Liquid-liquid phase separation (LLPS) in DNA and chromatin systems from the perspective of colloid physical chemistry.

DNA is a highly charged polyelectrolyte and is prone to associative phase separation driven by the presence of multivalent cations, charged surfactants, proteins, polymers and colloids. The process of DNA phase separation induced by positively charged species is often called DNA condensation. Generally, it refers to either intramolecular DNA compaction (coil-globule transition) or intermolecular DNA aggregation with macroscopic phase separation, but the formation of a DNA liquid crystalline system is also displayed. This has traditionally been described by polyelectrolyte theory and qualitative (Flory-Huggins-based) polymer theory approaches. DNA in the cell nucleus is packed into chromatin wound around the histone octamer (a protein complex comprising two copies each of the four histone proteins H2A, H2B, H3 and H4) to form nucleosomes separated by linker DNA. During the last decade, the phenomenon of the formation of biomolecular condensates (dynamic droplets) by liquid-liquid phase separation (LLPS) has emerged as a generally important mechanism for the formation of membraneless organelles from proteins, nucleic acids and their complexes. DNA and chromatin droplet formation through LLPS has recently received much attention by in vitro as well as in vivo studies that established the importance of this for compartmentalisation in the cell nucleus. Here, we review DNA and chromatin LLPS from a general colloid physical chemistry perspective. We start with a general discussion of colloidal phase separation in aqueous solutions and review the original (pre-LLPS era) work on DNA (macroscopic) phase separation for simpler systems with DNA in the presence of multivalent cations and well-defined surfactants and colloids. Following that, we discuss and illustrate the similarities of such macroscopic phase separation with the general behaviour of LLPS droplet formation by associative phase separation for DNA-protein systems, including chromatin; we also note cases of segregative association. The review ends with a discussion of chromatin LLPS in vivo and its physiological significance.

The shelterin component TRF2 mediates columnar stacking of human telomeric chromatin.

Telomere repeat binding factor 2 (TRF2) is an essential component of the telomeres and also plays an important role in a number of other non-telomeric processes. Detailed knowledge of the binding and interaction of TRF2 with telomeric nucleosomes is limited. Here, we study the binding of TRF2 to in vitro-reconstituted kilobasepair-long human telomeric chromatin fibres using electron microscopy, single-molecule force spectroscopy and analytical ultracentrifugation sedimentation velocity. Our electron microscopy results revealed that full-length and N-terminally truncated TRF2 promote the formation of a columnar structure of the fibres with an average width and compaction larger than that induced by the addition of Mg2+, in agreement with the in vivo observations. Single-molecule force spectroscopy showed that TRF2 increases the mechanical and thermodynamic stability of the telomeric fibres when stretched with magnetic tweezers. This was in contrast to the result for fibres reconstituted on the 'Widom 601' high-affinity nucleosome positioning sequence, where minor effects on fibre stability were observed. Overall, TRF2 binding induces and stabilises columnar fibres, which may play an important role in telomere maintenance.

Multiscale modeling reveals the ion-mediated phase separation of nucleosome core particles.

Due to the vast length scale inside the cell nucleus, multiscale models are required to understand chromatin folding, structure, and dynamics and how they regulate genomic activities such as DNA transcription, replication, and repair. We study the interactions and structure of condensed phases formed by the universal building block of chromatin, the nucleosome core particle (NCP), using bottom-up multiscale coarse-grained (CG) simulations with a model extracted from all-atom MD simulations. In the presence of the multivalent cations Mg(H2O)62+ or CoHex3+, we analyze the internal structures of the NCP aggregates and the contributions of histone tails and ions to the aggregation patterns. We then derive a "super" coarse-grained (SCG) NCP model to study the macroscopic scale phase separation of NCPs. The SCG simulations show the formation of NCP aggregates with Mg(H2O)62+ concentration-dependent densities and sizes. Variation of the CoHex3+ concentrations results in highly ordered lamellocolumnar and hexagonal columnar phases in agreement with experimental data. The results give detailed insights into nucleosome interactions and for understanding chromatin folding in the cell nucleus.

