Statistical-mechanical lattice models for protein-DNA binding in chromatin

DNA sequence-dependent formation of heterochromatin nanodomains

The mammalian epigenome contains thousands of heterochromatin nanodomains (HNDs) marked by di- and trimethylation of histone H3 at lysine 9 (H3K9me2/3), which have a typical size of 3–10 nucleosomes. However, what governs HND location and extension is only partly understood. Here, we address this issue by introducing the chromatin hierarchical lattice framework (ChromHL) that predicts chromatin state patterns with single-nucleotide resolution. ChromHL is applied to analyse four HND types in mouse embryonic stem cells that are defined by histone methylases SUV39H1/2 or GLP, transcription factor ADNP or chromatin remodeller ATRX. We find that HND patterns can be computed from PAX3/9, ADNP and LINE1 sequence motifs as nucleation sites and boundaries that are determined by DNA sequence (e.g. CTCF binding sites), cooperative interactions between nucleosomes as well as nucleosome-HP1 interactions. Thus, ChromHL rationalizes how patterns of H3K9me2/3 are established and changed via the activity of protein factors in processes like cell differentiation.

The ability to predict epigenetic regulation is an important challenge in biology. Here the authors describe heterochromatin nanodomains (HNDs) and compare four different types of H3K9me2/3-marked HNDs in mouse embryonic stem cells. They further develop a computational framework to predict genome-wide HND maps from DNA sequence and protein concentrations, at single-nucleotide resolution.

High fidelity epigenetic inheritance: Information theoretic model predicts threshold filling of histone modifications post replication

During cell devision, maintaining the epigenetic information encoded in histone modification patterns is crucial for survival and identity of cells. The faithful inheritance of the histone marks from the parental to the daughter strands is a puzzle, given that each strand gets only half of the parental nucleosomes. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that enzymes may implement a critical threshold filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum à posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.

Liquid-Liquid Phase Separation in Chromatin

In eukaryotic cells, protein and RNA factors involved in genome activities like transcription, RNA processing, DNA replication, and repair accumulate in self-organizing membraneless chromatin subcompartments. These structures contribute to efficiently conduct chromatin-mediated reactions and to establish specific cellular programs. However, the underlying mechanisms for their formation are only partly understood. Recent studies invoke liquid-liquid phase separation (LLPS) of proteins and RNAs in the establishment of chromatin activity patterns. At the same time, the folding of chromatin in the nucleus can drive genome partitioning into spatially distinct domains. Here, the interplay between chromatin organization, chromatin binding, and LLPS is discussed by comparing and contrasting three prototypical chromatin subcompartments: the nucleolus, clusters of active RNA polymerase II, and pericentric heterochromatin domains. It is discussed how the different ways of chromatin compartmentalization are linked to transcription regulation, the targeting of soluble factors to certain parts of the genome, and to disease-causing genetic aberrations.

Cooperative kinetics of ligand binding to linear polymers

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Cooperative kinetic equation for large ligands binding to long polymers.

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Cooperativity in general affects binding and release rates.

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Appropriate counting of the available binding sites for a ligand to a linear polymer.

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Positive cooperativity increases polymer coverage by the ligand.

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Large ligand size reduces cooperativity effects.

Ligands change the chemical and mechanical properties of polymers. In particular, single strand binding protein (SSB) non-specifically bounds to single-stranded DNA (ssDNA), modifying the ssDNA stiffness and the DNA replication rate, as recently measured with single-molecule techniques. SSB is a large ligand presenting cooperativity in some of its binding modes. We aim to develop an accurate kinetic model for the cooperative binding kinetics of large ligands. Cooperativity accounts for the changes in the affinity of a ligand to the polymer due to the presence of another bound ligand. Large ligands, attaching to several binding sites, require a detailed counting of the available binding possibilities. This counting has been done by McGhee and von Hippel to obtain the equilibrium state of the ligands-polymer complex. The same procedure allows to obtain the kinetic equations for the cooperative binding of ligands to long polymers, for all ligand sizes. Here, we also derive approximate cooperative kinetic equations in the large ligand limit, at the leading and next-to-leading orders. We found cooperativity is negligible at the leading-order, and appears at the next-to-leading order. Positive cooperativity (increased affinity) can be originated by increased binding affinity or by decreased release affinity, implying different kinetics. Nevertheless, the equilibrium state is independent of the origin of cooperativity and only depends on the overall increase in affinity. Next-to-leading approximation is found to be accurate, particularly for small cooperativity. These results allow to understand and characterize relevant ligand binding processes, as the binding kinetics of SSB to ssDNA, which has been reported to affect the DNA replication rate for several SSB-polymerase pairs.

