Statistical mechanics of nucleosome ordering by chromatin-structure-induced two-body interactions

Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation

We construct and analyze monomeric and multimeric models of the stochastic disassembly of a single nucleosome. Our monomeric model predicts the time needed for a number of histone-DNA contacts to spontaneously break, leading to dissociation of a non-fragmented histone from DNA. The dissociation process can be facilitated by DNA binding proteins or processing molecular motors that compete with histones for histone-DNA contact sites. Eigenvalue analysis of the corresponding master equation allows us to evaluate histone detachment times under both spontaneous detachment and protein-facilitated processes. We find that competitive DNA binding of remodeling proteins can significantly reduce the typical detachment time but only if these remodelers have DNA-binding affinities comparable to those of histone-DNA contact sites. In the presence of processive motors, the histone detachment rate is shown to be proportional to the product of the histone single-bond dissociation constant and the speed of motor protein procession. Our simple intact-histone model is then extended to allow for multimeric nucleosome kinetics that reveal additional pathways of disassembly. In addition to a dependence of complete disassembly times on subunit-DNA contact energies, we show how histone subunit concentrations in bulk solutions can mediate the disassembly process by rescuing partially disassembled nucleosomes. Moreover, our kinetic model predicts that remodeler binding can also bias certain pathways of nucleosome disassembly, with higher remodeler binding rates favoring intact-histone detachment.

A unified computational framework for modeling genome-wide nucleosome landscape

Nucleosomes form the fundamental building blocks of eukaryotic chromatin, and previous attempts to understand the principles governing their genome-wide distribution have spurred much interest and debate in biology. In particular, the precise role of DNA sequence in shaping local chromatin structure has been controversial. This paper rigorously quantifies the contribution of hitherto-debated sequence features-including G+C content, 10.5 bp periodicity, and poly(dA:dT) tracts-to three distinct aspects of genome-wide nucleosome landscape: occupancy, translational positioning and rotational positioning. Our computational framework simultaneously learns nucleosome number and nucleosome-positioning energy from genome-wide nucleosome maps. In contrast to other previous studies, our model can predict both in vitro and in vivo nucleosome maps in Saccharomyces cerevisiae. We find that although G+C content is the primary determinant of MNase-derived nucleosome occupancy, MNase digestion biases may substantially influence this GC dependence. By contrast, poly(dA:dT) tracts are seen to deter nucleosome formation, regardless of the experimental method used. We further show that the 10.5 bp nucleotide periodicity facilitates rotational but not translational positioning. Applying our method to in vivo nucleosome maps demonstrates that, for a subset of genes, the regularly-spaced nucleosome arrays observed around transcription start sites can be partially recapitulated by DNA sequence alone. Finally, in vivo nucleosome occupancy derived from MNase-seq experiments around transcription termination sites can be mostly explained by the genomic sequence. Implications of these results and potential extensions of the proposed computational framework are discussed.

Major Determinants of Nucleosome Positioning

The compact structure of the nucleosome limits DNA accessibility and inhibits the binding of most sequence-specific proteins. Nucleosomes are not randomly located on the DNA but positioned with respect to the DNA sequence, suggesting models in which critical binding sites are either exposed in the linker, resulting in activation, or buried inside a nucleosome, resulting in repression. The mechanisms determining nucleosome positioning are therefore of paramount importance for understanding gene regulation and other events that occur in chromatin, such as transcription, replication, and repair. Here, we review our current understanding of the major determinants of nucleosome positioning: DNA sequence, nonhistone DNA-binding proteins, chromatin-remodeling enzymes, and transcription. We outline the major challenges for the future: elucidating the precise mechanisms of chromatin opening and promoter activation, identifying the complexes that occupy promoters, and understanding the multiscale problem of chromatin fiber organization.