Telomeric chromatin structure.

Eukaryotic DNA is packaged into nucleosomes, which further condenses into chromosomes. The telomeres, which form the protective end-capping of chromosomes, play a pivotal role in ageing and cancer. Recently, significant advances have been made in understanding the nucleosomal and telomeric chromatin structure at the molecular level. In addition, recent studies shed light on the nucleosomal organisation at telomeres revealing its ultrastructural organisation, the atomic structure at the nucleosome level, its dynamic properties, and higher-order packaging of telomeric chromatin. Considerable advances have furthermore been made in understanding the structure, function and organisation of shelterin, telomerase and CST complexes. Here we discuss these recent advances in the organisation of telomeric nucleosomes and chromatin and highlight progress in the structural understanding of shelterin, telomerase and CST complexes.

Reconstituted TAD-size chromatin fibers feature heterogeneous nucleosome clusters.

Large topologically associated domains (TADs) contain irregularly spaced nucleosome clutches, and interactions between such clutches are thought to aid the compaction of these domains. Here, we reconstituted TAD-sized chromatin fibers containing hundreds of nucleosomes on native source human and lambda-phage DNA and compared their mechanical properties at the single-molecule level with shorter '601' arrays with various nucleosome repeat lengths. Fluorescent imaging showed increased compaction upon saturation of the DNA with histones and increasing magnesium concentration. Nucleosome clusters and their structural fluctuations were visualized in confined nanochannels. Force spectroscopy revealed not only similar mechanical properties of the TAD-sized fibers as shorter fibers but also large rupture events, consistent with breaking the interactions between distant clutches of nucleosomes. Though the arrays of native human DNA, lambda-phage and '601' DNA featured minor differences in reconstitution yield and nucleosome stability, the fibers' global structural and mechanical properties were similar, including the interactions between nucleosome clutches. These single-molecule experiments quantify the mechanical forces that stabilize large TAD-sized chromatin domains consisting of disordered, dynamically interacting nucleosome clutches and their effect on the condensation of large chromatin domains.

Columnar structure of human telomeric chromatin.

Telomeres, the ends of eukaryotic chromosomes, play pivotal parts in ageing and cancer and are targets of DNA damage and the DNA damage response1-5. Little is known about the structure of telomeric chromatin at the molecular level. Here we used negative stain electron microscopy and single-molecule magnetic tweezers to characterize 3-kbp-long telomeric chromatin fibres. We also obtained the cryogenic electron microscopy structure of the condensed telomeric tetranucleosome and its dinucleosome unit. The structure displayed close stacking of nucleosomes with a columnar arrangement, and an unusually short nucleosome repeat  length that comprised about 132 bp DNA wound in a continuous superhelix around histone octamers. This columnar structure is primarily stabilized by the H2A carboxy-terminal and histone amino-terminal tails in a synergistic manner. The columnar conformation results in exposure of the DNA helix, which may make it susceptible to both DNA damage and the DNA damage response. The conformation also exists in an alternative open state, in which one nucleosome is unstacked and flipped out, which exposes the acidic patch of the histone surface. The structural features revealed in this work suggest mechanisms by which protein factors involved in telomere maintenance can access telomeric chromatin in its compact form.

A Bottom-Up Coarse-Grained Model for Nucleosome-Nucleosome Interactions with Explicit Ions.

The nucleosome core particle (NCP) is a large complex of 145-147 base pairs of DNA and eight histone proteins and is the basic building block of chromatin that forms the chromosomes. Here, we develop a coarse-grained (CG) model of the NCP derived through a systematic bottom-up approach based on underlying all-atom MD simulations to compute the necessary CG interactions. The model produces excellent agreement with known structural features of the NCP and gives a realistic description of the nucleosome-nucleosome attraction in the presence of multivalent cations (Mg(H2O)62+ or Co(NH3)63+) for systems comprising 20 NCPs. The results of the simulations reveal structural details of the NCP-NCP interactions unavailable from experimental approaches, and this model opens the prospect for the rigorous modeling of chromatin fibers.

