Dynamics of Chromatin Fibers: Comparison of Monte Carlo Simulations with Force Spectroscopy

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

Studies of the Mechanism of Nucleosome Dynamics: A Review on Multifactorial Regulation from Computational and Experimental Cases

The nucleosome, which organizes the long coil of genomic DNA in a highly condensed, polymeric way, is thought to be the basic unit of chromosomal structure. As the most important protein–DNA complex, its structural and dynamic features have been successively revealed in recent years. However, its regulatory mechanism, which is modulated by multiple factors, still requires systemic discussion. This study summarizes the regulatory factors of the nucleosome’s dynamic features from the perspective of histone modification, DNA methylation, and the nucleosome-interacting factors (transcription factors and nucleosome-remodeling proteins and cations) and focuses on the research exploring the molecular mechanism through both computational and experimental approaches. The regulatory factors that affect the dynamic features of nucleosomes are also discussed in detail, such as unwrapping, wrapping, sliding, and stacking. Due to the complexity of the high-order topological structures of nucleosomes and the comprehensive effects of regulatory factors, the research on the functional modulation mechanism of nucleosomes has encountered great challenges. The integration of computational and experimental approaches, the construction of physical modes for nucleosomes, and the application of deep learning techniques will provide promising opportunities for further exploration.

An associative memory Hamiltonian model for DNA and nucleosomes

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), reproduces the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similar to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM is designed to emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, is ready to be scaled up to molecular systems large enough to investigate the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use.

Genome modeling: From chromatin fibers to genes

The intricacies of the 3D hierarchical organization of the genome have been approached by many creative modeling studies. The specific model/simulation technique combination defines and restricts the system and phenomena that can be investigated. We present the latest modeling developments and studies of the genome, involving models ranging from nucleosome systems and small polynucleosome arrays to chromatin fibers in the kb-range, chromosomes, and whole genomes, while emphasizing gene folding from first principles. Clever combinations allow the exploration of many interesting phenomena involved in gene regulation, such as nucleosome structure and dynamics, nucleosome-nucleosome stacking, polynucleosome array folding, protein regulation of chromatin architecture, mechanisms of gene folding, loop formation, compartmentalization, and structural transitions at the chromosome and genome levels. Gene-level modeling with full details on nucleosome positions, epigenetic factors, and protein binding, in particular, can in principle be scaled up to model chromosomes and cells to study fundamental biological regulation.

Chromatin fiber breaks into clutches under tension and crowding

The arrangement of nucleosomes inside chromatin is of extensive interest. While in vitro experiments have revealed the formation of 30 nm fibers, most in vivo studies have failed to confirm their presence in cell nuclei. To reconcile the diverging experimental findings, we characterized chromatin organization using a residue-level coarse-grained model. The computed force–extension curve matches well with measurements from single-molecule experiments. Notably, we found that a dodeca-nucleosome in the two-helix zigzag conformation breaks into structures with nucleosome clutches and a mix of trimers and tetramers under tension. Such unfolded configurations can also be stabilized through trans interactions with other chromatin chains. Our study suggests that unfolding from chromatin fibers could contribute to the irregularity of in vivo chromatin configurations. We further revealed that chromatin segments with fibril or clutch structures engaged in distinct binding modes and discussed the implications of these inter-chain interactions for a potential sol–gel phase transition.

CENP-N promotes the compaction of centromeric chromatin

The histone variant CENP-A is the epigenetic determinant for the centromere, where it is interspersed with canonical H3 to form a specialized chromatin structure that nucleates the kinetochore. How nucleosomes at the centromere arrange into higher order structures is unknown. Here we demonstrate that the human CENP-A-interacting protein CENP-N promotes the stacking of CENP-A-containing mononucleosomes and nucleosomal arrays through a previously undefined interaction between the α6 helix of CENP-N with the DNA of a neighboring nucleosome. We describe the cryo-EM structures and biophysical characterization of such CENP-N-mediated nucleosome stacks and nucleosomal arrays and demonstrate that this interaction is responsible for the formation of densely packed chromatin at the centromere in the cell. Our results provide first evidence that CENP-A, together with CENP-N, promotes specific chromatin higher order structure at the centromere.

