Pulling chromatin fibers: computer simulations of direct physical micromanipulations

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.

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.

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.

Bridging chromatin structure and function over a range of experimental spatial and temporal scales by molecular modeling

Chromatin structure, dynamics, and function are being intensely investigated by a variety of methods, including microscopy, X-ray diffraction, nuclear magnetic resonance, biochemical crosslinking, chromosome conformation capture, and computation. A range of experimental techniques combined with modeling is clearly valuable to help interpret experimental data and, importantly, generate configurations and mechanisms related to the 3D organization and function of the genome. Contact maps, in particular, as obtained by a variety of chromosome conformation capture methods, are of increasing interest due to their implications on genome structure and regulation on many levels. In this perspective, using seven examples from our group's studies, we illustrate how molecular modeling can help interpret such experimental data. Specifically, we show how computed contact maps related to experimental systems can be used to explain structures of nucleosomes, chromatin higher-order folding, domain segregation mechanisms, gene organization, and the effect on chromatin structure of external and internal fiber parameters, such as nucleosome positioning, presence of nucleosome free regions, histone posttranslational modifications, and linker histone binding. We argue that such computations on multiple spatial and temporal scales will be increasingly important for the integration of genomic, epigenomic, and biophysical data on chromatin structure and related cellular processes.

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

To elucidate conformational dynamics of chromatin fibers, we compared available force-spectroscopy measurements with extensive Monte Carlo simulations of nucleosome arrays under external force. Our coarse-grained model of chromatin includes phenomenological energy terms for the DNA-histone adhesion and the internucleosome stacking interactions. We found that the Monte Carlo fiber ensembles simulated with increasing degrees of DNA unwrapping and the stacking energy 8 kT can account for the intricate force-extension response observed experimentally. Our analysis shows that at low external forces (F < 3.0 picoNewtons), the DNA ends in nucleosomes breathe by ∼10 bp. Importantly, under these conditions, the fiber is highly dynamic, exhibiting continuous unstacking-restacking transitions, allowing accessibility of transcription factors to DNA, while maintaining a relatively compact conformation. Of note, changing the stacking interaction by a few kT, an in silico way to mimic histone modifications, is sufficient to transform an open chromatin state into a compact fiber. The fibers are mostly two-start zigzag folds with rare occurrences of three- to five-start morphologies. The internucleosome stacking is lost during the linear response regime. At the higher forces exceeding 4 picoNewtons, the nucleosome unwrapping becomes stochastic and asymmetric, with one DNA arm opened by ∼55 bp and the other arm only by ∼10 bp. Importantly, this asymmetric unwrapping occurs for any kind of sequence, including the symmetric ones. Our analysis brings new, to our knowledge, insights in dynamics of chromatin modulated by histone epigenetic modifications and molecular motors such as RNA polymerase.

Transfer-matrix calculations of the effects of tension and torque constraints on DNA-protein interactions

Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such proteins is frequently subject to force and torque constraints applied to the DNA. Although the existing experimental techniques allow to exert these type of mechanical constraints on individual DNA biopolymers, their exact effects in regulation of DNA-protein interactions are still not completely understood due to the lack of systematic theoretical methods able to efficiently interpret complex experimental observations. To fill this gap, we have developed a general theoretical framework based on the transfer-matrix calculations that can be used to accurately describe behaviour of DNA-protein interactions under force and torque constraints. Potential applications of the constructed theoretical approach are demonstrated by predicting how these constraints affect the DNA-binding properties of different types of architectural proteins. Obtained results provide important insights into potential physiological functions of mechanical forces in the chromosomal DNA organization by architectural proteins as well as into single-DNA manipulation studies of DNA-protein interactions.

Towards quantitative analysis of gene regulation by enhancers

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

Binding of DNA-bending non-histone proteins destabilizes regular 30-nm chromatin structure

Why most of the in vivo experiments do not find the 30-nm chromatin fiber, well studied in vitro, is a puzzle. Two basic physical inputs that are crucial for understanding the structure of the 30-nm fiber are the stiffness of the linker DNA and the relative orientations of the DNA entering/exiting nucleosomes. Based on these inputs we simulate chromatin structure and show that the presence of non-histone proteins, which bind and locally bend linker DNA, destroys any regular higher order structures (e.g., zig-zag). Accounting for the bending geometry of proteins like nhp6 and HMG-B, our theory predicts phase-diagram for the chromatin structure as a function of DNA-bending non-histone protein density and mean linker DNA length. For a wide range of linker lengths, we show that as we vary one parameter, that is, the fraction of bent linker region due to non-histone proteins, the steady-state structure will show a transition from zig-zag to an irregular structure-a structure that is reminiscent of what is observed in experiments recently. Our theory can explain the recent in vivo observation of irregular chromatin having co-existence of finite fraction of the next-neighbor (i + 2) and neighbor (i + 1) nucleosome interactions.

