New Results

Estimating the Selective Effect of Heterozygous Protein Truncating Variants from Human Exome Data

Christopher A. Cassa, Donate Weghorn, Daniel J. Balick, Daniel M. Jordan, David Nusinow, Kaitlin E. Samocha, Anne O'Donnell Luria, Daniel G. MacArthur, Mark J. Daly, David R. Beier, Shamil R. Sunyaev
doi: https://doi.org/10.1101/075523

Abstract

The dispensability of individual genes for viability has interested generations of geneticists. For some genes it is essential to maintain two functional chromosomal copies, while other genes may tolerate the loss of one or both copies. Exome sequence data from 60,706 individuals provide sufficient observations of rare protein truncating variants (PTVs) to make genome-wide estimates of selection against heterozygous loss of gene function. The cumulative frequency of rare deleterious PTVs is primarily determined by the balance between incoming mutations and purifying selection rather than genetic drift. This enables the estimation of the genome-wide distribution of selection coefficients for heterozygous PTVs and corresponding Bayesian estimates for individual genes. The strength of selection can help discriminate the severity, age of onset, and mode of inheritance in Mendelian exome sequencing cases. We find that genes under the strongest selection are enriched in embryonic lethal mouse knockouts, putatively cell-essential genes inferred from human tumor cells, Mendelian disease genes, and regulators of transcription. Using an essentiality screen, we find a large set of genes under strong selection that are likely to have critical function but that have not yet been studied extensively.

The evolutionary cost of gene loss is a central question in genetics and has been investigated in model organisms and human cell lines1–3. In humans, the question of dispensability and haploinsufficiency of individual genes is intimately related to their causal role in genetic disease. However, estimates of the selection and dominance coefficients in humans have proved elusive as inference techniques used in other sexual organisms generally require cross-breeding over several generations.

The analysis of patterns of natural genetic variation in humans provides an alternative approach to estimating selection intensity and dispensability of individual genes. Despite substantial methodological progress in the ascertainment and analysis of population sequence data4–8, estimation of parameters of natural selection in humans has been complicated by genetic drift, complexities of human demographic history4,7,9–13 and the role of non-additive genetic variation14–16. Additionally, naturally occurring PTVs are infrequent in the population and as a result, datasets of even thousands of individuals are underpowered for the estimation of gene dispensability in humans.

The Exome Aggregation Consortium (ExAC) dataset now provides a sufficiently powered sample to assess the selection that constrains the number of gene-specific PTVs in the general population17. We restrict our analysis to PTVs predicted to be consequential18, which allows us to assume that all PTVs within a gene likely incur the same selective disadvantage. We can then treat each gene as a bi-allelic locus with a functional state and a loss-of-function state. In each gene, the cumulative frequency of rare deleterious PTVs (the sum of PTV allele frequencies throughout the gene) is then primarily determined by the balance between incoming mutations and selection rather than through reassortment of alleles by stochastic drift. This makes our estimates robust to drift, population structure and historical changes in population size, which we evaluate analytically and with simulations (Methods and Supplementary Figure 1).

Figure 1:
Figure 1: Inferred distribution of fitness effects for heterozygous loss of gene function. Estimates of parameters Embedded Imagefrom maximum likelihood fit to the observed distribution of PTV counts across 15,998 genes in terciles of mutation rate, assuming Shet~IG (α, β). Shaded areas show 95% CI obtained from 100 bootstrapping replicates, intended to quantify the influence of sampling noise in the data set on parameter inference, with fixed estimates of local mutation rate.

Using population frequency data from 60,706 jointly-called exomes from individuals without severe Mendelian disorders, we estimate both the overall distribution of gene-based fitness effects and individual gene fitness cost in heterozygotes. Given gene-specific estimates of the de novo mutation rate19,20, the observed number of PTV alleles throughout each gene, and the number of chromosomes sampled, we estimate the distribution of the genome-wide selective effect of PTVs on heterozygote carriers, Shet. We parameterize the distribution of selective effects using an inverse Gaussian, which is fit using maximum likelihood (Figure 1). We then estimate the selection coefficient for each gene using the posterior probability for Shet given gene-specific values of the observed number of PTVs, the number of chromosomes sampled and the estimated mutation rate (Supplementary Table 1).

