Geometrical, conformational and topological restraints in regular nucleosome compaction in chromatin

Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome

Motivation: We present a user-friendly 3D chromatin simulation model for the human genome based on OpenMM, addressing the challenges posed by existing models with use-specific implementations. Our approach employs a multi-scale energy minimization strategy, capturing chromatin's hierarchical structure. Initiating with a Hilbert curve-based structure, users can input files specifying nucleosome positioning, loops, compartments, or subcompartments. Results: The model utilizes an energy minimization approach with a large choice of numerical integrators, providing the entire genome's structure within minutes. Output files include the generated structures for each chromosome, offering a versatile and accessible tool for chromatin simulation in bioinformatics studies. Furthermore, MultiMM is capable of producing nucleosome-resolution structures by making simplistic geometric assumptions about the structure and the density of nucleosomes on the DNA. Code availability: Open-source software and the manual are freely available on https://github.com/SFGLab/MultiMM or via pip https://pypi.org/project/MultiMM/.

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.

Geometrical Heterogeneity Dominates Thermal Fluctuations in Facilitating Chromatin Contacts

Within a living cell, the myriad of proteins that bind DNA introduce heterogeneously spaced kinks into an otherwise semiflexible DNA double helix. To investigate the effects of heterogeneous nucleosome binding on chromatin organization, we extend the wormlike chain model to include statistically spaced, rigid kinks. On timescales where nucleosome positions are fixed, we find that the probability of chromatin loop formation can vary by up to six orders of magnitude between two sets of nucleosome positions drawn from the same distribution. On longer timescales, we show that continuous rerandomization due to nucleosome turnover results in chromatin tracing out an effective WLC with a dramatically smaller Kuhn length than bare DNA. Together, these observations demonstrate that nucleosome spacing acts as the primary source of the structural heterogeneity that dominates local and global chromatin organization.

Chromatin Higher-Order Folding: A Perspective with Linker DNA Angles

The mechanism by which the "beads-on-a-string" nucleosome chain folds into various higher-order chromatin structures in eukaryotic cell nuclei is still poorly understood. The various models depicting higher-order chromatin as regular helical fibers and the very opposite "polymer melt" theory imply that interactions between nucleosome "beads" make the main contribution to the chromatin compaction. Other models in which the geometry of linker DNA "strings" entering and exiting the nucleosome define the three-dimensional structure predict that small changes in the linker DNA configuration may strongly affect nucleosome chain folding and chromatin higher-order structure. Among those studies, the cross-disciplinary approach pioneered by Jörg Langowski that combines computational modeling with biophysical and biochemical experiments was most instrumental for understanding chromatin higher-order structure in vitro. Strikingly, many recent studies, including genome-wide nucleosome interaction mapping and chromatin imaging, show an excellent agreement with the results of three-dimensional computational modeling based on the primary role of linker DNA geometry in chromatin compaction. This perspective relates nucleosome array models with experimental studies of nucleosome array folding in vitro and in situ. I argue that linker DNA configuration plays a key role in determining nucleosome chain flexibility, topology, and propensity for self-association, thus providing new implications for regulation of chromatin accessibility to DNA binding factors and RNA transcription machinery as well as long-range communications between distant genomic sites.

Towards quantitative analysis of gene regulation by enhancers

Enhancers are regulatory DNA sequences that can activate transcription over large distances. Recent studies have revealed the widespread role of distant activation in eukaryotic gene regulation and in the development of various human diseases, including cancer. Here we review recent progress in the field, focusing on new experimental and computational approaches that quantify the role of chromatin structure and dynamics during enhancer-promoter interactions in vitro and in vivo.

Contributions of Sequence to the Higher-Order Structures of DNA

One of the critical unanswered questions in genome biophysics is how the primary sequence of DNA bases influences the global properties of very-long-chain molecules. The local sequence-dependent features of DNA found in high-resolution structures introduce irregularities in the disposition of adjacent residues that facilitate the specific binding of proteins and modulate the global folding and interactions of double helices with hundreds of basepairs. These features also determine the positions of nucleosomes on DNA and the lengths of the interspersed DNA linkers. Like the patterns of basepair association within DNA, the arrangements of nucleosomes in chromatin modulate the properties of longer polymers. The intrachromosomal loops detected in genomic studies contain hundreds of nucleosomes, and given that the simulated configurations of chromatin depend on the lengths of linker DNA, the formation of these loops may reflect sequence-dependent information encoded within the positioning of the nucleosomes. With knowledge of the positions of nucleosomes on a given genome, methods are now at hand to estimate the looping propensities of chromatin in terms of the spacing of nucleosomes and to make a direct connection between the DNA base sequence and larger-scale chromatin folding.

