable feedback and discussions. This work was supported by the National Institutes of Health (NIH; grants R01HG011432, R01HG008140 and U01HG009431 to J.K.P. and R01AG066490 to S. Montgomery). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the paper.

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Author notes

  1. These authors contributed equally: Tony Zeng, Jeffrey P. Spence.

Authors and Affiliations

  1. Department of Genetics, Stanford University, Stanford, CA, USA

    Tony Zeng, Jeffrey P. Spence, Hakhamanesh Mostafavi & Jonathan K. Pritchard

  2. Department of Population Health, New York University, New York, NY, USA

    Hakhamanesh Mostafavi

  3. Department of Biology, Stanford University, Stanford, CA, USA

    Jonathan K. Pritchard

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  1. Tony Zeng
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Contributions

J.P.S., H.M. and J.K.P. conceived and designed the study. T.Z. and J.P.S. performed all data analyses and developed the model. H.M. provided intellectual contributions to all aspects of the study. T.Z., J.P.S., H.M. and J.K.P. wrote the paper. J.K.P. supervised the study and acquired funding.

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Correspondence to Tony Zeng, Jeffrey P. Spence or Jonathan K. Pritchard.

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Nature Genetics thanks Zilin Li and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Performance of shet estimates from a model with some features removed.

a, Scatterplot of posterior mean shet estimated from a model trained without missense constraint or cross-species conservation features (y axis) against shet estimated from the full model (x axis). b, Precision–recall curves comparing the performance of shet estimated from the full model (blue) and from the model without missense/conservation features (orange) in classifying essential genes. c, Precision–recall curves comparing the performance of shet estimated from the two models in classifying developmental disorder genes.

Extended Data Fig. 2 Comparison of shet estimates from models trained on subsets of gnomAD.

a, Scatterplot of posterior mean shet estimated from a model trained with non-NFE individuals (y axis) against shet estimated from the full model (x axis). NFE, Non-Finnish European. This subset consists of 56,000 individuals or 45% of the total dataset. b, Scatterplot of posterior mean shet estimated from a model trained with NFE individuals (y axis) against shet estimated from the full model (x axis). This subset consists of 67,000 individuals or 55% of the total dataset.

Extended Data Fig. 3 shet distributions for additional example genes.

Left: posterior distributions and rescaled likelihoods for genes with few expected LOFs (genes in the bottom quartile). Right: posterior distributions and rescaled likelihoods for genes with many expected LOFs (genes in the top quartile).

Extended Data Fig. 4 Additional validation analyses.

a, Precision–recall curves comparing the performance of shet estimates from GeneBayes against LOEUF from gnomAD v4.0.0 (731k exomes) or LOEUF from gnomAD v2.1.1 (125k exomes) in classifying essential genes. b, Precision–recall curves comparing the performance of shet estimates from GeneBayes against other constraint metrics in classifying nonessential genes. c, Precision–recall curves comparing the performance of shet against other constraint metrics in classifying developmental disorder genes. d, Enrichment of de novo mutations in patients with developmental disorders, calculated as the observed number of mutations over the expected number under a null mutational model (n = 31,058 parent–offspring trios). We plot the enrichment of synonymous, missense, splice and nonsense variants in the 10% of genes considered most constrained by shet (blue) and the enrichment of these variants in all other genes (gray), including (left) and excluding (right) known developmental disorder genes. Bars represent 95% confidence intervals, centered around the mean. e, Scatterplot of the enrichment of common variant heritability in the 10% of genes considered most constrained by shet (y axis) or LOEUF (x axis), normalized by the enrichment of heritability in all genes. Each point represents one trait.

Extended Data Fig. 5 Performance of shet and LOEUF for genes with differing numbers of expected LOFs.

Left: precision–recall curves comparing the performance of shet against LOEUF in classifying essential genes for groups of genes binned by their expected number of LOFs. Right: precision–recall curves comparing the performance of shet against LOEUF in classifying developmental disorder genes for binned genes.

Extended Data Fig. 6 Correlation of gene features with gene length.

a, Histogram of the Spearman ρ between gene features and coding sequence (CDS) length. b, Histogram of the Spearman ρ between gene features and CDS length for gene expression features, colored by category. c, Spearman ρ between gene features and CDS length for additional features of interest. d, Scatterplot of the Spearman ρ between gene features and posterior mean shet (y axis) against the partial Spearman ρ (x axis) after controlling for the effect of gene (CDS) length.

Supplementary information

Supplementary Information

Supplementary Note and Figs. 1–4.

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Supplementary Tables

Supplementary Table 1: Posterior means and 95% credible intervals for GeneBayes estimates of shet. Supplementary Table 2: LOEUF and shet for ribosomal proteins associated with Diamond–Blackfan anemia. Supplementary Table 3: Terms used to define tissues for expression features. Supplementary Table 4: Filtering criteria for LOF variant curation. Supplementary Table 5: Sources for the LOF data. Supplementary Table 6: Parameters for fitting the gradient-boosted trees. Supplementary Table 7: Parameters for fitting the gradient-boosted trees for models trained on feature subsets. Supplementary Table 8a–k: Gene feature descriptions.

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Zeng, T., Spence, J.P., Mostafavi, H. et al. Bayesian estimation of gene constraint from an evolutionary model with gene features. Nat Genet 56, 1632–1643 (2024). https://doi.org/10.1038/s41588-024-01820-9

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