Although the distribution is broad, suggesting that the effect of losing one copy of a gene is variable, the mode of the distribution corresponds to a fitness loss of about 0.5% (Shet = 0.005). Despite the large sample size, resolution to distinguish between very high selective effects is still limited. There are 2,984 genes with Shet > 0.1, a result concordant with previous estimates of loss of function intolerance derived from population data17. Even though some genes are heavily depleted of PTVs in ExAC as compared with mutational expectation, these values suggest that heterozygote PTVs in many genes are not necessarily responsible for observable, severe clinical consequences.

Unsurprisingly however, genes known to be involved in rare Mendelian diseases have higher Shet values. Among them, genes annotated exclusively as autosomal dominant (AD, N=867) have significantly higher Shet values than those annotated as autosomal recessive (AR, N=1,482)21 [Mann-Whitney p-value 3.14×10−64] (Figure 2[a,b]). This suggests that it may be possible to prioritize candidate disease genes identified in clinical exome sequencing analysis using the observed mode of inheritance and Shet value.

Figure 2:
Figure 2: Separation of disease genes and clinical cases by mode of inheritance. [a] The distribution of genes associated with exclusively autosomal dominant (AD, N=867) disorders versus autosomal recessive (AR, N=1,482) disorders as annotated by the Clinical Genomics Database (CGD). Logarithmic bins are ordered from greatest to smallest Shet values. [b] Overall, AD genes have significantly higher Shet values than AR genes [Mann-Whitney p-value 3.14×10−64]. [c] Similarly, in solved Mendelian clinical exome sequencing cases (Baylor)22, Shet values can help discriminate between AR and AD disease genes, as annotated by clinical geneticists. [d] A Shet value of 0.04 can be used as a simple classification threshold for AD genes with a PPV of 96%. [e] This finding is replicated in a separately ascertained sample from UCLA. Box plots range from 25th–75th percentile values and whiskers include 1.5 times the interquartile range.

In a set of 504 clinical exome cases that resulted in a Mendelian diagnosis22, we find a similar enrichment of cases by MOI and selection value (Figure 2[c]). We find that 90.4% of novel, dominant variants are associated with heterozygous fitness loss greater than 0.04 (Figure 2[d]). Among disease variants, a cutoff of Shet > 0.04 provides a 96% positive predictive value for discriminating between AD and AR modes of inheritance.

To test the generalizable utility of Shet values in prioritizing candidate genes in Mendelian sequencing studies, we compared the overall prevalence of genes with Shet > 0.04 to the corresponding fraction in an independently ascertained dataset of new dominant Mendelian diagnoses (Figure 2[e])23. This analysis suggests that restricting to genes with Shet > 0.04 would provide a three-fold reduction of candidate variants, given the overall distribution of Shet values. Thus, initial effort in clinical cases can be focused on just a few genes for functional validation, familial segregation studies, and patient matching. We summarize the classification accuracy for all possible thresholds (AUC 0.9312) and probabilities for the mode of inheritance in each gene, generated using the full set of clinical sequencing cases (Supplementary Figure 2 and Supplementary Table 2).

Beyond mode of inheritance, we find that Shet can help predict phenotypic severity, age of onset, penetrance, and the fraction of de novo variants in a set of high-confidence haploinsufficient disease genes (Figure 3). In broader sets of known disease genes, Shet estimates significantly correlate with the number of references in OMIM MorbidMap and the number of HGMD disease “DM” variants (Supplementary Figure 3).

Figure 3:
Figure 3: Enrichments of Shet in known haploinsufficient disease genes of high confidence (ClinGen Project). In (N=127) autosomal genes, we annotate the Shet scores of genes associated with each disease category and classification. Higher Shet values are associated with increased phenotypic severity (Mann-Whitney p-value 4.87×10−3), earlier age of onset (p=1.46 ×10−2), high or unspecified penetrance (p=1.79×10−2), and a larger fraction of de novo variants (p=8×10−5). Box plots range from 25th-75th percentile values and whiskers include 1.5 times the interquartile range.

Gene-specific fitness loss values allow us to plot the distribution of selective effects for different disorders. This provides information about the breadth and severity of selection associated with various disorder groups using both well-established genes (Figure 4[a]) and new findings from Mendelian exome cases (Figure 4[b]). Overall, genes involved in neurologic phenotypes and congenital heart disease appear to be under more intense selection when compared with other disorder groups, tolerated knockouts in a consanguineous cohort, or in all genes (Figure 4[c,d])24. Interestingly, genes recessive for these disorders appear to have only partially recessive effects on fitness, so selection on heterozygotes is not negligible in these genes (Figure 4).