Effects of size, cooperativity, and competitive binding on protein positioning on DNA

Accurate positioning of proteins on chromosomal DNA is crucial for its proper organization as well as gene transcription regulation. Recent experiments revealed existence of periodic patterns of nucleoprotein complexes on DNA, which frequently cannot be explained by sequence-dependent binding of proteins. Previous theoretical studies suggest that such patterns typically emerge as a result of the proteins' volume-exclusion effect. However, the role of other physical factors in patterns' formation, such as the length of DNA, its sequence heterogeneity, and protein binding cooperativity/binding competition to DNA, remains unclear. To address these less understood yet important aspects, we investigated potential effects of these factors on protein positioning on finite-size DNA by using transfer-matrix calculations. It has been found that upon binding to DNA, proteins form oscillatory patterns that span over the length of up to ∼10 times the size of the protein binding site, with the shape of the patterns being strongly dependent on the length of DNA and the proteins' binding cooperativity to DNA. Furthermore, calculations showed that small variations in the proteins' affinity to DNA due to its sequence heterogeneity do not much change the main geometric characteristics of the observed protein patterns. Finally, competition between two different types of proteins for binding to DNA has been found to lead to formation of highly diverse and complex alternating positioning of the two proteins. Altogether, these results provide new insights into the roles of physicochemical properties of proteins, the DNA length, and DNA-binding competition between proteins in formation of protein positioning patterns on DNA.

Predicting Genome Architecture: Challenges and Solutions

Genome architecture plays a pivotal role in gene regulation. The use of high-throughput methods for chromatin profiling and 3-D interaction mapping provide rich experimental data sets describing genome organization and dynamics. These data challenge development of new models and algorithms connecting genome architecture with epigenetic marks. In this review, we describe how chromatin architecture could be reconstructed from epigenetic data using biophysical or statistical approaches. We discuss the applicability and limitations of these methods for understanding the mechanisms of chromatin organization. We also highlight the emergence of new predictive approaches for scoring effects of structural variations in human cells.

Protein-ligand binding interactions of imidazolium salts with SARS CoV-2

The disease called severe acute respiratory syndrome (SARS) is a lifestyle intimidating viral contamination affected by a positive, single stranded novel RNA virus (COVID-2019) from the enveloped coronaviruse family. The COVID-2019 virus has affected many people, scattering promptly, and researchers are attempting to find out medicines for its effectual cure in all over the globe. Chloroquine (ChQ) and its derivatives, an older drug used for the cure of malaria, is exposed to encompass a perceptible feasibility and commendable well-being in opposition to SARS CoV-2 associated pneumonia clinical trials conducted in China. Later on, a few investigations have been directed to find and present SARS CoV-2 antiviral medications. The aim of this present work deals with the potential binding interactions of some imidazolium salts with Nsp9 (Nonstructural protein 9) RNA binding protein of SARS CoV-2.

Noncooperative thermodynamics and kinetic models of ligand binding to polymers: Connecting McGhee-von Hippel model with the Tonks gas model

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages.