emDNA - A Tool for Modeling Protein-decorated DNA Loops and Minicircles at the Base-pair Step Level

Computational modeling of nucleic acids plays an important role in molecular biology, enhancing our general understanding of the relationship between structure and function. Biophysical studies have provided a wealth of information on how double-helical DNA responds to proteins and other molecules in its local environment but far less understanding of the larger scale structural responses found in protein-decorated loops and minicircles. Current computational models of DNA range from detailed all-atom molecular dynamics studies, which produce rich time and spatially dependent depictions of small DNA fragments, to coarse-grained simulations, which sacrifice detailed physical and chemical information to treat larger scale systems. The treatment of DNA used here, at the base-pair step level with rigid-body parameters, allows one to develop quality models hundreds of base pairs long from local, sequence-specific features found from experiment. The emDNA software takes advantage of this framework, producing elastically optimized models of DNA at thermal equilibrium with built-in or user-generated elastic models. This versatile program, in combination with case studies included in this article, allows users of any skill level to develop and investigate mesoscale models of their own design. The functionality of emDNA includes a tool to incorporate experiment-specific configurations, e.g. protein-bound and/or melted DNA from known high-resolution structures, within higher-order 3D models by fixing the orientation and position of user-specified base pairs. The software provides a new avenue into multiscale genetic modeling, giving a wide range of users a deeper understanding of DNA mesoscale organization and the opportunity to pose new questions in genetic research. The publicly available emDNA software, including build instructions and usage information, is available on GitHub (https://nicocvn.github.io/emDNA/).

Differences in nanoscale organization of regulatory active and inactive human chromatin

Methodological advances in conformation capture techniques have fundamentally changed our understanding of chromatin architecture. However, the nanoscale organization of chromatin and its cell-to-cell variance are less studied. Analyzing genome-wide data from 733 human cell and tissue samples, we identified 2 prototypical regions that exhibit high or absent hypersensitivity to deoxyribonuclease I, respectively. These regulatory active or inactive regions were examined in the lymphoblast cell line K562 by using high-throughput super-resolution microscopy. In both regions, we systematically measured the physical distance of 2 fluorescence in situ hybridization spots spaced by only 5 kb of DNA. Unexpectedly, the resulting distance distributions range from very compact to almost elongated configurations of more than 200-nm length for both the active and inactive regions. Monte Carlo simulations of a coarse-grained model of these chromatin regions based on published data of nucleosome occupancy in K562 cells were performed to understand the underlying mechanisms. There was no parameter set for the simulation model that can explain the microscopically measured distance distributions. Obviously, the chromatin state given by the strength of internucleosomal interaction, nucleosome occupancy, or amount of histone H1 differs from cell to cell, which results in the observed broad distance distributions. This large variability was not expected, especially in inactive regions. The results for the mechanisms for different distance distributions on this scale are important for understanding the contacts that mediate gene regulation. Microscopic measurements show that the inactive region investigated here is expected to be embedded in a more compact chromatin environment. The simulation results of this region require an increase in the strength of internucleosomal interactions. It may be speculated that the higher density of chromatin is caused by the increased internucleosomal interaction strength.

DNA methylation cues in nucleosome geometry, stability and unwrapping

Cytosine methylation at the 5-carbon position is an essential DNA epigenetic mark in many eukaryotic organisms. Although countless structural and functional studies of cytosine methylation have been reported, our understanding of how it influences the nucleosome assembly, structure, and dynamics remains obscure. Here, we investigate the effects of cytosine methylation at CpG sites on nucleosome dynamics and stability. By applying long molecular dynamics simulations on several microsecond time scale, we generate extensive atomistic conformational ensembles of full nucleosomes. Our results reveal that methylation induces pronounced changes in geometry for both linker and nucleosomal DNA, leading to a more curved, under-twisted DNA, narrowing the adjacent minor grooves, and shifting the population equilibrium of sugar-phosphate backbone geometry. These DNA conformational changes are associated with a considerable enhancement of interactions between methylated DNA and the histone octamer, doubling the number of contacts at some key arginines. H2A and H3 tails play important roles in these interactions, especially for DNA methylated nucleosomes. This, in turn, prevents a spontaneous DNA unwrapping of 3-4 helical turns for the methylated nucleosome with truncated histone tails, otherwise observed in the unmethylated system on several microseconds time scale.