Figure 4:
Figure 4: Distribution of Shet values for phenotypes in known disease genes and clinical cases. We plot the distribution of selective effects for different disorder groups, providing information about the breadth and severity of selection associated with each group. [a] We include known Mendelian disease genes (Clinical Genomic Database) annotated as either Autosomal Recessive or Autosomal Dominant and [b] clinical exome sequencing cases22. We contrast these with [c] all tolerated knockouts in a consanguineous cohort (PROMIS)24 and [d] the distribution of selective effects in all scored genes. Logarithmic bins are ordered from greatest to smallest Shet values.

In germline cancer predisposition, genes with higher selection values are enriched in individuals with cancer over those in ExAC (Supplementary Figure 4). This suggests that genes with low Shet values should not be prioritized in the prospective genetic screening for cancer predisposition. Consistent with previous studies19, we find that de novo mutations in patients with autism spectrum disorder are significantly enriched in genes with higher selective effects than those identified in controls (Supplementary Figure 5 and Supplementary Table 3).

Figure 5:
Figure 5: High-throughput screens of gene essentiality in mice and cell assays. [a] Proportion of orthologous mouse knockout genes by phenotype, from a neutrally-ascertained set of genes generated by the International Mouse Phenotyping Consortium (IMCP). Logarithmic bins are ordered from greatest to smallest Shet values. [b] ICMP mice are separated into viable (N=1,057), sub-viable (N=211) and lethal knockouts (N=477), and lethal knockouts have significantly higher Shet values than viable [Mann-Whitney p-value 2.95×10−28]. [c] Cell-essential genes as reported by Wang et al. from genome-wide KBM-7 tumor cell CRISPR assay (N=1,740) have significantly higher Shet values [p-value 5.13×10−16] and [d] as do genes that were characterized as essential in a gene trap assay (N= 1,081) [p-value = 4.90×10−18]. In the CRISPR assay, all genes with adjusted p-values < 0.05 and negative assay scores are included, and genes with gene trap scores < 0.4 or lower are included. Box plots range from 25th–75th percentile values and whiskers include 1.5 times the interquartile range.

Next, we analyze Shet in the context of developmental and functional assays. In a large set of neutrally-ascertained mouse knockouts (N=2,179 genes)25, mice that are null mutant for orthologous genes with higher Shet estimates are enriched for embryonic lethality or sub-viability, while those with the lowest Shet estimates are depleted for embryonic lethality [Mann-Whitney p=2.95×10−28] (Figure 5[a,b]).

It is well known that mutations that are haploinsufficient in humans can often be well-tolerated when heterozygous in mice26. A classic example is SHH; heterozygous null mutations in this important developmental signaling gene result in holoprosencephaly27. Haploinsufficiency for other genes in this signaling pathway also results in developmental defects; e.g. GLI3 (Pallister-Hall syndrome and Greig cephalopolysyndactyly syndrome)28–30 and GLI2 (Holoprosencephaly 9)31. Interestingly, haploinsufficiency for these genes is tolerated in mouse models; mice heterozygous for null variation in the SHH signaling pathway are phenotypically normal, while homozygous mutant mice have defects that recapitulate features of the human syndrome32–34. This extends to many other human developmental disorders, enabling the experimental characterization of the molecular consequences of these mutations. Thus, it is notable that mice that are homozygous for null mutations in orthologous genes with higher Shet values are enriched for lethality.

High-throughput genetic analysis of cell-essentiality provides an orthogonal dataset for comparison with our estimates of Shet. In genes that are predicted to be essential for human cell proliferation using CRISPR-based inactivation (Figure 5[c]) and gene trap inactivation assays3(Figure 5[d]), we find that putatively essential genes are heavily enriched in genes with high Shet values [p-values 5.13×10−16, 4.90×10−18, respectively].

Key developmental pathways are dramatically enriched in genes with high Shet values (Figure 6[a]). We also find a significant positive correlation between the number of protein-protein interactions for each gene and its Shet value (Figure 6[b,c]), identified from high-throughput mass spectroscopy data. In the context of molecular and cellular function, a set of genes with very high estimated selective effects (Shet > 0.15, 2,072 genes) is statistically enriched in biological process categories “transcription regulation” (Bonferroni corrected p=1.8×10−39), “transcription” (7.5×10−36), and “negative regulators of biosynthetic processes” (see Supplementary Material)35. Consistent with this finding, nucleus was the most enriched cellular compartment for products of these genes (4.8×10−76). The enrichment of this set of high-Shet genes for transcription factors is consistent with literature that describes dosage dependence for enzymatic proteins and haploinsufficiency for transcriptional regulators36.