Contributions of Sequence to the Higher-Order Structures of DNA

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

The chromatin fiber: multiscale problems and approaches

The structure of chromatin, affected by many factors from DNA linker lengths to posttranslational modifications, is crucial to the regulation of eukaryotic cells. Combined experimental and computational methods have led to new insights into its structural and dynamical features, from interactions due to the flexible core histone tails or linker histones to the physical mechanism driving the formation of chromosomal domains. Here we present a perspective of recent advances in chromatin modeling techniques at the atomic, mesoscopic, and chromosomal scales with a view toward developing multiscale computational strategies to integrate such findings. Innovative modeling methods that connect molecular to chromosomal scales are crucial for interpreting experiments and eventually deciphering the complex dynamic organization and function of chromatin in the cell.

Forced unraveling of chromatin fibers with nonuniform linker DNA lengths

The chromatin fiber undergoes significant structural changes during the cell's life cycle to modulate DNA accessibility. Detailed mechanisms of such structural transformations of chromatin fibers as affected by various internal and external conditions such as the ionic conditions of the medium, the linker DNA length, and the presence of linker histones, constitute an open challenge. Here we utilize Monte Carlo (MC) simulations of a coarse grained model of chromatin with nonuniform linker DNA lengths as found in vivo to help explain some aspects of this challenge. We investigate the unfolding mechanisms of chromatin fibers with alternating linker lengths of 26-62 bp and 44-79 bp using a series of end-to-end stretching trajectories with and without linker histones and compare results to uniform-linker-length fibers. We find that linker histones increase overall resistance of nonuniform fibers and lead to fiber unfolding with superbeads-on-a-string cluster transitions. Chromatin fibers with nonuniform linker DNA lengths display a more complex, multi-step yet smoother process of unfolding compared to their uniform counterparts, likely due to the existence of a more continuous range of nucleosome-nucleosome interactions. This finding echoes the theme that some heterogeneity in fiber component is biologically advantageous.

The polymorphisms of the chromatin fiber

In eukaryotes, the genome is packed into chromosomes, each consisting of large polymeric fibers made of DNA bound with proteins (mainly histones) and RNA molecules. The nature and precise 3D organization of this fiber has been a matter of intense speculations and debates. In the emerging picture, the local chromatin state plays a critical role in all fundamental DNA transactions, such as transcriptional control, DNA replication or repair. However, the molecular and structural mechanisms involved remain elusive. The purpose of this review is to give an overview of the tremendous efforts that have been made for almost 40 years to build physiologically relevant models of chromatin structure. The motivation behind building such models was to shift our representation and understanding of DNA transactions from a too simplistic 'naked DNA' view to a more realistic 'coated DNA' view, as a step towards a better framework in which to interpret mechanistically the control of genetic expression and other DNA metabolic processes. The field has evolved from a speculative point of view towards in vitro biochemistry and in silico modeling, but is still longing for experimental in vivo validations of the proposed structures or even proof of concept experiments demonstrating a clear role of a given structure in a metabolic transaction. The mere existence of a chromatin fiber as a relevant biological entity in vivo has been put into serious questioning. Current research is suggesting a possible reconciliation between theoretical studies and experiments, pointing towards a view where the polymorphic and dynamic nature of the chromatin fiber is essential to support its function in genome metabolism.

Pack, unpack, bend, twist, pull, push: the physical side of gene expression

Molecular motors such as polymerases produce physical constraints on DNA and chromatin. Recent techniques, in particular single-molecule micromanipulation, provide estimation of the forces and torques at stake. These biophysical approaches have improved our understanding of chromatin behaviour under physiological physical constraints and should, in conjunction with genome wide and in vivo studies, help to build more realistic mechanistic models of transcription in the context of chromatin. Here, we wish to provide a brief overview of our current knowledge in the field, and emphasize at the same time the importance of DNA supercoiling as a major parameter in gene regulation.

Insights into chromatin fibre structure by in vitro and in silico single-molecule stretching experiments

The detailed structure and dynamics of the chromatin fibre and their relation to gene regulation represent important open biological questions. Recent advances in single-molecule force spectroscopy experiments have addressed these questions by directly measuring the forces that stabilize and alter the folded states of chromatin, and by investigating the mechanisms of fibre unfolding. We present examples that demonstrate how complementary modelling approaches have helped not only to interpret the experimental findings, but also to advance our knowledge of force-induced events such as unfolding of chromatin with dynamically bound linker histones and nucleosome unwrapping.

