Limited spreading enzyme stabilizes epigenetic memory*

The epigenetic state of a cell is characterized by patterns of covalent histone modifications ("marks") across the genome, with different marks typical of active (euchromatic) and silenced (heterochromatic) regions. These mark patterns can be stable over many cell generations—a form of epigenetic memory—despite continuous loss due to replication. Here, we investigate the possibility that the increased density of heterochromatin and its phase separation could contribute to this stability. We introduce a minimal biophysical model stylizing chromatin and its dynamics through the cell cycle, in which modifying enzymes "spread" marks between nearby histones and marked histones experience self-attraction. We find that marks localize sharply and stably to denser regions, but if the density differences are allowed to arise endogenously from the self-attraction, the model generically exhibits uncontrolled spread or global loss of heterochromatin. Limitation of the modifying enzymes relative to their histone substrates—a plausible but oft-neglected element—totally changes this picture, yielding a memory system, stable for hundreds of cell generations, that depends on self-attraction and dense heterochromatin, suggesting a functional role for this hallmark of nuclear organization.