Precise genome-wide mapping of single nucleosomes and linkers in vivo

We developed a chemical cleavage method that releases single nucleosome dyad-containing fragments, allowing us to precisely map both single nucleosomes and linkers with high accuracy genome-wide in yeast. Our single nucleosome positioning data reveal that nucleosomes occupy preferred positions that differ by integral multiples of the DNA helical repeat. By comparing nucleosome dyad positioning maps to existing genomic and transcriptomic data, we evaluated the contributions of sequence, transcription, and histones H1 and H2A.Z in defining the chromatin landscape. We present a biophysical model that neglects DNA sequence and shows that steric occlusion suffices to explain the salient features of nucleosome positioning.

MNase-Sensitive Complexes in Yeast: Nucleosomes and Non-histone Barriers

Micrococcal nuclease (MNase) is commonly used to map nucleosomes genome-wide, but nucleosome maps are affected by the degree of digestion. It has been proposed that many yeast promoters are not nucleosome-free but instead occupied by easily digested, unstable, "fragile" nucleosomes. We analyzed the histone content of all MNase-sensitive complexes by MNase-ChIP-seq and sonication-ChIP-seq. We find that yeast promoters are predominantly bound by non-histone protein complexes, with little evidence for fragile nucleosomes. We do detect MNase-sensitive nucleosomes elsewhere in the genome, including at transcription termination sites. However, they have high A/T content, suggesting that MNase sensitivity does not indicate instability, but rather the preference of MNase for A/T-rich DNA, such that A/T-rich nucleosomes are digested faster than G/C-rich nucleosomes. We confirm our observations by analyzing ChIP-exo, chemical mapping, and ATAC-seq data from other laboratories. Thus, histone ChIP-seq experiments are essential to distinguish nucleosomes from other DNA-binding proteins that protect against MNase.

Genome-wide profiling of nucleosome sensitivity and chromatin accessibility in Drosophila melanogaster

Nucleosomal DNA is thought to be generally inaccessible to DNA-binding factors, such as micrococcal nuclease (MNase). Here, we digest Drosophila chromatin with high and low concentrations of MNase to reveal two distinct nucleosome types: MNase-sensitive and MNase-resistant. MNase-resistant nucleosomes assemble on sequences depleted of A/T and enriched in G/C-containing dinucleotides, whereas MNase-sensitive nucleosomes form on A/T-rich sequences found at transcription start and termination sites, enhancers and DNase I hypersensitive sites. Estimates of nucleosome formation energies indicate that MNase-sensitive nucleosomes tend to be less stable than MNase-resistant ones. Strikingly, a decrease in cell growth temperature of about 10°C makes MNase-sensitive nucleosomes less accessible, suggesting that observed variations in MNase sensitivity are related to either thermal fluctuations of chromatin fibers or the activity of enzymatic machinery. In the vicinity of active genes and DNase I hypersensitive sites nucleosomes are organized into periodic arrays, likely due to 'phasing' off potential barriers formed by DNA-bound factors or by nucleosomes anchored to their positions through external interactions. The latter idea is substantiated by our biophysical model of nucleosome positioning and energetics, which predicts that nucleosomes immediately downstream of transcription start sites are anchored and recapitulates nucleosome phasing at active genes significantly better than sequence-dependent models.

Conditions for positioning of nucleosomes on DNA

Positioning of nucleosomes along a eukaryotic genome plays an important role in its organization and regulation. There are many different factors affecting the location of nucleosomes. Some can be viewed as preferential binding of a single nucleosome to different locations along the DNA and some as interactions between neighboring nucleosomes. In this study, we analyze positioning of nucleosomes and derive conditions for their good positioning. Using analytic and numerical approaches we find that, if the binding preferences are very weak, an interplay between the interactions and the binding preferences is essential for a good positioning of nucleosomes, especially on correlated energy landscapes. Analyzing the empirical energy landscape, we conclude that good positioning of nucleosomes in vivo is possible only if they strongly interact. In this case, our model, predicting long-length-scale fluctuations of nucleosomes' occupancy along the DNA, accounts well for the empirical observations.

