General transfer matrix formalism to calculate DNA-protein-drug binding in gene regulation: application to OR operator of phage lambda

Random sampling of ligand arrangements on a one-dimensional lattice

We introduce a transfer-matrix-based sequential sampling scheme for generating random samples of ligand arrangements on one-dimensional templates. The number of ligand types is arbitrary, the binding constants can have positional dependence, and cooperativity parameters are included. From the random arrangements, any (linear or nonlinear) observable can be calculated using sample averaging. As an example case study, we investigate the competitive binding of three ligand types (the sequence-specific binder netropsin, YOYO-1, and ethidium bromide) to a DNA molecule. We also employ our random sampling method of ligands to determine the quality of synthetically generated DNA barcodes as a function of concentration of a ligand (e.g., netropsin) in optical DNA mapping (ODM) experiments. We provide publically available softwares, with a computational time that scales linearly with the lattice size, for generating random ligand arrangements and for generating synthetic barcodes.

Theoretical investigation of functional responses of bio-molecular assembly networks

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Quantitative Frameworks for Multivalent Macromolecular Interactions in Biological Linear Lattice Systems

Multivalent macromolecular interactions underlie dynamic regulation of diverse biological processes in ever-changing cellular states. These interactions often involve binding of multiple proteins to a linear lattice including intrinsically disordered proteins and the chromosomal DNA with many repeating recognition motifs. Quantitative understanding of such multivalent interactions on a linear lattice is crucial for exploring their unique regulatory potentials in the cellular processes. In this review, the distinctive molecular features of the linear lattice system are first discussed with a particular focus on the overlapping nature of potential protein binding sites within a lattice. Then, we introduce two general quantitative frameworks, combinatorial and conditional probability models, dealing with the overlap problem and relating the binding parameters to the experimentally measurable properties of the linear lattice-protein interactions. To this end, we present two specific examples where the quantitative models have been applied and further extended to provide biological insights into specific cellular processes. In the first case, the conditional probability model was extended to highlight the significant impact of nonspecific binding of transcription factors to the chromosomal DNA on gene-specific transcriptional activities. The second case presents the recently developed combinatorial models to unravel the complex organization of target protein binding sites within an intrinsically disordered region (IDR) of a nucleoporin. In particular, these models have suggested a unique function of IDRs as a molecular switch coupling distinct cellular processes. The quantitative models reviewed here are envisioned to further advance for dissection and functional studies of more complex systems including phase-separated biomolecular condensates.

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.

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.

A Predictive Model of Antibody Binding in the Presence of IgG-Interacting Bacterial Surface Proteins

Many bacteria can interfere with how antibodies bind to their surfaces. This bacterial antibody targeting makes it challenging to predict the immunological function of bacteria-associated antibodies. The M and M-like proteins of group A streptococci (GAS) exhibit IgGFc-binding regions, which they use to reverse IgG binding orientation depending on the host environment. Unraveling the mechanism behind these binding characteristics may identify conditions under which bound IgG can drive an efficient immune response. Here, we have developed a biophysical model for describing these complex protein-antibody interactions. We show how the model can be used as a tool for studying the binding behavior of various IgG samples to M protein by performing in silico simulations and correlating this data with experimental measurements. Besides its use for mechanistic understanding, this model could potentially be used as a tool to aid in the development of antibody treatments. We illustrate this by simulating how IgG binding to GAS in serum is altered as specified amounts of monoclonal or pooled IgG is added. Phagocytosis experiments link this altered antibody binding to a physiological function and demonstrate that it is possible to predict the effect of an IgG treatment with our model. Our study gives a mechanistic understanding of bacterial antibody targeting and provides a tool for predicting the effect of antibody treatments in the presence of bacteria with IgG-modulating surface proteins.

An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-Bénard Convection

Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh–Bénard convection system which when driven out of equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out of equilibrium. This study, thus acts as a foundation for modeling a complex system as a two-state system, where the states: order and disorder can coexist as the system is driven away from equilibrium.

DNA Supercoiling: an Ancestral Regulator of Gene Expression in Pathogenic Bacteria?

DNA supercoiling acts as a global and ancestral regulator of bacterial gene expression. In this review, we advocate that it plays a pivotal role in host-pathogen interactions by transducing environmental signals to the bacterial chromosome and coordinating its transcriptional response. We present available evidence that DNA supercoiling is modulated by environmental stress conditions relevant to the infection process according to ancestral mechanisms, in zoopathogens as well as phytopathogens. We review the results of transcriptomics studies obtained in widely distant bacterial species, showing that such structural transitions of the chromosome are associated to a complex transcriptional response affecting a large fraction of the genome. Mechanisms and computational models of the transcriptional regulation by DNA supercoiling are then discussed, involving both basal interactions of RNA Polymerase with promoter DNA, and more specific interactions with regulatory proteins. A final part is specifically focused on the regulation of virulence genes within pathogenicity islands of several pathogenic bacterial species.

