Spatio-temporal patterns of active epigenetic turnover

DNA methylation is a primary layer of epigenetic modification that plays a pivotal role in the regulation of development, aging, and cancer. The concurrent activity of opposing enzymes that mediate DNA methylation and demethylation gives rise to a biochemical cycle and active turnover of DNA methylation. While the ensuing biochemical oscillations have been implicated in the regulation of cell differentiation, their functional role and spatio-temporal dynamics are, however, unknown. In this work, we demonstrate that chromatin-mediated coupling between these local biochemical cycles can lead to the emergence of phase-locked domains, regions of locally synchronized turnover activity, whose coarsening is arrested by genomic heterogeneity. We introduce a minimal model based on stochastic oscillators with constrained long-range and non-reciprocal interactions, shaped by the local chromatin organization. Through a combination of analytical theory and stochastic simulations, we predict both the degree of synchronization and the typical size of emergent phase-locked domains. We qualitatively test these predictions using single-cell sequencing data. Our results show that DNA methylation turnover exhibits surprisingly rich spatio-temporal patterns which may be used by cells to control cell differentiation.