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Design principles of 3D epigenetic memory systems

The epigenetic state of a cell is associated with patterns of chemical modifications of histones (“marks”) across the genome, with different marks typical of active (euchromatic) and inactive (heterochromatic) genomic regions. These mark patterns can be stable over many cell generations—a form of epigenetic memory—despite their constant erosion due to replication and other processes. Enzymes that place histone marks are often stimulated by the same marks, as if “spreading” marks between neighboring histones. But this positive feedback may not be sufficient for stable memory, raising the question of what is. In this work, we show how 3D genome organization—in particular, the compartmental segregation of euchromatin and heterochromatin— could serve to stabilize an epigenetic memory, as long as (1) there is a large density difference between the compartments, (2) the modifying enzymes can spread marks in 3D, and (3) the enzymes are limited in abundance relative to their histone substrates. We introduce a biophysical model stylizing chromatin and its dynamics through the cell cycle, in which enzymes spread self-attracting marks on a polymer. We find that marks localize sharply and stably to the denser compartment, but over several cell generations, the model generically exhibits uncontrolled spread or global loss of marks. Strikingly, imposing limitation of the modifying enzymes—a plausible but oft-neglected element—totally changes this picture, yielding an epigenetic memory system, stable for hundreds of cell generations. Our model predicts a rich phenomenology to compare to experiments, and reveals basic design principles of putative epigenetic memory systems relying on compartmentalized 3D genome structure for their function.