The Dissection of Expression Quantitative Trait Locus Hotspots

Abstract

Studies of the genetic loci that contribute to variation in gene expression frequently identify loci with broad effects on gene expression: expression quantitative trait locus hotspots. We describe a set of exploratory graphical methods as well as a formal likelihood-based test for assessing whether a given hotspot is due to one or multiple polymorphisms. We first look at the pattern of effects of the locus on the expression traits that map to the locus: the direction of the effects and the degree of dominance. A second technique is to focus on the individuals that exhibit no recombination event in the region, apply dimensionality reduction (e.g., with linear discriminant analysis), and compare the phenotype distribution in the nonrecombinant individuals to that in the recombinant individuals: if the recombinant individuals display a different expression pattern than the nonrecombinant individuals, this indicates the presence of multiple causal polymorphisms. In the formal likelihood-based test, we compare a two-locus model, with each expression trait affected by one or the other locus, to a single-locus model. We apply our methods to a large mouse intercross with gene expression microarray data on six tissues.

Keywords: data visualization; eQTL; gene expression; multivariate analysis; pleiotropy.

Figure 1

Inferred eQTL with LOD score ≥ 5 by tissue. Points correspond to peak LOD scores from single-QTL genome scans with each microarray probe with known genomic position. The y-axis is the position of the probe, and the x-axis is the inferred QTL position. Points are shaded according to the corresponding LOD score, although we threshold at 100: all points with a LOD score ≥ 100 are black. [A version of this figure appeared as figure 1 in Tian et al. (2015).]

Figure 2

Visualizations of the QTL effects on the multiple expression traits that map with LOD score ≥ 10 to a trans-eQTL hotspot. Each row is a hotspot. The left panels are scatter plots of signed LOD scores (with positive values indicating that the BTBR allele is associated with larger average gene expression and negative values indicating that the B6 allele is associated with larger average gene expression) vs. the estimated QTL location. Each point is a single expression trait. Tick marks at the bottom indicate the locations of the genetic markers. The right panels are scatter plots of the estimated dominance effects vs. the estimated additive effects.

Figure 3

Scatter plots of the first two linear discriminants from application of linear discriminant analysis to data on the mice that show no recombination event in the region of a trans-eQTL hotspot, using the 100 expression traits that map to the region with the highest LOD score. Blue, orange, and green points correspond to the nonrecombinant mice with genotype BB, BR, and RR, respectively, at the eQTL. Yellow points correspond to recombinant mice.

Figure 4

Scatter plots of the first two linear discriminants, as in Figure 3E, for the trans-eQTL hotspot on chromosome 10, here considering three tissues: adipose, kidney, and liver. Points correspond to mice, and they are colored according to their two-locus genotypes, for the inferred two QTL model, with one locus at ∼48 cM and the other at ∼54 cM.

Figure 5

Results of a test of one vs. two QTL at a trans-eQTL hotspot, considering the top 50 traits, in terms of LOD score, that map to the region. Each row is a hotspot. In the left panels, the black curve is the LOD score curve for the single-QTL model, with estimated QTL location indicated by a black triangle. The blue and pink curves are profile LOD score curves for the left and right QTL, respectively, for the estimated two-QTL model (with the estimated cut point). Points indicate the LOD score and estimated QTL position for the 50 expression traits, analyzed separately. The points are colored according to whether they are estimated to be affected by the left QTL (blue) or the right QTL (pink). The right panels show the ${\text{LOD}}_{\text{2v1}}^{\left(\text{c}\right)}$ score, indicating evidence for two vs. one QTL, for each possible cut point c of the list of expression traits in those that map to the left QTL and those that map to the right QTL.

Figure 6

Power to detect two QTL as a function of the distance between the QTL for varying QTL effects. (A) Ten traits, with each QTL affecting five traits. (B) Forty traits, with each QTL affecting 20 traits. (C) Forty traits, with the left QTL affecting 5 traits and the right QTL affecting 35 traits.