In silico evidence for sequence-dependent nucleosome sliding

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally-defined domains observed by single cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as Rad21 degradation.

Sequence Dependence in Nucleosome Dynamics

The basic packaging unit of eukaryotic chromatin is the nucleosome that contains 145-147 base pair duplex DNA wrapped around an octameric histone protein. While the DNA sequence plays a crucial role in controlling the positioning of the nucleosome, the molecular details behind the interplay between DNA sequence and nucleosome dynamics remain relatively unexplored. This study analyzes this interplay in detail by performing all-atom molecular dynamics simulations of nucleosomes, comparing the human α-satellite palindromic (ASP) and the strong positioning "Widom-601" DNA sequence at time scales of 12 μs. The simulations are performed at salt concentrations 10-20 times higher than physiological salt concentrations to screen the electrostatic interactions and promote unwrapping. These microsecond-long simulations give insight into the molecular-level sequence-dependent events that dictate the pathway of DNA unwrapping. We find that the "ASP" sequence forms a loop around SHL ± 5 for three sets of simulations. Coincident with loop formation is a cooperative increase in contacts with the neighboring N-terminal H2B tail and C-terminal H2A tail and the release of neighboring counterions. We find that the Widom-601 sequence exhibits a strong breathing motion of the nucleic acid ends. Coincident with the breathing motion is the collapse of the full N-terminal H3 tail and formation of an α-helix that interacts with the H3 histone core. We postulate that the dynamics of these histone tails and their modification with post-translational modifications (PTMs) may play a key role in governing this dynamics.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Brewing COFFEE: A Sequence-Specific Coarse-Grained Energy Function for Simulations of DNA-Protein Complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA-protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA-protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

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.

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that is able to capture the observed behavior across imaging and sequencing based measures of chromatin organization. The SR-EV model takes the return rules of the Self Returning Random Walk, incorporates excluded volume interactions, chain connectivity and expands the length scales range from 10 nm to over 1 micron. The model is computationally fast and we created thousands of configurations that we grouped in twelve different ensembles according to the two main parameters of the model. The analysis of the configurations was done in a way completely analogous to the experimental treatments used to determine chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. We find a robust agreement between the theoretical and experimental results. The overall organization of the model chromatin is corrugated, with dense packing domains alternating with a very dilute regions in a manner that resembles the mixing of two disordered bi-continuous phases. The return rules combined with excluded volume interactions lead to the formation of packing domains. We observed a transition from a short scale regime to a long scale regime occurring at genomic separations of ~ 4 × 104 base pairs or ~ 100 nm in distance. The contact probability reflects this transition with a change in the scaling exponent from larger than -1 to approximately -1. The analysis of the pair correlation function reveals that chromatin organizes following a power law scaling with exponent D ∈ { 2 , 3 } in the transition region between the short and long distance regimes.

The role of transcript regions and amino acid choice in nucleosome positioning

Eukaryotic DNA is organized and compacted in a string of nucleosomes, DNA-wrapped protein cylinders. The positions of nucleosomes along DNA are not random but show well-known base pair sequence preferences that result from the sequence-dependent elastic and geometric properties of the DNA double helix. Here, we focus on DNA around transcription start sites, which are known to typically attract nucleosomes in multicellular life forms through their high GC content. We aim to understand how these GC signals, as observed in genome-wide averages, are produced and encoded through different genomic regions (mainly 5' UTRs, coding exons, and introns). Our study uses a bioinformatics approach to decompose the genome-wide GC signal into between-region and within-region signals. We find large differences in GC signal contributions between vertebrates and plants and, remarkably, even between closely related species. Introns contribute most to the GC signal in vertebrates, while in plants the exons dominate. Further, we find signal strengths stronger on DNA than on mRNA, suggesting a biological function of GC signals along the DNA itself, as is the case for nucleosome positioning. Finally, we make the surprising discovery that both the choice of synonymous codons and amino acids contribute to the nucleosome positioning signal.

Role of Nucleosome Sliding in the Protein Target Search for Covered DNA Sites

Associations of transcription factors (TFs) with specific sites on DNA initiate major cellular processes. But DNA in eukaryotic cells is covered by nucleosomes which prevent TFs from binding. However, nucleosome structures on DNA are not static and exhibit breathing and sliding. We develop a theoretical framework to investigate the effect of nucleosome sliding on a protein target search. By analysis of a discrete-state stochastic model of nucleosome sliding, search dynamics are explicitly evaluated. It is found that for long sliding lengths the target search dynamics are faster for normal TFs that cannot enter the nucleosomal DNA. But for more realistic short sliding lengths, the so-called pioneer TFs, which can invade nucleosomal DNA, locate specific sites faster. It is also suggested that nucleosome breathing, which is a faster process, has a stronger effect on protein search dynamics than that of nucleosome sliding. Theoretical arguments to explain these observations are presented.