Crucial role of dynamic linker histone binding and divalent ions for DNA accessibility and gene regulation revealed by mesoscale modeling of oligonucleosomes

Monte Carlo simulations of a mesoscale model of oligonucleosomes are analyzed to examine the role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to further interpret noted chromatin fiber softening by dynamic LH in monovalent salt conditions. We find that divalent ions produce a fiber stiffening effect that competes with, but does not overshadow, the dramatic softening triggered by dynamic-LH behavior. Indeed, we find that in typical in vivo conditions, dynamic-LH binding/unbinding reduces fiber stiffening dramatically (by a factor of almost 5, as measured by the elasticity modulus) compared with rigidly fixed LH, and also the force needed to initiate chromatin unfolding, making it consistent with those of molecular motors. Our data also show that, during unfolding, divalent ions together with LHs induce linker-DNA bending and DNA–DNA repulsion screening, which guarantee formation of heteromorphic superbeads-on-a-string structures that combine regions of loose and compact fiber independently of the characteristics of the LH–core bond. These structures might be important for gene regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding, either globally or locally, in the presence of divalent ions, might constitute a mechanism for regulation of gene expression.

Internucleosomal interactions mediated by histone tails allow distant communication in chromatin

Action across long distances on chromatin is a hallmark of eukaryotic transcriptional regulation. Although chromatin structure per se can support long-range interactions, the mechanisms of efficient communication between widely spaced DNA modules in chromatin remain a mystery. The molecular simulations described herein suggest that transient binary internucleosomal interactions can mediate distant communication in chromatin. Electrostatic interactions between the N-terminal tails of the core histones and DNA enhance the computed probability of juxtaposition of sites that lie far apart along the DNA sequence. Experimental analysis of the rates of communication in chromatin constructs confirms that long-distance communication occurs efficiently and independently of distance on tail-containing, but not on tailless, chromatin. Taken together, our data suggest that internucleosomal interactions involving the histone tails are essential for highly efficient, long-range communication between regulatory elements and their targets in eukaryotic genomes.

The effect of linker histone's nucleosome binding affinity on chromatin unfolding mechanisms

Eukaryotic gene activation requires selective unfolding of the chromatin fiber to access the DNA for processes such as DNA transcription, replication, and repair. Mutation/modification experiments of linker histone (LH) H1 suggest the importance of dynamic mechanisms for LH binding/dissociation, but the effects on chromatin's unfolding pathway remain unclear. Here we investigate the stretching response of chromatin fibers by mesoscale modeling to complement single-molecule experiments, and present various unfolding mechanisms for fibers with different nucleosome repeat lengths (NRLs) with/without LH that are fixed to their cores or bind/unbind dynamically with different affinities. Fiber softening occurs for long compared to short NRL (due to facile stacking rearrangements), dynamic compared to static LH/core binding as well as slow rather than fast dynamic LH rebinding (due to DNA stem destabilization), and low compared to high LH concentration (due to DNA stem inhibition). Heterogeneous superbead constructs--nucleosome clusters interspersed with extended fiber regions--emerge during unfolding of medium-NRL fibers and may be related to those observed experimentally. Our work suggests that fast and slow LH binding pools, present simultaneously in vivo, might act cooperatively to yield controlled fiber unfolding at low forces. Medium-NRL fibers with multiple dynamic LH pools offer both flexibility and selective DNA exposure, and may be evolutionarily suitable to regulate chromatin architecture and gene expression.

Salt-modulated structure of polyelectrolyte-macroion complex fibers

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5-6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.

Chromatin under mechanical stress: from single 30 nm fibers to single nucleosomes

About a decade ago, the elastic properties of a single chromatin fiber and, subsequently, those of a single nucleosome started to be explored using optical and magnetic tweezers. These techniques have allowed direct measurements of several essential physical parameters of individual nucleosomes and nucleosomal arrays, including the forces responsible for the maintenance of the structure of both the chromatin fiber and the individual nucleosomes, as well as the mechanism of their unwinding under mechanical stress. Experiments on the assembly of individual chromatin fibers have illustrated the complexity of the process and the key role of certain specific components. Nevertheless a substantial disparity exists in the data reported from various experiments. Chromatin, unlike naked DNA, is a system which is extremely sensitive to environmental conditions, and studies carried out under even slightly different conditions are difficult to compare directly. In this review we summarize the available data and their impact on our knowledge of both nucleosomal structure and the dynamics of nucleosome and chromatin fiber assembly and organization.

