Multiple locus linkage analysis of genomewide expression in yeast

Abstract

With the ability to measure thousands of related phenotypes from a single biological sample, it is now feasible to genetically dissect systems-level biological phenomena. The genetics of transcriptional regulation and protein abundance are likely to be complex, meaning that genetic variation at multiple loci will influence these phenotypes. Several recent studies have investigated the role of genetic variation in transcription by applying traditional linkage analysis methods to genomewide expression data, where each gene expression level was treated as a quantitative trait and analyzed separately from one another. Here, we develop a new, computationally efficient method for simultaneously mapping multiple gene expression quantitative trait loci that directly uses all of the available data. Information shared across gene expression traits is captured in a way that makes minimal assumptions about the statistical properties of the data. The method produces easy-to-interpret measures of statistical significance for both individual loci and the overall joint significance of multiple loci selected for a given expression trait. We apply the new method to a cross between two strains of the budding yeast Saccharomyces cerevisiae, and estimate that at least 37% of all gene expression traits show two simultaneous linkages, where we have allowed for epistatic interactions. Pairs of jointly linking quantitative trait loci are identified with high confidence for 170 gene expression traits, where it is expected that both loci are true positives for at least 153 traits. In addition, we are able to show that epistatic interactions contribute to gene expression variation for at least 14% of all traits. We compare the proposed approach to an exhaustive two-dimensional scan over all pairs of loci. Surprisingly, we demonstrate that an exhaustive two-dimensional scan is less powerful than the sequential search used here. In addition, we show that a two-dimensional scan does not truly allow one to test for simultaneous linkage, and the statistical significance measured from this existing method cannot be interpreted among many traits.

Figure 1. A Power Comparison of the 2D Locus Pair Search and the Sequential Search

The number of significant traits over a range of p-value thresholds are shown. Since any given p-value threshold results in the same number of expected false positives, these plots give empirical evidence that the sequential search is more powerful than the 2D search. (A) Plot of the number of traits significant for linkage versus the p-value threshold. (B) Plot of the number of traits significant for epistasis versus the p-value threshold. The gray line, which shows the number of expected false positives for each p-value cut-off, is similar to the number called significant under the exhaustive 2D search.

Figure 2. An Example of the Locus-Specific Linkage Probability Estimation Applied to the Secondary Loci

The estimated density of the observed statistics is plotted (solid black). This density is modeled as a weighted mixture of probability densities corresponding to the “null” unlinked secondary loci (solid grey) and the “alternative” linked secondary loci (dashed grey). The estimated posterior probability of linkage is also shown (dashed black).

Figure 3. A Plot of the Locus Pair Positions Corresponding to the 170 Traits Significant for Joint Linkage

(A) A plot of the significant locus pair positions when each chromosome has been partitioned into equally sized bins less than or equal to 550 kb. The number of significant traits showing linkage to locus pairs in each pair-wise bin is denoted. The number on each axis indicates the chromosome number; a dash denotes a bin division. (B) A plot constructed analogously to (A), except bins less than or equal to 50 kb are used, and only bins with three or more traits significant for joint linkage are numbered.