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

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.

Development of a bottom-up coarse-grained model for interactions of lipids with TiO 2 nanoparticles

Understanding interactions of inorganic nanoparticles with biomolecules is important in many biotechnology, nanomedicine, and toxicological research, however, the size of typical nanoparticles makes their direct modeling by atomistic simulations unfeasible. Here, we present a bottom-up coarse-graining approach for modeling titanium dioxide (TiO  2 ) nanomaterials in contact with phospholipids that uses the inverse Monte Carlo method to optimize the effective interactions from the structural data obtained in small-scale all-atom simulations of TiO  2 surfaces with lipids in aqueous solution. The resulting coarse-grained models are able to accurately reproduce the structural details of lipid adsorption on different titania surfaces without the use of an explicit solvent, enabling significant computational resource savings and favorable scaling. Our coarse-grained simulations show that small spherical TiO  2 nanoparticles ( r = 2 nm) can only be partially wrapped by a lipid bilayer with phosphoethanolamine headgroups, however, the lipid adsorption increases with the radius of the nanoparticle. The current approach can be used to study the effect of the size and shape of TiO  2 nanoparticles on their interactions with cell membrane lipids, which can be a determining factor in membrane wrapping as well as the recently discovered phenomenon of nanoquarantining, which involves the formation of layered nanomaterial-lipid structures.

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.

Explicit ion modeling predicts physicochemical interactions for chromatin organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono- and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Explicit Ion Modeling Predicts Physicochemical Interactions for Chromatin Organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Coarse-Grained Modeling Using Neural Networks Trained on Structural Data

We propose a method of bottom-up coarse-graining, in which interactions within a coarse-grained model are determined by an artificial neural network trained on structural data obtained from multiple atomistic simulations. The method uses ideas of the inverse Monte Carlo approach, relating changes in the neural network weights with changes in average structural properties, such as radial distribution functions. As a proof of concept, we demonstrate the method on a system interacting by a Lennard-Jones potential modeled by a simple linear network and a single-site coarse-grained model of methanol-water solutions. In the latter case, we implement a nonlinear neural network with intermediate layers trained by atomistic simulations carried out at different methanol concentrations. We show that such a network acts as a transferable potential at the coarse-grained resolution for a wide range of methanol concentrations, including those not included in the training set.

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.

C-B-A Test of DNA Force Fields

The DNA duplex may be locally strongly bent in complexes with proteins, for example, with polymerases or in a nucleosome. At such bends, the DNA helix is locally in the noncanonical forms A (with a narrow major groove and a large amount of north sugars) or C (with a narrow minor groove and a large share of BII phosphates). To model the formation of such complexes by molecular dynamics methods, the force field is required to reproduce these conformational transitions for a naked DNA. We analyzed the available experimental data on the B-C and B-A transitions under the conditions easily implemented in modeling: in an aqueous NaCl solution. We selected six DNA duplexes which conformations at different salt concentrations are known reliably enough. At low salt concentrations, poly(GC) and poly(A) are in the B-form, classical and slightly shifted to the A-form, respectively. The duplexes ATAT and GGTATACC have a strong and salt concentration dependent bias toward the A-form. The polymers poly(AC) and poly(G) take the C- and A-forms, respectively, at high salt concentrations. The reproduction of the behavior of these oligomers can serve as a test for the balance of interactions between the base stacking and the conformational flexibility of the sugar-phosphate backbone in a DNA force field. We tested the AMBER bsc1 and CHARMM36 force fields and their hybrids, and we failed to reproduce the experiment. In all the force fields, the salt concentration dependence is very weak. The known B-philicity of the AMBER force field proved to result from the B-philicity of its excessively strong base stacking. In the CHARMM force field, the B-form is a result of a fragile balance between the A-philic base stacking (especially for G:C pairs) and the C-philic backbone. Finally, we analyzed some recent simulations of the LacI-, SOX-4-, and Sac7d-DNA complex formation in the framework of the AMBER force field.

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.

Molecular dynamics simulations for the study of chromatin biology

The organization of Eukaryotic DNA into chromatin has profound implications for the processing of genetic information. In the past years, molecular dynamics (MD) simulations proved to be a powerful tool to investigate the mechanistic basis of chromatin biology. We review recent all-atom and coarse-grained MD studies revealing how the structure and dynamics of chromatin underlie its biological functions. We describe the latest method developments; the structural fluctuations of nucleosomes and the various factors affecting them; the organization of chromatin fibers, with particular emphasis on its liquid-like character; the interactions and dynamics of transcription factors on chromatin; and how chromatin organization is modulated by molecular motors acting on DNA.