Mechanistic stochastic model of histone modification pattern formation

\noindent \textbf{Background} \\ The activity of a single gene is influenced by the composition of the chromatin in which it is embedded. Nucleosome turnover, conformational dynamics, and covalent histone modifications each induce changes in the structure of chromatin and its affinity for regulatory proteins. The dynamics of histone modifications and the persistence of modification patterns for long periods are still largely unknown. \noindent \textbf{Results} \\ In this study, we present a stochastic mathematical model that describes the molecular mechanisms of histone modification pattern formation along a single gene, with non-phenomenological, physical parameters. We find that diffusion and recruitment properties of histone modifying enzymes together with chromatin connectivity allow for a rich repertoire of stochastic histone modification dynamics and pattern formation. We demonstrate that histone modification patterns at a single gene can be established or removed within a few minutes through diffusion and weak recruitment mechanisms of histone modification spreading. Moreover, we show that strong synergism between diffusion and weak recruitment mechanisms leads to nearly irreversible transitions in histone modification patterns providing stable patterns. In the absence of chromatin connectivity spontaneous and dynamic histone modification boundaries can be formed that are highly unstable, spontaneous fluctuations causing them to diffuse randomly. Chromatin connectivity destabilizes this synergistic system and introduces bistability, illustrating state switching between opposing modification states of the model gene. The observed bistable long-range and localized pattern formation and are critical effectors of gene expression regulation. \noindent \textbf{Conclusion} \\ This study illustrates how the cooperative interactions between regulatory proteins and the chromatin state generate complex stochastic dynamics of gene expression regulation.