mod-eQTL discovery in the GTEx dataset

Benjamin Iriarte, Yongjin Park, and Manolis Kellis

• Contact: ypp@csail.mit.edu and manoli@mit.edu
• Equal contribution of BI and YP.

Experimental procedure

1. STEP1 Data collection

• Get genotype matrix per each chromosome using VCFtools
• MAF  ≥  0.05; no missing data; no in/dels --missing --geno 1 --maf 0.05 --remove-indels --remove-filtered-all

• Stored in DATA/genotype/Chr1.mat ...

• Get the list of protein coding genes (GenCode V18)
• Collect RPKM matrix for each tissue (on the same set of genes)
• Collapse RPKM per gene by simply summing them up ( ≈  same length)

• Stored in DATA/expr/Tis1.mat ...

2. STEP2 Expression quality control and normalization

• Consider tissues with  ≥  50 samples

• Retain genes if 10% of individuals have RPKM > 0.1 in all retained tissues

  retained number of genes = 12945
  retained number of tissues = 48
  retained number of samples = 8495

• Take log(1+RPKM) and perform quantile normalization
• Rescale each gene's expression (row vector) to standard Gaussian ~ N(0, 1) to prevent outliers from biasing downstream analyses.
• saved in RESULT/STEP02/Tis1.mat and so on; RESULT/STEP02/GENE_NAME.mat for gene names

• Here are the list of retained tissues:

1   Adipose - Subcutaneous  350
2   Adipose - Visceral (Omentum)    227
3   Adrenal Gland   145
4   Artery - Aorta  224
5   Artery - Coronary   133
6   Artery - Tibial 332
7   Bladder 11
8   Brain - Amygdala    72
9   Brain - Anterior cingulate cortex (BA24)    84
10  Brain - Caudate (basal ganglia) 117
11  Brain - Cerebellar Hemisphere   105
12  Brain - Cerebellum  125
13  Brain - Cortex  114
14  Brain - Frontal Cortex (BA9)    108
15  Brain - Hippocampus 94
16  Brain - Hypothalamus    96
17  Brain - Nucleus accumbens (basal ganglia)   113
18  Brain - Putamen (basal ganglia) 97
19  Brain - Spinal cord (cervical c-1)  71
20  Brain - Substantia nigra    63
21  Breast - Mammary Tissue 214
22  Cells - EBV-transformed lymphocytes 118
23  Cells - Transformed fibroblasts 284
24  Cervix - Ectocervix 6
25  Cervix - Endocervix 5
26  Colon - Sigmoid 149
27  Colon - Transverse  196
28  Esophagus - Gastroesophageal Junction   153
29  Esophagus - Mucosa  286
30  Esophagus - Muscularis  247
31  Fallopian Tube  6
32  Heart - Atrial Appendage    194
33  Heart - Left Ventricle  218
34  Kidney - Cortex 32
35  Liver   119
36  Lung    320
37  Minor Salivary Gland    57
38  Muscle - Skeletal   430
39  Nerve - Tibial  304
40  Ovary   97
41  Pancreas    171
42  Pituitary   103
43  Prostate    106
44  Skin - Not Sun Exposed (Suprapubic) 250
45  Skin - Sun Exposed (Lower leg)  357
46  Small Intestine - Terminal Ileum    88
47  Spleen  104
48  Stomach 193
49  Testis  172
50  Thyroid 323
51  Uterus  83
52  Vagina  96
53  Whole Blood 393

3. STEP3 Tissue-by-tissue confounder correction/identification of hidden covariates
   X = BC
   where X is gene by samples.

   • PEER factors 5, 10, 15, 20, 30

     PEER_setNmax_iterations(peer.model,1000)
     PEER_setTolerance(peer.model,0.01)
     PEER_setVarTolerance(peer.model,0.0001)

     stored in RESULT/STEP03/PEER/${NF}/Tis${TIS}.mat

   • MFGL factors with max 30 factors; note: we use expected E[C] not C directly

     [B,C,lambda,sigma,tau,lambda] = mfgl_gibbs(NormalizedTis${TIS},30,1000,1000);

     stored in RESULT/STEP03/MFGL/Tis${TIS}.mat

   • Difference between PEER and MFGL

     1. Prior on B and C:

        • PEER: B_gj ∼ exp( − 0.5β_j²B_gj²) and C_ji ∼ exp( − 0.5C_ji²), where β_j values are also inferred with Gamma prior (with fixed hyper-parameters).

        • MFGL: B_gj ∼ exp( − 0.5β²B_gj²) but C ∼ exp( − λ∥c_j∥), where β = 0.01m fixed; regularization parameter λ is sampled from Gamma prior.

     2. Inference : PEER uses variationa Bayes; MFGL Gibbs sampling on Bayesian group lasso model (Kyung et al. 2010). For matrix factorization problem (of moderate size), we do not need to use variational approximation. Using Gibbs sampling we are allowed to take model-average over many possible choices of λ, which then implicitly allows to select right model complexity.

   • Fig1 shows confounding factors found in Tissue #1 (Adipose - Subcutaneous).
   • Top 3-4 factors explain much of variation.
   • In Fig2 we see different patterns (Tissue #19; Brain - Spinal cord). The very first factor dominates and segregate population, and inference algorithm picks up the right amount of factors.

   • Results on the other tissues can be found in here

4. STEP4 Imputation of each gene's tissue x individual matrix

• Demonstration of imputation method:
  • Generate X = UV where the ranks of U and V are both 3 (in this example).
  • The matrix X is 50 x 450.
  • Factored matrices U and V are from from N(0, 1).
  • X was row-wise normalized.
  • Remove 80% of elements from X.
  • We can perform imputation while estimating MFGL by sampling missing values given current U and V.
  • We term this MFGL-impute.
  • Our matrix MFGL-impute accurately impute missing values:
  • We also recover correct dimensionality:
  • Penalty parameter also reached equilibrium:

• We tested from K = 1 to K = 5 and found MFGL-impute accurately estimate missing values and dimensionality.

• An example of imputed gene:

5. STEP5 Vanilla eQTL calling per tissue

• MatrixEQTL
• Number of eQTL discovery