Geometrical Heterogeneity Dominates Thermal Fluctuations in Facilitating Chromatin Contacts

Within a living cell, the myriad of proteins that bind DNA introduce heterogeneously spaced kinks into an otherwise semiflexible DNA double helix. To investigate the effects of heterogeneous nucleosome binding on chromatin organization, we extend the wormlike chain model to include statistically spaced, rigid kinks. On timescales where nucleosome positions are fixed, we find that the probability of chromatin loop formation can vary by up to six orders of magnitude between two sets of nucleosome positions drawn from the same distribution. On longer timescales, we show that continuous rerandomization due to nucleosome turnover results in chromatin tracing out an effective WLC with a dramatically smaller Kuhn length than bare DNA. Together, these observations demonstrate that nucleosome spacing acts as the primary source of the structural heterogeneity that dominates local and global chromatin organization.

The theory of interceptor-protector action of DNA binding drugs

The review discusses the theory of interceptor-protector action (the IPA theory) as the new self-consistent biophysical theory establishing a quantitative interrelation between parameters measured in independent physico-chemical experiment and in vitro biological experiment for the class of DNA binding drugs. The elements of the theory provide complete algorithm of analysis, which may potentially be applied to any system of DNA targeting aromatic drugs. Such analytical schemes, apart from extension of current scientific knowledge, are important in the context of rational drug design for managing drug's response by changing the physico-chemical parameters of molecular complexation.

Removing Background Co-occurrences of Transcription Factor Binding Sites Greatly Improves the Prediction of Specific Transcription Factor Cooperations

Today, it is well-known that in eukaryotic cells the complex interplay of transcription factors (TFs) bound to the DNA of promoters and enhancers is the basis for precise and specific control of transcription. Computational methods have been developed for the identification of potentially cooperating TFs through the co-occurrence of their binding sites (TFBSs). One challenge of these methods is the differentiation of TFBS pairs that are specific for a given sequence set from those that are ubiquitously appearing, rendering the results highly dependent on the choice of a proper background set. Here, we present an extension of our previous PC-TraFF approach that estimates the background co-occurrence of any TF pair by preserving the (oligo-) nucleotide composition and, thus, the core of TFBSs in the sequences of interest. Applying our approach to a simulated data set with implanted TFBS pairs, we could successfully identify them as sequence-set specific under a variety of conditions. When we analyzed the gene expression data sets of five breast cancer associated subtypes, the number of overlapping pairs could be dramatically reduced in comparison to our previous approach. As a result, we could identify potentially cooperating transcriptional regulators that are characteristic for each of the five breast cancer subtypes. This indicates that our approach is able to discriminate specific potential TF cooperations against ubiquitously occurring combinations. The results obtained with our method may help to understand the genetic programs governing specific biological processes such as the development of different tumor types.

Unexpected heat shock element binding ability and tumor-killing activity of the combinatorial function domain of apoptin

Apoptin, derived from the chicken anemia virus, has been found to exert tumor-preferential apoptotic activity. It is a potential anticancer agent with direct clinical applications. However, if this viral protein were to be used as a new drug, it might also induce a strong immune response, causing toxic side effects. In a previous study, our group showed that TAT-apoptin downregulates the stress expression of heat shock protein 70 by competing with heat shock factor protein 1 in binding to the heat shock element (HSE) of the promoter region of heat shock protein 70, thus inducing specific apoptosis in HepG2 cells. In this study, we investigated the HSE-binding properties of the minimal functional region of apoptin. We showed that apoptin's nuclear localization signals 1 and nuclear localization signals 2 represented functional regions that could bind with HSE and that this binding capacity was increased by polymers formed through the introduction of a leucine-rich stretch. Our data also showed that truncated combinatorial apoptin peptide has greater tumor-specific cell-killing activity and could be a potential antitumor agent.

