Methylation of histone H3K9 is a hallmark of epigenetic silencing in eukaryotes. Nucleosome modifications often rely on positive feedback where enzymes are recruited by modified nucleosomes. A combination of local and global feedbacks has been proposed to account for some dynamic properties of heterochromatin, but the range at which the global feedbacks operate and the exact mode of heterochromatin propagation are not known. We investigated these questions in fission yeast. Guided by mathematical modeling, we incrementally increased the size of the mating-type region and profiled heterochromatin establishment over time. We observed exponential decays in the proportion of cells with active reporters, with rates that decreased with domain size. Establishment periods varied from a few generations in wild type to >200 generations in the longest region examined, and highly correlated silencing of two reporters located outside the nucleation center was observed. On a chromatin level, this indicates that individual regions are silenced in sudden bursts. Mathematical modeling accounts for these bursts if heterochromatic nucleosomes facilitate a deacetylation or methylation reaction at long range, in a distance-independent manner. A likely effector of three-dimensional interactions is the evolutionarily conserved Swi6HP1 H3K9me reader, indicating the bursting behavior might be a general mode of heterochromatin propagation.

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Nucleosomes and their modifications often facilitate gene regulation in eukaryotes. Certain genomic regions may obtain alternate epigenetic states through enzymatic reactions forming positive feedback between nucleosome states. How a system of nucleosome states maintains confinement is an open question. Here we explore a family of stochastic dynamic models with combinations of read-write enzymes. We find that a larger number of intermediate nucleosome states increases both the robustness of linear spreading in models with only local recruitment processes and the degree of bi-stability under conditions with at least one non-local recruitment. Further, supplementing the positive feedback with one negative feedback acting over long distances along the genome enables effective confinement of epigenetic, bistable regions. Our study emphasizes the importance of determining whether each particular read-write enzyme acts only locally or between distant nucleosomes.