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Numerous studies have employed genome-wide measures of mRNA abundance (typically assayed using DNA microarrays, and more recently RNA-seq) in combination with high-resolution genotyping (often supplemented with statistical imputation to loci not directly assayed, leading to genotype calls with quantified uncertainty) to search for genetic determinants of variation in gene expression. Key references in human applications include Cheung et al. (2005), Majewski & Pastinen (2011), and Gaffney et al. (2012); Shabalin (2012) addresses computational concerns.
This document focuses on searches for eQTL
A typical report describes tuning of the search (including, for example, boundaries on minor allele frequencies of variants to be tested, approach to correction for batch effects and other forms of confounding, scope of search in terms of distance from gene coding region), enumerates variants with evidence of association to expression variation in nearby genes, and then characterizes the biological roles of the discovered variants.
Suppose there are \(N\) independently sampled individuals with gene expression measures on \(G\) genes or probes. Each individual is genotyped (or has genotype statistically imputed) at \(S\) DNA locations, catalogued by NCBI dbSNP or 1000 genomes. We are given a \(G \times N\) matrix of expression assay results, and \(N \times S\) genotyping results in the form of the number of B alleles (or expected number of B alleles) for each of the loci. Select the search radius &rho \(\rho\) (for example, 100kb) and for each gene \(g\), determine the search neighborhoods \(Ng = N{g,\rho} = [a_g-\rho, b_g+\rho]\), where \(a_g\) denotes the genomic coordinate of the 5' end of the transcript region for gene \(g\), and \(b_g\) is the coordinate at the 3' end. Let \(|N_g|\) denote the number of SNP in that neighborhood. Key objectives are
The code in the example for the GGtools function All.cis() yields an example of a sharply restricted search for cis eQTL on chr21, using data on the HapMap CEU population.
cc = new("CisConfig") # take a default configuration
chrnames(cc) = "21" # confine to chr21
estimates(cc) = FALSE # no point estimates neede
f1 <- All.cis(cc) # compute the tests; can be slow without attendance
# to parallelization
The result of the function inherits from GRanges, and includes metadata concerning its generation.
length(f1)
## [1] 6060
f1[1:3]
## cisRun with 3 ranges and 10 metadata columns:
## seqnames ranges strand | snp
## <Rle> <IRanges> <Rle> | <character>
## GI_11342663-S 21 [42683950, 42830869] + | rs2838008
## GI_11342663-S 21 [42683950, 42830869] + | rs9985079
## GI_11342663-S 21 [42683950, 42830869] + | rs12627067
## snplocs score fdr probeid MAF
## <integer> <numeric> <numeric> <character> <numeric>
## GI_11342663-S 42685044 0.44 0.8945 GI_11342663-S 0.3483
## GI_11342663-S 42687136 0.40 0.9070 GI_11342663-S 0.4156
## GI_11342663-S 42689443 0.21 0.9171 GI_11342663-S 0.2697
## dist.mid permScore_1 permScore_2 permScore_3
## <numeric> <numeric> <numeric> <numeric>
## GI_11342663-S -72366 0.10 1.57 0.44
## GI_11342663-S -70274 0.40 0.25 0.08
## GI_11342663-S -67966 0.35 0.00 0.09
## ---
## seqlengths:
## 21
## NA
metadata(f1)
## $call
## All.cis(config = cc)
##
## $config
## CisConfig instance. Key parameters:
## smpack = GGdata ; chrnames = 21
## nperm = 3 ; radius = 50000
## ====
## Configure using
## [1] "smpack<-" "rhs<-" "nperm<-"
## [4] "folderStem<-" "radius<-" "shortfac<-"
## [7] "chrnames<-" "smchrpref<-" "gchrpref<-"
## [10] "schrpref<-" "geneApply<-" "geneannopk<-"
## [13] "snpannopk<-" "smFilter<-" "exFilter<-"
## [16] "keepMapCache<-" "SSgen<-" "excludeRadius<-"
## [19] "estimates<-"
Use of GRanges for the organization of association test statistics allows easy amalgamation of findings with other forms of genomic annotation. Retention of the association scores achieved under permutation allows recomputation of plug-in FDR after combination or filtering.