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.

Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long-Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Physics behind the mechanical nucleosome positioning code

The positions along DNA molecules of nucleosomes, the most abundant DNA-protein complexes in cells, are influenced by the sequence-dependent DNA mechanics and geometry. This leads to the "nucleosome positioning code", a preference of nucleosomes for certain sequence motives. Here we introduce a simplified model of the nucleosome where a coarse-grained DNA molecule is frozen into an idealized superhelical shape. We calculate the exact sequence preferences of our nucleosome model and find it to reproduce qualitatively all the main features known to influence nucleosome positions. Moreover, using well-controlled approximations to this model allows us to come to a detailed understanding of the physics behind the sequence preferences of nucleosomes.

Affinity, stoichiometry and cooperativity of heterochromatin protein 1 (HP1) binding to nucleosomal arrays

Heterochromatin protein 1 (HP1) participates in establishing and maintaining heterochromatin via its histone-modification-dependent chromatin interactions. In recent papers HP1 binding to nucleosomal arrays was measured in vitro and interpreted in terms of nearest-neighbour cooperative binding. This mode of chromatin interaction could lead to the spreading of HP1 along the nucleosome chain. Here, we reanalysed previous data by representing the nucleosome chain as a 1D binding lattice and showed how the experimental HP1 binding isotherms can be explained by a simpler model without cooperative interactions between neighboring HP1 dimers. Based on these calculations and spatial models of dinucleosomes and nucleosome chains, we propose that binding stoichiometry depends on the nucleosome repeat length (NRL) rather than protein interactions between HP1 dimers. According to our calculations, more open nucleosome arrays with long DNA linkers are characterized by a larger number of binding sites in comparison to chains with a short NRL. Furthermore, we demonstrate by Monte Carlo simulations that the NRL dependent folding of the nucleosome chain can induce allosteric changes of HP1 binding sites. Thus, HP1 chromatin interactions can be modulated by the change of binding stoichiometry and the type of binding to condensed (methylated) and non-condensed (unmethylated) nucleosome arrays in the absence of direct interactions between HP1 dimers.

Competitive binding-based optical DNA mapping for fast identification of bacteria--multi-ligand transfer matrix theory and experimental applications on Escherichia coli

We demonstrate a single DNA molecule optical mapping assay able to resolve a specific Escherichia coli strain from other strains. The assay is based on competitive binding of the fluorescent dye YOYO-1 and the AT-specific antibiotic netropsin. The optical map is visualized by stretching the DNA molecules in nanofluidic channels. We optimize the experimental conditions to obtain reproducible barcodes containing as much information as possible. We implement a multi-ligand transfer matrix method for calculating theoretical barcodes from known DNA sequences. Our method extends previous theoretical approaches for competitive binding of two types of ligands to many types of ligands and introduces a recursive approach that allows long barcodes to be calculated with standard computer floating point formats. The identification of a specific E. coli strain (CCUG 10979) is based on mapping of 50-160 kilobasepair experimental DNA fragments onto the theoretical genome using the developed theory. Our identification protocol introduces two theoretical constructs: a P-value for a best experiment-theory match and an information score threshold. The developed methods provide a novel optical mapping toolbox for identification of bacterial species and strains. The protocol does not require cultivation of bacteria or DNA amplification, which allows for ultra-fast identification of bacterial pathogens.

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.

Nucleosome repositioning links DNA (de)methylation and differential CTCF binding during stem cell development

During differentiation of embryonic stem cells, chromatin reorganizes to establish cell type-specific expression programs. Here, we have dissected the linkages between DNA methylation (5mC), hydroxymethylation (5hmC), nucleosome repositioning, and binding of the transcription factor CTCF during this process. By integrating MNase-seq and ChIP-seq experiments in mouse embryonic stem cells (ESC) and their differentiated counterparts with biophysical modeling, we found that the interplay between these factors depends on their genomic context. The mostly unmethylated CpG islands have reduced nucleosome occupancy and are enriched in cell type-independent binding sites for CTCF. The few remaining methylated CpG dinucleotides are preferentially associated with nucleosomes. In contrast, outside of CpG islands most CpGs are methylated, and the average methylation density oscillates so that it is highest in the linker region between nucleosomes. Outside CpG islands, binding of TET1, an enzyme that converts 5mC to 5hmC, is associated with labile, MNase-sensitive nucleosomes. Such nucleosomes are poised for eviction in ESCs and become stably bound in differentiated cells where the TET1 and 5hmC levels go down. This process regulates a class of CTCF binding sites outside CpG islands that are occupied by CTCF in ESCs but lose the protein during differentiation. We rationalize this cell type-dependent targeting of CTCF with a quantitative biophysical model of competitive binding with the histone octamer, depending on the TET1, 5hmC, and 5mC state.