Topological polymorphism of the two-start chromatin fiber

Specific details concerning the spatial organization of nucleosomes in 30 nm fibers remain unknown. To investigate this, we analyzed all stereochemically possible configurations of two-start nucleosome fibers with short DNA linkers L = 13-37 bp (nucleosome repeat length (NRL) = 160-184 bp). Four superhelical parameters-inclination of nucleosomes, twist, rise, and diameter-uniquely describe a regular symmetric fiber. The energy of a fiber is defined as the sum of four terms: elastic energy of the linker DNA, steric repulsion, electrostatics, and a phenomenological (H4 tail-acidic patch) interaction between two stacked nucleosomes. By optimizing the fiber energy with respect to the superhelical parameters, we found two types of topological transition in fibers (associated with the change in inclination angle): one caused by an abrupt 360° change in the linker DNA twisting (change in the DNA linking number, ΔLk = 1), and another caused by overcrossing of the linkers (ΔLk = 2). To the best of our knowledge, this topological polymorphism of the two-start fibers was not reported in the computations published earlier. Importantly, the optimal configurations of the fibers with linkers L = 10n and 10n + 5 bp are characterized by different values of the DNA linking number-that is, they are topologically different. Our results are consistent with experimental observations, such as the inclination 60° to 70° (the angle between the nucleosomal disks and the fiber axis), helical rise, diameter, and left-handedness of the fibers. In addition, we make several testable predictions, among them different degrees of DNA supercoiling in fibers with L = 10n and 10n + 5 bp, different flexibility of the two types of fibers, and a correlation between the local NRL and the level of transcription in different parts of the yeast genome.

Topological diversity of chromatin fibers: Interplay between nucleosome repeat length, DNA linking number and the level of transcription

The spatial organization of nucleosomes in 30-nm fibers remains unknown in detail. To tackle this problem, we analyzed all stereochemically possible configurations of two-start chromatin fibers with DNA linkers L = 10–70 bp (nucleosome repeat length NRL = 157–217 bp). In our model, the energy of a fiber is a sum of the elastic energy of the linker DNA, steric repulsion, electrostatics, and the H4 tail-acidic patch interaction between two stacked nucleosomes. We found two families of energetically feasible conformations of the fibers—one observed earlier, and the other novel. The fibers from the two families are characterized by different DNA linking numbers—that is, they are topologically different. Remarkably, the optimal geometry of a fiber and its topology depend on the linker length: the fibers with linkers L = 10n and 10n + 5 bp have DNA linking numbers per nucleosome ΔLk ≈ −1.5 and −1.0, respectively. In other words, the level of DNA supercoiling is directly related to the length of the inter-nucleosome linker in the chromatin fiber (and therefore, to NRL). We hypothesize that this topological polymorphism of chromatin fibers may play a role in the process of transcription, which is known to generate different levels of DNA supercoiling upstream and downstream from RNA polymerase. A genome-wide analysis of the NRL distribution in active and silent yeast genes yielded results consistent with this assumption.

Nucleosome spacing and chromatin higher-order folding

Packing of about two meters of the human genome DNA into chromatin occupying a several micron-sized cell nucleus requires a high degree of compaction in a manner that allows the information encoded on DNA to remain easily accessible. This packing is mediated by repeated coiling of DNA double helix around histones to form nucleosome arrays that are further folded into higher-order structures. Relatively straight DNA linkers separate the nucleosomes and the spacing between consecutive nucleosome varies between different cells and between different chromosomal loci. In a recent work¹ our group used a biochemically defined in vitro reconstituted system to explore how do various DNA linkers mediate nucleosome array packing into higher-order chromatin structures. For long nucleosome linkers (about 60 bp) we observed a more open chromatin structure and no effect of small linker length alterations (±2−4 bp) on chromatin folding. In striking contrast, for shorter linkers (20−32 bp) we found more compact packing with strong periodical dependence upon the linker DNA lengths. Our data together with high-resolution nucleosome position mapping provide evidence for the natural nucleosome repeats to support a chromatin architecture that, by default, restricts spontaneous folding of nucleosome arrays into compact chromatin fibers. We suggest that incomplete folding of the nucleosome arrays may promote global inter-array interactions that lead to chromatin condensation in metaphase chromosomes and heterochromatin.