Correcting binding parameters for interacting ligand-lattice systems

Binding of ligands to macromolecules is central to many functional and regulatory biological processes. Key parameters characterizing ligand-macromolecule interactions are the stoichiometry, inducing the number of ligands per macromolecule binding site, and the dissociation constant, quantifying the ligand-binding site affinity. Both these parameters can be obtained from analyses of classical saturation experiments using the standard binding equation that offers the great advantage of mathematical simplicity but becomes an approximation for situations of interest when a ligand binds and covers more than one single binding site on the macromolecule. Using the framework of car-parking problem with latticelike macromolecules where each ligand can cover simultaneously several consecutive binding sites, we showed that employing the standard analysis leads to underestimation of binding parameters, i.e., ligands appear larger than they actually are and their affinity is also greater than it is. Therefore, we have derived expressions allowing to determine the ligand size and true binding parameters (stoichiometry and dissociation constant) as a function of apparent binding parameters retrieved from standard saturation experiments.

DNA Occupancy of Polymerizing Transcription Factors: A Chemical Model of the ETS Family Factor Yan

Transcription factors use both protein-DNA and protein-protein interactions to assemble appropriate complexes to regulate gene expression. Although most transcription factors operate as monomers or dimers, a few, including the E26 transformation-specific family repressors Drosophila melanogaster Yan and its human homolog TEL/ETV6, can polymerize. Although polymerization is required for both the normal and oncogenic function of Yan and TEL/ETV6, the mechanisms by which it influences the recruitment, organization, and stability of transcriptional complexes remain poorly understood. Further, a quantitative description of the DNA occupancy of a polymerizing transcription factor is lacking, and such a description would have broader applications to the conceptually related area of polymerizing chromatin regulators. To expand the theoretical basis for understanding how the oligomeric state of a transcriptional regulator influences its chromatin occupancy and function, we leveraged the extensive biochemical characterization of E26 transformation-specific factors to develop a mathematical model of Yan occupancy at chemical equilibrium. We find that spreading condensation from a specific binding site can take place in a path-independent manner given reasonable values of the free energies of specific and non-specific DNA binding and protein-protein cooperativity. Our calculations show that polymerization confers upon a transcription factor the unique ability to extend occupancy across DNA regions far from specific binding sites. In contrast, dimerization promotes recruitment to clustered binding sites and maximizes discrimination between specific and non-specific sites. We speculate that the association with non-specific DNA afforded by polymerization may enable regulatory behaviors that are well-suited to transcriptional repressors but perhaps incompatible with precise activation.

Reverse engineering gene regulatory networks from measurement with missing values

Background

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values.

Results

We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.

Conclusion

PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

Electronic supplementary material

The online version of this article (doi:10.1186/s13637-016-0055-8) contains supplementary material, which is available to authorized users.

Genomic Targets and Features of BarA-UvrY (-SirA) Signal Transduction Systems

The two-component signal transduction system BarA-UvrY of Escherichia coli and its orthologs globally regulate metabolism, motility, biofilm formation, stress resistance, virulence of pathogens and quorum sensing by activating the transcription of genes for regulatory sRNAs, e.g. CsrB and CsrC in E. coli. These sRNAs act by sequestering the RNA binding protein CsrA (RsmA) away from lower affinity mRNA targets. In this study, we used ChIP-exo to identify, at single nucleotide resolution, genomic sites for UvrY (SirA) binding in E. coli and Salmonella enterica. The csrB and csrC genes were the strongest targets of crosslinking, which required UvrY phosphorylation by the BarA sensor kinase. Crosslinking occurred at two sites, an inverted repeat sequence far upstream of the promoter and a site near the -35 sequence. DNAse I footprinting revealed specific binding of UvrY in vitro only to the upstream site, indicative of additional binding requirements and/or indirect binding to the downstream site. Additional genes, including cspA, encoding the cold-shock RNA-binding protein CspA, showed weaker crosslinking and modest or negligible regulation by UvrY. We conclude that the global effects of UvrY/SirA on gene expression are primarily mediated by activating csrB and csrC transcription. We also used in vivo crosslinking and other experimental approaches to reveal new features of csrB/csrC regulation by the DeaD and SrmB RNA helicases, IHF, ppGpp and DksA. Finally, the phylogenetic distribution of BarA-UvrY was analyzed and found to be uniquely characteristic of γ-Proteobacteria and strongly anti-correlated with fliW, which encodes a protein that binds to CsrA and antagonizes its activity in Bacillus subtilis. We propose that BarA-UvrY and orthologous TCS transcribe sRNA antagonists of CsrA throughout the γ-Proteobacteria, but rarely or never perform this function in other species.

