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Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale T t , polymer relaxation timescale τ can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when p , and segmental relaxation timescale τ s can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when T . We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate. t ≈ τ p and a maximum when T t ≈ τ s . We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations., (© 2023. The Author(s).)

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation, and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction-strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its three-dimensional organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid- and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops., (Copyright © 2022 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The establishment of centromeric chromatin and its propagation by the centromere-specific histone CENPA is mediated by epigenetic mechanisms in most eukaryotes. DNA replication origins, origin binding proteins, and replication timing of centromere DNA are important determinants of centromere function. The epigenetically regulated regional centromeres in the budding yeast Candida albicans have unique DNA sequences that replicate earliest in every chromosome and are clustered throughout the cell cycle. In this study, the genome-wide occupancy of the replication initiation protein Orc4 reveals its abundance at all centromeres in C. albicans Orc4 is associated with four different DNA sequence motifs, one of which coincides with tRNA genes (tDNA) that replicate early and cluster together in space. Hi-C combined with genome-wide replication timing analyses identify that early replicating Orc4-bound regions interact with themselves stronger than with late replicating Orc4-bound regions. We simulate a polymer model of chromosomes of C. albicans and propose that the early replicating and highly enriched Orc4-bound sites preferentially localize around the clustered kinetochores. We also observe that Orc4 is constitutively localized to centromeres, and both Orc4 and the helicase Mcm2 are essential for cell viability and CENPA stability in C. albicans Finally, we show that new molecules of CENPA are recruited to centromeres during late anaphase/telophase, which coincides with the stage at which the CENPA-specific chaperone Scm3 localizes to the kinetochore. We propose that the spatiotemporal localization of Orc4 within the nucleus, in collaboration with Mcm2 and Scm3, maintains centromeric chromatin stability and CENPA recruitment in C. albicans ., (© 2021 Sreekumar et al.; Published by Cold Spring Harbor Laboratory Press.)

An important question in the context of the three-dimensional organization of chromosomes is the mechanism of formation of large loops between distant basepairs. Recent experiments suggest that the formation of loops might be mediated by loop extrusion factor proteins such as cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low-effective-diffusion constants leads to times that are unphysically large. The puzzle then is the following: how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle and show that although at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration they can reduce loop formation times because of a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

How chromatin is folded on the length scale of a gene is an open question. Recent experiments have suggested that, in vivo, chromatin is folded in an irregular manner and not as an ordered fiber with a width of 30 nm that is expected from theories of higher order packaging. Using computational methods, we examine how the interplay between DNA-bending nonhistone proteins, histone tails, intrachromatin electrostatic, and other interactions decide the nature of the packaging of chromatin. We show that although the DNA-bending nonhistone proteins make the chromatin irregular, they may not alter the packing density and size of the fiber. We find that the length of the interacting region and intrachromatin electrostatic interactions influence the packing density, clustering of nucleosomes, and the width of the chromatin fiber. Our results suggest that the heterogeneity in the interaction pattern will play an important role in deciding the nature of the packaging of chromatin., (Copyright © 2019 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We present a physics-based polymer model that can investigate 3D organization of chromatin accounting for DNA elasticity, DNA-bending due to nucleosomes, and 1D organization of nucleosomes along DNA. We find that the packing density of chromatin oscillates between densities corresponding to highly folded and extended configurations as we change the nucleosome organization (length of linker DNA). We compute the looping probability of chromatin and show that the presence of nucleosomes increases the looping probability of the chain compared to that of a bare DNA. We also show that looping probability has a large variability depending on the nature of nucleosome organization and density of linker histones.