Brewing COFFEE: A sequence-specific coarse-grained energy function for simulations of DNA-protein complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription, gene expression, to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse grained force field for energy estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the Self-Organized Polymer model with Side Chains for proteins and the Three Interaction Site model for DNA in a modular fashion, without re-calibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a dataset of high-resolution crystal structures. The only parameter in COFFEE is the strength (λ D N A P R O ) of the DNA-protein contact potential. For an optimal choice of λ D N A P R O , the crystallographic B-factors for DNA-protein complexes, with varying sizes and topologies, are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts the scattering profiles that are in quantitative agreement with SAXS experiments as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which does not alter the balance of electrostatic interactions, but affects chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

A coarse-grained DNA model to study protein-DNA interactions and liquid-liquid phase separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define non-bonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), that is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond timescale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micron-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

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.

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.

Nucleosome breathing facilitates cooperative binding of pluripotency factors Sox2 and Oct4 to DNA

Critical lineage commitment events are staged by multiple transcription factors (TFs) binding to their cognate motifs, often positioned at nucleosome-enriched regions of chromatin. The underlying mechanism remains elusive due to difficulty in disentangling the heterogeneity in chromatin states. Using a novel coarse-grained model and molecular dynamics simulations, here we probe the association of Sox2 and Oct4 proteins that show clustered binding at the entry-exit region of a nucleosome. The model captures the conformational heterogeneity of nucleosome breathing dynamics that features repeated wrap-unwrap transitions of a DNA segment from one end of the nucleosome. During the dynamics, DNA forms bulges that diffuse stochastically and may regulate the target search dynamics of a protein by nonspecifically interacting with it. The overall search kinetics of the TF pair follows a "dissociation-compensated-association" mechanism, where Oct4 binding is facilitated by the association of Sox2. The cooperativity stems from a change in entropy caused by an alteration in the nucleosome dynamics upon TF binding. The binding pattern is consistent with a live-cell single-particle tracking experiment, suggesting the mechanism observed for clustered binding of a TF pair, which is a hallmark of cis-regulatory elements, has broader implications in understanding gene regulation in a complex chromatin environment.

Understanding protein diffusion on force-induced stretched DNA conformation

DNA morphology is subjected to environmental conditions and is closely coupled with its function. For example, DNA experiences stretching forces during several biological processes, including transcription and genome transactions, that significantly alter its conformation from that of B-DNA. Indeed, a well-defined 1.5 times extended conformation of dsDNA, known as Σ-DNA, has been reported in DNA complexes with proteins such as Rad51 and RecA. A striking feature in Σ-DNA is that the nucleobases are partitioned into triplets of three locally stacked bases separated by an empty rise gap of ∼ 5 Å. The functional role of such a DNA base triplet was hypothesized to be coupled with the ease of recognition of DNA bases by DNA-binding proteins (DBPs) and the physical origin of three letters (codon/anti-codon) in the genetic code. However, the underlying mechanism of base-triplet formation and the ease of DNA base-pair recognition by DBPs remain elusive. To investigate, here, we study the diffusion of a protein on a force-induced stretched DNA using coarse-grained molecular dynamics simulations. Upon pulling at the 3' end of DNA by constant forces, DNA exhibits a conformational transition from B-DNA to a ladder-like S-DNA conformation via Σ-DNA intermediate. The resulting stretched DNA conformations exhibit non-uniform base-pair clusters such as doublets, triplets, and quadruplets, of which triplets are energetically more stable than others. We find that protein favors the triplet formation compared to its unbound form while interacting non-specifically along DNA, and the relative population of it governs the ruggedness of the protein-DNA binding energy landscape and enhances the efficiency of DNA base recognition. Furthermore, we analyze the translocation mechanism of a DBP under different force regimes and underscore the significance of triplet formation in regulating the facilitated diffusion of protein on DNA. Our study, thus, provides a plausible framework for understanding the structure-function relationship between triplet formation and base recognition by a DBP and helps to understand gene regulation in complex regulatory processes.

Multiplexing mechanical and translational cues on genes

The genetic code gives precise instructions on how to translate codons into amino acids. Due to the degeneracy of the genetic code-18 out of 20 amino acids are encoded for by more than one codon-more information can be stored in a basepair sequence. Indeed, various types of additional information have been discussed in the literature, e.g., the positioning of nucleosomes along eukaryotic genomes and the modulation of the translating efficiency in ribosomes to influence cotranslational protein folding. The purpose of this study is to show that it is indeed possible to carry more than one additional layer of information on top of a gene. In particular, we show how much translation efficiency and nucleosome positioning can be adjusted simultaneously without changing the encoded protein. We achieve this by mapping genes on weighted graphs that contain all synonymous genes, and then finding shortest paths through these graphs. This enables us, for example, to readjust the disrupted translational efficiency profile after a gene has been introduced from one organism (e.g., human) into another (e.g., yeast) without greatly changing the nucleosome landscape intrinsically encoded by the DNA molecule.

