P LOTS

We use plot to assess genetic characteristics of gene expressions that are identified as the endophenotypes.

3.6.1 Density plot of PHEs

We plot density plots and observe the variations of PHEs’ distributions under four conditions of PHEs, there are total PHEs, PHEs >0, PHEs with unadjusted p-value <

0.05 and PHEs with q-value < 0.05.

3.6.2 The scatter plot of heritability of gene expressions versus PHEs

We calculate the heritability of gene expression in each probe set. Then we plot the scatter plot under four conditions: (1) total heritability of gene expressions for all probe sets versus total PHEs, (2) heritability of gene expressions for probe sets with PHEs >0 versus PHEs >0, (3) heritability of gene expressions for probe sets with significant PHEs with unadjusted p-values < 0.05 versus significant PHEs with unadjusted p-values < 0.05, (4) heritability of gene expressions for probe sets with significant PHEs with q-values < 0.05 versus significant PHEs with q-values < 0.05.

Under four conditions, we observe the relationship between heritability of gene expressions and PHEs.

3.6.3 The bar-plot of proportions of probe sets with max significant SNPs’ LOD

>6 versus PHEs

We derive four conditions of significant SNP’s LOD >6, there are the results of genome-wide association tests for (1) gene expressions for all probe sets, (2) probe sets with PHEs >0, (3) gene expressions for probe sets with PHEs with unadjusted p-values < 0.05, (4) gene expressions for probe sets with PHEs with q-value < 0.05.

Under four conditions, we plot the bar-plot of proportions of probe sets with max significant SNP’s LOD >6 versus PHEs. The purpose of these plot is to observe variable numbers of underlying genes by observing proportions of probe sets with

max significant SNPs’ LOD >6.

The steps of plot:

Step1. No matter which conditions, we divide the PHEs into 5 groups according to 5 quantiles.

Step2. To evaluate the number of probe sets with eSNPs in each quantile of PHEs.

Step3. Each quantile of PHEs, to evaluate the proportion

=# of probe sets with significant SNPs (max LOD >6)

# of probe sets .

Step4. The bar-plot: Proportions versus quantiles of PHEs.

3.6.4 The bar-plot of number of cis eSNPs <100 kb or cis eSNPs >100 kb or trans versus PHEs

A cis-regulatory element or cis-element is a region of DNA or RNA that regulates the expression of genes located on that same strand. These cis-regulatory elements are often binding sites of one or more trans-acting factors. In contrast, trans-regulatory elements are species which may modify the expression of genes distant from the gene that was originally transcribed to create them. To demonstrate the concept (this is not a specific example), a transcription factor which regulates a gene on chromosome 6 might itself have been transcribed from a gene on chromosome 11.

To summarize, cis-elements are present on the same strand as the gene they regulate whereas trans-elements can regulate genes distant from the gene from which they were transcribed (⁸http://en.wikipedia.org/wiki/Cis-regulatory_element).

So we defined the cis eSNPs is that the strongest cis effect for a given expression values of probe sets was then mapped by testing SNPs located at the location of this probe set in the same chromosome. If cis eSNPs located within 100 kb window centered at the location of this probe set in the same chromosome, we define them as

location of this probe set in the same chromosome, we define them as “cis eSNPs

>100 kb”. Trans is that eSNPs are in other chromosomes and not the same chromosomes of this probe set.

We derive four conditions of significant SNP’s LOD >6 (eSNPs), there are the results of genome-wide association tests for (1) gene expressions for all probe sets, (2) probe sets with PHEs >0, (3) for gene expressions for probe sets with PHEs with unadjusted p-values < 0.05, (4) for gene expressions for probe sets with PHEs with q-value < 0.05.

Under four conditions, we plot

a. The bar-plot of number of cis eSNPs <100 kb versus PHEs.

b. The bar-plot of number of cis eSNPs >100 kb versus PHEs.

c. The bar-plot of number of trans versus PHEs.

The purpose of these plots is to observe the various numbers of cis eSNPs < 100 kb, cis eSNPs > 100 kb or trans and infer the various number of underlying genes.

The steps of plot:

Step1. No matter which conditions, we divide PHEs into 5 groups according to 5 quantiles.

Step2. To evaluate the number of cis eSNPs <100 kb, cis eSNPs >100 kb and trans separately in each quantile.

Step3. The bar-plots: Number (cis eSNPs <100kb, cis eSNPs >100kb and trans) versus quantiles of PHEs.

3.6.5 The bar-plot of number of cis eSNPs <100 kb or cis eSNPs >100 kb or trans versus heritability of gene expressions and differential expressions.

Heritability of gene expression is the proportion of gene expressional variation that is attributable to genetic variation. We calculate the heritability of gene expression value in each probe set and use the q-values from output of SAM as differential

expression value.

We calculate heritability of gene expressions (differential expressions) under four conditions: (1) gene expressions for all probe sets, (2) gene expressions for probe sets with PHEs >0, (3) gene expressions for probe sets with PHEs with unadjusted p-values < 0.05, (4) gene expressions for probe sets with PHEs with q-value < 0.05.

Under four conditions, we plot

a. The bar-plot: numbers of cis eSNPs <100 kb versus heritability of gene expressions and differential expressions.

b. The bar-plot: numbers of cis eSNPs >100 kb versus heritability of gene expressions and differential expressions.

c. The bar-plot: numbers of trans versus heritability of gene expressions and differential expressions.

The purpose of these plots is to observe that the various numbers of cis eSNPs <

100 kb, cis eSNPs > 100 kb or trans corresponding to heritability of gene expressions and differential expression values.

The steps of plot:

Step1. No matter which conditions, we divide heritability of gene expressions and differential expressions into 5 groups according to 5 quantiles.

Step2. To evaluate the numbers of cis eSNPs <100 kb, cis eSNPs >100 kb and trans separately in each quantile of heritability of gene expressions and differential expressions.

Step3. The bar-plots: Numbers (cis eSNPs <100kb, cis eSNPs >100kb and trans) versus quantiles of heritability of gene expressions and differential expressions.

3.6.6 The density plot of LOD score for cis eSNPs <100 kb, cis eSNPs >100 kb and trans

We derive four conditions of SNP’s LOD scores, there are the result of genome-wide association tests for (1) gene expressions for all probe sets, (2) for gene expressions for probe sets with PHEs >0, (3) gene expressions for probe sets with PHEs with unadjusted p-values < 0.05, (4) gene expressions for probe sets with PHEs with q-value < 0.05.

Under four conditions, we plot the density plot of LOD scores for cis eSNPs <100 kb, cis eSNPs >100 kb and trans and observe these distributions of cis eSNPs <100 kb, cis eSNPs > 100 kb and trans.