Essential life processes take place across multiple space and time scales in living organisms but understanding their mechanistic interactions remains an ongoing challenge. Advanced multiscale modeling techniques are providing new opportunities and insights into these complex processes. In cells, meters of chromatin are folded into a nucleus with a diameter on the order of microns. The three-dimensional chromatin structure coupled with biochemical processes that turn genes on or off, specify a given cell type through a complicated set of interactions collectively referred to as epigenetics. Important epigenetic processes include the differential accessibility of genomic loci to transcription factors and chemical modifications to DNA and DNA-binding molecules such as histones. The dynamics of these epigenetic processes span timescales from milliseconds to years. How do chemical modifications consisting of a handful of atoms cooperate to modulate genome folding at the scale of the nucleus and impact organism outcomes? In this review, we highlight the inherently multiscale nature of chromatin organization, with a focus on computational modeling to bridge the gaps in our understanding
Topologically Associating Chromatin Domains are spatially distinct chromatin regions that regulate transcription by segregating active and inactive genomic elements. Empirical studies show that their formation correlates with local patterns of epigenetic markers, yet the precise mechanisms linking 1D epigenetic landscapes to 3D chromatin folding remain unclear. Recent models represent chromatin as a spin system, where nucleosomes are treated as discrete-state variables coupled by interaction strengths derived from genomic and epigenetic data. Classical samplers struggle with these models due to high frustration and dense couplings. Here, we present a quantum annealing (QA) approach to efficiently sample chromatin states, embedding an epigenetic Ising model into the topology of D-Wave quantum processors. Rather than reconstructing exact TAD size distributions or insulation scores, our method reproduces statistical features, such as mean marker incidences and intra-/inter-nucleosome correlations, while generating configurations that exhibit TAD-like structural motifs. These results demonstrate QA as an alternative to explore the chromatin architecture and provide a foundation in epig
Epigenetic landscapes, represented by patterns of chemical modifications on histone tails, are essential for maintaining cell identity and tissue homeostasis. These landscapes are shaped by multiple factors, including local biochemical signals and the three-dimensional organisation of chromatin. However, their response to genomic stress, such as DNA double-strand breaks (DSBs), remains incompletely understood. Here, we use a stochastic model of histone modification dynamics integrated with chromatin architecture to investigate how local depletion of sirtuins, histone deacetylases involved in DSB repair, destabilises epigenetic patterns. Our simulations recapitulate experimental findings in which sirtuin relocalisation to DSB sites leads to the epigenetic erosion and suggest that the resulting landscape depends on enzyme levels and chromatin geometry. Importantly, chromatin regions with large domains of long-range contacts are more resilient to epigenetic destabilisation. These findings suggest that chromatin folding can buffer against relocation of histone-modifying enzymes, highlighting a structural mechanism for preserving epigenetic integrity under stress.
Epigenetic changes -- heritable, long-lived, yet actively reversible modifications of the chromatin state -- display memory, threshold activation and hysteresis, features that are the hallmark of rate-independent dissipative evolution. We propose a mathematical framework, Rate-Independent Epigenetics, that models epigenetic change within the theory of rate-independent systems and is consistent with two fundamental principles identified with the laws of thermodynamics. In this framework, a model is specified by a state space of epigenetic configurations, a stored-energy functional depending on the state and on an external loading, and a 1-homogeneous dissipation potential encoding the resistance of the epigenetic machinery to change. Assuming an energetic evolution principle, the governing equations follow, with no further modelling hypotheses. The energy balance is exact energy conservation, and the 1-homogeneity of the dissipation potential forces a non-negative, minimal (economical) dissipation. Under natural coercivity and continuity assumptions we establish existence of energetic solutions and, via vanishing viscosity, of balanced-viscosity solutions that resolve the ambiguity
In recent years, multiplexed Fluorescence In Situ Hybridization (FISH) or FISH-omics methods have rapidly expanded, enabling the quantification of chromatin organization in single cells, often in conjunction with measurements of RNA and protein. These approaches have deepened our understanding of how 3D chromosome architecture relates to transcriptional activity and cell states in health and disease. Despite these advances, results from Chromatin Tracing FISH-omics experiments remain challenging to share, reuse, and analyze due to the absence of standardized data exchange specifications. Building on the release of microscopy metadata standards, we introduce the FISH Omics Format-Chromatin Tracing (FOF-CT), a community-developed standard for processed results from diverse imaging modalities. We describe the FOF-CT file format and present a curated collection of datasets deposited in the 4DN Data Portal and the OME Image Data Resource (IDR). We also highlight their potential for reuse, integration, and modeling by outlining example analysis pipelines and illustrating biological insights enabled by standardized, FAIR-compliant Chromatin Tracing datasets. While this manuscript focuses
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
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 c
By means of a minimal physical model, we investigate the interplay of two phase transitions at play in chromatin organization: (1) liquid-liquid phase separation (LLPS) within the fluid solvating chromatin, resulting in the formation of biocondensates, and (2) the coil-globule crossover of the chromatin fiber, which drives the condensation or extension of the chain. In our model, a species representing a domain of chromatin is embedded in a binary fluid. This fluid phase separates to form a droplet rich in a macromolecule (B). Chromatin particles are trapped in a harmonic potential to reproduce the coil and globular phases of an isolated polymer chain. We investigate the role of the droplet material B on the radius of gyration of this polymer and find that this radius varies nonmonotonically with respect to the volume fraction of B. This behavior is reminiscent of a phenomenon known as $\textit{co-non-solvency}$: a polymer chain in good solvent (S) may collapse when a second good solvent (here B) is added in low quantity, and expand at higher B concentration. Additionally, the presence of finite-size effects on the coil-globule transition results in a qualitatively different impact
