  Epigenetic histone modifications play an important role in the maintenance of
different cell phenotypes. The exact molecular mechanism for inheritance of the
modification patterns over cell generations remains elusive. We construct a
Potts-type model based on experimentally observed nearest-neighbor enzyme
lateral interactions and nucleosome covalent modification state biased enzyme
recruitment. The model can lead to effective nonlocal interactions among
nucleosomes suggested in previous theoretical studies, and epigenetic memory is
robustly inheritable against stochastic cellular processes.

Genomics