Hierarchies in eukaryotic genome organization: Insights from polymer theory and simulations

Eukaryotic genomes possess an elaborate and dynamic higher-order structure within the limiting confines of the cell nucleus. Knowledge of the physical principles and the molecular machinery that govern the 3D organization of this structure and its regulation are key to understanding the relationship between genome structure and function. Elegant microscopy and chromosome conformation capture techniques supported by analysis based on polymer models are important steps in this direction. Here, we review results from these efforts and provide some additional insights that elucidate the relationship between structure and function at different hierarchical levels of genome organization.

Intermediate structure between chromatin fibers and chromosome revealed by mechanical stretching and SPM measurement

The morphology of chromosomes (certain rod-shaped structures) is highly reproducible despite the high condensation of chromatin fibers (∼1 mm) into chromosomes (∼1 μm). However, the mechanism underlying the condensation of chromatin fibers into chromosomes is unclear. We assume that investigation of the internal structure of chromosomes will aid in elucidating the condensation process. In order to observe the detailed structure of a chromosome, we stretched a human chromosome by using a micromanipulator and observed its morphology along the stretched region by scanning probe microscopy (SPM). We found that the chromosome consisted of some fibers that were thicker than chromatin fibers. The found fiber was composed of approximately 90-nm-wide beads that were linked linearly. To explore the components of the fiber, we performed immunofluorescence staining of the stretched chromosome. Fluorescence signals of topoisomerase (Topo) IIα, which is known to interact with and support chromatin fibers, and DNA were detected both on the found fiber and beads. Furthermore, after micrococcal nuclease and trypsin treatments, the fibers were found to be mechanically supported by proteins. These results suggest that chromosome comprises an intermediate structure between chromatin fibers and chromosomes.

Exploring the conformational space of chromatin fibers and their stability by numerical dynamic phase diagrams

The three-dimensional structure of chromatin affects DNA accessibility and is therefore a key regulator of gene expression. However, the path of the DNA between consecutive nucleosomes, and the resulting chromatin fiber organization remain controversial. The conformational space available for the folding of the nucleosome chain has been analytically described by phase diagrams with a two-angle model, which describes the chain trajectory by a DNA entry-exit angle at the nucleosome and a torsion angle between consecutive nucleosomes. Here, a novel type of numerical phase diagrams is introduced that relates the geometric phase space to the energy associated with a given chromatin conformation. The resulting phase diagrams revealed differences in the energy landscape that reflect the probability of a given conformation to form in thermal equilibrium. Furthermore, we investigated the effects of entropy and additional degrees of freedom in the dynamic phase diagrams by performing Monte Carlo simulations of the initial chain trajectories. Using our approach, we were able to demonstrate that conformations that initially were geometrically impossible could evolve into energetically favorable states in thermal equilibrium due to DNA bending and torsion. In addition, dynamic phase diagrams were applied to identify chromatin fibers that reflect certain experimentally determined features.

Chromatin fiber dynamics under tension and torsion

Genetic and epigenetic information in eukaryotic cells is carried on chromosomes, basically consisting of large compact supercoiled chromatin fibers. Micromanipulations have recently led to great advances in the knowledge of the complex mechanisms underlying the regulation of DNA transaction events by nucleosome and chromatin structural changes. Indeed, magnetic and optical tweezers have allowed opportunities to handle single nucleosomal particles or nucleosomal arrays and measure their response to forces and torques, mimicking the molecular constraints imposed in vivo by various molecular motors acting on the DNA. These challenging technical approaches provide us with deeper understanding of the way chromatin dynamically packages our genome and participates in the regulation of cellular metabolism.

Evidence for heteromorphic chromatin fibers from analysis of nucleosome interactions

The architecture of the chromatin fiber, which determines DNA accessibility for transcription and other template-directed biological processes, remains unknown. Here we investigate the internal organization of the 30-nm chromatin fiber, combining Monte Carlo simulations of nucleosome chain folding with EM-assisted nucleosome interaction capture (EMANIC). We show that at physiological concentrations of monovalent ions, linker histones lead to a tight 2-start zigzag dominated by interactions between alternate nucleosomes (i +/- 2) and sealed by histone N-tails. Divalent ions further compact the fiber by promoting bending in some linker DNAs and hence raising sequential nucleosome interactions (i +/- 1). Remarkably, both straight and bent linker DNA conformations are retained in the fully compact chromatin fiber as inferred from both EMANIC and modeling. This conformational variability is energetically favorable as it helps accommodate DNA crossings within the fiber axis. Our results thus show that the 2-start zigzag topology and the type of linker DNA bending that defines solenoid models may be simultaneously present in a structurally heteromorphic chromatin fiber with uniform 30 nm diameter. Our data also suggest that dynamic linker DNA bending by linker histones and divalent cations in vivo may mediate the transition between tight nucleosome packing within discrete 30-nm fibers and self-associated higher-order chromosomal forms.