Functional roles of nucleosome stability and dynamics

Nucleosome is a histone-DNA complex known as the fundamental repeating unit of chromatin. Up to 90% of eukaryotic DNA is wrapped around consecutive octamers made of the core histones H2A, H2B, H3 and H4. Nucleosome positioning affects numerous cellular processes that require robust and timely access to genomic DNA, which is packaged into the tight confines of the cell nucleus. In living cells, nucleosome positions are determined by intrinsic histone-DNA sequence preferences, competition between histones and other DNA-binding proteins for genomic sequence, and ATP-dependent chromatin remodelers. We discuss the major energetic contributions to nucleosome formation and remodeling, focusing especially on partial DNA unwrapping off the histone octamer surface. DNA unwrapping enables efficient access to nucleosome-buried binding sites and mediates rapid nucleosome removal through concerted action of two or more DNA-binding factors. High-resolution, genome-scale maps of distances between neighboring nucleosomes have shown that DNA unwrapping and nucleosome crowding (mutual invasion of nucleosome territories) are much more common than previously thought. Ultimately, constraints imposed by nucleosome energetics on the rates of ATP-dependent and spontaneous chromatin remodeling determine nucleosome occupancy genome-wide, and shape pathways of cellular response to environmental stresses.

RSC-dependent constructive and destructive interference between opposing arrays of phased nucleosomes in yeast

RSC and SWI/SNF are related ATP-dependent chromatin remodeling machines that move nucleosomes, regulating access to DNA. We addressed their roles in nucleosome phasing relative to transcription start sites in yeast. SWI/SNF has no effect on phasing at the global level. In contrast, RSC depletion results in global nucleosome repositioning: Both upstream and downstream nucleosomal arrays shift toward the nucleosome-depleted region (NDR), with no change in spacing, resulting in a narrower and partly filled NDR. The global picture of RSC-depleted chromatin represents the average of a range of chromatin structures, with most genes showing a shift of the +1 or the -1 nucleosome into the NDR. Using RSC ChIP data reported by others, we show that RSC occupancy is highest on the coding regions of heavily transcribed genes, though not at their NDRs. We propose that RSC has a role in restoring chromatin structure after transcription. Analysis of gene pairs in different orientations demonstrates that phasing patterns reflect competition between phasing signals emanating from neighboring NDRs. These signals may be in phase, resulting in constructive interference and a regular array, or out of phase, resulting in destructive interference and fuzzy positioning. We propose a modified barrier model, in which a stable complex located at the NDR acts as a bidirectional phasing barrier. In RSC-depleted cells, this barrier has a smaller footprint, resulting in narrower NDRs. Thus, RSC plays a critical role in organizing yeast chromatin.

Regulation of the nucleosome repeat length in vivo by the DNA sequence, protein concentrations and long-range interactions

The nucleosome repeat length (NRL) is an integral chromatin property important for its biological functions. Recent experiments revealed several conflicting trends of the NRL dependence on the concentrations of histones and other architectural chromatin proteins, both in vitro and in vivo, but a systematic theoretical description of NRL as a function of DNA sequence and epigenetic determinants is currently lacking. To address this problem, we have performed an integrative biophysical and bioinformatics analysis in species ranging from yeast to frog to mouse where NRL was studied as a function of various parameters. We show that in simple eukaryotes such as yeast, a lower limit for the NRL value exists, determined by internucleosome interactions and remodeler action. For higher eukaryotes, also the upper limit exists since NRL is an increasing but saturating function of the linker histone concentration. Counterintuitively, smaller H1 variants or non-histone architectural proteins can initiate larger effects on the NRL due to entropic reasons. Furthermore, we demonstrate that different regimes of the NRL dependence on histone concentrations exist depending on whether DNA sequence-specific effects dominate over boundary effects or vice versa. We consider several classes of genomic regions with apparently different regimes of the NRL variation. As one extreme, our analysis reveals that the period of oscillations of the nucleosome density around bound RNA polymerase coincides with the period of oscillations of positioning sites of the corresponding DNA sequence. At another extreme, we show that although mouse major satellite repeats intrinsically encode well-defined nucleosome preferences, they have no unique nucleosome arrangement and can undergo a switch between two distinct types of nucleosome positioning.

