Epigenetic state encodes locus-specific chromatin mechanics

TL;DR

The paper addresses how locus-specific chromatin mechanics depend on 3D genome organization and epigenetic state. It introduces the HIPPS-DIMES framework to infer locus-level viscoelastic moduli $G'(ω)$ and $G''(ω)$ from Hi-C derived structures. Key findings include region-scale Rouse-like scaling with $G'(ω)$ and $G''(ω) \sim ω^{1/2}$, a bimodal distribution of relaxation times $τ_{\max}$, enrichment of active marks among long-relaxing loci, and the emergence of viscoelastic islands at regulatory elements, tied to fractal organization and local stiffness $κ_i$ via $τ_{\max} \sim κ_i^{-1}$. The results connect epigenetic state, 3D structure, and mechanics, offering testable predictions for enhancer-promoter interactions, condensate dynamics, and mechanical responses across cell types and perturbations.

Abstract

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.

Figures (10)

• Figure 1: Region-averaged viscoelastic properties of chromosomes in GM12878. (a) Comparison of the contact map between Hi-C and HIPPS-DIMES for a 10 Mb region in chromosome 1. Contact maps are calculated directly from the 3D structures determined using the HIPPS-DIMES framework. (b) Same as (a) but for Chr17: 47 Mb to 57 Mb. (c) Storage ($G^{\prime}$) and loss modulus ($G^{\prime\prime}$) for GM12878. Solid lines are $G^{\prime\prime}(\omega)$ and dashed lines are $G^{\prime}(\omega)$. The colors represent different regions. All regions studied are 10 Mb long. Solid black line is a guide to the eye showing $\sim \omega^{1/2}$ dependence. (d) Logarithm of the ratio between loss modulus and storage modulus, $\tan(\delta) = G^{\prime\prime}(\omega)/G^{\prime}(\omega)$.
• Figure 2: Locus-specific viscoelasticity in GM12878 chromosomes. (a) Frequency dependence of $\tan_{i}(\delta)$ for individual loci from all 5 regions investigated, with each curve representing a single locus. Several representative loci are highlighted in black. Distinct crossing behavior at $\tan_{i}(\delta)=1$ reveals variations in the relaxation dynamics across the loci. For selected loci, arrows indicate $\omega_{\min}$ and $\omega_{\max}$, the lowest- and highest-frequency crossings of $\tan_i(\delta)=1$, and the corresponding relaxation timescales $\tau_{\max}=1/\omega_{\min}$ and $\tau_{\min}=1/\omega_{\max}$. (b) Histogram of the largest relaxation time, $\tau_{\text{max}} = 1/\omega_{\text{min}}$, showing a bimodal distribution that points to two distinct subpopulations of loci with different viscoelasticity. Vertical dashed line marks the separation of two subpopulations. (c) $\ln \tan_i(\delta)$ as a function of $\omega$ for Chr 17: 47 Mb - 57 Mb and Chr1: 31 Mb - 41 Mb. (d) Hi-C contact map (top) and the corresponding heatmap of $\ln\tan_i(\delta)$ (bottom) for the same genomic region, with loci aligned along the horizontal axis. In the $\ln\tan_i(\delta)$ panel, the vertical axis denotes $\omega$ (increasing from top to bottom), and the colormap encodes the sign of $\ln\tan_i(\delta)$ (blue: $G"_i > G'_i$, white: $G"_i = G'_i$, orange/red: $G'_i > G"_i$). Shaded boxes highlight examples where "islands’’ of complex viscoelastic behavior coincide with domain-like structures in the contact map.
• Figure 3: Association between chromatin viscoelastic properties and histone modifications in GM12878 cells. (a) Average $\ln\overline{\tan(\delta)}$ profiles for loci grouped by their largest relaxation time, $\tau_{\text{max}}$. Loci with $\log_{10}\tau_{\text{max}} > 1$ (long relaxation times) exhibit complex behavior with three zero crossings, whereas loci with $\log_{10}\tau_{\text{max}} \leq 1$ (short relaxation times) show a simpler profile with a single crossing. (b) Mean histone modification ChIP-seq read counts per million (RPM) across the two groups. Loci with long relaxation times are enriched for active chromatin marks (H3K27ac, H3K4me1, H3K4me3, H3K36me3), while loci with short relaxation times are relatively enriched in repressive marks (H3K27me3, H3K9me3). (c) Representative genomic regions from chromosomes 1, 7, and 17 illustrating the correspondence between high H3K27ac RPM and loci with long relaxation times $\tau_{\text{max}}$.
• Figure 4: Structural organization of slow- and fast-relaxing loci in GM12878 cells. (a) Locus-specific fractal dimension $D_f$ for chromosome 17 (47–57 Mb), computed from the scaling of the number of neighbors with distance. (b) Representative 3D structures at 100 kb resolution sampled from the HIPPS-DIMES ensemble, with loci colored by relaxation group: slow-relaxing loci (orange) and fast-relaxing loci (blue). The slow-relaxing loci form spatially loose but distinct clusters. In the structure, each 100 kb segment is represented by a single 3D coordinate, and the structures are visualized using the licorice representation. (c) Distributions of $D_f$ for slow and fast-relaxing loci are broad, reflecting the variations in the local environment. Slow-relaxing loci exhibit lower average fractal dimension ($\overline{D_f} = 2.71$) compared to fast-relaxing loci ($\overline{D_f} = 2.75$), indicating that active loci are organized in looser, less compact structures, whereas repressive loci are more structurally compact. (d) Longest relaxation time $\tau_{\max}$ for each locus plotted against the locus-specific local stiffness $\kappa_i$ (scatter). The orange curve shows the binned mean. The black dashed line is a guide to the eye with slope $-1$. $\kappa_i$ is computed from the connectivity-spectrum response to a perturbation that rescales all the couplings $k_{ij}$ associated with locus $i$.
• Figure 5: Force extension and recoil dynamics of genomic loci in GM12878 cells. (a) Schematic showing application of mechanical force $F$ on an individual locus labeled by the position $x_i$. (b) Displacement $\Delta x_i$ of individual loci as a function of time at $F=5$ directed along the positive $x$-axis (released at $t=300$, with relaxation followed until $t=1000$). Each curve represents a single locus (the black trajectories are shown as examples), with the substantial variations illustrating heterogeneous mechanical responses. The recoil dynamics is surprisingly slow. (c) Box plot for recoil ratio (defined as $(\Delta x_i(t=300) - \Delta x_i(t=1000)) / \Delta x_i(t=300)$) of individual loci. (d) Trajectory-averaged final displacement $\langle \Delta x\rangle$ for locus $i=50$ (32.25 Mb on Chr 1) at the end of force application as a function of force amplitude $F$. The force is applied for a duration $T$. $\langle \cdot \rangle$ denotes average over multiple trajectories. (e) Mean force–recoil dynamics for loci grouped by H3K27ac enrichment, $\overline{\Delta x}$, obtained by averaging over individual loci shown in (a). Loci in the top 5% of H3K27ac signal display the largest displacement, followed by those in the 50–95th percentile, while loci in the bottom 50% show the smallest displacement. (f) The locus-average displacement, $\overline{\Delta x}$, with $F=50$ applied for a duration $T=1$ grouped by H3K27ac enrichment. $\overline{\Delta x} = 6.4,\ 6.2,\ 6.0$ for loci with low, medium, and high H3K27ac enrichment, respectively.