Targeted visualization of association is supported with the plot_EvG function in GGBase. To obtain the figure on the right, the expression matrix has been transformed by removing the principal components corresponding to the 10 largest eigenvalues. This is a crude approach to reducing “expression heterogeneity'', a main concern of eQTL analyses to date (Leek & Storey, 2007).
## Warning: harmonizeSamples TRUE and sampleNames for es not coincident with
## rownames(sml[[1]]); harmonizing...
plot_EvG(probeId("o67h4JQSuEa02CJJIQ"), rsid("rs2259928"), c20f, main = "10 expr. PC removed")
Above we have a single SNP-gene association.
The family of
associations observed cis to ABHD12 can also be
visualized in conjunction with the transcript models.
As of November 2013, a reasonably efficient representation of expression, sample and genotype data is defined using an R package containing
Elements of the sampleNames of the ExpressionSet instance must coincide with elements of the row names of the SnpMatrix instances. At time of analysis, warnings will be issued and harmonization attempts will be made when the coincidence is not exact.
The SnpMatrix instances make use of a byte code for (potentially) imputed genotypes.
Each element of the code defines a point on the simplex displayed below, allowing
a discrete but rich set of the key quantities of interest, the expected number of B alleles.
Note that the nucleotide codes are not carried in this representation. Typically for a diallelic SNP, B denotes the alphabetically later nucleotide.
We can illustrate the basic operations with this overall structure, using data collected on Yoruban (YRI) HapMap cell lines. Expression data were obtained at ArrayExpression E-MTAB-264 (Stranger et al. 2012).
library(GGtools)
library(yri1kgv)
library(lumiHumanAll.db)
## Warning: package 'lumiHumanAll.db' was built under R version 3.0.2
## Loading required package: AnnotationDbi
## Warning: package 'AnnotationDbi' was built under R version 3.0.2
## Loading required package: org.Hs.eg.db
##
##
## lumiHumanAll.db is using or is likely to need access to special
## nuID identifiers. Users can learn about these identifiers from
## vignette documentation provided with the lumi package.
if (!exists("y22")) y22 = getSS("yri1kgv", "chr22")
## Warning: harmonizeSamples TRUE and sampleNames for es not coincident with
## rownames(sml[[1]]); harmonizing...
y22
## SnpMatrix-based genotype set:
## number of samples: 79
## number of chromosomes present: 1
## annotation: lumiHumanAll.db
## Expression data dims: 21800 x 79
## Total number of SNP: 494322
## Phenodata: An object of class 'AnnotatedDataFrame'
## sampleNames: NA18486 NA18487 ... NA19257 (79 total)
## varLabels: Source.Name Material.Type ... Factor.Value.SIGNAL.
## (26 total)
## varMetadata: labelDescription
dim(exprs(y22))
## [1] 21800 79
fn = featureNames(y22)[1:5]
The annotation of expression features can be explored in several directions. First, the probe names themselves encode the 50mers on the chip.
library(lumi)
id2seq(fn) # get the 50mer for each probe
## NQqs8dKRwVSgI4SRPk
## "CAAGGGGTATTACTCAGGCACTAACCCCAGGAAAGATGACAGCACATTGC"
## BvIpQQ9yzp__kCLnEU
## "GTTAGAGGCCAACAATTCTAGTATGGCTTGTTGGCAAAGAGTGCTACACC"
## NH1MoTHk7CULTog3nk
## "ACTTCCATAGGACATACTGCATGTAAGCCAAGTCATGGAGAATCTGCTGC"
## KNJlVFShMX1UoyIkRc
## "ATCAGCGCCCCCACCCAGGACATACCTTCCCCAGGATAGAGAGCACACCT"
## fuplG2R3erO3QrujDk
## "GTGGGCGCCACGTCGCACTCTCTGGGTATGTCTCAAGGTGTGGATAATGC"
# and some annotation
Second, the mapping to institutionally curated gene identifiers is available.
select(lumiHumanAll.db, keys = fn, keytype = "PROBEID", columns = c("SYMBOL",
"CHR", "ENTREZID"))
## PROBEID SYMBOL CHR ENTREZID
## 1 NQqs8dKRwVSgI4SRPk THBS3 1 7059
## 2 BvIpQQ9yzp__kCLnEU SLC38A2 12 54407
## 3 NH1MoTHk7CULTog3nk CCNB1 5 891
## 4 KNJlVFShMX1UoyIkRc ZNF496 1 84838
## 5 fuplG2R3erO3QrujDk LOC100130238 12 100130238
Finally, we can look at the genotype information. This can be voluminous and is managed in an environment to reduce potential copying expenses.
