Random positioning of nucleosomes enhances heritable bistability.

Chromosomal regions are often dynamically modified by histones, leading to the uncertainty of nucleosome positions. Experiments have provided evidence for this randomness, but it is unclear how it impacts epigenetic heritability. Here, by analyzing a mechanic model at the molecular level, which considers three representative types of nucleosomes (unmodified, methylated, and acetylated) and dynamic nucleosome modifications, we find that in contrast to the equidistance partition of nucleosomes, random partition can significantly enhance heritable bistability. Moreover, the more "chaotic" the nucleosome positions are, the better the heritable bistability is, in contrast to the previous view. In both cases of nucleosome positioning, heritable bistability occurs only when the total nucleosome number is beyond a threshold, and it depends strongly on the allocation rate that enzymes regulate transitions between different nucleosome types. Thus, we conclude that random positioning of nucleosomes is an unneglectable factor impacting heritable bistability. A point worth mentioning is that our model established on a master equation can easily be extended to include other more complex processes underlying dynamic nucleosome modifications.