A Soft Sensor for Measuring the Wear of an Induction Motor Bearing by the Park's Vector Components of Current and Voltage.

This paper presents a methodology for creating a soft sensor for predicting the bearing wear of electrical machines. The technique is based on a combination of Park vector methods and a classifier based on an artificial neural network (ANN-classifier). Experiments are carried out in laboratory conditions on an asynchronous motor of AIR132M4 brand. For the experiment, the inner rings of the bearing are artificially degraded. The filtered and processed data obtained from the installation are passed through the ANN-classifier. A method of providing the data into the classifier is shown. The result is a convergence of 99% and an accuracy of 98% on the test data.

Bottom-Up Coarse-Grained Modeling of DNA.

Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.

Linker histone defines structure and self-association behaviour of the 177 bp human chromatosome.

Linker histones play essential roles in the regulation and maintenance of the dynamic chromatin structure of higher eukaryotes. The influence of human histone H1.0 on the nucleosome structure and biophysical properties of the resulting chromatosome were investigated and compared with the 177-bp nucleosome using Cryo-EM and SAXS. The 4.5 Å Cryo-EM chromatosome structure showed that the linker histone binds at the nucleosome dyad interacting with both linker DNA arms but in a tilted manner leaning towards one of the linker sides. The chromatosome is laterally compacted and rigid in the dyad and linker DNA area, in comparison with the nucleosome where linker DNA region is more flexible and displays structural variability. In solution, the chromatosomes appear slightly larger than the nucleosomes, with the volume increase compared to the bound linker histone, according to solution SAXS measurements. SAXS X-ray diffraction characterisation of Mg-precipitated samples showed that the different shapes of the 177 chromatosome enabled the formation of a highly ordered lamello-columnar phase when precipitated by Mg2+, indicating the influence of linker histone on the nucleosome stacking. The biological significance of linker histone, therefore, may be affected by the change in the polyelectrolyte and DNA conformation properties of the chromatosomes, in comparison to nucleosomes.

How potassium came to be the dominant biological cation: of metabolism, chemiosmosis, and cation selectivity since the beginnings of life.

In the cytoplasm of practically all living cells, potassium is the major cation while sodium dominates in the media (seawater, extracellular fluids). Both prokaryotes and eukaryotes have elaborate mechanisms and spend significant energy to maintain this asymmetric K+ /Na+ distribution. This essay proposes an original line of evidence to explain how bacteria selected potassium at the very beginning of the evolutionary process and why it remains essential for eukaryotes.

The human telomeric nucleosome displays distinct structural and dynamic properties.

Telomeres protect the ends of our chromosomes and are key to maintaining genomic integrity during cell division and differentiation. However, our knowledge of telomeric chromatin and nucleosome structure at the molecular level is limited. Here, we aimed to define the structure, dynamics as well as properties in solution of the human telomeric nucleosome. We first determined the 2.2 Å crystal structure of a human telomeric nucleosome core particle (NCP) containing 145 bp DNA, which revealed the same helical path for the DNA as well as symmetric stretching in both halves of the NCP as that of the 145 bp '601' NCP. In solution, the telomeric nucleosome exhibited a less stable and a markedly more dynamic structure compared to NCPs containing DNA positioning sequences. These observations provide molecular insights into how telomeric DNA forms nucleosomes and chromatin and advance our understanding of the unique biological role of telomeres.

High resolution 3D visualization of the spinal cord in a post-mortem murine model.

A crucial issue in the development of therapies to treat pathologies of the central nervous system is represented by the availability of non-invasive methods to study the three-dimensional morphology of spinal cord, with a resolution able to characterize its complex vascular and neuronal organization. X-ray phase contrast micro-tomography enables a high-quality, 3D visualization of both the vascular and neuronal network simultaneously without the need of contrast agents, destructive sample preparations or sectioning. Until now, high resolution investigations of the post-mortem spinal cord in murine models have mostly been performed in spinal cords removed from the spinal canal. We present here post-mortem phase contrast micro-tomography images reconstructed using advanced computational tools to obtain high-resolution and high-contrast 3D images of the fixed spinal cord without removing the bones and preserving the richness of micro-details available when measuring exposed spinal cords. We believe that it represents a significant step toward the in-vivo application.