DNA Sequence-Dependent Binding of Linker Histone gH1 Regulates Nucleosome Conformations

Sequence-dependent binding between DNA and proteins in chromatin is an essential part of gene expression. Linker histone H1 is an important protein in the regulation of chromatin compartmentalization and compaction, and its binding with the nucleosome is sensitive to the DNA sequence. Although the interactions of H1 and DNA have been widely investigated, the mechanism of nucleosome conformation changes induced by the DNA-sequence-dependent binding with gH1 (globular H1.0) remains largely unclear at the atomic level. In the present molecular dynamics simulations, both linker and dyad DNAs were mutated to investigate the conformational changes of the nucleosome induced by the sequence-dependent binding of gH1 based on the on-dyad binding mode. Our results indicate that gH1 is insensitive to the DNA sequence of the dyad DNA but presents an apparent preference to linker DNA with an AT-rich sequence. Moreover, this specific binding induces the entry/exit region of a nucleosome to a tight conformation and regulates the accessibility of core histones. Considering that the entry/exit region of the nucleosome is a crucial binding site for many functional proteins related to gene expression, the conformational change at this region could represent an important gene regulation signal.

A simulation model of heterochromatin formation at submolecular detail

Heterochromatin is a physical state of the chromatin fiber that maintains gene repression during cell development. Although evidence exists on molecular mechanisms involved in heterochromatin formation, a detailed structural mechanism of heterochromatin formation needs a better understanding. We made use of a simple Monte Carlo simulation model with explicit representation of key molecular events to observe molecular self-organization leading to heterochromatin formation. Our simulations provide a structural interpretation of several important traits of the heterochromatinization process. In particular, this study provides a depiction of how small amounts of HP1 are able to induce a highly condensed chromatin state through HP1 dimerization and bridging of sequence-remote nucleosomes. It also elucidates structural roots of a yet poorly understood phenomenon of a nondeterministic nature of heterochromatin formation and subsequent gene repression. Experimental chromatin in vivo assay provides an unbiased estimate of time scale of repressive response to a heterochromatin-triggering event.

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.

Implementation of residue-level coarse-grained models in GENESIS for large-scale molecular dynamics simulations

Residue-level coarse-grained (CG) models have become one of the most popular tools in biomolecular simulations in the trade-off between modeling accuracy and computational efficiency. To investigate large-scale biological phenomena in molecular dynamics (MD) simulations with CG models, unified treatments of proteins and nucleic acids, as well as efficient parallel computations, are indispensable. In the GENESIS MD software, we implement several residue-level CG models, covering structure-based and context-based potentials for both well-folded biomolecules and intrinsically disordered regions. An amino acid residue in protein is represented as a single CG particle centered at the Cα atom position, while a nucleotide in RNA or DNA is modeled with three beads. Then, a single CG particle represents around ten heavy atoms in both proteins and nucleic acids. The input data in CG MD simulations are treated as GROMACS-style input files generated from a newly developed toolbox, GENESIS-CG-tool. To optimize the performance in CG MD simulations, we utilize multiple neighbor lists, each of which is attached to a different nonbonded interaction potential in the cell-linked list method. We found that random number generations for Gaussian distributions in the Langevin thermostat are one of the bottlenecks in CG MD simulations. Therefore, we parallelize the computations with message-passing-interface (MPI) to improve the performance on PC clusters or supercomputers. We simulate Herpes simplex virus (HSV) type 2 B-capsid and chromatin models containing more than 1,000 nucleosomes in GENESIS as examples of large-scale biomolecular simulations with residue-level CG models. This framework extends accessible spatial and temporal scales by multi-scale simulations to study biologically relevant phenomena, such as genome-scale chromatin folding or phase-separated membrane-less condensations.

Modeling DNA Opening in the Eukaryotic Transcription Initiation Complexes via Coarse-Grained Models

Recently, the molecular mechanisms of transcription initiation have been intensively studied. Especially, the cryo-electron microscopy revealed atomic structure details in key states in the eukaryotic transcription initiation. Yet, the dynamic processes of the promoter DNA opening in the pre-initiation complex remain obscured. In this study, based on the three cryo-electron microscopic yeast structures for the closed, open, and initially transcribing complexes, we performed multiscale molecular dynamics (MD) simulations to model structures and dynamic processes of DNA opening. Combining coarse-grained and all-atom MD simulations, we first obtained the atomic model for the DNA bubble in the open complexes. Then, in the MD simulation from the open to the initially transcribing complexes, we found a previously unidentified intermediate state which is formed by the bottleneck in the fork loop 1 of Pol II: The loop opening triggered the escape from the intermediate, serving as a gatekeeper of the promoter DNA opening. In the initially transcribing complex, the non-template DNA strand passes a groove made of the protrusion, the lobe, and the fork of Rpb2 subunit of Pol II, in which several positively charged and highly conserved residues exhibit key interactions to the non-template DNA strand. The back-mapped all-atom models provided further insights on atomistic interactions such as hydrogen bonding and can be used for future simulations.

Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy

A robust understanding of the sequence-dependent thermodynamics of DNA hybridization has enabled rapid advances in DNA nanotechnology. A fundamental understanding of the sequence-dependent kinetics and mechanisms of hybridization and dehybridization remains comparatively underdeveloped. In this work, we establish new understanding of the sequence-dependent hybridization/dehybridization kinetics and mechanism within a family of self-complementary pairs of 10-mer DNA oligomers by integrating coarse-grained molecular simulation, machine learning of the slow dynamical modes, data-driven inference of long-time kinetic models, and experimental temperature-jump infrared spectroscopy. For a repetitive ATATATATAT sequence, we resolve a rugged dynamical landscape comprising multiple metastable states, numerous competing hybridization/dehybridization pathways, and a spectrum of dynamical relaxations. Introduction of a G:C pair at the terminus (GATATATATC) or center (ATATGCATAT) of the sequence reduces the ruggedness of the dynamics landscape by eliminating a number of metastable states and reducing the number of competing dynamical pathways. Only by introducing a G:C pair midway between the terminus and the center to maximally disrupt the repetitive nature of the sequence (ATGATATCAT) do we recover a canonical "all-or-nothing" two-state model of hybridization/dehybridization with no intermediate metastable states. Our results establish new understanding of the dynamical richness of sequence-dependent kinetics and mechanisms of DNA hybridization/dehybridization by furnishing quantitative and predictive kinetic models of the dynamical transition network between metastable states, present a molecular basis with which to understand experimental temperature jump data, and furnish foundational design rules by which to rationally engineer the kinetics and pathways of DNA association and dissociation for DNA nanotechnology applications.

The kinetic landscape of nucleosome assembly: A coarse-grained molecular dynamics study

The organization of nucleosomes along the Eukaryotic genome is maintained over time despite disruptive events such as replication. During this complex process, histones and DNA can form a variety of non-canonical nucleosome conformations, but their precise molecular details and roles during nucleosome assembly remain unclear. In this study, employing coarse-grained molecular dynamics simulations and Markov state modeling, we characterized the complete kinetics of nucleosome assembly. On the nucleosome-positioning 601 DNA sequence, we observe a rich transition network among various canonical and non-canonical tetrasome, hexasome, and nucleosome conformations. A low salt environment makes nucleosomes stable, but the kinetic landscape becomes more rugged, so that the system is more likely to be trapped in off-pathway partially assembled intermediates. Finally, we find that the co-operativity between DNA bending and histone association enables positioning sequence motifs to direct the assembly process, with potential implications for the dynamic organization of nucleosomes on real genomic sequences.

Nucleosomes are biomolecular complexes formed by DNA wrapped around histone proteins. They represent the basic units of Eukaryotic chromosomes, compacting the genome so that it fits into the small nucleus, and regulating important biological processes such as gene expression. Nucleosomes are disassembled during disruptive events such as DNA replication, and re-assembled afterwards to preserve the correct organization of chromatin. However, the molecular details of nucleosome assembly are still not well understood. In particular, experiments found that histones and DNA may associate into a variety of non-canonical complexes, but their precise conformation and role during assembly remain unclear. In this study, we addressed these problems by performing extensive molecular dynamics simulations of nucleosomes undergoing assembly and disassembly. The simulations reveal many insights into the kinetics of assembly, the structure of non-canonical nucleosome intermediates, and the influence of salt concentration and DNA sequence on the assembly process.

Cooperative DNA looping by PRC2 complexes

Polycomb repressive complex 2 (PRC2) is an essential protein complex that silences gene expression via post-translational modifications of chromatin. This paper combined homology modeling, atomistic and coarse-grained molecular dynamics simulations, and single-molecule force spectroscopy experiments to characterize both its full-length structure and PRC2-DNA interactions. Using free energy calculations with a newly parameterized protein-DNA force field, we studied a total of three potential PRC2 conformations and their impact on DNA binding and bending. Consistent with cryo-EM studies, we found that EZH2, a core subunit of PRC2, provides the primary interface for DNA binding, and its curved surface can induce DNA bending. Our simulations also predicted the C2 domain of the SUZ12 subunit to contact DNA. Multiple PRC2 complexes bind with DNA cooperatively via allosteric communication through the DNA, leading to a hairpin-like looped configuration. Single-molecule experiments support PRC2-mediated DNA looping and the role of AEBP2 in regulating such loop formation. The impact of AEBP2 can be partly understood from its association with the C2 domain, blocking C2 from DNA binding. Our study suggests that accessory proteins may regulate the genomic location of PRC2 by interfering with its DNA interactions.

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.