Genetic algorithms are a well-known example of bio-inspired heuristic methods. They mimic natural selection by modeling several operators such as mutation, crossover, and selection. Recent discoveries about Epigenetics regulation processes that occur "on top of" or "in addition to" the genetic basis for inheritance involve changes that affect and improve gene expression. They raise the question of improving genetic algorithms (GAs) by modeling epigenetics operators. This paper proposes a new epigenetics algorithm that mimics the epigenetics phenomenon known as DNA methylation. The novelty of our epigenetics algorithms lies primarily in taking advantage of attention mechanisms and deep learning, which fits well with the genes enhancing/silencing concept. The paper develops theoretical arguments and presents empirical studies to exhibit the capability of the proposed epigenetics algorithms to solve more complex problems efficiently than has been possible with simple GAs; for example, facing two Non-convex (multi-peaks) optimization problems as presented in this paper, the proposed epigenetics algorithm provides good performances and shows an excellent ability to overcome the lack of
We solve a hydrodynamic model of active chromatin dynamics, within a confined geometry simulating the cell nucleus. Using both analytical and numerical methods, we describe the behavior of the chromatin polymer driven by the activity of motors having polar symmetry, both in the linear response regime as well as in the long-term, fully nonlinear regime of the flows. The introduction of a boundary induces a particular geometry in the flows of chromatin, which we describe using vector spherical harmonics, a tool which greatly simplifies both our analytical and numerical approaches. We find that the long-term behavior of this model in confinement is dominated by steady, transverse flows of chromatin which circulate around the spherical domain. These circulating flows are found to be robust to perturbations, and their characteristic size is set by the size of the domain. This gives us further insight into active chromatin dynamics in the cell nucleus, and provides a foundation for development of further, more complex models of active chromatin dynamics.
We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular motors tethered to chromatin. Cooperation occurs if each motor acts simultaneously on the polymer and the surrounding solvent, exerting on them equal and opposite forces. This drives the flow of solvent past the polymer, which in turn affects the orientation of nearby motors and, if the drive is strong enough, an active polar (``ferromagnetic'') phase of motors can spontaneously form. Depending on boundary conditions, either transverse flows, or sustained longitudinal oscillations and waves are possible. Predicted time and length scales are consistent with experiments. We now have in hand a coarse-grained description of chromatin dynamics which reproduces the directed coherent flows of chromatin seen in experiments. This field-theoretic description can be analytically coupled to other features of the nuclear environment such as fluctuating or porous boundaries, local heterogeneities in the distribution of chromatin or its activity, leading to in
Network analysis is a powerful way of modeling chromatin interactions. Assortativity is a network property used in social sciences to identify factors affecting how people establish social ties. We propose a new approach, using chromatin assortativity to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network and thus investigate which proteins or chromatin marks mediate genomic contacts. We use high-resolution Promoter Capture Hi-C and Hi-Cap data as well as ChIA-PET data from mouse embryonic stem cells to investigate promoter-centered chromatin interaction networks and calculate the presence of specific epigenomic features in the chromatin fragments constituting the nodes of the network. We estimate the association of these features to the topology of four chromatin interaction networks and identify features localized in connected areas of the network. Polycomb Group proteins and associated histone marks are the features with the highest chromatin assortativity in promoter-centred networks. We then ask which features distinguish contacts amongst promoters from contacts between promoters and other genomic elements. We observe higher chroma
The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fibre is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to the natural emergence of clusters of proteins and binding sites, accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. Here we combine numerics and analytics to first classify these networks and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and this leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favour rosette-like structures with a local cloud of loops with respect to more complicated non-local topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, whi
Chromatin is a complex of DNA and specific proteins forming an intermediary level of organization of eukaryotic genomes, between double-stranded DNA and chromosome. Within a generic modeling of the chromatin assembly, we investigate the interplay between the mechanical properties of the chromatin fiber and its biological functions. A quantitative step is to relate the mechanics at the DNA level and the mechanics described at the chromatin fiber level. It allows to calculate the complete set of chromatin elastic constants (twist and bend persistence lengths, stretch modulus and twist-stretch coupling constant), in terms of DNA elastic properties and geometric features of the fiber. These elastic constants are strongly sensitive to the local architecture of the fiber and we argue that this tunable elasticity might be a key feature in chromatin functions, for instance in the initiation and regulation of transcription. Moreover, this analysis provides a framework to interpret micromanipulations studies of chromatin fiber and suggests further experiments involving intercalators to scan the tunable elasticity of the fiber.