Figure 6:
Figure 6: Protein pathways and protein-protein interactions. [a] In key developmental pathways in KEGG, we find that genes with higher Shet values are enriched in genes important to development. [b] We plot the distribution of the number of protein-protein interactions for each gene, as determined by a genome-wide Mass Spectrometry assay37 versus Shet value. [c] We find that Shet values are positively correlated with the number of observed interactors for each gene. Box plots range from 25th-75th percentile values and whiskers include 1.5 times the interquartile range.

Estimation of the strength of purifying selection on PTVs provides a measure of gene dispensability unbiased with respect to existing knowledge. Thus, it has the potential to highlight genes that play a key role in development or in maintaining core functions in human cells. There are many genes with high estimated fitness costs that have not been previously described in human genetics studies. Given the marked enrichment of genes with high Shet values associated with Mendelian disorders, cell essentiality, embryonic lethality and development, it is plausible that many genes with high Shet values that have not been previously associated with human disease may be so detrimental that they are required for embryonic development.

We inspect the set of genes that lack disease annotations and publications but that have high Shet values to determine whether they share functional and genetic features reminiscent of known genes with central roles in cell housekeeping and developmental biology. We measure the relative knowledge about each gene in the primary literature from Entrez and PubMed38 using the number of gene reports connected with each manuscript, and sum the weighted contributions across all available manuscripts39 (PubMed score, Methods). While the PubMed score is positively correlated with Shet values, a substantial number of understudied genes fall in the highest Shet decile (Supplementary Figure 6).

We selected the 250 most cited and least cited genes within the top Shet decile, and compared their frequency of protein-protein interactions, viability of orthologous mouse knockouts and cell essentiality assays. Genes with the fewest publications have nearly the same number of embryonic lethal mouse knockouts as genes with the most publications. Other assays are only slightly depleted in the set of genes with the fewest publications (Supplementary Figure 7). These findings suggest that there may be additional essential developmental pathways yet to be uncovered in the set of genes under strong selection that lack functional or disease annotations, and provides a very promising gene set for further exploration. We have created a prioritized list of genes using a heuristic score developed from functional evidence to indicate the most promising candidates for future functional screening (Supplementary Table 4).

To place our inferences in the broader evolutionary context, we use comparable estimates from model organisms including flies and yeast, based on knockout competition with wild type or explicit crosses. In yeast, the analysis of a library of PTV knockouts provides a mean estimate of Shet ≈ 0.013, which is close to our inferred results (Shet ≈ 0.059) in humans40, given that the functional experiments excluded genes with very high s. Estimates in flies derived from homozygote lethal mutations which reduce viability in heterozygotes (rather than only PTVs) suggest values of Shet on the order of 1-3%, which is also in broad agreement with our estimates in humans1,41. While values of s in this range have a small impact in each generation, they may have dramatic evolutionary consequences42.

In conclusion, we use the genome-wide distribution of PTVs to estimate the fitness loss due to the heterozygous loss of each gene. Unlike recent work on intolerance to variation and its utility in human genetics19,43, we attempt to explicitly estimate the distribution of selection coefficients for PTVs. Our estimates are also distinct from the earlier work on the estimation of fitness effects of allelic variants in humans44 as the large sample size coupled with the assumption of strong selection makes our approach robust with respect to complexities of demographic history and dominance, and allows gene-based inferences. Conversely, our assumptions are justified for many but not all genes, as the method has limited resolution for genes under the strongest and weakest selection. We find significant enrichments in genes under strong selection in orthologous lethal mouse knockouts, genes that are essential for cell proliferation, and transcription factors. Additionally, these results may be useful in Mendelian disease gene discovery efforts and provide clinical utility in the inference of severity and mode of inheritance underlying Mendelian disease.

