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Histone modifications play a crucial role in regulating chromatin architecture and gene expression. Here we develop a multiscale model for incorporating methylation in our nucleosome-resolution physics-based chromatin model to investigate the mechanisms by which H3K9 and H3K27 trimethylation (H3K9me3 and H3K27me3) influence chromatin structure and gene regulation. We apply three types of energy terms for this purpose: short-range potentials are derived from all-atom molecular dynamics simulations of wildtype and methylated chromatosomes, which revealed subtle local changes; medium-range potentials are derived by incorporating contacts between HP1 and nucleosomes modified by H3K9me3, to incorporate experimental results of enhanced contacts for short chromatin fibers (12 nucleosomes); for long-range interactions we identify H3K9me3- and H3K27me3-associated contacts based on Hi-C maps with a machine learning approach. These combined multiscale effects can model methylation as a first approximation in our mesoscale chromatin model, and applications to gene systems offer new insights into the epigenetic regulation of genomes mediated by H3K9me3 and H3K27me3.