Asymmetry in histone rotation in forced unwrapping and force quench rewrapping in a nucleosome

Single molecule pulling experiments have shown that DNA in the nucleosomes unwraps in two stages from the histone protein core (HPC). The first stage, attributed to the rupture of the outer DNA turn, occurs between 3 and 5 pNs, and is reversible. The inner DNA turn ruptures irreversibly at forces between 9 and 15 pNs (or higher) in the second stage. Molecular simulations using the Self-Organized Polymer model capture the experimental findings. The unwrapping of the outer DNA turn is independent of the pulling direction. The rupture of the DNA inner turn depends on the pulling direction and involves overcoming substantial energetic (most likely electrostatic in origin) and kinetic barriers. They arise because the mechanical force has to generate sufficient torque to rotate the HPC by 180°. On the other hand, during the rewrapping process, HPC rotation is stochastic, with force playing no role. The assembly of the outer DNA wrap upon force quench nearly coincides with the unwrapping process, confirming the reversibility of the outer turn rupture. The asymmetry in HPC rotation during unwrapping and rewrapping explains the observed hysteresis in the stretch-release cycles in experiments. We propose experiments to test the prediction that HPC rotation produces kinetic barriers in the unwrapping process.

Tetranucleosome Interactions Drive Chromatin Folding

The multiscale organizational structure of chromatin in eukaryotic cells is instrumental to DNA transcription, replication, and repair. At mesoscopic length scales, nucleosomes pack in a manner that serves to regulate gene expression through condensation and expansion of the genome. The particular structures that arise and their respective thermodynamic stabilities, however, have yet to be fully resolved. In this study, we combine molecular modeling using the 1CPN mesoscale model of chromatin with nonlinear manifold learning to identify and characterize the structure and free energy of metastable states of short chromatin segments comprising between 4- and 16-nucleosomes. Our results reveal the formation of two previously characterized tetranucleosomal conformations, the "α-tetrahedron" and the "β-rhombus", which have been suggested to play an important role in the accessibility of DNA and, respectively, induce local chromatin compaction or elongation. The spontaneous formation of these motifs is potentially responsible for the slow nucleosome dynamics observed in experimental studies. Increases of the nucleosome repeat length are accompanied by more pronounced structural irregularity and flexibility and, ultimately, a dynamic liquid-like behavior that allows for frequent structural reorganization. Our findings indicate that tetranucleosome motifs are intrinsically stable structural states, driven by local internucleosomal interactions, and support a mechanistic picture of chromatin packing, dynamics, and accessibility that is strongly influenced by emergent local mesoscale structure.

Histone tails cooperate to control the breathing of genomic nucleosomes

Genomic DNA is packaged in chromatin, a dynamic fiber variable in size and compaction. In chromatin, repeating nucleosome units wrap 145–147 DNA basepairs around histone proteins. Genetic and epigenetic regulation of genes relies on structural transitions in chromatin which are driven by intra- and inter-nucleosome dynamics and modulated by chemical modifications of the unstructured terminal tails of histones. Here we demonstrate how the interplay between histone H3 and H2A tails control ample nucleosome breathing motions. We monitored large openings of two genomic nucleosomes, and only moderate breathing of an engineered nucleosome in atomistic molecular simulations amounting to 24 μs. Transitions between open and closed nucleosome conformations were mediated by the displacement and changes in compaction of the two histone tails. These motions involved changes in the DNA interaction profiles of clusters of epigenetic regulatory aminoacids in the tails. Removing the histone tails resulted in a large increase of the amplitude of nucleosome breathing but did not change the sequence dependent pattern of the motions. Histone tail modulated nucleosome breathing is a key mechanism of chromatin dynamics with important implications for epigenetic regulation.

In the cell, the DNA is packed in chromatin. Chromatin is a highly dynamic fiber structure made of arrays of nucleosomes with different degrees of compaction. Each nucleosome has 145–147 basepairs of DNA wrapped around a protein octamer made of four unique histone proteins. Each histone is present twice and has a structured part and one or two disordered terminal tails. The regulation of gene expression in the cell and during cellular transitions depends on dynamic changes in chromatin structure. Chromatin dynamics are modulated by intra and inter nucleosome motions and by posttranslational chemical modifications of the histone tails. Here we reveal how histone tails control the intra nucleosome dynamics at atomic resolution. From extensive sampling of nucleosome dynamics in atomistic molecular simulations, we show that genomic nucleosomes breath more extensively than engineered ones and we describe how two histone tails cooperate to control nucleosome breathing through interactions between clusters of positively charged residues and the DNA. Nucleosome conformations with different degrees of opening are associated with different conformations, positions, and DNA interaction patterns of the tails. With this mechanism, we contribute to the understanding of chromatin dynamics at atomic resolution.

