Mathematical model for the role of multiple pericentromeric repeats on heterochromatin assembly

Although the length and constituting sequences for pericentromeric repeats are highly variable across eukaryotes, the presence of multiple pericentromeric repeats is one of the conserved features of the eukaryotic chromosomes. Pericentromeric heterochromatin is often misregulated in human diseases, with the expansion of pericentromeric repeats in human solid cancers. In this article, we have developed a mathematical model of the RNAi-dependent methylation of H3K9 in the pericentromeric region of fission yeast. Our model, which takes copy number as an explicit parameter, predicts that the pericentromere is silenced only if there are many copies of repeats. It becomes bistable or desilenced if the copy number of repeats is reduced. This suggests that the copy number of pericentromeric repeats alone can determine the fate of heterochromatin silencing in fission yeast. Through sensitivity analysis, we identified parameters that favor bistability and desilencing. Stochastic simulation shows that faster cell division and noise favor the desilenced state. These results show the unexpected role of pericentromeric repeat copy number in gene silencing and provide a quantitative basis for how the copy number allows or protects repetitive and unique parts of the genome from heterochromatin silencing, respectively.