Modeling Heterochromatin Spreading in Schizosaccharomyces pombe via a Steady-State Reaction–Diffusion Framework

Heterochromatin spreading in Schizosaccharomyces pombe must be tightly regulated to preserve epigenetic inheritance while preventing inappropriate silencing of essential genes. In mutants lacking the Leo1–Paf1 subcomplex, boundary function is compromised, enabling histone H3K9me2 domains to invade euchromatic regions. Although this phenomenon is well documented, the quantitative rules governing the spatial dynamics of spreading remain poorly defined. Here, we introduce a reaction–diffusion framework that integrates position-dependent nucleation, nonlinear reader–writer feedback, and histone turnover kinetics. Focusing on a structurally insulated chromatin globule on Chromosome II (1.15–1.20 Mb), we fit the model to published ChIP-seq data, achieving excellent agreement with experiment (R2 = 0.9914, MSE = 4.14 × 10−11). Parameter inference suggests moderate diffusivity (D = 100), negligible feedback strength (β = 10−5), balanced turnover (γ = 1.0), and modest cooperativity (n = 2). Linear stability analysis identifies a critical β/γ threshold that governs domain persistence. Gene-level mapping further links ectopic spreading to loci involved in telomere maintenance (Stn1 ), DNA repair (Saw1), and ribosome biogenesis (Tsr2 ). This quantitative framework unifies chromatin architecture with nucleosome turnover and enzymatic feedback, providing a predictive tool for understanding boundary control of epigenetic inheritance.