Histone dynamics mediate DNA unwrapping and sliding in nucleosomes

Nucleosomes are elementary building blocks of chromatin in eukaryotes. They tightly wrap ∼147 DNA base pairs around an octamer of histone proteins. How nucleosome structural dynamics affect genome functioning is not completely clear. Here we report all-atom molecular dynamics simulations of nucleosome core particles at a timescale of 15 microseconds. At this timescale, functional modes of nucleosome dynamics such as spontaneous nucleosomal DNA breathing, unwrapping, twisting, and sliding were observed. We identified atomistic mechanisms of these processes by analyzing the accompanying structural rearrangements of the histone octamer and histone-DNA contacts. Octamer dynamics and plasticity were found to enable DNA unwrapping and sliding. Through multi-scale modeling, we showed that nucleosomal DNA dynamics contribute to significant conformational variability of the chromatin fiber at the supranucleosomal level. Our study further supports mechanistic coupling between fine details of histone dynamics and chromatin functioning, provides a framework for understanding the effects of various chromatin modifications.

Remodeler Catalyzed Nucleosome Repositioning: Influence of Structure and Stability

The packaging of the eukaryotic genome into chromatin regulates the storage of genetic information, including the access of the cell’s DNA metabolism machinery. Indeed, since the processes of DNA replication, translation, and repair require access to the underlying DNA, several mechanisms, both active and passive, have evolved by which chromatin structure can be regulated and modified. One mechanism relies upon the function of chromatin remodeling enzymes which couple the free energy obtained from the binding and hydrolysis of ATP to the mechanical work of repositioning and rearranging nucleosomes. Here, we review recent work on the nucleosome mobilization activity of this essential family of molecular machines.

Constructing arrays of nucleosome positioning sequences using Gibson Assembly for single-molecule studies

As the basic building blocks of chromatin, nucleosomes play a key role in dictating the accessibility of the eukaryotic genome. Consequently, nucleosomes are involved in essential genomic transactions such as DNA transcription, replication and repair. In order to unravel the mechanisms by which nucleosomes can influence, or be altered by, DNA-binding proteins, single-molecule techniques are increasingly employed. To this end, DNA molecules containing a defined series of nucleosome positioning sequences are often used to reconstitute arrays of nucleosomes in vitro. Here, we describe a novel method to prepare DNA molecules containing defined arrays of the ‘601’ nucleosome positioning sequence by exploiting Gibson Assembly cloning. The approaches presented here provide a more accessible and efficient means to generate arrays of nucleosome positioning motifs, and facilitate a high degree of control over the linker sequences between these motifs. Nucleosomes reconstituted on such arrays are ideal for interrogation with single-molecule techniques. To demonstrate this, we use dual-trap optical tweezers, in combination with fluorescence microscopy, to monitor nucleosome unwrapping and histone localisation as a function of tension. We reveal that, although nucleosomes unwrap at ~20 pN, histones (at least histone H3) remain bound to the DNA, even at tensions beyond 60 pN.

Bottom-Up Meets Top-Down: The Crossroads of Multiscale Chromatin Modeling

Chromatin can be viewed as a hierarchically structured fiber that regulates gene expression. It consists of a complex network of DNA and proteins whose characteristic dynamical modes facilitate compaction and rearrangement in the cell nucleus. These modes stem from chromatin's fundamental unit, the nucleosome, and their effects are propagated across length scales. Understanding the effects of nucleosome dynamics on the chromatin fiber, primarily through post-translational modifications that occur on the histones, is of central importance to epigenetics. Within the last decade, imaging and chromosome conformation capture techniques have revealed a number of structural and statistical features of the packaged chromatin fiber at a hitherto unavailable level of resolution. Such experiments have led to increased efforts to develop polymer models that aim to reproduce, explain, and predict the contact probability scaling and density heterogeneity. At nanometer scales, available models have focused on the role of the nucleosome and epigenetic marks on local chromatin structure. At micrometer scales, existing models have sought to explain scaling laws and density heterogeneity. Less work, however, has been done to reconcile these two approaches: bottom-up and top-down models of chromatin. In this perspective, we highlight the multiscale simulation models that are driving toward an understanding of chromatin structure and function, from the nanometer to the micron scale, and we highlight areas of opportunity and some of the prospects for new frameworks that bridge these two scales. Taken together, experimental and modeling advances over the last few years have established a robust platform for the study of chromatin fiber structure and dynamics, which will be of considerable use to the chromatin community in developing an understanding of the interplay between epigenomic regulation and molecular structure.

Translational nucleosome positioning: A computational study

About three-quarters of eukaryotic DNA is wrapped into nucleosomes; DNA spools with a protein core. The affinity of a given DNA stretch to be incorporated into a nucleosome is known to depend on the base-pair sequence-dependent geometry and elasticity of the DNA double helix. This causes the rotational and translational positioning of nucleosomes. In this study we ask the question whether the latter can be predicted by a simple coarse-grained DNA model with sequence-dependent elasticity, the rigid base-pair model. Whereas this model is known to be rather robust in predicting rotational nucleosome positioning, we show that the translational positioning is a rather subtle effect that is dominated by the guanine-cytosine content dependence of entropy rather than energy. A correct qualitative prediction within the rigid base-pair framework can only be achieved by assuming that DNA elasticity effectively changes on complexation into the nucleosome complex. With that extra assumption we arrive at a model which gives an excellent quantitative agreement to experimental in vitro nucleosome maps, under the additional assumption that nucleosomes equilibrate their positions only locally.