Methods

Model of deterministic mutation-selection balance

For most genes, protein-truncating alleles are both individually and collectively rare. For genes where they are collectively rare, estimation of the selective effect against heterozygous PTVs (Shet) can be greatly simplified. We model each gene as a single bi-allelic locus with cumulative frequency X = ∑ jxj where the sum is over PTVs in gene i for PTV sites j. This is motivated by the simplifying assumption of identical selection coefficients for all PTVs within a gene, and the observation that the frequency of the vast majority of PTVs is extremely low such that the occurrence of multiple variable sites within a gene on a single haplotype is also extremely low (2Nxijxik < 1 for sample size N). Moreover, multiple PTVs in a gene in an individual would be functionally equivalent to a single PTV resulting in a loss of function state.

Then for each gene, the cumulative allele frequency X is influenced by incoming mutation, selection and the random reassortment of alleles (genetic drift). When selection is strong, S ≫ 2.5×10−5 (i.e. when 4NeS ≫ 1, with effective population size Ne = 104), drift is much smaller than the contribution of selection. Furthermore, the strength of genetic drift is weakest for genes at low frequencies: for a variant with cumulative frequency of X = 0.001 the expected frequency change due to drift is only 〈ΔX2〉 ~ X/4Ne = 2.5×10−8 per generation. Notably, at the locus level assuming X ≪ 1 the drift contribution is also much smaller than the mutational influx. Hence under strong selection and for small allele frequencies the expected cumulative frequency of PTVs is determined by the equilibrium between the influx of de novo mutations (estimated to increase the cumulative frequency by an average 1.4×10−6 per locus per generation by mutational model) and the outflux due to natural selection.

In the presence of selection on both heterozygotes and homozygotes and ignoring back mutations, the dynamics of X are captured by the following equation: Embedded Image

Here U represents the PTV mutation rate at the gene locus per individual per generation, and Shet = hS > 0 and Shom = S > 0 represent the strength of negative selection against PTV heterozygotes and homozygotes, respectively. We note that compound heterozygotes (with a single PTV on each chromosome) are treated as homozygotes under the bi-allelic assumption. Provided X ≪ 1, as is the case for PTVs under strong selection (2NeS ≫ 1), this equation simplifies dramatically: Embedded Image

Because X ≪ 1, selection against heterozygotes (the linear term) generally also dominates over selection against homozygotes (the quadratic term), provided Shet/Shom ≫ X. This is only violated in cases of extreme recessivity (where the dominance coefficient h ≪ 0.001), but even in that case the expected cumulative frequency of PTVs in essential genes is unlikely to exceed 0.001 (the characteristic X in the completely recessive case is Embedded Image when S~1, see simulations in Supplementary Figure 1). The strong selection regime thus corresponds to mutation-selection balance in the heterozygote state of a PTV mutation. Notably, there is no dependence on the demography or population size in this regime, as the contribution from drift vanishes because selection drives alleles out of the population efficiently and on very short time scales.

From Eq. 2 follows that for a population sample of size N, sample allele counts Embedded Image are expected to be Poisson distributed around the expectation given by: Embedded Image

Generally, genes under the strongest and weakest selection are expected to have greater estimation uncertainty, as the resolution to estimate Shet deteriorates when variants are so common that they may not only be controlled by heterozygote selection, but also by drift or complex demography. However, the overwhelming majority of genes conform to our assumptions of cumulative PTV allele frequency not exceeding 0.001. Despite issues such as the admixture of populations, consanguineous samples in ExAC24, and the Wahlund effect, very few genes (1,201 of 17,199 covered genes) have higher estimated cumulative allele frequencies Embedded Image, which we restrict from the estimation procedure. On the other end of the spectrum, genes under strong selection may lack PTVs by chance alone in ExAC, which limits the ability to distinguish between large selective effects.

Population genetics simulations of model assumptions

To validate the assumption that estimates of selection can be made under mutation-selection balance independent of demography or population size for variants under sufficiently strong selection, we used SLiM 2.0 to conduct forward population genetics simulations45. We ran 10 replicates each of simulations with selection coefficients of −5×10−2, −5×10−3, −5×10−4, −5×10−5, and −5×10−6 through the demography published in Tennessen et al.46 for Africans and Europeans (Supplementary Figure 1). We compare the theoretical mutation load (U/Shet) with the simulated mutation load in three groups (African, European and Combined, which includes pooled site frequency spectra from both African and European populations in proportions represented in the EXAC dataset). The simulations support our assumption of mutation-selection balance in the strong selection regime (|Shet| >= 1×10−3), which appears to be appropriate for PTVs.