Why most of the in vivo experiments do not find the 30-nm chromatin fiber, well studied in vitro, is a puzzle. Two basic physical inputs that are crucial for understanding the structure of the 30-nm fiber are the stiffness of the linker DNA and the relative orientations of the DNA entering/exiting nucleosomes. Based on these inputs we simulate chromatin structure and show that the presence of non-histone proteins, which bind and locally bend linker DNA, destroys any regular higher order structures (e.g., zig-zag). Accounting for the bending geometry of proteins like nhp6 and HMG-B, our theory predicts phase-diagram for the chromatin structure as a function of DNA-bending non-histone protein density and mean linker DNA length. For a wide range of linker lengths, we show that as we vary one parameter, that is, the fraction of bent linker region due to non-histone proteins, the steady-state structure will show a transition from zig-zag to an irregular structure-a structure that is reminiscent of what is observed in experiments recently. Our theory can explain the recent in vivo observation of irregular chromatin having co-existence of finite fraction of the next-neighbor (i + 2) and neighbor (i + 1) nucleosome interactions., Competing Interests: The authors have declared that no competing interests exist.

Cells switch genes ON or OFF by altering the state of chromatin via histone modifications at specific regulatory locations along the chromatin polymer. These gene regulation processes are carried out by a network of reactions in which the histone marks spread to neighboring regions with the help of enzymes. In the literature, this spreading has been studied as a purely kinetic, non-diffusive process considering the interactions between neighboring nucleosomes. In this work, we go beyond this framework and study the spreading of modifications using a reaction-diffusion (RD) model accounting for the diffusion of the constituents. We quantitatively segregate the modification profiles generated from kinetic and RD models. The diffusion and degradation of enzymes set a natural length scale for limiting the domain size of modification spreading, and the resulting enzyme limitation is inherent in our model. We also demonstrate the emergence of confined modification domains without the explicit requirement of a nucleation site. We explore polymer compaction effects on spreading and show that single-cell domains may differ from averaged profiles. We find that the modification profiles from our model are comparable with existing H3K9me3 data of S. pombe. Author summary: DNA is folded into chromatin by wrapping it around histone protein octamers, forming a string of nucleosome beads. The chemical modifications on histone proteins along the one-dimensional string form a significant part of the epigenetic code. This code determines whether a chromatin region is likely to be active or repressed. How the chemical modification patterns arise, and their stability along the histone proteins is a question of great interest. While some players in this process are known, how the physical process of diffusion and reaction of the enzymes collectively dictate the pattern formation is unknown. In this work, we simulate histone modification spreading accounting for explicit diffusion and reaction of the essential constituents. We show that the diffusion and degradation processes of the constituents limit the size of the modification domain. We also show how the availability of enzymes and the compaction of the chromatin affect the spreading of the histone modification. [ABSTRACT FROM AUTHOR]

In our cells, DNA is folded and packed with the help of many proteins into chromatin whose basic unit is a nucleosome—DNA wrapped around octamer of histone proteins. The chain of nucleosomes is further folded and arranged into many layers and has a dynamic organization. How does the complex chromatin organization emerge from interactions among DNA, histones, and non-histone proteins have been a question of great interest. Here we review recent literature that investigated how nucleosome positioning and nucleosome-mediated interactions drive chromatin organization. Unlike our earlier understanding, chromatin is organized into 3D domains of various sizes having irregularly organized nucleosomes. These domains emerge due to heterogeneous nucleosome positioning and diverse inter-nucleosome interactions that vary in space and time. [ABSTRACT FROM AUTHOR]

Accounting for enzyme-mediated active sliding, disassembly, and sequence-dependent positioning of nucleosomes, we simulate nucleosome occupancy over cell-cycle-scale times using a stochastic kinetic model. We show that ATP-dependent active nucleosome sliding and nucleosome removal processes are essential to obtain in vivo-like nucleosome positioning. While active sliding leads to dense nucleosome filling, sliding events alone cannot ensure sequence-dependent nucleosome positioning: Active nucleosome removal is the crucial remodeling event that drives positioning. We also show that remodeling activity changes nucleosome dynamics from glassy to liquid-like, and that remodeling dramatically influences exposure dynamics of promoter regions. [ABSTRACT FROM AUTHOR]