Nucleosomal DNA Dynamics Mediate Oct4 Pioneer Factor Binding

Transcription factor (TF) proteins bind to DNA to regulate gene expression. Normally, accessibility to DNA is required for their function. However, in the nucleus, the DNA is often inaccessible, wrapped around histone proteins in nucleosomes forming the chromatin. Pioneer TFs are thought to induce chromatin opening by recognizing their DNA binding sites on nucleosomes. For example, Oct4, a master regulator and inducer of stem cell pluripotency, binds to DNA in nucleosomes in a sequence-specific manner. Here, we reveal the structural dynamics of nucleosomes that mediate Oct4 binding from molecular dynamics simulations. Nucleosome flexibility and the amplitude of nucleosome motions such as breathing and twisting are enhanced in nucleosomes with multiple TF binding sites. Moreover, the regions around the binding sites display higher local structural flexibility. Probing different structures of Oct4-nucleosome complexes, we show that alternative configurations in which Oct4 recognizes partial binding sites display stable TF-DNA interactions similar to those observed in complexes with free DNA and compatible with the DNA curvature and DNA-histone interactions. Therefore, we propose a structural basis for nucleosome recognition by a pioneer TF that is essential for understanding how chromatin is unraveled during cell fate conversions.

Nucleosomes as allosteric scaffolds for genetic regulation

Nucleosomes are stable yet highly dynamic complexes exhibiting diverse types of motions, such as sliding, DNA unwrapping, and disassembly, encoding a landscape with a large number of metastable states. In this review, describing recent studies on these nucleosome structure changes, we propose that the nucleosome can be viewed as an ideal allosteric scaffold: regulated by effector molecules such as transcription factors and chromatin remodelers, the nucleosome controls the downstream gene activity. Binding of transcription factors to the nucleosome can enhance DNA unwrapping or slide the DNA, altering either the binding or the unbinding of other transcription factors to nearby sites. ATP-dependent chromatin remodelers induce a series of DNA deformations, which allosterically propagate throughout the nucleosome to induce DNA sliding or histone exchange.

Ensembles of Breathing Nucleosomes: A Computational Study

About three-fourths of the human DNA molecules are wrapped into nucleosomes, protein spools with DNA. Nucleosomes are highly dynamic, transiently exposing their DNA through spontaneous unspooling. Recent experiments allowed to observe the DNA of an ensemble of such breathing nucleosomes through x-ray diffraction with contrast matching between the solvent and the protein core. In this study, we calculate such an ensemble through a Monte Carlo simulation of a coarse-grained nucleosome model with sequence-dependent DNA mechanics. Our analysis gives detailed insights into the sequence dependence of nucleosome breathing observed in the experiment and allows us to determine the adsorption energy of the DNA bound to the protein core as a function of the ionic strength. Moreover, we predict the breathing behavior of other potentially interesting sequences and compare the findings to earlier related experiments.

Consequences of Hydrophobic Nanotube Binding on the Functional Dynamics of Signaling Protein Calmodulin

The wide applications of nanomaterials in industry and our daily life have raised growing concerns on their toxicity to human body. Increasing evidence links the cytotoxicity of nanoparticles to the disruption of cellular signaling pathways. Here, we report a computational study on the mechanisms of the cytotoxicity of carbon nanotubes (CNTs) by investigating the direct impacts of CNTs on the functional motions of calmodulin (CaM), which is one of the most important signaling proteins in a cell, and its signaling function relies on the Ca2+ binding-coupled conformational switching. Computational simulations with a coarse-grained model showed that binding of CNTs modifies the conformational equilibrium of CaM and induces the closed-to-open conformational transition, leading to the loss of its Ca2+-sensing ability. In addition, the binding of CNTs drastically increases the calcium affinity of CaM, which may disrupt the Ca2+ homeostasis in a cell. These results suggest that the binding of hydrophobic nanotubes not only inhibits the signaling function of CaM as a calcium sensor but also renders CaM to toxic species through sequestering Ca2+ from other competing calcium-binding proteins, suggesting a new physical mechanism of the cytotoxicity of nanoparticles.

1CPN: A coarse-grained multi-scale model of chromatin

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

The base pair-scale diffusion of nucleosomes modulates binding of transcription factors

The structure of promoter chromatin determines the ability of transcription factors (TFs) to bind to DNA and therefore has a profound effect on the expression levels of genes. However, the role of spontaneous nucleosome movements in this process is not fully understood. Here, we developed a single-molecule optical tweezers assay capable of simultaneously characterizing the base pair-scale diffusion of a nucleosome on DNA and the binding of a TF, using the luteinizing hormone β subunit gene (Lhb) promoter and Egr-1 as a model system. Our results demonstrate that nucleosomes undergo confined diffusion, and that the incorporation of the histone variant H2A.Z serves to partially relieve this confinement, inducing a different type of nucleosome repositioning. The increase in diffusion leads to exposure of a TF's binding site and facilitates its association with the DNA, which, in turn, biases the subsequent movement of the nucleosome. Our findings suggest the use of mobile nucleosomes as a general transcriptional regulatory mechanism.