All simulations had a length of 1 kilobase, mutation rate of 2×10−8 per generation per base pair, and recombination rate of 1×10−5 per generation per base pair. The high recombination rate was chosen to simulate largely unlinked sites, as we are simulating PTVs which are infrequent enough that they are expected not to be in linkage with other PTVs in the same gene.

Dataset for Shet estimation

In this analysis, we use Exome Aggregation Consortium (ExAC) dataset version 0.3, a set of jointly-called exomes from 60,706 individuals ascertained with no known severe, early-onset Mendelian disorders. The mean coverage depth was calculated for each gene (canonical transcript from Ensembl v75, GENCODE v19) in the ExAC dataset (mean 57.75; s.d. 20.96).

Genes with average coverage depth of at least 30x were used in further analysis (N=17,199). Single nucleotide substitution variants annotated as PASS quality with predicted functional effects in the canonical transcript of stop-gain, splice donor, or splice acceptor (Variant Effect Predictor) were included in the analysis.

We are mindful that not all PTVs will result in complete loss of gene function, due to alternative transcripts or nonsense mediated decay. To address this, variants were filtered using LOFTEE47 and restricted to those predicted with high confidence to have consequences in the canonical transcript.

For each of the 17,199 genes we have observable values for (n, U, N), where n denotes the total number of observed PTV alleles in the population sample of N chromosomes covered in the gene, and U the PTV mutation rate across the canonical gene transcript from a mutational model19,20. Values of N and U for each gene from Samocha et. al. were used along with the number of well-covered chromosomes in each gene to generate the null mutational expectation of neutral evolution, NU. Incorrectly specified values from this mutational model could alter estimates of selection for individual genes, as higher estimates of selection are made in genes with greater depletions from the null expectation model. Our inference of selection coefficients relies on the assumption that the cumulative population frequency of PTV mutations, X, is small due to strong negative selection, so genes with Embedded Image are omitted from the analysis, leaving 15,998 genes.

Estimation of P(Shet)

A genome-wide ensemble of observed (n) and expected (NU ≡ v) genic PTV counts enables the inference of the distribution of heterozygous loss-of-function fitness effects, P(Shet), which underlies the evolutionary dynamics of this class of mutations. We estimate the parameters (α, β) of this distribution by fitting the observed distribution of PTV counts across genes: Embedded Image

For a given gene under negative selection PTV mutations are rare events, such that we expect a Poisson distribution for the likelihood of the observed number of PTVs

P(n|Shet;v) = Poiss n; λ), where λ = v/Shet (Eq. 3). We parameterize by using the functional form of an inverse Gaussian distribution, i.e. P (Shet; α, β = IG(Shet; α, β), so Eq. 4 becomes: Embedded Image where Kn(Z) is the modified Bessel function of the second kind. To estimate parameters of the distribution of selection coefficients, P(Shet; α, β), we fit Eq. 5 to the observed distribution of PTV counts, Qn, by maximizing the log-likelihood

Embedded Image on the regime α ∈ [10−3, 2] and β ∈ [10−4, 2], where G is the number of genes. In order to account for a slight positive correlation between the mutation rate and selection strength (Supplementary Figure 8), we separately perform the fit on U terciles of the data set and combine the results in a mixture distribution with equal weights. The mean mutation rates in the three terciles are Embedded Image. We estimate Embedded ImageEmbedded ImageEmbedded Image, with error margins denoting two s.d. from 100 bootstrapping replicates of the set of ~5,333 genes in each tercile. This error estimate is intended to quantify the effect of the sampling noise in the data set on the parameter inference while local mutation rate estimates are assumed fixed. The resulting fitted distributions of counts are shown in Supplementary Figure 9 together with the corresponding Q (n), while Figure 1 shows the inferred Embedded Image. The choice for the functional form of P (Shet) is motivated by the shape of the empirical distribution of the naïve estimator v/n (given by a simple inversion of Eq. 3). We also compared the log-likelihood of the fit to Q(n) obtained with this model to that obtained from two other two-parameter distributions, Shet ~ Gamma and Shet ~ InvGamma, and chose the model with the highest likelihood, which is Shet ~ IG.

Inference of Shet on individual genes

From the inferred distributions Embedded Image in each tercile t of the mutation rate U, we construct a per-gene estimator of Shet for genes in the tercile using the posterior probability given n, which mitigates the stochasticity of the observed PTV count: Embedded Image where the denominator is given by Eq. 5. Supplementary Table 1 provides the mean values derived from these posterior probabilities for each gene.