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.

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.

Binding polynomial in molecular self-assembly

In the present work the concept of a binding polynomial is revisited for the most widely used case of self-assembly of identical molecular units and results in the re-construction of a link to the grand partition function of such a system. It is found that if the self-assembly process is not pronounced (i.e., the product of the equilibrium constant and the monomer concentration is close to zero), the binding polynomial has the meaning of a molecular partition function that is given by the summation over energy levels of any molecule in the system. In other cases the concept of a binding polynomial may be misleading.

Genome-wide analysis of H4K5 acetylation associated with fear memory in mice

BACKGROUND

Histone acetylation has been implicated in learning and memory in the brain, however, its function at the level of the genome and at individual genetic loci remains poorly investigated. This study examines a key acetylation mark, histone H4 lysine 5 acetylation (H4K5ac), genome-wide and its role in activity-dependent gene transcription in the adult mouse hippocampus following contextual fear conditioning.

RESULTS

Using ChIP-Seq, we identified 23,235 genes in which H4K5ac correlates with absolute gene expression in the hippocampus. However, in the absence of transcription factor binding sites 150 bp upstream of the transcription start site, genes were associated with higher H4K5ac and expression levels. We further establish H4K5ac as a ubiquitous modification across the genome. Approximately one-third of all genes have above average H4K5ac, of which ~15% are specific to memory formation and ~65% are co-acetylated for H4K12. Although H4K5ac is prevalent across the genome, enrichment of H4K5ac at specific regions in the promoter and coding region are associated with different levels of gene expression. Additionally, unbiased peak calling for genes differentially acetylated for H4K5ac identified 114 unique genes specific to fear memory, over half of which have not previously been associated with memory processes.

CONCLUSIONS

Our data provide novel insights into potential mechanisms of gene priming and bookmarking by histone acetylation following hippocampal memory activation. Specifically, we propose that hyperacetylation of H4K5 may prime genes for rapid expression following activity. More broadly, this study strengthens the importance of histone posttranslational modifications for the differential regulation of transcriptional programs in cognitive processes.

Taking into account nucleosomes for predicting gene expression

The eukaryotic genome is organized in a chain of nucleosomes that consist of 145-147 bp of DNA wrapped around a histone octamer protein core. Binding of transcription factors (TF) to nucleosomal DNA is frequently impeded, which makes it a challenging task to calculate TF occupancy at a given regulatory genomic site for predicting gene expression. Here, we review methods to calculate TF binding to DNA in the presence of nucleosomes. The main theoretical problems are (i) the computation speed that is becoming a bottleneck when partial unwrapping of DNA from the nucleosome is considered, (ii) the perturbation of the binding equilibrium by the activity of ATP-dependent chromatin remodelers, which translocate nucleosomes along the DNA, and (iii) the model parameterization from high-throughput sequencing data and fluorescence microscopy experiments in living cells. We discuss strategies that address these issues to efficiently compute transcription factor binding in chromatin.

Computational models for large-scale simulations of facilitated diffusion

The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process.

Conformational fluctuations of a protein-DNA complex and the structure and ordering of water around it

Protein-DNA binding is an important process responsible for the regulation of genetic activities in living organisms. The most crucial issue in this problem is how the protein recognizes the DNA and identifies its target base sequences. Water molecules present around the protein and DNA are also expected to play an important role in mediating the recognition process and controlling the structure of the complex. We have performed atomistic molecular dynamics simulations of an aqueous solution of the protein-DNA complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. The conformational fluctuations of the protein and DNA and the microscopic structure and ordering of water around them in the complex have been explored. In agreement with experimental studies, the calculations reveal conformational immobilization of the terminal segments of the protein on complexation. Importantly, it is discovered that both structural adaptations of the protein and DNA, and the subsequent correlation between them to bind, contribute to the net entropy loss associated with the complex formation. Further, it is found that water molecules around the DNA are more structured with significantly higher density and ordering than that around the protein in the complex.