Torsional stress can regulate the unwrapping of two outer half superhelical turns of nucleosomal DNA

Torsional stress has a significant impact on the structure and stability of the nucleosome. RNA polymerase imposes torsional stress on the DNA in chromatin and unwraps the DNA from the nucleosome to access the genetic information encoded in the DNA. To understand how the torsional stress affects the stability of the nucleosome, we examined the unwrapping of two half superhelical turns of nucleosomal DNA from either end of the DNA under torsional stress with all-atom molecular dynamics simulations. The free energies for unwrapping the DNA indicate that positive stress that overtwists DNA facilitates a large-scale asymmetric unwrapping of the DNA without a large extension of the DNA. During the unwrapping, one end of the DNA was dissociated from H3 and H2A-H2B, while the other end of the DNA stably remained wrapped. The detailed analysis indicates that this asymmetric dissociation is facilitated by the geometry and bendability of the DNA under positive stress. The geometry stabilized the interaction between the major groove of the twisted DNA and the H3 αN-helix, and the straightened DNA destabilized the interaction with H2A-H2B. Under negative stress, the DNA became more bendable and flexible, which facilitated the binding of the unwrapped DNA to the octamer in a stable state. Consequently, we conclude that the torsional stress has a significant impact on the affinity of the DNA and the octamer through the inherent nature of the DNA and can change the accessibility of regulatory proteins.

Soft-matter properties of multilayer chromosomes

This perspective aims to identify the relationships between the structural and dynamic properties of chromosomes and the fundamental properties of soft-matter systems. Chromatin is condensed into metaphase chromosomes during mitosis. The resulting structures are elongated cylinders having micrometer-scale dimensions. Our previous studies, using transmission electron microscopy, atomic force microscopy, and cryo-electron tomography, suggested that metaphase chromosomes have a multilayered structure, in which each individual layer has the width corresponding to a mononucleosome sheet. The self-assembly of multilayer chromatin plates from small chromatin fragments suggests that metaphase chromosomes are self-organized hydrogels (in which a single DNA molecule crosslinks the whole structure) with an internal liquid-crystal order produced by the stacking of chromatin layers along the chromosome axis. This organization of chromatin was unexpected, but the spontaneous assembly of large structures has been studied in different soft-matter systems and, according to these studies, the self-organization of chromosomes could be justified by the interplay between weak interactions of repetitive nucleosome building blocks and thermal fluctuations. The low energy of interaction between relatively large building blocks also justifies the easy deformation and structural fluctuations of soft-matter structures and the changes of phase caused by diverse external factors. Consistent with these properties of soft matter, different experimental results show that metaphase chromosomes are easily deformable. Furthermore, at the end of mitosis, condensed chromosomes undergo a phase transition into a more fluid structure, which can be correlated to the decrease in the Mg²⁺concentration and to the dissociation of condensins from chromosomes. Presumably, the unstacking of layers and chromatin fluctuations driven by thermal energy facilitate gene expression during interphase.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Solution structure(s) of trinucleosomes from contrast variation SAXS

