Understanding How Chromatin Folding and Enzyme Competition Affect Rugged Epigenetic Landscapes.

Epigenetics plays a key role in cellular differentiation and maintaining cell identity, enabling cells to regulate their genetic activity without altering the DNA sequence. Epigenetic regulation occurs within the context of hierarchically folded chromatin, yet the interplay between the dynamics of epigenetic modifications and chromatin architecture remains poorly understood. In addition, it remains unclear what mechanisms drive the formation of rugged epigenetic patterns, characterised by alternating genomic regions enriched in activating and repressive marks. In this study, we focus on post-translational modifications of histone H3 tails, particularly H3K27me3, H3K4me3, and H3K27ac. We introduce a mesoscopic stochastic model that incorporates chromatin architecture and competition of histone-modifying enzymes into the dynamics of epigenetic modifications in small genomic loci comprising several nucleosomes. Our approach enables us to investigate the mechanisms by which epigenetic patterns form on larger scales of chromatin organisation, such as loops and domains. Through bifurcation analysis and stochastic simulations, we demonstrate that the model can reproduce uniform chromatin states (open, closed, and bivalent) and generate previously unexplored rugged profiles. Our results suggest that enzyme competition and chromatin conformations with high-frequency interactions between distant genomic loci can drive the emergence of rugged epigenetic landscapes. Additionally, we hypothesise that bivalent chromatin can act as an intermediate state, facilitating transitions between uniform and rugged landscapes. This work offers a powerful mathematical framework for understanding the dynamic interactions between chromatin architecture and epigenetic regulation, providing new insights into the formation of complex epigenetic patterns.