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.

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.

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

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibria measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical-mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.

Predicting gene-regulation functions: lessons from temperate bacteriophages

Gene-regulation functions (GRF) provide a unique characteristic of a cis-regulatory module (CRM), relating the concentrations of transcription factors (input) to the promoter activities (output). The challenge is to predict GRFs from the sequence. Here we systematically consider the lysogeny-lysis CRMs of different temperate bacteriophages such as the Lactobacillus casei phage A2, Escherichia coli phages lambda, and 186 and Lactococcal phage TP901-1. This study allowed explaining a recent experimental puzzle on the role of Cro protein in the lambda switch. Several general conclusions have been drawn: 1), long-range interactions, multilayer assembly and DNA looping may lead to complex GRFs that cannot be described by linear functions of binding site occupancies; 2), in general, GRFs cannot be described by the Boolean logic, whereas a three-state non-Boolean logic suffices for the studied examples; 3), studied CRMs of the intact phages seemed to have a similar GRF topology (the number of plateaus and peaks corresponding to different expression regimes); we hypothesize that functionally equivalent CRMs might have topologically equivalent GRFs for a larger class of genetic systems; and 4) within a given GRF class, a set of mechanistic-to-mathematical transformations has been identified, which allows shaping the GRF before carrying out a system-level analysis.

Thermodynamics-based models of transcriptional regulation by enhancers: the roles of synergistic activation, cooperative binding and short-range repression

Quantitative models of cis-regulatory activity have the potential to improve our mechanistic understanding of transcriptional regulation. However, the few models available today have been based on simplistic assumptions about the sequences being modeled, or heuristic approximations of the underlying regulatory mechanisms. We have developed a thermodynamics-based model to predict gene expression driven by any DNA sequence, as a function of transcription factor concentrations and their DNA-binding specificities. It uses statistical thermodynamics theory to model not only protein-DNA interaction, but also the effect of DNA-bound activators and repressors on gene expression. In addition, the model incorporates mechanistic features such as synergistic effect of multiple activators, short range repression, and cooperativity in transcription factor-DNA binding, allowing us to systematically evaluate the significance of these features in the context of available expression data. Using this model on segmentation-related enhancers in Drosophila, we find that transcriptional synergy due to simultaneous action of multiple activators helps explain the data beyond what can be explained by cooperative DNA-binding alone. We find clear support for the phenomenon of short-range repression, where repressors do not directly interact with the basal transcriptional machinery. We also find that the binding sites contributing to an enhancer's function may not be conserved during evolution, and a noticeable fraction of these undergo lineage-specific changes. Our implementation of the model, called GEMSTAT, is the first publicly available program for simultaneously modeling the regulatory activities of a given set of sequences.

The development of complex multicellular organisms requires genes to be expressed at specific stages and in specific tissues. Regulatory DNA sequences, often called cis-regulatory modules, drive the desired gene expression patterns by integrating information about the environment in the form of the activities of transcription factors. The rules by which regulatory sequences read this type of information, however, are unclear. In this work, we developed quantitative models based on physicochemical principles that directly map regulatory sequences to the expression profiles they generate. We evaluated these models on the segmentation network of the model organism Drosophila melanogaster. Our models incorporate mechanistic features that attempt to capture how activating and repressing transcription factors work in the segmentation system. By evaluating the importance of these features, we were able to gain insights on the quantitative regulatory rules. We found that two different mechanisms may contribute to cooperative gene activation and that repressors often have a short range of influence in DNA sequences. Combining the quantitative modeling with comparative sequence analysis, we also found that even functional sequences may be lost during evolution.

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.

A biophysical model for analysis of transcription factor interaction and binding site arrangement from genome-wide binding data

Background

How transcription factors (TFs) interact with cis-regulatory sequences and interact with each other is a fundamental, but not well understood, aspect of gene regulation.