Forces and torques in the nucleus: chromatin under mechanical constraints

Genomic DNA in eukaryotic cells is organized in discrete chromosome territories, each consisting of a single huge hierarchically supercoiled nucleosomal fiber. Through dynamic changes in structure, resulting from chemical modifications and mechanical constraints imposed by numerous factors in vivo, chromatin plays a critical role in the regulation of DNA metabolism processes, including replication and transcription. Indeed, DNA-translocating enzymes, such as polymerases, produce physical constraints that chromatin has to overcome. Recent techniques, in particular single-molecule micromanipulation, have allowed precise quantization of forces and torques at work in the nucleus and have greatly improved our understanding of chromatin behavior under physiological mechanical constraints. These new biophysical approaches should enable us to build realistic mechanistic models and progressively specify the ad hoc and hazy "because of chromatin structure" argument often used to interpret experimental studies of biological function in the context of chromatin.

A tale of tails: how histone tails mediate chromatin compaction in different salt and linker histone environments

To elucidate the role of the histone tails in chromatin compaction and in higher-order folding of chromatin under physiological conditions, we extend a mesoscale model of chromatin (Arya, Zhang, and Schlick. Biophys. J. 2006, 91, 133; Arya and Schlick. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16236) to account for divalent cations (Mg(2+)) and linker histones. Configurations of 24-nucleosome oligonucleosomes in different salt environments and in the presence and absence of linker histones are sampled by a mixture of local and global Monte Carlo methods. Analyses of the resulting ensembles reveal a dynamic synergism between the histone tails, linker histones, and ions in forming compact higher-order structures of chromatin. In the presence of monovalent salt alone, oligonucleosomes remain relatively unfolded, and the histone tails do not mediate many internucleosomal interactions. Upon the addition of linker histones and divalent cations, the oligonucleosomes undergo a significant compaction triggered by a dramatic increase in the internucleosomal interactions mediated by the histone tails, formation of a rigid linker DNA "stem" around the linker histones' C-terminal domains, and reduction in the electrostatic repulsion between linker DNAs via sharp bending in some linker DNAs caused by the divalent cations. Among all histone tails, the H4 tails mediate the most internucleosomal interactions, consistent with experimental observations, followed by the H3, H2A, and H2B tails in decreasing order. Apart from mediating internucleosomal interactions, the H3 tails also contribute to chromatin compaction by attaching to the entering and exiting linker DNA to screen electrotatic repulsion among the linker DNAs. This tendency of the H3 tails to attach to linker DNA, however, decreases significantly upon the addition of linker histones due to competition effects. The H2A and H2B tails do not mediate significant internucleosomal interactions but are important for mediating fiber/fiber intractions, especially in relatively unfolded chromatin in monovalent salt environments.

The effect of internucleosomal interaction on folding of the chromatin fiber

The folding of the nucleosome chain into a chromatin fiber modulates DNA accessibility and is therefore an important factor for the control of gene expression. The fiber conformation depends crucially on the interaction between individual nucleosomes. However, this parameter has not been accurately determined experimentally, and it is affected by posttranslational histone modifications and binding of chromosomal proteins. Here, the effect of different internucleosomal interaction strengths on the fiber conformation was investigated by Monte Carlo computer simulations. The fiber geometry was modeled to fit that of chicken erythrocyte chromatin, which has been examined in numerous experimental studies. In the Monte Carlo simulation, the nucleosome shape was described as an oblate spherocylinder, and a replica exchange protocol was developed to reach thermal equilibrium for a broad range of internucleosomal interaction energies. The simulations revealed the large impact of the nucleosome geometry and the nucleosome repeat length on the compaction of the chromatin fiber. At high internucleosomal interaction energies, a lateral self-association of distant fiber parts and an interdigitation of nucleosomes were apparent. These results identify key factors for the control of the compaction and higher order folding of the chromatin fiber.

Nucleosome geometry and internucleosomal interactions control the chromatin fiber conformation

Based on model structures with atomic resolution, a coarse-grained model for the nucleosome geometry was implemented. The dependence of the chromatin fiber conformation on the spatial orientation of nucleosomes and the path and length of the linker DNA was systematically explored by Monte Carlo simulations. Two fiber types were analyzed in detail that represent nucleosome chains without and with linker histones, respectively: two-start helices with crossed-linker DNA (CL conformation) and interdigitated one-start helices (ID conformation) with different nucleosome tilt angles. The CL conformation was derived from a tetranucleosome crystal structure that was extended into a fiber. At thermal equilibrium, the fiber shape persisted but relaxed into a structure with a somewhat lower linear mass density of 3.1 +/- 0.1 nucleosomes/11 nm fiber. Stable ID fibers required local nucleosome tilt angles between 40 degrees and 60 degrees. For these configurations, much higher mass densities of up to 7.9 +/- 0.2 nucleosomes/11 nm fiber were obtained. A model is proposed, in which the transition between a CL and ID fiber is mediated by relatively small changes of the local nucleosome geometry. These were found to be in very good agreement with changes induced by linker histone H1 binding as predicted from the high resolution model structures.