Ubiquitous nucleosome crowding in the yeast genome

Nucleosomes may undergo a conformational change in which a stretch of DNA peels off the histone octamer surface as a result of thermal fluctuations or interactions with chromatin remodelers. Thus, neighboring nucleosomes may invade each other's territories by DNA unwrapping and translocation, or through initial assembly in partially wrapped states. A recent high-resolution map of distances between dyads of neighboring nucleosomes in Saccharomyces cerevisiae reveals that nucleosomes frequently overlap DNA territories of their neighbors. This conclusion is supported by lower-resolution maps of S. cerevisiae nucleosome lengths based on micrococcal nuclease digestion and paired-end sequencing. The average length of wrapped DNA follows a stereotypical pattern in genes and promoters, correlated with the well-known distribution of nucleosome occupancy: nucleosomal DNA tends to be shorter in promoters and longer in coding regions. To explain these observations, we have developed a biophysical model that uses a 10-11-bp periodic histone-DNA binding energy profile. The profile is based on the pattern of histone-DNA contacts in nucleosome crystal structures, as well as the idea of linker length discretization caused by higher-order chromatin structure. Our model is in agreement with the observed genome-wide distributions of interdyad distances, wrapped DNA lengths, and nucleosome occupancies. Furthermore, our approach explains in vitro measurements of the accessibility of nucleosome-covered target sites and nucleosome-induced cooperativity between DNA-binding factors. We rule out several alternative scenarios of histone-DNA interactions as inconsistent with the genomic data.

Quantifying the role of steric constraints in nucleosome positioning

Statistical positioning, the localization of nucleosomes packed against a fixed barrier, is conjectured to explain the array of well-positioned nucleosomes at the 5′ end of genes, but the extent and precise implications of statistical positioning in vivo are unclear. We examine this hypothesis quantitatively and generalize the idea to include moving barriers as well as nucleosomes actively packed against a barrier. Early experiments noted a similarity between the nucleosome profile aligned and averaged across genes and that predicted by statistical positioning; however, we demonstrate that aligning random nucleosomes also generates the same profile, calling the previous interpretation into question. New rigorous results reformulate statistical positioning as predictions on the variance structure of nucleosome locations in individual genes. In particular, a quantity termed the variance gradient, describing the change in variance between adjacent nucleosomes, is tested against recent high-throughput nucleosome sequencing data. Constant variance gradients provide support for generalized statistical positioning in ∼50% of long genes. Genes that deviate from predictions have high nucleosome turnover and cell-to-cell gene expression variability. The observed variance gradient suggests an effective nucleosome size of 158 bp, instead of the commonly perceived 147 bp. Our analyses thus clarify the role of statistical positioning in vivo.

Global remodeling of nucleosome positions in C. elegans

Background

Eukaryotic chromatin architecture is affected by intrinsic histone-DNA sequence preferences, steric exclusion between nucleosome particles, formation of higher-order structures, and in vivo activity of chromatin remodeling enzymes.

Results

To disentangle sequence-dependent nucleosome positioning from the other factors, we have created two high-throughput maps of nucleosomes assembled in vitro on genomic DNA from the nematode worm Caenorhabditis elegans. A comparison of in vitro nucleosome positions with those observed in a mixed-stage, mixed-tissue population of C. elegans cells reveals that in vivo sequence preferences are modified on the genomic scale. Indeed, G/C dinucleotides are predicted to be most favorable for nucleosome formation in vitro but not in vivo. Nucleosome sequence read coverage in vivo is distinctly lower in chromosome arms than in central regions; the observed changes in apparent nucleosome sequence specificity, likely due to genome-wide chromatin remodeler activity, contribute to the formation of these megabase-scale chromatin domains. We also observe that the majority of well-positioned in vivo nucleosomes do not occupy thermodynamically favorable sequences observed in vitro. Finally, we find that exons are intrinsically more amenable to nucleosome formation compared to introns. Nucleosome occupancy of introns and exons consistently increases with G/C content in vitro but not in vivo, in agreement with our observation that G/C dinucleotide enrichment does not strongly promote in vivo nucleosome formation.