gt22 <- smList(y22)[[1]] # access to genotypes
as(gt22[1:5, 1:5], "character")
## rs149201999 rs146752890 rs139377059 rs188945759 rs6518357
## NA18486 "A/A" "A/A" "A/A" "A/A" "A/A"
## NA18487 "A/A" "A/A" "A/A" "A/A" "A/A"
## NA18489 "A/A" "A/A" "A/A" "A/A" "A/A"
## NA18498 "A/A" "A/A" "A/A" "A/A" "A/A"
## NA18499 "A/A" "A/A" "A/A" "A/A" "A/A"
cs22 = col.summary(gt22) # some information on genotypes
cs22[1:10, ]
## Calls Call.rate Certain.calls RAF MAF P.AA P.AB
## rs149201999 79 1 1 0.094937 0.094937 0.8101 0.18987
## rs146752890 79 1 1 0.069620 0.069620 0.8608 0.13924
## rs139377059 79 1 1 0.069620 0.069620 0.8608 0.13924
## rs188945759 79 1 1 0.006329 0.006329 0.9873 0.01266
## rs6518357 79 1 1 0.075949 0.075949 0.8481 0.15190
## rs62224609 79 1 1 0.000000 0.000000 1.0000 0.00000
## rs62224610 79 1 1 0.297468 0.297468 0.4937 0.41772
## rs143503259 79 1 1 0.000000 0.000000 1.0000 0.00000
## rs192339082 79 1 1 0.000000 0.000000 1.0000 0.00000
## rs79725552 79 1 1 0.075949 0.075949 0.8481 0.15190
## P.BB z.HWE
## rs149201999 0.00000 0.932328
## rs146752890 0.00000 0.665103
## rs139377059 0.00000 0.665103
## rs188945759 0.00000 0.056613
## rs6518357 0.00000 0.730537
## rs62224609 0.00000 NA
## rs62224610 0.08861 -0.005111
## rs143503259 0.00000 NA
## rs192339082 0.00000 NA
## rs79725552 0.00000 0.730537
This workflow is based on Amazon EC2 computation managed using the MIT starcluster utilities. Configuration and management of EC2 based machinery is quite simple. The bulk of the partial run described here used configuration variables
In a complete run, for chromosome 1, a rescue run was required with a larger instance type (m3.2xlarge).
We will describe an essentially monolithic approach to using a cluster to search for eQTL in which evaluation of a single R function drives the search. The master process will communicate with slaves via sockets; slaves will write results to disk and ship back to master. The task is executed across chromosomes that have been split roughly in thirds to reduce RAM consumption.
The ciseqByCluster function of GGtools is the workhorse for the search. Arguments to this function determine how the search will be configured and executed. The invocation here asks for a search on four chromosomes, dispatching work from a master R process to a four node cluster, with multicore concurrency for gene-specific searches on eight cores per node. Three output files are generated in the folder identified as targetfolder:
The following script is available on the AMI noted above and will generate the partceu100k_dt data.table instance used for analysis below.
library(parallel)
newcl = makePSOCKcluster(c("master", paste0("node00", 1:3)))
library(foreach)
library(doParallel)
registerDoParallel(cores = 8) # may want to keep at 5
library(GGtools)
ceuDemoRecov = try(ciseqByCluster(newcl, chromsToRun = 19:22, finaltag = "partceu100k",
outprefix = "ceurun", ncoresPerNode = 8, targetfolder = "/freshdata/CEU_DEMO"))
save(ceuDemoRecov, file = "ceuDemoRecov.rda")
stopCluster(newcl)
stopImplicitCluster()
sessionInfo()
The full set of arguments and defaults for ciseqByCluster is
The GFF3 file that is generated along with the data.table instance is useful for targeted queries, potentially from external applications. The primary difficulty with using this in R is the need to parse the optional data subfields of field 9.
It is customary to inspect QQ-plots for genome-wide association studies. For eQTL searches, the number of test results can range into the billions, so a binned approach is taken.
binnedQQ(partceu100k_dt, ylim = c(0, 30), xlim = c(-2, 15), end45 = 12)
This gives an indication that the distribution of the vast majority of observed SNP-gene pair association statistics is consistent with the null model.
