Chromatin architecture dictates epigenetic memory

Epigenetic memory encoded via histone modifications must remain robust across cell divisions. However, the physical rules governing how chromatin architecture regulates the maintenance and reorganization of epigenetic patterns remain unclear. Here, we develop a spreading-writing-erasing theory of epigenetic memory incorporating chromatin compartmentalization, enzyme limitation, and mark spreading. Our model demonstrates that self-sustaining epigenetic patterns emerge naturally without sequence insulators, while the establishment and erasure of heterochromatic compartments is governed by finite thresholds. Crucially, we uncover that the power-law exponent of chromatin contact probability dictates memory stability by buffering against spontaneous compartment collapse or expansion. Our theory also predicts progressive compartment fusion over cell generations, setting an upper limit of about 60 generations before senescence for human cells and explaining Hi-C map dynamics in senescent cells. Our theory also predicts a positive correlation between the contact-decay exponent and organismal complexity across species, supported by analysis of Hi-C maps across 873 species.