Critical role of histone tail entropy in nucleosome unwinding

The nucleosome is the fundamental packaging unit for the genome. It must remain tightly wound to ensure genome stability while simultaneously being flexible enough to keep the DNA molecule accessible for genome function. The set of physicochemical interactions responsible for the delicate balance between these naturally opposed processes have not been determined due to challenges in resolving partially unwound nucleosome configurations at atomic resolution. Using a near atomistic protein-DNA model and advanced sampling techniques, we calculate the free energy cost of nucleosome DNA unwinding. Our simulations identify a large energetic barrier that decouples the outer and the inner DNA unwinding into two separate processes, occurring on different time scales. This dynamical decoupling allows the exposure of outer DNA at a modest cost to ensure accessibility while keeping the inner DNA and the histone core intact to maintain stability. We also reveal that this energetic barrier arises from a delayed loss of contacts between disordered histone tails and the DNA and is, surprisingly, largely offset by an entropic contribution from these tails. Implications of this enthalpy entropy compensation for the regulation of nucleosome stability and genome function are discussed.

Overtwisting induces polygonal shapes in bent DNA

By combining analytical results and simulations of various coarse-grained models, we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternation of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, rather than the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.

Shortest paths through synonymous genomes

The elasticity of the DNA double helix varies with the underlying base pair sequence. This allows one to put mechanical cues into sequences that in turn influence the packaging of DNA into nucleosomes, DNA-wrapped protein cylinders. Nucleosomes dictate a broad range of biological processes, ranging from gene regulation, recombination, and replication to chromosome condensation. Here we map base pair sequences onto graphs and use shortest paths algorithms to determine which DNA stretches are easiest or hardest to bend inside a nucleosome. We further demonstrate how genetic and mechanical information can be multiplexed by studying paths through graphs of synonymous codons. Using this method we find that nucleosomes can be placed by mechanical cues nearly everywhere on the genome of baker's yeast (Saccharomyces cerevisiae).

The Free Energy Landscape of Internucleosome Interactions and Its Relation to Chromatin Fiber Structure

The supramolecular chromatin fiber is governed by molecular scale energetics and interactions. Such energetics originate from the fiber's building block, the nucleosome core particle (NCP). In recent years, the chromatin fiber has been examined through perturbative methods in attempts to extract the energetics of nucleosome association in the fiber. This body of work has led to different results from experiments and simulations concerning the nucleosome-nucleosome energetics. Here, we expand on previous experiments and use coarse-grained simulations to evaluate the energetics inherent to nucleosomes across a variety of parameters in configurational and environmental space. Through this effort, we are able to uncover molecular processes that are critical to understanding the 30 nm chromatin fiber structure. In particular, we describe the NCP-NCP interactions by relying on an anisotropic energetic landscape, rather than a single potential energy value. The attractions in that landscape arise predominantly from the highly anisotropic interactions provided by the NCP histone N-terminal domain (NTD) tails. Our results are found to be in good agreement with recent nucleosome interaction experiments that suggest a maximum interaction energy of 2.69k _B T. Furthermore, we examine the influence of crucial epigenetic modifications, such as acetylation of the H4 tail, and how they modify the underlying landscape. Our results for acetylated NCP interactions are also in agreement with experiment. We additionally find an induced chirality in NCP-NCP interactions upon acetylation that reduces interactions which would correspond to a left-handed superhelical chromatin fiber.

Molecular Mechanism of Spontaneous Nucleosome Unraveling

Meters of DNA wrap around histone proteins to form nucleosomes and fit inside the micron-diameter nucleus. For the genetic information encoded in the DNA to become available for transcription, replication, and repair, the DNA-histone assembly must be disrupted. Experiment has indicated that the outer stretches of nucleosomal DNA "breathe" by spontaneously detaching from and reattaching to the histone core. Here, we report direct observation of spontaneous DNA breathing in atomistic molecular dynamics simulations, detailing a microscopic mechanism of the DNA breathing process. According to our simulations, the outer stretches of nucleosomal DNA detach in discrete steps involving 5 or 10 base pairs, with the detachment process being orchestrated by the motion of several conserved histone residues. The inner stretches of nucleosomal DNA are found to be more stably associated with the histone core by more abundant nonspecific DNA-protein contacts, providing a microscopic interpretation of nucleosome unraveling experiments. The CG content of nucleosomal DNA is found to anticorrelate with the extent of unwrapping, supporting the possibility that AT-rich segments may signal the start of transcription by forming less stable nucleosomes.