Because our data.table output retains information on association scores achieved after permuting expression against genotype, we can recompute plug-in FDRs for loci that remain after filtering the full set of records in various ways. The eqsens_dt function allows exploration of sensitivity of eQTL enumerations across various dimensions, and users can add additional dimension through suitable programming. The default behavior is illustrated first:
load("partceu100k_dt.rda")
library(foreach) # basic function includes a %dopar%
library(doParallel)
## Warning: package 'doParallel' was built under R version 3.0.2
## Loading required package: iterators
library(parallel)
dcdown = max(c(detectCores() - 1, 1))
registerDoSEQ()
if (.Platform$OS.type != "windows") {
cl = makeForkCluster(dcdown)
registerDoParallel(cl, cores = 1) # nesting?
}
eq1 = eqsens_dt(partceu100k_dt)
plotsens(eq1)
## Loading required package: reshape2
## Loading required package: ggplot2
The arguments to eqsens_dt are
args(eqsens_dt)
## function (dtab, filtgen = filtgen.maf.dist, by = c("pairs", "snps",
## "probes")[1], targfdrs = c(0.05, 0.01, 0.005), parmslist = list(mafs = c(0.025,
## 0.05, 0.075, 0.1, 0.125), dists = c(1000, 5000, 10000, 25000,
## 50000, 1e+05)))
## NULL
and setting components of the parmslist argument governs the set of tuning parameter vectors that will be used. Exploration of additional dimensions would involve passing a different function for the filtgen parameter; filtgen.maf.dist assumes a 2-vector of (MAF, dist) will be used to retain rows with MAF exceeding the input MAF, and dist no greater than the input mindist from SNP to gene.
As of 1/20/2014 the call to scoresCis() can only be executed with R-devel and GGtools 4.11.28+.
We will focus on the data.table output. A basic objective is targeted visualization. The scoresCis function helps with this. We load the data.table instance first.
library(data.table)
load("partceu100k_dt.rda")
scoresCis("CPNE1", partceu100k_dt)
In this section we consider how structural and genetic information can be used to distinguish conditional probabilities of SNP genotypes being associated with phenotypic variation. We use some additional data provided in the GGtools package concerning a) chromatin state of the lymphoblastoid cell line GM12878, a line similar to those form which expression data were generated, and b) identities of SNP that have been found to be hits or are in LD with hits at \( R2 > 0.80 \) in the NHGRI GWAS catalog. See man pages for hmm878 in GGtools package and gwastagger in gwascat package for more information. These data are automatically propagated to ciseqByCluster data.table output.
Our approach is to use logistic regression on 1.5 million records. We use the biglm package to keep memory images modest.
We discretize some of the key factors, and form an indicator variable for the event that the SNP is in a region of active or poised promoter chromatin state, as determined by ChromHMM on GM12878.
distcat = cut(partceu100k_dt$mindist, c(-1, 1, 1000, 5000, 10000, 50000, 100001))
fdrcat = cut(partceu100k_dt$fdr, c(-0.01, 0.005, 0.05, 0.1, 0.2, 1.01))
fdrcat = relevel(fdrcat, "(0.2,1.01]")
mafcat = cut(partceu100k_dt$MAF, c(0, 0.05, 0.1, 0.2, 0.3, 0.51))
approm = 1 * partceu100k_dt$chromcat878 %in% c("1_Active_Promoter", "3_Poised_Promoter")
Now we rebuild the data.table and fit the model to a randomly selected training set of about half the total number of records.
partceu100k_dt = cbind(partceu100k_dt, distcat, fdrcat, mafcat, approm)
set.seed(1234)
train = sample(1:nrow(partceu100k_dt), size = floor(nrow(partceu100k_dt)/2),
replace = FALSE)
library(biglm)
b1 = bigglm(isgwashit ~ distcat + fdrcat + mafcat + approm, fam = binomial(),
data = partceu100k_dt[train, ], maxit = 30)
A source of figures of merit is the calibration of predictions against actual hit events in the test set.
