Physical theory of epigenetic memory and its biological implications

Epigenetic marks are essential for maintaining cell identity, yet how epigenetic memory is robustly preserved across cell cycles while remaining plastic during cell-state transitions remains unclear. Here, we develop a theory of epigenetic memory that incorporates chromatin compartmentalization and mark modifications, including long-range spreading, writing, and erasing. The spreading-writing-erasing model generates self-sustaining epigenetic mark patterns across multiple cell generations. The model also reveals that to induce or remove a heterochromatic compartment, the writing or erasing strength must exceed a finite threshold, which depends on the long-distance scaling of the contact probability between two chromatin loci. Intriguingly, the scaling exponent for human cells appears to be evolutionarily selected for stability and plasticity in epigenetic memory. We demonstrate that adding noise in parental histone segregation during DNA replication and accelerating cell proliferation significantly enhance reprogramming efficiency in induced pluripotent stem cells. Finally, our theory also predicts cellular senescence arising from chromatin reorganization after many cell generations.