Nucleosomes in all eukaryotic cells are organized into higher order structures that facilitate genome compaction. Visualizing these organized structures is an important step in understanding how genomic DNA is efficiently stored yet remains accessible to information-processing machinery. Arrays of linked nucleosomes serve as useful models for understanding how the properties of both DNA and protein partners affect their arrangement. A number of important questions are also associated with understanding how the spacings between nucleosomes are affected by the histone proteins, chromatin remodelers, or other chromatin-associated protein partners. Contrast variation small angle X-ray scattering (CVSAXS) reports the DNA conformation within protein-DNA complexes and here is applied to measure the conformation(s) of trinucleosomes in solution, with specific sensitivity to the distance between and relative orientation of linked nucleosomes. These data are interpreted in conjunction with DNA models that account for its sequence dependent mechanical properties, and Monte-Carlo techniques that generate realistic structures for comparison with measured scattering profiles. In solution, trinucleosomes segregate into two dominant populations, with the flanking nucleosomes stacked or nearly equilaterally separated, e.g. with roughly equal distance between all pairs of nucleosomes. These populations are consistent with previously observed magnesium-dependent structures of trinucleosomes with shorter linkers.

Surprising Twists in Nucleosomal DNA with Implication for Higher-order Folding

While nucleosomes are dynamic entities that must undergo structural deformations to perform their functions, the general view from available high-resolution structures is a largely static one. Even though numerous examples of twist defects have been documented, the DNA wrapped around the histone core is generally thought to be overtwisted. Analysis of available high-resolution structures from the Protein Data Bank reveals a heterogeneous distribution of twist along the nucleosomal DNA, with clear patterns that are consistent with the literature, and a significant fraction of structures that are undertwisted. The subtle differences in nucleosomal DNA folding, which extend beyond twist, have implications for nucleosome disassembly and modeled higher-order structures. Simulations of oligonucleosome arrays built with undertwisted models behave very differently from those constructed from overtwisted models, in terms of compaction and inter-nucleosome contacts, introducing configurational changes equivalent to those associated with 2-3 base-pair changes in nucleosome spacing. Differences in the nucleosomal DNA pathway, which underlie the way that DNA enters and exits the nucleosome, give rise to different nucleosome-decorated minicircles and affect the topological mix of configurational states.

A critical role for linker DNA in higher-order folding of chromatin fibers

Nucleosome-nucleosome interactions drive the folding of nucleosomal arrays into dense chromatin fibers. A better physical account of the folding of chromatin fibers is necessary to understand the role of chromatin in regulating DNA transactions. Here, we studied the unfolding pathway of regular chromatin fibers as a function of single base pair increments in linker length, using both rigid base-pair Monte Carlo simulations and single-molecule force spectroscopy. Both computational and experimental results reveal a periodic variation of the folding energies due to the limited flexibility of the linker DNA. We show that twist is more restrictive for nucleosome stacking than bend, and find the most stable stacking interactions for linker lengths of multiples of 10 bp. We analyzed nucleosomes stacking in both 1- and 2-start topologies and show that stacking preferences are determined by the length of the linker DNA. Moreover, we present evidence that the sequence of the linker DNA also modulates nucleosome stacking and that the effect of the deletion of the H4 tail depends on the linker length. Importantly, these results imply that nucleosome positioning in vivo not only affects the phasing of nucleosomes relative to DNA but also directs the higher-order structure of chromatin.

Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber.

The three-dimensional organization of chromatin plays critical roles in regulating genome function. Here the authors apply a near atomistic model to study the structure and dynamics of the chromatin folding unit - the tetra-nucleosome - to provide insight into how chromatin folds.

Topological polymorphism of nucleosome fibers and folding of chromatin

We discuss recent observations of polymorphic chromatin packaging at the oligonucleosomal level and compare them with computer simulations. Our computations reveal two topologically different families of two-start 30-nm fiber conformations distinguished by the linker length L; fibers with L ≈ 10n and L ≈ 10n+5 basepairs have DNA linking numbers per nucleosome of ΔLk ≈ -1.5 and -1.0, respectively (where n is a natural number). Although fibers with ΔLk ≈ -1.5 were observed earlier, the topoisomer with ΔLk ≈ -1.0 is novel. These predictions were confirmed experimentally for circular nucleosome arrays with precisely positioned nucleosomes. We suggest that topological polymorphism of chromatin may play a role in transcription, with the {10n+5} fibers producing transcriptionally competent chromatin structures. This hypothesis is consistent with available data for yeast and, partially, for fly. We show that both fiber topoisomers (with ΔLk ≈ -1.5 and -1.0) have to be taken into account to interpret experimental data obtained using new techniques: genome-wide Micro-C, Hi-CO, and RICC-seq, as well as self-association of nucleosome arrays in vitro. The relative stability of these topoisomers is likely to depend on epigenetic histone modifications modulating the strength of internucleosome interactions. Potentially, our findings may reflect a general tendency of functionally distinct parts of the genome to retain topologically different higher-order structures.