pp = predict(b1, newdata = partceu100k_dt[-train, ], type = "response")
summary(pp)
## V1
## Min. :0.00241
## 1st Qu.:0.00661
## Median :0.01670
## Mean :0.01593
## 3rd Qu.:0.02733
## Max. :0.20005
cpp = cut(pp, c(0, 0.025, 0.05, 0.12, 0.21))
table(cpp)
## cpp
## (0,0.025] (0.025,0.05] (0.05,0.12] (0.12,0.21]
## 1026788 467427 1701 1473
sapply(split(partceu100k_dt$isgwashit[-train], cpp), mean)
## (0,0.025] (0.025,0.05] (0.05,0.12] (0.12,0.21]
## 0.009177 0.030655 0.061141 0.158859
It seems that the model, fit using data on a small number of chromosomes, has some predictive utility. We can visualize the coefficients:
tmat = matrix(rownames(summary(b1)$mat), nc = 1)
est = summary(b1)$mat[, 1]
library(rmeta)
forestplot(tmat, est, est - 0.01, est + 0.01, xlog = TRUE, boxsize = 0.35, graphwidth = unit(3,
"inches"), xticks = exp(seq(-4, 2, 2)))
Standard errors in the presence of correlations among responses require further methodological development.
sessionInfo()
## R version 3.0.1 (2013-05-16)
## Platform: x86_64-apple-darwin10.8.0 (64-bit)
##
## locale:
## [1] C
##
## attached base packages:
## [1] grid parallel splines stats4 stats graphics grDevices
## [8] utils datasets methods base
##
## other attached packages:
## [1] ggplot2_0.9.3.1 reshape2_1.2.2 doParallel_1.0.8
## [4] iterators_1.0.6 lumiHumanAll.db_1.22.0 org.Hs.eg.db_2.10.1
## [7] RSQLite_0.11.4 AnnotationDbi_1.24.0 Cairo_1.5-5
## [10] rmeta_2.16 biglm_0.9-1 DBI_0.2-7
## [13] foreach_1.4.1 lumi_2.14.2 Biobase_2.22.0
## [16] scatterplot3d_0.3-35 yri1kgv_0.5.2 GGtools_4.10.0
## [19] Rsamtools_1.14.3 Biostrings_2.30.1 GenomicRanges_1.14.4
## [22] XVector_0.2.0 IRanges_1.20.7 BiocGenerics_0.8.0
## [25] GGBase_3.24.0 snpStats_1.12.0 Matrix_1.0-12
## [28] lattice_0.20-27 survival_2.37-4 knitcitations_0.5-0
## [31] bibtex_0.3-6 knitr_1.5
##
## loaded via a namespace (and not attached):
## [1] BSgenome_1.30.0 BiocInstaller_1.12.0
## [3] GenomicFeatures_1.14.5 KernSmooth_2.23-10
## [5] MASS_7.3-26 R.methodsS3_1.6.1
## [7] RColorBrewer_1.0-5 RCurl_1.95-4.1
## [9] Rcpp_0.11.1 VariantAnnotation_1.8.13
## [11] XML_3.95-0.2 affy_1.40.0
## [13] affyio_1.30.0 annotate_1.40.1
## [15] base64_1.1 beanplot_1.1
## [17] biomaRt_2.18.0 bit_1.1-11
## [19] bitops_1.0-6 bumphunter_1.2.0
## [21] codetools_0.2-8 colorspace_1.2-4
## [23] compiler_3.0.1 dichromat_2.0-0
## [25] digest_0.6.4 doRNG_1.6
## [27] evaluate_0.5.1 ff_2.2-12
## [29] formatR_0.10 genefilter_1.44.0
## [31] gtable_0.1.2 httr_0.2
## [33] illuminaio_0.4.0 itertools_0.1-3
## [35] labeling_0.2 limma_3.18.13
## [37] locfit_1.5-9.1 matrixStats_0.8.14
## [39] mclust_4.2 methylumi_2.8.0
## [41] mgcv_1.7-22 minfi_1.8.9
## [43] multtest_2.18.0 munsell_0.4.2
## [45] nleqslv_2.1.1 nlme_3.1-109
## [47] nor1mix_1.1-4 pkgmaker_0.20
## [49] plyr_1.8.1 preprocessCore_1.24.0
## [51] proto_0.3-10 registry_0.2
## [53] reshape_0.8.4 rngtools_1.2.4
## [55] rtracklayer_1.22.6 scales_0.2.3
## [57] siggenes_1.36.0 stringr_0.6.2
## [59] tools_3.0.1 xtable_1.7-3
## [61] zlibbioc_1.8.0