Uncovering correlated variability in epigenomic datasets using the Karhunen-Loeve transform.

Larger variation exists in epigenomes than in genomes, as a single genome shapes the identity of multiple cell types. With the advent of next-generation sequencing, one of the key problems in computational epigenomics is the poor understanding of correlations and quantitative differences between large scale data sets. Here we bring to genomics a scenario of functional principal component analysis, a finite Karhunen-Loève transform, and explicitly decompose the variation in the coverage profiles of 27 chromatin mark ChIP-seq datasets at transcription start sites for H1, one of the most used human embryonic stem cell lines. Using this approach we identify positive correlations between H3K4me3 and H3K36me3, as well as between H3K9ac and H3K36me3, so far undetected by the most commonly used Pearson correlation between read enrichment coverages. We uncover highly negative correlations between H2A.Z, H3K4me3, and several histone acetylation marks, but these occur only between principal components of first and second order. We also demonstrate that levels of gene expression correlate significantly with scores of components of order higher than one, demonstrating that transcriptional regulation by histone marks escapes simple one-to-one relationships. This correlations were higher in significance and magnitude in protein coding genes than in non-coding RNAs. In summary, we present a methodology to explore and uncover novel patterns of epigenomic variability and covariability in genomic data sets by using a functional eigenvalue decomposition of genomic data. R code is available at: http://github.com/pmb59/KLTepigenome.