Conditional entropy in variation-adjusted windows detects selection signatures associated with expression quantitative trait loci (eQTLs)

Abstract

Background: Over the past 50,000 years, shifts in human-environmental or human-human interactions shaped genetic differences within and among human populations, including variants under positive selection. Shaped by environmental factors, such variants influence the genetics of modern health, disease, and treatment outcome. Because evolutionary processes tend to act on gene regulation, we test whether regulatory variants are under positive selection. We introduce a new approach to enhance detection of genetic markers undergoing positive selection, using conditional entropy to capture recent local selection signals.

Results: We use conditional logistic regression to compare our Adjusted Haplotype Conditional Entropy (H|H) measure of positive selection to existing positive selection measures. H|H and existing measures were applied to published regulatory variants acting in cis (cis-eQTLs), with conditional logistic regression testing whether regulatory variants undergo stronger positive selection than the surrounding gene. These cis-eQTLs were drawn from six independent studies of genotype and RNA expression. The conditional logistic regression shows that, overall, H|H is substantially more powerful than existing positive-selection methods in identifying cis-eQTLs against other Single Nucleotide Polymorphisms (SNPs) in the same genes. When broken down by Gene Ontology, H|H predictions are particularly strong in some biological process categories, where regulatory variants are under strong positive selection compared to the bulk of the gene, distinct from those GO categories under overall positive selection. . However, cis-eQTLs in a second group of genes lack positive selection signatures detectable by H|H, consistent with ancient short haplotypes compared to the surrounding gene (for example, in innate immunity GO:0042742); under such other modes of selection, H|H would not be expected to be a strong predictor.. These conditional logistic regression models are adjusted for Minor allele frequency(MAF); otherwise, ascertainment bias is a huge factor in all eQTL data sets. Relationships between Gene Ontology categories, positive selection and eQTL specificity were replicated with H|H in a single larger data set. Our measure, Adjusted Haplotype Conditional Entropy (H|H), was essential in generating all of the results above because it: 1) is a stronger overall predictor for eQTLs than comparable existing approaches, and 2) shows low sequential auto-correlation, overcoming problems with convergence of these conditional regression statistical models.

Conclusions: Our new method, H|H, provides a consistently more robust signal associated with cis-eQTLs compared to existing methods. We interpret this to indicate that some cis-eQTLs are under positive selection compared to their surrounding genes. Conditional entropy indicative of a selective sweep is an especially strong predictor of eQTLs for genes in several biological processes of medical interest. Where conditional entropy is a weak or negative predictor of eQTLs, such as innate immune genes, this would be consistent with balancing selection acting on such eQTLs over long time periods. Different measures of selection may be needed for variant prioritization under other modes of evolutionary selection.

Figure 1

Example showing positive selection predictors and eQTLs for a single gene. This figure shows the input to the conditional logistic regression associated with a single gene (Cholesterol Ester Transfer Protein, or CETP) from the Zeller 2010 data set. The purposes of this figure are to illustrate the prediction problem in a single gene/strata, and to showcase the relative degree of serial auto-correlation (smoothness) associated with the different predictors. At the top of the figure, each SNP is indicated with a symbol reflecting the location within the gene, only one, rs1532625, is an eQTL in the Zeller data set (indicated with a large orange hourglass symbol), and it happens to be in an Intron; the two major splice isoforms of CETP are illustrated at the bottom of the figure for reference. rs1532625 does NOT show any particular sign of being under positive selection. The conditional logistic regression used in this manuscript is fit to eQTLs such as rs1532625, with genes such as CETP treated as individual strata (equivalent to a 1-to-many case-control matching in a clinical trial.) In this data set CETP contains only a single eQTL but this is not always the case. Four predictors used in this manuscript are scaled to empirical Z-scores in order to fit on the same chart; a fifth potential predictor (composite of multiple signals, cms), very powerful in other contexts, is also shown to illustrate the issue with auto-correlation. Conditional logistic models depend on a degree of independence among the predictors - because the cms score (blue line) has such a strong serial auto-correlation (as would any positive selection measure that is smoothed in a window of any size), it is not independent of the within-gene location (symbols at the top) which are used as an independent predictor. Even Fst (the green line) shows too much serial auto-correlation to converge in the Mangravite data set, which was part of the motivation in developing H|H. The other three positive selection measures, including H|H, are highly non-smooth, so they can be fit to logistic models where individual strata contain short regions of DNA.