Modeling DNA Flexibility: Comparison of Force Fields from Atomistic to Multiscale Levels.

Accurate parametrization of force fields (FFs) is of ultimate importance for computer simulations to be reliable and to possess a predictive power. In this work, we analyzed, in multi-microsecond simulations of a 40-base-pair DNA fragment, the performance of four force fields, namely, the two recent major updates of CHARMM and two from the AMBER family. We focused on a description of double-helix DNA flexibility and dynamics both at atomistic and at mesoscale level in coarse-grained (CG) simulations. In addition to the traditional analysis of different base-pair and base-step parameters, we extended our analysis to investigate the ability of the force field to parametrize a CG DNA model by structure-based bottom-up coarse-graining, computing DNA persistence length as a function of ionic strength. Our simulations unambiguously showed that the CHARMM36 force field is unable to preserve DNA's structural stability at over-microsecond time scale. Both versions of the AMBER FF, parmbsc0 and parmbsc1, showed good agreement with experiment, with some bias of parmbsc0 parameters for intermediate A/B form DNA structures. The CHARMM27 force field provides stable atomistic trajectories and overall (among the considered force fields) the best fit to experimentally determined DNA flexibility parameters both at atomistic and at mesoscale level.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level.

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex3+). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex3+ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

The effect of linker DNA on the structure and interaction of nucleosome core particles.

In eukaryotes, the compaction of chromatin fibers composed of nucleosome core particles (NCPs) connected by a linker DNA into chromosomes is highly efficient; however, the underlying folding mechanisms remain elusive. We used small angle X-ray scattering (SAXS) to investigate the influence of linker DNA length on the local structure and the interparticle interactions of the NCPs. In the presence of the linker DNA of 30 bp or less in length, the results suggest partial unwrapping of nucleosomal DNA on the NCP irrespective of the linker DNA length. Moreover, the presence of 15 bp linker DNA alleviated the electrostatic repulsion between the NCPs and prevented the formation of an ordered columnar hexagonal phase, demonstrating that the linker DNA plays an active role in chromatin folding.

A systematic analysis of nucleosome core particle and nucleosome-nucleosome stacking structure.

Chromatin condensation is driven by the energetically favourable interaction between nucleosome core particles (NCPs). The close NCP-NCP contact, stacking, is a primary structural element of all condensed states of chromatin in vitro and in vivo. However, the molecular structure of stacked nucleosomes as well as the nature of the interactions involved in its formation have not yet been systematically studied. Here we undertake an investigation of both the structural and physico-chemical features of NCP structure and the NCP-NCP stacking. We introduce an "NCP-centred" set of parameters (NCP-NCP distance, shift, rise, tilt, and others) that allows numerical characterisation of the mutual positions of the NCPs in the stacking and in any other structures formed by the NCP. NCP stacking in more than 140 published NCP crystal structures were analysed. In addition, coarse grained (CG) MD simulations modelling NCP condensation was carried out. The CG model takes into account details of the nucleosome structure and adequately describes the long range electrostatic forces as well as excluded volume effects acting in chromatin. The CG simulations showed good agreement with experimental data and revealed the importance of the H2A and H4 N-terminal tail bridging and screening as well as tail-tail correlations in the stacked nucleosomes.

Single-molecule compaction of megabase-long chromatin molecules by multivalent cations.

