Spatial statistical modelling of epigenomic variability

Each cell in our body carries the same genetic information encoded in the DNA, yet the human organism contains hundreds of cell types which differ substantially in physiology and functionality. This variability stems from the existence of regulatory mechanisms that control gene expression, and hence phenotype. The field of epigenetics studies how changes in biochemical factors, other than the DNA sequence itself, might affect gene regulation. The advent of high throughput sequencing platforms has enabled the profiling of different epigenetic marks on a genome-wide scale; however, bespoke computational methods are required to interpret these high-dimensional data and investigate the coupling between the epigenome and transcriptome. This thesis contributes to the development of statistical models to capture spatial correlations of epigenetic marks, with the main focus being DNA methylation. To this end, we developed BPRMeth (Bayesian Probit Regression for Methylation), a probabilistic model for extracting higher order methylation features that precisely quantify the spatial variability of bulk DNA methylation patterns. Using such features, we constructed an accurate machine learning predictor of gene expression from DNA methylation and identified prototypical methylation profiles that explain most of the variability across promoter regions. The BPRMeth model, and its algorithmic implementation, were subsequently substantially extended both to accommodate different data types, and to improve the scalability of the algorithm. Bulk experiments have paved the way for mapping the epigenetic landscape, nonetheless, they fall short of explaining the epigenetic heterogeneity and quantifying its dynamics, which inherently occur at the single cell level. Single cell bisulfite sequencing protocols have been recently developed, however, due to intrinsic limitations of the technology they result in extremely sparse coverage of CpG sites, effectively limiting the analysis repertoire to a semi-quantitative level. To overcome these difficulties we developed Melissa (MEthyLation Inference for Single cell Analysis), a Bayesian hierarchical model that leverages local correlations between neighbouring CpGs and similarity between individual cells to jointly impute missing methylation states, and cluster cells based on their genome-wide methylation profiles. A recent experimental innovation enables the parallel profiling of DNA methylation, transcription and chromatin accessibility (scNMT-seq), making it possible to link transcriptional and epigenetic heterogeneity at the single cell resolution. For the scNMT-seq study, we applied the extended BPRMeth model to quantify cell-to-cell chromatin accessibility heterogeneity around promoter regions and subsequently link it to transcript abundance. This revealed that genes with conserved accessibility profiles are associated with higher average expression levels. In summary, this thesis proposes statistical methods to model and interpret epigenomic data generated from high throughput sequencing experiments. Due to their statistical power and flexibility we anticipate that these methods will be applicable to future sequencing technologies and become widespread tools in the high throughput bioinformatics workbench for performing biomedical data analysis