Epigenetic state encodes locus-specific chromatin mechanics

Chromatin is repeatedly deformed in vivo during transcription, nuclear remodeling, and confined migration - yet how mechanical response varies from locus to locus, and how it relates to epigenetic state, remains unclear. We develop a theory to infer locus-specific viscoelasticity from three-dimensional genome organization. Using chromatin structures derived from contact maps, we calculate frequency-dependent storage and loss moduli for individual loci and establish that the mechanical properties are determined both by chromatin epigenetic marks and organization. On large length scales, chromatin exhibits Rouse-like viscoelastic scaling, but this coarse behavior masks extensive heterogeneity at the single-locus level. Loci segregate into two mechanical subpopulations with distinct longest relaxation times: one characterized by single-timescale and another by multi-timescale relaxation. The multi-timescale loci are strongly enriched in active marks, and the longest relaxation time for individual loci correlates inversely with effective local stiffness. Pull-release simulations further predict a time-dependent susceptibility: H3K27ac-rich loci deform more under sustained forcing yet can resist brief, large impulses. At finer genomic scales, promoters, enhancers, and gene bodies emerge as "viscoelastic islands" aligned with their focal interactions. Together, these results suggest that chromatin viscoelasticity is an organized, epigenetically coupled property of the 3D genome, providing a mechanistic layer that may influence enhancer-promoter communication, condensate-mediated organization, and response to cellular mechanical stress. The prediction that locus-specific mechanics in chromatin are controlled by 3D structures as well as the epigenetic states is amenable to experimental test.