# Contents

This tutorial exemplifies how the covRNA package uses fourthcorner analysis and RLQ to discover covariate associations in transcriptomic data. Here, an RNA-Seq dataset of Bacillus anthracis containing different stress conditions as sample covariates and COG annotations (Clusters of Orthologous Groups) as gene covariates will be analysed. Further, it will be shown how gene covariates can be assigned to the dataset by using other R packages.

Please install the package as follows.

> source("https://bioconductor.org/biocLite.R")
> biocLite("covRNA")

# 1 1. Overview of the Analysis

Gene expression data normally comes with covariates of the samples and of the genes. To analyze associations between sample and gene covariates, the fourthcorner analysis tests the statistical significance of the associations by permutation tests (Legendre et al., 1997) while the RLQ visualizes associations within and between the covariates (Doledec et al., 1996).

The fourthcorner analysis and rlq implemented in the ade4 package (Dray et al., 2007, and Dray et al., 2014) are adapted to easily analyze large-scale transcriptomic data. The functions stat and ord of this package can be used for fourthcorner analysis and rlq, respectively; hereby 1. runtime and storage space are significantly reduced; 2. the analysis accounts for transcriptome-specific shapes of the empirical permutation distributions; 3. the analysis is rendered user-friendly by supplying automation, simple designing of plots and unsupervised gene filtering.

Please refer to the manpages for details about the functions. The package covRNA is implemented to be easily combinable with other packages and objects of the Bioconductor project (Gentleman et al., 2004).

input An ExpressionSet object of the package Biobase can be used as input. Then, the ExpressionSet has to contain transcriptomic data in its argument assayData, the sample covariates in phenoData and the gene covariates in featureData.

Alternatively to an ExpressionSet, the three data.frames R, L and Q can be used as input. Here, data.frame L contains transcriptomic data, Q the sample covariates and R the gene functions.

stat The function stat takes each combination between one sample covariate and one gene covariate and calculates a statistic. If at least one the covariates is quantitative, a correlation coeffcient is calculated. If both covariates are categorical, a Chi-Square test (Fisher, 1922) related statistic is calculated. Significance of the associations is assessed by permutation tests. By default, multiple testing correction according to Benjamini and Hochberg (1995) is applied. The resulting p-values are plotted as cross-tabulation of the sample covariates and the gene functions; by default, red and blue cells show negative and positive significant associations at $$\alpha$$=0.05, respectively.

ord The function ord automatically applies singular matrix ordination to each of the three data.frames R, L and Q. Correspondence Analysis (CA) is applied to L. Principal Component Analysis (PCA) or Hillsmith Analysis (HA) or Multiple Correspondence Analysis (MCA) are applied to R and Q, depending on the type of variables they contain. Then, the rlq function of the ade4 package is applied and the results can be plotted.

# 2 2. Analysis of an RNA-Seq Dataset

Here, an RNA-Seq dataset of Bacillus anthracis (ExpressionSet Baca) containing different stress conditions as sample covariates and COG annotations (Clusters of Orthologous Groups, Tatusov et al., 2000) as gene covariates will be analysed.

## 2.1 2.1 Preparation of the dataset

We load the covRNA package and the integrated Baca dataset, which contains the ExpressionSet Baca. The assayData contains deep sequenced RNA-Seq data of B. anthracis under four stress conditions (with four replicates per stress conditions). The raw sequence reads derive from Passalacqua et al. (2012) and are availaible at Gene Expression Omnibus (GEO, accession number GSE36506). We have already mapped, counted and DESeq2 (Love et al., 2014) normalised these counts. The phenoData assigns the stress condition, i.e. ctrl, cold, salt and alcohol stress, to the samples. The featureData contains COG annotations of the genes.

library(covRNA)
## Loading required package: ade4
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data(Baca)

## 2.2 2.2 Fourthcorner Analysis with stat

We use the function stat to statistically analyse associations between gene and sample covariates.

statBaca <- stat(ExprSet = Baca, npermut = 999, padjust = "BH", nrcor = 2, exprvar = 1)

statBaca is then an object of type stat. As a list, it saves all results as well as the input of the function. For instance, we can access the adjusted p-values of all covariate combinations.

ls(statBaca)
adjp <- statBaca\$adj.pvalue; adjp

To visualise the results, the stat object can be plotted (Figure 1). If the plot shall be shown in high quality, we advise to use the default setting pdf=TRUE.

plot(statBaca, xnames = c('cold','ctrl','etoh','salt'), shiftx = -0.1)

Figure 1: Cross-tabulation of the adjusted p-values between the sample covariates and the gene functions of the ExpressionSet Baca. Red and blue cells show negative and positive significant associations at $$\alpha$$=0.05, respectively.

The cross-tabulation of the sample covariates and the gene functions visualises negative and positive significant associations at $$\alpha$$=0.05. Five significant associations can be discovered.

## 2.3 2.3 RLQ with ord

We use the function ord to visualise sample and gene covariates in one coordinate system.

ordBaca <- ord(Baca)

ordBaca is then an object of type ord. Different features of this object can be plotted by using the feature argument of the plot function (see manpages for more information). For instance, we can plot the amount of variance explained by each axis (Figure 2).

plot(ordBaca, feature = "variance")

Figure 2: Barplot of the amount of variance explained by each axis of the ordination ordBaca. As the number of axes to be taken into account by ordination is by default set to 2, the bars of the first two axes are shown in black.