To gain insight into the conformational properties and compaction of megabase-long chromatin molecules, we reconstituted chromatin from T4 phage DNA (165 kb) and recombinant human histone octamers (HO). The unimolecular compaction, induced by divalent Mg2+ or tetravalent spermine4+ cations, studied by single-molecule fluorescence microscopy (FM) and dynamic light scattering (DLS) techniques, resulted in the formation of 250-400 nm chromatin condensates. The compaction on this scale of DNA size is comparable to that of chromatin topologically associated domains (TAD) in vivo. Variation of HO loading revealed a number of unique features related to the efficiency of chromatin compaction by multivalent cations, the mechanism of compaction, and the character of partly compact chromatin structures. The observations may be relevant for how DNA accessibility in chromatin is maintained. Compaction of saturated chromatin, in turn, is accompanied by an intra-chain segregation at the level of single chromatin molecules, suggesting an intriguing scenario of selective activation/deactivation of DNA as a result of chromatin fiber heterogeneity due to the nucleosome positioning. We suggest that this chromatin, reconstituted on megabase-long DNA because of its large size, is a useful model of eukaryotic chromatin.

All-Atom MD Simulation of DNA Condensation Using Ab Initio Derived Force Field Parameters of Cobalt(III)-Hexammine.

It is well established that the presence of the trivalent cobalt(III)-hexammine cation (CoHex3+) at submillimolar concentrations leads to bundling (condensation) of double-stranded DNA molecules, which is caused by DNA-DNA attraction induced by the multivalent counterions. However, the detailed mechanism of this process is still not fully understood. Furthermore, in all-atom molecular dynamics (MD) simulations, spontaneous aggregation of several DNA oligonucleotides in the presence of CoHex3+ has previously not been demonstrated. In order to obtain a rigorous description of CoHex3+-nucleic acid interactions and CoHex3+-induced DNA condensation to be used in MD simulations, we have derived optimized force field parameters of the CoHex3+ ion. They were obtained from Car-Parrinello molecular dynamics simulation of a single CoHex3+ ion in the presence of 125 water molecules. The new set of force field parameters reproduces the experimentally known transition of DNA from B- to A-form, and qualitatively describes changes of DNA and RNA persistence lengths. We then carried out a 2 µs long atomistic simulation of four DNA oligomers each consisting of 36 base pairs in the presence of CoHex3+. We demonstrate that, in this system, DNA molecules display attractive interactions and aggregate into bundle-like structures. This behavior depends critically on the details of the CoHex3+ interaction with DNA. A control simulation with a similar setup but in the presence of Mg2+ does not induce DNA-DNA attraction, which is also in agreement with experiment.

Regulation of Nucleosome Stacking and Chromatin Compaction by the Histone H4 N-Terminal Tail-H2A Acidic Patch Interaction.

Chromatin folding and dynamics are critically dependent on nucleosome-nucleosome interactions with important contributions from internucleosome binding of the histone H4 N-terminal tail K16-R23 domain to the surface of the H2A/H2B dimer. The H4 Lys16 plays a pivotal role in this regard. Using in vitro reconstituted 12-mer nucleosome arrays, we have investigated the mechanism of the H4 N-terminal tail in maintaining nucleosome-nucleosome stacking and mediating intra- and inter-array chromatin compaction, with emphasis on the role of K16 and the positive charge region, R17-R23. Analytical ultracentrifugation sedimentation velocity experiments and precipitation assays were employed to analyze effects on chromatin folding and self-association, respectively. Effects on chromatin folding caused by various mutations and modifications at position K16 in the H4 histone were studied. Additionally, using charge-quenching mutations, we characterized the importance of the interaction of the residues within the H4 positive charge region R17-R23 with the H2A acidic patch of the adjacent nucleosome. Furthermore, crosslinking experiments were conducted to establish the proximity of the basic tail region to the acidic patch. Our data indicate that the positive charge and length of the side chain of H4 K16 are important for its access to the adjacent nucleosome in the process of nucleosome-nucleosome stacking and array folding. The location and orientation of the H4 R17-R23 domain on the H2A/H2B dimer surface of the neighboring nucleosome core particle (NCP) in the compacted chromatin fiber were established. The dominance of electrostatic interactions in maintaining intra-array interaction was demonstrated.