Chromatin fiber structure: Where is the problem now?

The structure of the "30 nm chromatin fiber", as observed in vitro, has been a matter of controversy for 30 years. Recent studies with new and more powerful techniques give some promise for resolution. However, this will not necessarily inform us as to the in vivo structure, which may be both heteromorphic and dynamic. In this chapter, we briefly review the older conjectures and some more recent studies of special interest. We attempt to point out the remaining contradictions and hopeful lines of future research.

Can visco-elastic phase separation, macromolecular crowding and colloidal physics explain nuclear organisation?

Background

The cell nucleus is highly compartmentalized with well-defined domains, it is not well understood how this nuclear order is maintained. Many scientists are fascinated by the different set of structures observed in the nucleus to attribute functions to them. In order to distinguish functional compartments from non-functional aggregates, I believe is important to investigate the biophysical nature of nuclear organisation.

Results

The various nuclear compartments can be divided broadly as chromatin or protein and/or RNA based, and they have very different dynamic properties. The chromatin compartment displays a slow, constrained diffusional motion. On the other hand, the protein/RNA compartment is very dynamic. Physical systems with dynamical asymmetry go to viscoelastic phase separation. This phase separation phenomenon leads to the formation of a long-lived interaction network of slow components (chromatin) scattered within domains rich in fast components (protein/RNA). Moreover, the nucleus is packed with macromolecules in the order of 300 mg/ml. This high concentration of macromolecules produces volume exclusion effects that enhance attractive interactions between macromolecules, known as macromolecular crowding, which favours the formation of compartments. In this paper I hypothesise that nuclear compartmentalization can be explained by viscoelastic phase separation of the dynamically different nuclear components, in combination with macromolecular crowding and the properties of colloidal particles.

Conclusion

I demonstrate that nuclear structure can satisfy the predictions of this hypothesis. I discuss the functional implications of this phenomenon.

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed "cold sites", which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.

Role of histone tails in chromatin folding revealed by a mesoscopic oligonucleosome model

The role of each histone tail in regulating chromatin structure is elucidated by using a coarse-grained model of an oligonucleosome incorporating flexible histone tails that reproduces the conformational and dynamical properties of chromatin. Specifically, a tailored configurational-bias Monte Carlo method that efficiently samples the possible conformational states of oligonucleosomes yields positional distributions of histone tails around nucleosomes and illuminates the nature of tail/core/DNA interactions at various salt milieus. Analyses indicate that the H4 histone tails are most important in terms of mediating internucleosomal interactions, especially in highly compact chromatin with linker histones, followed by H3, H2A, and H2B tails in decreasing order of importance. In addition to mediating internucleosomal interactions, the H3 histone tails crucially screen the electrostatic repulsion between the entering/exiting DNA linkers. The H2A and H2B tails distribute themselves along the periphery of chromatin fibers and are important for mediating fiber/fiber interactions. A delicate balance between tail-mediated internucleosomal attraction and repulsion among linker DNAs allows the entering/exiting linker DNAs to align perpendicular to each other in linker-histone deficient chromatin, leading to the formation of an irregular zigzag-folded fiber with dominant pair-wise interactions between nucleosomes i and i +/- 4.

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SMEs) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SMEs it is possible to manipulate molecules one at a time and measure distributions describing molecular properties, characterize the kinetics of biomolecular reactions and detect molecular intermediates. SMEs provide additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SMEs it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level, emphasizing the importance of SMEs to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SMEs from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOTs), magnetic tweezers (MTs), biomembrane force probes (BFPs) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation) and proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SMEs to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.

Modeling a self-avoiding chromatin loop: relation to the packing problem, action-at-a-distance, and nuclear context

There is now convincing evidence that genomes are organized into loops, and that looping brings distant genes together so that they can bind to local concentrations of polymerases in "factories" or "hubs." As there remains no systematic analysis of how looping affects the probability that a gene can access binding sites in such factories/hubs, we used an algorithm that we devised and Monte Carlo methods to model a DNA or chromatin loop as a semiflexible (self-avoiding) tube attached to a sphere; we examine how loop thickness, rigidity, and contour length affect where particular segments of the loop lie relative to binding sites on the sphere. Results are compared with those obtained with the traditional model of an (infinitely thin) freely jointed chain. They provide insights into the packing problem (how long genomes are packed into small nuclei), and action-at-a-distance (how firing of one origin or gene can prevent firing of an adjacent one).