Calculating transcription factor binding maps for chromatin

Current high-throughput experiments already generate enough data for retrieving the DNA sequence-dependent binding affinities of transcription factors (TF) and other chromosomal proteins throughout the complete genome. However, the reverse task of calculating binding maps in a chromatin context for a given set of concentrations and TF affinities appears to be even more challenging and computationally demanding. The problem can be addressed by considering the DNA sequence as a one-dimensional lattice with units of one or more base pairs. To calculate protein occupancies in chromatin, one needs to consider the competition of TF and histone octamers for binding sites as well as the partial unwrapping of nucleosomal DNA. Here, we consider five different classes of algorithms to compute binding maps that include the binary variable, combinatorial, sequence generating function, transfer matrix and dynamic programming approaches. The calculation time of the binary variable algorithm scales exponentially with DNA length, which limits its use to the analysis of very small genomic regions. For regulatory regions with many overlapping binding sites, potentially applicable algorithms reduce either to the transfer matrix or dynamic programming approach. In addition to the recently proposed transfer matrix formalism for TF access to the nucleosomal organized DNA, we develop here a dynamic programming algorithm that accounts for this feature. In the absence of nucleosomes, dynamic programming outperforms the transfer matrix approach, but the latter is faster when nucleosome unwrapping has to be considered. Strategies are discussed that could further facilitate calculations to allow computing genome-wide TF binding maps.

Nucleosome mediated crosstalk between transcription factors at eukaryotic enhancers

A recent study of transcription regulation in Drosophila embryonic development revealed a complex non-monotonic dependence of gene expression on the distance between binding sites of repressor and activator proteins at the corresponding enhancer cis-regulatory modules (Fakhouri et al 2010 Mol. Syst. Biol. 6 341). The repressor efficiency was high at small separations, low around 30 bp, reached a maximum at 50-60 bp, and decreased at larger distances to the activator binding sites. Here, we propose a straightforward explanation for the distance dependence of repressor activity by considering the effect of the presence of a nucleosome. Using a method that considers partial unwrapping of nucleosomal DNA from the histone octamer core, we calculated the dependence of activator binding on the repressor-activator distance and found a quantitative agreement with the distance dependence reported for the Drosophila enhancer element. In addition, the proposed model offers explanations for other distance-dependent effects at eukaryotic enhancers.

A lattice model for transcription factor access to nucleosomal DNA

Nucleosomes, the basic repeating unit of chromatin, consist of 147 basepairs of DNA that are wrapped in almost two turns around a histone protein octamer core. Because ∼3/4 of the human genomic DNA is found within nucleosomes, their position and DNA interaction is an essential determinant for the DNA access of gene-specific transcription factors and other proteins. Here, a DNA lattice model was developed for describing ligand binding in the presence of a nucleosome. The model takes into account intermediate states, in which DNA is partially unwrapped from the histone octamer. This facilitates access of transcription factors to up to 60 DNA basepairs located in the outer turn of nucleosomal DNA, while the inner DNA turn was found to be more resistant to competitive ligand binding. As deduced from quantitative comparisons with recently published experimental data, our model provides a better description than the previously used all-or-none lattice-binding model. Importantly, nucleosome-occupancy maps predicted by the nucleosome-unwrapping model also differed significantly when partial unwrapping of nucleosomal DNA was considered. In addition, large effects on the cooperative binding of transcription factors to multiple binding sites occluded by the nucleosome were apparent. These findings indicate that partial unwrapping of DNA from the histone octamer needs to be taken into account in quantitative models of gene regulation in chromatin.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.