Chromatin moves dynamically inside the cell nucleus, and its motion is often correlated with gene functions such as DNA recombination and transcription. A recent study has shown that during early embryogenesis of the nematode, Caenorhabiditis elegans, the chromatin motion markedly decreases. However, the underlying mechanism for this transition has yet to be elucidated. We systematically investigated the impact of nuclear size to demonstrate that it is indeed a decisive factor in chromatin mobility. To this end, we established a method to quantify chromatin motion inside the nucleus, while excluding the contribution of the movement of the nucleus itself, which allowed us to extract the intrinsic mean-squared displacement (iMSD) of individual chromosomal loci in moving nuclei from the correlated motion of two loci. We show that a simple theoretical description, which takes into account the topological constraints of chromatin polymers, can quantitatively describe the relationship between the nucleus size and the chromatin motion in vivo. Our results emphasize a regulatory role of nuclear size in restricting chromatin motion, and a generic polymer physics model plays a guiding role i
Cellular functions crucially depend on the precise execution of complex biochemical reactions taking place on the chromatin fiber in the tightly packed environment of the cell nucleus. Despite the availability of large data sets probing this process from multiple angles, we still lack a bottom-up framework which can incorporate the sequence-specific nature of biochemistry in a unified model of 3D chromatin dynamics. Here we propose SEMPER (Sequence Enhanced Magnetic PolymER), a novel stochastic polymer model which naturally incorporates observational data about sequence-driven biochemical processes, such as binding of transcription factor proteins, in a 3D model of chromatin structure. By introducing a new algorithm for approximate Bayesian inference, we discuss how to estimate in a robust manner the relative importance of biochemical vs. polymer signals in the determination of the chromatin epigenetic states which is leading to a significant revision of the interpretation of previous models. Furthermore we show that, without additional input from the genome 3D structure, our model can predict with reasonable accuracy some notable and non trivial conformational features of chromati
We use Brownian dynamics simulations to study the formation of chromatin loops through diffusive sliding of slip-link-like proteins, mimicking the behaviour of cohesin molecules. We recently proposed that diffusive sliding is sufficient to explain the extrusion of chromatin loops of hundreds of kilo-base-pairs (kbp), which may then be stabilised by interactions between cohesin and CTCF proteins. Here we show that the flexibility of the chromatin fibre strongly affects this dynamical process, and find that diffusive loop extrusion is more efficient on stiffer chromatin regions. We also show that the dynamics of loop formation are faster in confined and collapsed chromatin conformations but that this enhancement is counteracted by the increased crowding. We provide a simple theoretical argument explaining why stiffness and collapsed conformations favour diffusive extrusion. In light of the heterogeneous physical and conformational properties of eukaryotic chromatin, we suggest that our results are relevant to understand the looping and organisation of interphase chromosomes in vivo.
We present a model improving the two-angle model for interphase chromatin (E2A model). This model takes into account the cylindrical shape of the histone octamers, the H1 histones in front of the nucleosomes and the vertical distance $d$ between the in and outgoing DNA strands. Factoring these chromatin features in, one gets essential changes in the chromatin phase diagram: Not only the shape of the excluded-volume borderline changes but also the vertical distance $d$ has a dramatic influence on the forbidden area. Furthermore, we examined the influence of H1 defects on the properties of the chromatin fiber. Thus we present two possible strategies for chromatin compaction: The use of very dense states in the phase diagram in the gaps in the excluded volume borderline or missing H1 histones which can lead to very compact fibers. The chromatin fiber might use both of these mechanisms to compact itself at least locally. Line densities computed within the model coincident with the experimental values.
The epigenome, i.e. the whole of chromatin modifications, is transferred from mother to daughter cells during cell differentiation. When de novo chromatin modifications (establishment or erasure of, respectively, new or pre-existing DNA methylations and/or histone modifications) are made in a daughter cell, however, it has a different epigenome than its mother cell. Although de novo chromatin modifications are an important event that comprises elementary processes of cell differentiation, its molecular mechanism remains poorly understood. We argue in this Letter that a key to solving this problem lies in understanding the role of long non-coding RNAs (lncRNAs)- a type of RNA that is becoming increasingly prominent in epigenetic studies. Many studies show that lncRNAs form ribonucleo-protein complexes in the nucleus and are involved in chromatin modifications. However, chromatin-modifying enzymes lack the information about genomic positions on which they act. It is known, on the other hand, that a single-stranded RNA in general can bind to a double-stranded DNA to form a triple helix. If each lncRNA forms a ribonucleo-protein complex with chromatin-modifying enzymes on one hand and,
We investigate the large-scale geometry of the DNA-protein complex of chromatin using a generalized optimality principle, which requires that not only should all sub-parts of a natural process be optimal but also the unfolding of higher recursive levels. It was shown previously that an information-theoretic geometry of the genetic code data, together with the principle of maximum entropy, explains the variation in the codon groupings that map into different amino acids and explain its underlying self-similar structure. Here we take that analysis forward and investigate the fundamental geometry underling physical and biological space as it gets reflected in aggregates associated with genomic DNA. The analysis is consistent with the measured fractal dimension of chromatin.