Flexible histone tails in a new mesoscopic oligonucleosome model

We describe a new mesoscopic model of oligonucleosomes that incorporates flexible histone tails. The nucleosome cores are modeled using the discrete surface-charge optimization model, which treats the nucleosome as an electrostatic surface represented by hundreds of point charges; the linker DNAs are treated using a discrete elastic chain model; and the histone tails are modeled using a bead/chain hydrodynamic approach as chains of connected beads where each bead represents five protein residues. Appropriate charges and force fields are assigned to each histone chain so as to reproduce the electrostatic potential, structure, and dynamics of the corresponding atomistic histone tails at different salt conditions. The dynamics of resulting oligonucleosomes at different sizes and varying salt concentrations are simulated by Brownian dynamics with complete hydrodynamic interactions. The analyses demonstrate that the new mesoscopic model reproduces experimental results better than its predecessors, which modeled histone tails as rigid entities. In particular, our model with flexible histone tails: correctly accounts for salt-dependent conformational changes in the histone tails; yields the experimentally obtained values of histone-tail mediated core/core attraction energies; and considers the partial shielding of electrostatic repulsion between DNA linkers as a result of the spatial distribution of histone tails. These effects are crucial for regulating chromatin structure but are absent or improperly treated in models with rigid histone tails. The development of this model of oligonucleosomes thus opens new avenues for studying the role of histone tails and their variants in mediating gene expression through modulation of chromatin structure.

Computer modeling demonstrates that electrostatic attraction of nucleosomal DNA is mediated by histone tails

We conducted molecular dynamics computer simulations of charged histone tail-DNA interactions in systems mimicking nucleosome core particles (NCP) . In a coarse-grained model, the NCP is modeled as a negatively charged spherical particle with flexible polycationic histone tails attached to it in a dielectric continuum with explicit mobile counterions and added salt. The size, charge, and distribution of the tails relative to the core were built to mimick real NCP. In this way, we incorporate attractive ion-ion correlation effects due to fluctuations in the ion cloud and the attractive entropic and energetic tail-bridging effects. In agreement with experimental data, increase of monovalent salt content from salt-free to physiological concentration leads to the formation of NCP aggregates; likewise, in the presence of MgCl2, the NCPs form condensed systems via histone-tail bridging and accumulation of counterions. More detailed mechanisms of the histone tail-DNA interactions and dynamics have been obtained from all-atom molecular dynamics simulations (including water), comprising three DNA 22-mers and 14 short fragments of the H4 histone tail (amino acids 5-12) carrying three positive charges on lysine+ interacting with DNA. We found correlation of the DNA-DNA distance with the presence and association of the histone tail between the DNA molecules.

The histone octamer influences the wrapping direction of DNA on it: Brownian dynamics simulation of the nucleosome chirality

In eukaryote nucleosome, DNA wraps around a histone octamer in a left-handed way. We study the process of chirality formation of nucleosome with Brownian dynamics simulation. We model the histone octamer with a quantitatively adjustable chirality: left-handed, right-handed or non-chiral, and simulate the dynamical wrapping process of a DNA molecule on it. We find that the chirality of a nucleosome formed is strongly dependent on that of the histone octamer, and different chiralities of the histone octamer induce its different rotation directions in the wrapping process of DNA. In addition, a very weak chirality of the histone octamer is quite enough for sustaining the correct chirality of the nucleosome formed. We also show that the chirality of a nucleosome may be broken at elevated temperature.

Electrostatic mechanism of nucleosomal array folding revealed by computer simulation

Although numerous experiments indicate that the chromatin fiber displays salt-dependent conformations, the associated molecular mechanism remains unclear. Here, we apply an irregular Discrete Surface Charge Optimization (DiSCO) model of the nucleosome with all histone tails incorporated to describe by Monte Carlo simulations salt-dependent rearrangements of a nucleosomal array with 12 nucleosomes. The ensemble of nucleosomal array conformations display salt-dependent condensation in good agreement with hydrodynamic measurements and suggest that the array adopts highly irregular 3D zig-zag conformations at high (physiological) salt concentrations and transitions into the extended "beads-on-a-string" conformation at low salt. Energy analyses indicate that the repulsion among linker DNA leads to this extended form, whereas internucleosome attraction drives the folding at high salt. The balance between these two contributions determines the salt-dependent condensation. Importantly, the internucleosome and linker DNA-nucleosome attractions require histone tails; we find that the H3 tails, in particular, are crucial for stabilizing the moderately folded fiber at physiological monovalent salt.