Conclusions

Our findings highlight the importance of both sequence specificity and active nucleosome repositioning in creating large-scale chromatin domains, and the antagonistic roles of intrinsic sequence preferences and chromatin remodelers in C. elegans.

Sequence read data has been deposited into Sequence Read Archive (http://www.ncbi.nlm.nih.gov/sra; accession number SRA050182). Additional data, software and computational predictions are available on the Nucleosome Explorer website (http://nucleosome.rutgers.edu).

Genome-wide nucleosome positioning during embryonic stem cell development

We determined genome-wide nucleosome occupancies in mouse embryonic stem cells and their neural progenitor and embryonic fibroblast counterparts to assess features associated with nucleosome positioning during lineage commitment. Cell-type- and protein-specific binding preferences of transcription factors to sites with either low (Myc, Klf4 and Zfx) or high (Nanog, Oct4 and Sox2) nucleosome occupancy as well as complex patterns for CTCF were identified. Nucleosome-depleted regions around transcription start and transcription termination sites were broad and more pronounced for active genes, with distinct patterns for promoters classified according to CpG content or histone methylation marks. Throughout the genome, nucleosome occupancy was correlated with certain histone methylation or acetylation modifications. In addition, the average nucleosome repeat length increased during differentiation by 5-7 base pairs, with local variations for specific regions. Our results reveal regulatory mechanisms of cell differentiation that involve nucleosome repositioning.

Nucleosome positioning and nucleosome stacking: two faces of the same coin

Nucleosomes are regularly spaced along eukaryotic genomes. In the emerging model, known as "statistical positioning", this spacing is due to steric repulsion between nucleosomes and to the presence of nucleosome excluding barriers on the genome. However, new experimental evidence recently challenged the "statistical positioning" model (Z. Zhang et al., Science, 2011, 332(6032), 977-980). We propose here that the regular spacing can be better explained by adding attractive interactions between nucleosomes. In our model those attractions are due to the fact that nucleosomes are stacked in regular chromatin fibers. In a self-reinforcing mechanism, regular nucleosome spacing promotes in turn nucleosome stacking. We first show that this model can precisely account for the nucleosome spacing observed in Saccharomyces cerevisiae. We then use a simple toy model to show that attraction between nucleosomes can fasten the formation of the chromatin fiber.

Statistical Mechanics of Nucleosomes Constrained by Higher-Order Chromatin Structure

Eukaryotic DNA is packaged into chromatin: one-dimensional arrays of nucleosomes separated by stretches of linker DNA are folded into 30-nm chromatin fibers which in turn form higher-order structures (Felsenfeld and Groudine in Nature 421:448, 2003). Each nucleosome, the fundamental unit of chromatin, has 147 base pairs (bp) of DNA wrapped around a histone octamer (Richmond and Davey in Nature 423:145, 2003). In order to describe how chromatin fiber formation affects nucleosome positioning and energetics, we have developed a thermodynamic model of finite-size particles with effective nearest-neighbor interactions and arbitrary DNA-binding energies. We show that both one-and two-body interactions can be extracted from one-particle density profiles based on high-throughput maps of in vitro or in vivo nucleosome positions. Although a simpler approach that neglects two-body interactions (even if they are in fact present in the system) can be used to predict sequence determinants of nucleosome positions, the full theory is required to disentangle one- and two-body effects. Finally, we construct a minimal model in which nucleosomes are positioned primarily by steric exclusion and two-body interactions rather than intrinsic histone-DNA sequence preferences. The model reproduces nucleosome occupancy patterns observed over transcribed regions in living cells.