The role of histone tails in nucleosome stability: An electrostatic perspective

We propose a methodology for the study of protein-DNA electrostatic interactions and apply it to clarify the effect of histone tails in nucleosomes. This method can be used to correlate electrostatic interactions to structural and functional features of protein-DNA systems, and can be combined with coarse-grained representations. In particular, we focus on the electrostatic field and resulting forces acting on the DNA. We investigate the electrostatic origins of effects such as different stages in DNA unwrapping, nucleosome destabilization upon histone tail truncation, and the role of specific arginines and lysines undergoing Post-Translational Modifications. We find that the positioning of the histone tails can oppose the attractive pull of the histone core, locally deform the DNA, and tune DNA unwrapping. Small conformational variations in the often overlooked H2A C-terminal tails had significant electrostatic repercussions near the DNA entry and exit sites. The H2A N-terminal tail exerts attractive electrostatic forces towards the histone core in positions where Polymerase II halts its progress. We validate our results with comparisons to previous experimental and computational observations.

Multi-contact 3C reveals that the human genome during interphase is largely not entangled

During interphase the eukaryotic genome is organized into chromosome territories that are spatially segregated into compartment domains. The extent to which interacting domains or chromosomes are entangled is not known. We analyze series of co-occurring chromatin interactions using multi-contact 3C (MC-3C) in human cells to provide insights into the topological entanglement of chromatin. Multi-contact interactions represent percolation paths (C-walks) through 3D chromatin space. We find that the order of interactions within C-walks that occur across interfaces where chromosomes or compartment domains interact is not random. Polymer simulations show that such C-walks are consistent with distal domains being topologically insulated, i.e. not catenated. Simulations show that even low levels of random strand passage, e.g. by topoisomerase II, would result in entanglements, increased mixing at domain interfaces and an order of interactions within C-walks not consistent with experimental MC-3C data. Our results indicate that during interphase entanglements between chromosomes and chromosomal domains are rare.

Chromatin Compaction Multiscale Modeling: A Complex Synergy Between Theory, Simulation, and Experiment

Understanding the mechanisms that trigger chromatin compaction, its patterns, and the factors they depend on, is a fundamental and still open question in Biology. Chromatin compacts and reinforces DNA and is a stable but dynamic structure, to make DNA accessible to proteins. In recent years, computational advances have provided larger amounts of data and have made large-scale simulations more viable. Experimental techniques for the extraction and reconstitution of chromatin fibers have improved, reinvigorating theoretical and experimental interest in the topic and stimulating debate on points previously considered as certainties regarding chromatin. A great assortment of approaches has emerged, from all-atom single-nucleosome or oligonucleosome simulations to various degrees of coarse graining, to polymer models, to fractal-like structures and purely topological models. Different fiber-start patterns have been studied in theory and experiment, as well as different linker DNA lengths. DNA is a highly charged macromolecule, making ionic and electrostatic interactions extremely important for chromatin topology and dynamics. Indeed, the repercussions of varying ionic concentration have been extensively examined at the computational level, using all-atom, coarse-grained, and continuum techniques. The presence of high-curvature AT-rich segments in DNA can cause conformational variations, attesting to the fact that the role of DNA is both structural and electrostatic. There have been some tentative attempts to describe the force fields governing chromatin conformational changes and the energy landscapes of these transitions, but the intricacy of the system has hampered reaching a consensus. The study of chromatin conformations is an intrinsically multiscale topic, influenced by a wide range of biological and physical interactions, spanning from the atomic to the chromosome level. Therefore, powerful modeling techniques and carefully planned experiments are required for an overview of the most relevant phenomena and interactions. The topic provides fertile ground for interdisciplinary studies featuring a synergy between theoretical and experimental scientists from different fields and the cross-validation of respective results, with a multi-scale perspective. Here, we summarize some of the most representative approaches, and focus on the importance of electrostatics and solvation, often overlooked aspects of chromatin modeling.

