Modeling DNA methylation by analyzing the individual configurations of single molecules

Abstract

DNA methylation is often analyzed by reporting the average methylation degree of each cytosine. In this study, we used a single molecule methylation analysis in order to look at the methylation conformation of individual molecules. Using D-aspartate oxidase as a model gene, we performed an in-depth methylation analysis through the developmental stages of 3 different mouse tissues (brain, lung, and gut), where this gene undergoes opposite methylation destiny. This approach allowed us to track both methylation and demethylation processes at high resolution. The complexity of these dynamics was markedly simplified by introducing the concept of methylation classes (MCs), defined as the number of methylated cytosines per molecule, irrespective of their position. The MC concept smooths the stochasticity of the system, allowing a more deterministic description. In this framework, we also propose a mathematical model based on the Markov chain. This model aims to identify the transition probability of a molecule from one MC to another during methylation and demethylation processes. The results of our model suggest that: 1) both processes are ruled by a dominant class of phenomena, namely, the gain or loss of one methyl group at a time; and 2) the probability of a single CpG site becoming methylated or demethylated depends on the methylation status of the whole molecule at that time.

Modeling DNA Methylation Profiles through a Dynamic Equilibrium between Methylation and Demethylation

“…In contrast to this heterogeneity among cells, we observed a low variability in the MC profiles of the same region and the same tissue, from different individuals. Also, this finding was consistent with the results from our previous papers, obtained from fewer samples [ 26 , 33 ].…”

“…In order to reduce the statistical noise of the samples, we adopted a coarse-grained description of the DNA methylation profiles, that is, instead of considering the exact equilibrium distribution for all epialleles, we considered the cumulative distribution of classes of epialleles (MCs), defined by the number of methylated CpGs they harbored, as introduced in [ 26 ]. In this framework, analogously to Affinito et al [ 26 ], we adopted the simplicity ansatz that the epiallele transitions involve only adjacent MCs, which means that in the unit time only one of the cytosines of an epiallele can change its status and become methylated or demethylated. According to our model, the equilibrium condition is reached when the methylation rate of a generic MC n is equal to the demethylation rate of the corresponding n + 1 MC.…”

“…According to our model, the equilibrium condition is reached when the methylation rate of a generic MC n is equal to the demethylation rate of the corresponding n + 1 MC. This is a key difference in respect of the approach we previously adopted [ 26 ], where the epialleles’ transitions were modeled as out-of-equilibrium dynamics.…”

“…Mathematical modeling has been extensively applied to DNA methylation and has provided useful insights on the regulatory mechanisms of this process. In a previous study, we used Markov’s hidden chains to model the DNA methylation changes of the D-aspartate oxidase gene promoter during mouse development [ 26 ]. The model was, indeed, aimed at capturing the dynamic of DNA methylation over time.…”

Ultra-Deep DNA Methylation Analysis of X-Linked Genes: GLA and AR as Model Genes

“…We recently provided evidence that studying DNA methylation at specific loci at a single-molecule resolution (epiallele distribution analysis) allows one to track the spatiotemporal evolution of cell-to-cell methylation differences in a given cell population [ 16 , 17 , 18 , 19 , 20 ]. In addition to the evaluation of the average methylation, this approach considers all possible different arrangements of methylated CpG sites present in each molecule (epialleles).…”