DNA methylation is a stable form of epigenetic memory used by cells to control gene expression. Whole genome bisulfite sequencing (WGBS) has emerged as a gold-standard experimental technique for studying DNA methylation by producing high resolution genome-wide methylation profiles. Statistical modeling and analysis is employed to computationally extract and quantify information from these profiles in an effort to identify regions of the genome that demonstrate crucial or aberrant epigenetic behavior. However, the performance of most currently available methods for methylation analysis is hampered by their inability to directly account for statistical dependencies between neighboring methylation sites, thus ignoring significant information available in WGBS reads.

We present a powerful information-theoretic approach for genome-wide modeling and analysis of WGBS data based on the 1D Ising model of statistical physics. This approach takes into account correlations in methylation by utilizing a joint probability model that encapsulates all information available in WGBS methylation reads and produces accurate results even when applied on single WGBS samples with low coverage. Using the Shannon entropy, our approach provides a rigorous quantification of methylation stochasticity in individual WGBS samples genome-wide. Furthermore, it utilizes the Jensen-Shannon distance to evaluate differences in methylation distributions between a test and a reference sample. Differential performance assessment using simulated and real human lung normal/cancer data demonstrate a clear superiority of our approach over DSS, a recently proposed method for WGBS data analysis. Critically, these results demonstrate that marginal methods become statistically invalid when correlations are present in the data.

This contribution demonstrates clear benefits and the necessity of modeling joint probability distributions of methylation using the 1D Ising model of statistical physics and of quantifying methylation stochasticity using concepts from information theory. By employing this methodology, substantial improvement of DNA methylation analysis can be achieved by effectively taking into account the massive amount of statistical information available in WGBS data, which is largely ignored by existing methods.