Computational and Analytical Approaches for DNA Methylation Pattern Modelling

DNA methylation is a modification of the biochemical environment of a nucleotide that can occur at so-called CpG sites in the DNA strand. Just as a genetic mutation, it can benefit or harm the organism, depending on where exactly it happens and to what ex- tent. This work focuses on two questions regarding the pattern evolution of methylation in certain DNA sequences, since the impact of methylation has been observed to depend on these patterns: does the size of (de-)methylated CpG clusters depend on reactions with other CpG sites? And can these reactions alter epigenetic variation, i.e. population-wide methylation patterns? To describe the methylome evolution within one individual (on a single cell basis), but also inter-generational developments, we formulate two mathemati- cal models and corresponding master equations: one considering the influence of a single neighboring CpG site and one regarding both nearest neighbors. As the master equations can only be solved for certain parameter values, we use numerical simulations for further analysis. The simulation is compared to the analytical solution for validation, and then it is used for the investigation of the aforementioned questions. We find that for the chosen parameters, the cluster size increases if neighboring interactions are involved, indepen- dently of methylation status. Our results suggest that the epigenetic variation is larger in the case of the models which include neighboring interactions.