Predicted mode of inheritance in clinical exome cases

We trained a Naïve Bayes classifier to predict the mode of inheritance in a set of solved clinical exome sequencing cases from Baylor College of Medicine (N=283 cases)22 and UCLA23 (N=176 cases). Using data from UCLA as the training dataset, we are able to cross-predict the mode of inheritance in separately ascertained Baylor cases with classification accuracy of 88.0%, sensitivity of 86.1%, specificity of 90.2%, and an AUC of 0.931. Genes that were related to diagnosis in both clinics (overlapping genes) were removed from the larger Baylor set (Supplementary Figure 2).

Using a logistic regression based on the full set of cases from Baylor and UCLA, we generated predictions for all 15,998 genes where there is a Shet value (Supplementary Table 4).

Mouse knockout comparative analysis

We reviewed mouse knockout enrichments from two datasets: the full set of mouse knockouts from a neutrally-ascertained mouse knockout screen (N=2,179 genes) generated by the International Mouse Phenotyping Consortium25. Genes were classified as ‘Viable’, ‘Sub-Viable’, or ‘Lethal’ based on the results for the assay.

PubMed gene score and enrichment analysis

We developed a score to estimate the relative importance of each gene in the published medical and scientific literature. First, we connected literature from Entrez which included both PubMed citations and references to Entrez genes. We assigned a weight to each article referencing a gene of 1/ai, where ai was the number of genes referred to by article i. For example, an article referring to four genes would receive a weight of 1/4. Finally, we assigned each gene a score which was the sum of the weighted article scores. These scores ranged from 4,672 articles per gene (p53) to 0.0001 articles/gene.

Next, we focused on genes that are estimated to be under very strong selection but that lack functional or clinical annotations. In the top decile of Shet values, we separated the top 250 and bottom 250 genes by PubMed score. We then annotated each of these with unbiased genome-wide assays, including the number of protein-protein interactions (as determined by a genome-wide Mass Spectrometry assay)37, whether each gene is determined to be cell-essential in genome-wide CRISPR and gene trap assays3, and whether there is a mouse knockout in the neutrally-ascertained orthologous nonviable mouse knockout48. To limit the number of genes with incorrect Shet estimates in this set of 500 genes, we pre-filtered any genes with only a single exon, as they may be enriched for recent pseudogenes, and also removed any olfactory, mucin, and zinc finger proteins.

Functional enrichment analysis

We inspected the functional annotations related to approximately the top 10% of selectively disadvantageous genes (with Shet > 0.15, N=2,072 genes) that were successfully mapped using Database for Annotation, Visualization, and Integrated Discovery (DAVID) version 6.735, DAVID. Separately, two other cutoffs (Shet > 0.25, N=897 genes and Shet > 0.5, N=32 genes) were also tested and similar results were identified.

Using DAVID, we identified functional annotation terms and keywords that were enriched and clustered. Functional annotation terms were generated using the Functional Annotation tool, which includes protein information resource keywords, GeneOntology (GO) terms, biological processes and pathways, and protein domains. Using the default settings (Count 2 and EASE 0.1), 247 statistically significant (Bonferroni corrected) terms were identified and are included in Supplementary Table 5.

Using the DAVID Functional Annotation clustering feature, we identified clusters using the same set of 2,072 genes with the default settings. The first annotation cluster includes core, essential cellular components including the nuclear lumen, nucleoplasm, organelle lumen (Enrichment score 32.63), and the second includes transcription regulation and transcription factor activity (Enrichment score 27.94), detailed in Supplementary Table 6.

Acknowledgements

This work was supported by National Institutes of Health Grant HG007229, GM078598, HG009088, MH101244, and GM105857. We thank Ivan Adzhubei, Konrad Karczewski, and Alexey Kondrashov for helpful advice.

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Posted September 16, 2016.
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Estimating the Selective Effect of Heterozygous Protein Truncating Variants from Human Exome Data
Christopher A. Cassa, Donate Weghorn, Daniel J. Balick, Daniel M. Jordan, David Nusinow, Kaitlin E. Samocha, Anne O'Donnell Luria, Daniel G. MacArthur, Mark J. Daly, David R. Beier, Shamil R. Sunyaev
bioRxiv 075523; doi: https://doi.org/10.1101/075523
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