DNA of a circular minichromosome linearized by restriction enzymes or other reagents is resistant to further cleavage: an influence of chromatin topology on the accessibility of DNA

The accessibility of DNA in chromatin is an essential factor in regulating its activities. We studied the accessibility of the DNA in a ∼170 kb circular minichromosome to DNA-cleaving reagents using pulsed-field gel electrophoresis and fibre-fluorescence in situ hybridization on combed DNA molecules. Only one of several potential sites in the minichromosome DNA was accessible to restriction enzymes in permeabilized cells, and in growing cells only a single site at an essentially random position was cut by poisoned topoisomerase II, neocarzinostatin and γ-radiation, which have multiple potential cleavage sites; further sites were then inaccessible in the linearized minichromosomes. Sequential exposure to combinations of these reagents also resulted in cleavage at only a single site. Minichromosome DNA containing single-strand breaks created by a nicking endonuclease to relax any unconstrained superhelicity was also cut at only a single position by a restriction enzyme. Further sites became accessible after ≥95% of histones H2A, H2B and H1, and most non-histone proteins were extracted. These observations suggest that a global rearrangement of the three-dimensional packing and interactions of nucleosomes occurs when a circular minichromosome is linearized and results in its DNA becoming inaccessible to probes.

Short nucleosome repeats impose rotational modulations on chromatin fibre folding

In eukaryotic cells, DNA is organized into arrays of repeated nucleosomes where the shorter nucleosome repeat length (NRL) types are associated with transcriptionally active chromatin. Here, we tested a hypothesis that systematic variations in the NRL influence nucleosome array folding into higher-order structures. For NRLs with fixed rotational settings, we observed a negative correlation between NRL and chromatin folding. Rotational variations within a range of longer NRLs (188 bp and above) typical of repressed chromatin in differentiated cells did not reveal any changes in chromatin folding. In sharp contrast, for the shorter NRL range of 165-177 bp, we observed a strong periodic dependence of chromatin folding upon the changes in linker DNA lengths, with the 172 bp repeat found in highly transcribed yeast chromatin imposing an unfolded state of the chromatin fibre that could be reversed by linker histone. Our results suggest that the NRL may direct chromatin higher-order structure into either a nucleosome position-dependent folding for short NRLs typical of transcribed genes or an architectural factor-dependent folding typical of longer NRLs prevailing in eukaryotic heterochromatin.

Nucleosome distribution and linker DNA: connecting nuclear function to dynamic chromatin structure

Genetic information in eukaryotes is managed by strategic hierarchical organization of chromatin structure. Primary chromatin structure describes an unfolded nucleosomal array, often referred to as "beads on a string". Chromatin is compacted by the nonlinear rearrangement of nucleosomes to form stable secondary chromatin structures. Chromatin conformational transitions between primary and secondary structures are mediated by both nucleosome-stacking interactions and the intervening linker DNA. Chromatin model system studies find that the topography of secondary structures is sensitive to the spacing of nucleosomes within an array. Understanding the relationship between nucleosome spacing and higher order chromatin structure will likely yield important insights into the dynamic nature of secondary chromatin structure as it occurs in vivo. Genome-wide nucleosome mapping studies find the distance between nucleosomes varies, and regions of uniformly spaced nucleosomes are often interrupted by regions of nonuniform spacing. This type of organization is found at a subset of actively transcribed genes in which a nucleosome-depleted region near the transcription start site is directly adjacent to uniformly spaced nucleosomes in the coding region. Here, we evaluate secondary chromatin structure and discuss the structural and functional implications of variable nucleosome distributions in different organisms and at gene regulatory junctions.

Predicting nucleosome positioning in genomes: physical and bioinformatic approaches

In eukaryotic genomes, nucleosomes are responsible for packaging DNA and controlling gene expression. For this reason, an increasing interest is arising on computational methods capable of predicting the nucleosome positioning along genomes. In this review we describe and compare bioinformatic and physical approaches adopted to predict nucleosome occupancy along genomes. Computational analyses attempt at decoding the experimental nucleosome maps of genomes in terms of certain dinucleotide step periodicity observed along DNA. Such investigations show that highly significant information about the occurrence of a nucleosome along DNA is intrinsic in certain features of the sequence suggesting that DNA of eukaryotic genomes encodes nucleosome organization. Besides the bioinformatic approaches, physical models were proposed based on the sequence dependent conformational features of the DNA chain, which govern the free energy needed to transform recurrent DNA tracts along the genome into the nucleosomal shape.