Mathematical modeling of histone modifications reveals the formation mechanism and function of bivalent chromatin

Bivalent chromatin is characterized by occupation of both activating and repressive histone modifications. Here, we develop a mathematical model that involves antagonistic histone modifications H3K4me3 and H3K27me3 to capture the key features of bivalent chromatin. Three necessary conditions for the emergence of bivalent chromatin are identified, including advantageous methylating activity over demethylating activity, frequent noise conversions of modifications, and sufficient nonlinearity. The first condition is further confirmed by analyzing the existing experimental data. Investigation of the composition of bivalent chromatin reveals that bivalent nucleosomes carrying both H3K4me3 and H3K27me3 account for no more than half of nucleosomes at the bivalent chromatin domain. We identify that bivalent chromatin not only allows transitions to multiple states but also serves as a stepping stone to facilitate a stepwise transition between repressive chromatin state and activating chromatin state and thus elucidate crucial roles of bivalent chromatin in mediating phenotypical plasticity during cell fate determination.