The first two axes of the RLQ explain a large amount of the variance of the data (93.81$$\%$$ and 4.09$$\%$$, respectively).

## 2.4 2.4 Combination of Results

The results of the functions stat and ord can be simultaneously visualised by the function vis (Figure 3).

vis(Stat = statBaca, Ord = ordBaca, rangex=4, rangey=4)

Figure 3: Simultaneous visualisation of the statistical analysis and of the ordination of Baca. Blue and red lines between the covariates represent positive and negative significant associations, respectively.

Here, covariates involved in at least one significant association are shown in black, others are shown in gray. All significant covariates are connected by lines which colour represents the character of their association. As expected, positively associated covariates are situated close to each other and at similar angles from the origin. On the contrary, negatively associated covariates are distant from each other.

We can further observe that the first axis seems to be spanned by the difference between the classes J and O. The second axis seems to be spanned between ctrl and the other treatments. Spatial proximity of cold and salt treatment in the second quadrant suggest that they have similar functional effects on the gene expression.

## 2.5 2.5 Comparison with Other Methods

To validate our results of the analysis of Baca, we compare them to traditional approaches like hypergeometric test (HG), Mann-Whitney rank test (RANK) und gene set enrichment analysis (GSEA, Subramanian et al., 2005) by using the R package BOG (see Park et al., 2015, for further details).

RANK and GSEA discover class J as significantly enriched (p=6.40e-11 and p=0.02, respectively). HG does not detect any significant gene functions.

# 3 3. Gene Annotation

If your dataset contains no gene covariates, but you would like to analyse the associations between sample covariates and gene functions, Bioconductor offers multiple ways to assign gene covariates to the genes. We propose to use the Bioconductor package biomaRt (Durinck et al., 2009).

> source("https://bioconductor.org/biocLite.R")
> biocLite("biomaRt")
> library(biomaRt)

Via the biomaRt package, different databases can be accessed. By using listEnsembl(), for example, all available ENSEMBL databases can be listed (Hubbard et al., 2002). After choosing a database, a dataset can be selected. This dataset will contain different gene functions and other information about genes which can be accessed by listAttributes().

> ensembl <- useEnsembl(biomart = "ensembl")
> listDatasets(ensembl)
> ensemblhuman <- useEnsembl(biomart = "ensembl", dataset = "hsapiens_gene_ensembl")
> listAttributes(ensemblhuman)

If the gene identifiers do not correspond to each other, the Bioconductor package annotate can be used to assign identifier to each other.

Like this, we receive a fully annotated dataset which can be analysed by functions of the covRNA package.

# 4 4. Installation

The covRNA package is freely available from Bioconductor at https://bioconductor.org/packages/devel/bioc/html/covRNA.html.

# 5 References

Benjamini, Y. and Hochberg, Y. (1995). . Journal of the Royal Statistical Society. Series B (Methodological). 289:300.

Chihara, L. M. and Hesterberg, T. C. (2011) . John Wiley & Sons, 35:75.

Doledec, S., Chessel, D., Ter Braak, C., and Champely, S. (1996) . Environmental and Ecological Statistics, 3(2), 143:166.

Dray, S., Choler, P., Doledec, S., Peres-Neto, P. R., Thuiller, W., Pavoine, S., and ter Braak, C. J. (2014) . Ecology, 95(1), 14:21.

Dray, S., Dufour, A.-B., et al. (2007) . Journal of statistical software, 22(4), 1:20.

Durinck, S., Spellman, P., Birney, E., Huber, W. (2009) Nature Protocols, 4, 1184:1191.

Fisher, R. A. (1922) . Journal of the Royal Statistical Society, 85 (1), 87:94.

Gentleman, R. C., Carey, V. J., Bates, D. M., Bolstad, B., Dettling, M., Dudoit, S., Ellis, B., Gautier, L., Ge, Y., Gentry, J., et al. (2004) . Genome Biology, 5(10), R80.

Hubbard, T., Barker, D., Birney, E., Cameron, G., Chen, Y. et al. (2002) Nucleic Acids Research 2002 30(1), 38:41.

Legendre, P., Galzin, R., and Harmelin-Vivien, M. L. (1997) . Ecology, 78(2), 547:562.

Love, M. I., Huber, W., Anders, S. (2014) . Genome Biology, 15(12), 550.

Park, J., Taslim, C., Lin, S. (2015) . Elsevier Computational and Structural Biotechnology Journal, 13, 366:369.

Passalacqua, K. D., Varadarajan, A., Weist, C., Ondov, B. D., Byrd, B. et al. (2012) . PLoS ONE, 7(8), e43350.

Subramanian, A., Tamayo, P., Mootha, V. K., Mukherjee, S., Ebert, B. L., Gillette, M. A., Paulovich, A., Pomeroy, S. L., Golub, T. R., Lander, E. S., et al. (2005) . Proceedings of the National Academy of Sciences of the United States of America, 102(43), 15545:15550.

Tatusov, R. L., Galperin, M. Y., Natale, D. A., Koonin, E. V. (2000) . Nucleic Acids Research, 28(1), 33:36.