Brownian dynamics simulation of nucleosome formation and disruption under stretching

Using a Brownian dynamics simulation, we numerically studied the interaction of DNA with histone and proposed an octamer-rotation model to describe the process of nucleosome formation. Nucleosome disruption under stretching was also simulated. The theoretical curves of extension versus time as well as of force versus extension are consistent with previous experimental results.

Nucleosome conformational flexibility and implications for chromatin dynamics

The active role of chromatin in the regulation of gene activity seems to imply a conformational flexibility of the basic chromatin structural unit, the nucleosome. This review is devoted to our recent results pertaining to this subject, using an original approach based on the topology of single particles reconstituted on DNA minicircles, combined with their theoretical simulation. Three types of chromatin particles have been studied so far: a subnucleosome, that is, the (H3-H4)(2) histone tetramer-containing particle, now known as the tetrasome; the nucleosome; and the linker histone H5/H1-bearing nucleosome (the chromatosome). All the particles were found to exist in two to three conformational states, which differ by their topological and mechanical properties. Our approach unveiled the molecular mechanisms of nucleosome conformational dynamics and will help to understand its functional relevance. A most surprising conclusion of the work was perhaps that DNA overall flexibility increases considerably upon particle formation, which might indeed be a requirement of genome function.

Nucleosome interactions in chromatin: fiber stiffening and hairpin formation

We use Monte Carlo simulations to study attractive and excluded volume interactions between nucleosome core particles in 30-nm chromatin fibers. The nucleosomes are treated as disklike objects having an excluded volume and short-range attraction modeled by a variant of the Gay-Berne potential. The nucleosomes are connected via bendable and twistable linker DNA in the crossed linker fashion. We investigate the influence of the nucleosomal excluded volume on the stiffness of the fiber. For parameter values that correspond to chicken erythrocyte chromatin, we find that the persistence length is governed to a large extent by that excluded volume whereas the soft linker backbone elasticity plays only a minor role. We further find that internucleosomal attraction can induce the formation of hairpin configurations. Tension-induced opening of such configurations into straight fibers manifests itself in a quasiplateau in the force-extension curve that resembles results from recent micromanipulation experiments. Such hairpins may play a role in the formation of higher-order structures in chromosomes like chromonema fibers.

Keeping fingers crossed: heterochromatin spreading through interdigitation of nucleosome arrays

Interphase eukaryotic nuclei contain diffuse euchromatin and condensed heterochromatin. Current textbook models suggest that chromatin condensation occurs via accordion-type compaction of nucleosome zigzag chains. Recent studies have revealed several structural aspects that distinguish the highly compact state of condensed heterochromatin. These include an extensive lateral self-association of chromatin fibers, prominent nucleosome linker 'stems', and special protein factors that promote chromatin self-association. Here I review the molecular and structural determinants of chromatin compaction and discuss how heterochromatin spreading may be mediated by lateral self-association of zigzag nucleosome arrays.

To the 30-nm chromatin fiber and beyond

Chromatin fibers are intrinsically dynamic macromolecular complexes whose biological functions are intimately linked with their structure and interactions with chromatin-associated proteins (CAPs). Three-dimensional architectural transitions between or within the two co-existing chromatin types referred to as euchromatin and heterochromatin have been associated with activation or repression of nuclear functions. The presence of specific subsets of chromosomal proteins co-existing with the different chromatin conformations suggests a functional significance for their co-localization. The major points of emphasis of this review will assess the structure, function and recently documented exchanges amongst various members of the CAP family.

Optical tweezers stretching of chromatin

Recently significant success has emerged from exciting research involving chromatin stretching using optical tweezers. These experiments, in which a single chromatin fibre is attached by one end to a micron-sized bead held in an optical trap and to a solid surface or second bead via the other end, allows manipulation and force detection at a single-molecule level. Through force-induced stretching of chromatin, mechanical properties, specific intermolecular bond strengths and DNA-protein association and dissociation kinetics have been determined. These studies will be extremely fruitful in terms of understanding the function of chromatin structure and its dynamics within the cell.

Modeling DNA structure, elasticity, and deformations at the base-pair level

We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between the neighboring base pairs. The sugar-phosphate backbones are taken into account by semirigid harmonic springs with a nonzero spring length. The competition between these two interactions and the introduction of a simple geometrical constraint lead to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the stack-of-plates model enables us to optimize the free model parameters so as to reproduce the experimentally known observables such as persistence lengths, mean and mean-squared base-pair step parameters. For the optimized model parameters, we measured the critical force where the transition from B- to S-DNA occurs to be approximately 140 pN. We observe an overstretched S-DNA conformation with highly inclined bases which partially preserves the stacking of successive base pairs.