Supramolecular multilayer organization of chromosomes: possible functional roles of planar chromatin in gene expression and DNA replication and repair

Experimental evidence indicates that the chromatin filament is self-organized into a multilayer planar structure that is densely stacked in metaphase and unstacked in interphase. This chromatin organization is unexpected, but it is shown that diverse supramolecular assemblies, including dinoflagellate chromosomes, are multilayered. The mechanical strength of planar chromatin protects the genome integrity, even when double-strand breaks are produced. Here, it is hypothesized that the chromatin filament in the loops and topologically associating domains is folded within the thin layers of the multilaminar chromosomes. It is also proposed that multilayer chromatin has two states: inactive when layers are stacked and active when layers are unstacked. Importantly, the well-defined topology of planar chromatin may facilitate DNA replication without entanglements and DNA repair by homologous recombination.

Nucleosome spacing periodically modulates nucleosome chain folding and DNA topology in circular nucleosome arrays

The length of linker DNA that separates nucleosomes is highly variable, but its mechanistic role in modulating chromatin structure and functions remains unknown. Here, we established an experimental system using circular arrays of positioned nucleosomes to investigate whether variations in nucleosome linker length could affect nucleosome folding, self-association, and interactions. We conducted EM, DNA topology, native electrophoretic assays, and Mg²⁺-dependent self-association assays to study intrinsic folding of linear and circular nucleosome arrays with linker DNA length of 36 bp and 41 bp (3.5 turns and 4 turns of DNA double helix, respectively). These experiments revealed that potential artifacts arising from open DNA ends and full DNA relaxation in the linear arrays do not significantly affect overall chromatin compaction and self-association. We observed that the 0.5 DNA helical turn difference between the two DNA linker lengths significantly affects DNA topology and nucleosome interactions. In particular, the 41-bp linkers promoted interactions between any two nucleosome beads separated by one bead as expected for a zigzag fiber, whereas the 36-bp linkers promoted interactions between two nucleosome beads separated by two other beads and also reduced negative superhelicity. Monte Carlo simulations accurately reproduce periodic modulations of chromatin compaction, DNA topology, and internucleosomal interactions with a 10-bp periodicity. We propose that the nucleosome spacing and associated chromatin structure modulations may play an important role in formation of different chromatin epigenetic states, thus suggesting implications for how chromatin accessibility to DNA-binding factors and the RNA transcription machinery is regulated.

Rigid Basepair Monte Carlo Simulations of One-Start and Two-Start Chromatin Fiber Unfolding by Force

The organization of chromatin in 30 nm fibers remains a topic of debate. Here, we quantify the mechanical properties of the linker DNA and evaluate the impact of these properties on chromatin fiber folding. We extended a rigid basepair DNA model to include (un)wrapping of nucleosomal DNA and (un)stacking of nucleosomes in one-start and two-start chromatin fibers. Monte Carlo simulations that mimic single-molecule force spectroscopy experiments of folded nucleosomal arrays reveal different stages of unfolding as a function of force and are largely consistent with a two-start folding for 167 and one-start folding for 197 nucleosome repeat length fibers. The major insight is that nucleosome unstacking and subsequent unwrapping is not necessary to obtain quantitative agreement with experimental force extension curves up to the overstretching plateau of folded chromatin fibers at 3-5 pN. Nucleosome stacking appears better accommodated in one-start than in two-start conformations, and we suggest that this difference can compensate the increased energy for bending the linker DNA. Overall, these simulations capture the dynamic structure of chromatin fibers while maintaining realistic physical properties of the linker DNA.