Applicability of the Mutation-Selection Balance Model to Population Genetics of Heterozygous Protein-Truncating Variants in Humans

Abstract

The fate of alleles in the human population is believed to be highly affected by the stochastic force of genetic drift. Estimation of the strength of natural selection in humans generally necessitates a careful modeling of drift including complex effects of the population history and structure. Protein-truncating variants (PTVs) are expected to evolve under strong purifying selection and to have a relatively high per-gene mutation rate. Thus, it is appealing to model the population genetics of PTVs under a simple deterministic mutation-selection balance, as has been proposed earlier (Cassa et al. 2017). Here, we investigated the limits of this approximation using both computer simulations and data-driven approaches. Our simulations rely on a model of demographic history estimated from 33,370 individual exomes of the Non-Finnish European subset of the ExAC data set (Lek et al. 2016). Additionally, we compared the African and European subset of the ExAC study and analyzed de novo PTVs. We show that the mutation-selection balance model is applicable to the majority of human genes, but not to genes under the weakest selection.

Keywords: genetic drift; protein-truncating variants; selection inference.

Fig. 1.

Comparison of the deterministic mutation–selection balance model with the model that includes the effects of genetic drift, in the NFE demography. (a) Fold change in the coefficient of variation (squares) and the mean (crosses) of the number of PTV mutations, k, relative to the deterministic case, obtained from simulations of a realistic demography of the ExAC NFE sample for different values of heterozygous selection strength s_het. (b) Heat map of gene-specific estimates for all 16,279 tested genes from the NFE sample, showing deterministic (x axis) and drift-inclusive (y axis) s_het estimates. Note the double-logarithmic axes in both panels.

Fig. 2.

In the strong selection limit, s_het is a predictor of the fraction of de novo PTVs, f. De novo fraction of PTV mutations was estimated for 6,203 (out of 16,279) genes with at least one PTV (de novo or transmitted) in an ASD cohort of ∼4,000 parent–child trios (y axis) and compared with the deterministic ${\widehat{s}}_{\text{het}}$ derived from the NFE sample (x axis). Red dots denote individual genes (genes with $\widehat{f}=0$ were assigned $\widehat{f}=2\times {10}^{-4}$ for illustration purposes). Black squares connected by black lines denote the mean in bins along the x axis of logarithmic width $\Delta \hspace{0.17em}\text{log}[{\widehat{s}}_{\text{het}}]=0.25$ (number of genes per bin from left to right: {1, 10, 43, 148, 400, 811, 1,117, 1,158, 870, 597, 359, 360, 236, 90, 3}). Vertical error bars show the standard error of the mean per bin for $\widehat{f}$. Corresponding error bars for ${\widehat{s}}_{\text{het}}$ are smaller than the marker size. Gray line denotes the diagonal.

Fig. 3.

Comparison of per-gene selection estimates, ${\widehat{s}}_{\text{het}}$, with a measure of probability of loss-of-function intolerance, pLI (Lek et al. 2016). Shown is the correlation with independent measures of gene importance. (a–c) Data on disease severity, penetrance, and age of onset (x axes) for a set of 113 haploinsufficient disease-associated genes of high confidence (ClinGen Dosage Sensitivity Project) were compared with deterministic NFE ${\widehat{s}}_{\text{het}}$ (top row) and pLI (bottom row) predictions (y axis). (d) The fraction of de novo PTVs ($\widehat{f}$), shown in bins of width 0.25 for 5,930 genes with at least one transmitted or de novo PTV and a pLI annotation (x axis), was derived from an ASD trio-sequencing data set (top: NFE ${\widehat{s}}_{\text{het}}$, bottom: pLI). Note that due to the small number of PTVs per gene in the ASD cohort, the distribution of $\widehat{f}$ on the range [0, 1] is not smooth. Red dots denote individual genes, gray boxes enclose the central quartiles of the distribution in each category, and black horizontal bars through gray boxes show the median. Note the logarithmic y axis in the top row, whereas the bottom row has a linear y axis.