Methodology/Principal Findings

We present a computational method to address this question, relying on the established biophysical principles. This method, STAP (sequence to affinity prediction), takes into account all combinations and configurations of strong and weak binding sites to analyze large scale transcription factor (TF)-DNA binding data to discover cooperative interactions among TFs, infer sequence rules of interaction and predict TF target genes in new conditions with no TF-DNA binding data. The distinctions between STAP and other statistical approaches for analyzing cis-regulatory sequences include the utility of physical principles and the treatment of the DNA binding data as quantitative representation of binding strengths. Applying this method to the ChIP-seq data of 12 TFs in mouse embryonic stem (ES) cells, we found that the strength of TF-DNA binding could be significantly modulated by cooperative interactions among TFs with adjacent binding sites. However, further analysis on five putatively interacting TF pairs suggests that such interactions may be relatively insensitive to the distance and orientation of binding sites. Testing a set of putative Nanog motifs, STAP showed that a novel Nanog motif could better explain the ChIP-seq data than previously published ones. We then experimentally tested and verified the new Nanog motif. A series of comparisons showed that STAP has more predictive power than several state-of-the-art methods for cis-regulatory sequence analysis. We took advantage of this power to study the evolution of TF-target relationship in Drosophila. By learning the TF-DNA interaction models from the ChIP-chip data of D. melanogaster (Mel) and applying them to the genome of D. pseudoobscura (Pse), we found that only about half of the sequences strongly bound by TFs in Mel have high binding affinities in Pse. We show that prediction of functional TF targets from ChIP-chip data can be improved by using the conservation of STAP predicted affinities as an additional filter.

Conclusions/Significance

STAP is an effective method to analyze binding site arrangements, TF cooperativity, and TF target genes from genome-wide TF-DNA binding data.

Predicting nucleosome positions on the DNA: combining intrinsic sequence preferences and remodeler activities

Nucleosome positions on the DNA are determined by the intrinsic affinities of histone proteins to a given DNA sequence and by the ATP-dependent activities of chromatin remodeling complexes that can translocate nucleosomes with respect to the DNA. Here, we report a theoretical approach that takes into account both contributions. In the theoretical analysis two types of experiments have been considered: in vitro experiments with a single reconstituted nucleosome and in vivo genome-scale mapping of nucleosome positions. The effect of chromatin remodelers was described by iteratively redistributing the nucleosomes according to certain rules until a new steady state was reached. Three major classes of remodeler activities were identified: (i) the establishment of a regular nucleosome spacing in the vicinity of a strong positioning signal acting as a boundary, (ii) the enrichment/depletion of nucleosomes through amplification of intrinsic DNA-sequence-encoded signals and (iii) the removal of nucleosomes from high-affinity binding sites. From an analysis of data for nucleosome positions in resting and activated human CD4(+) T cells [Schones et al., Cell 132, p. 887] it was concluded that the redistribution of a nucleosome map to a new state is greatly facilitated if the remodeler complex translocates the nucleosome with a preferred directionality.

An ensemble model of competitive multi-factor binding of the genome

Hundreds of different factors adorn the eukaryotic genome, binding to it in large number. These DNA binding factors (DBFs) include nucleosomes, transcription factors (TFs), and other proteins and protein complexes, such as the origin recognition complex (ORC). DBFs compete with one another for binding along the genome, yet many current models of genome binding do not consider different types of DBFs together simultaneously. Additionally, binding is a stochastic process that results in a continuum of binding probabilities at any position along the genome, but many current models tend to consider positions as being either binding sites or not. Here, we present a model that allows a multitude of DBFs, each at different concentrations, to compete with one another for binding sites along the genome. The result is an "occupancy profile," a probabilistic description of the DNA occupancy of each factor at each position. We implement our model efficiently as the software package COMPETE. We demonstrate genome-wide and at specific loci how modeling nucleosome binding alters TF binding, and vice versa, and illustrate how factor concentration influences binding occupancy. Binding cooperativity between nearby TFs arises implicitly via mutual competition with nucleosomes. Our method applies not only to TFs, but also recapitulates known occupancy profiles of a well-studied replication origin with and without ORC binding. Importantly, the sequence preferences our model takes as input are derived from in vitro experiments. This ensures that the calculated occupancy profiles are the result of the forces of competition represented explicitly in our model and the inherent sequence affinities of the constituent DBFs.

Role of nucleic acid binding in Sir3p-dependent interactions with chromatin fibers

Recent studies of the mechanisms involved in the regulation of gene expression in eukaryotic organisms depict a highly complex process requiring a coordinated rearrangement of numerous molecules to mediate DNA accessibility. Silencing in Saccharomyces cerevisiae involves the Sir family of proteins. Sir3p, originally described as repressing key areas of the yeast genome through interactions with the tails of histones H3 and H4, appears to have additional roles in that process, including involvement with a DNA binding component. Our in vitro studies focused on the characterization of Sir3p-nucleic acid interactions and their biological functions in Sir3p-mediated silencing using binding assays, EM imaging, and theoretical modeling. Our results suggest that the initial Sir3p recruitment is partially DNA-driven, highly cooperative, and dependent on nucleosomal features other than histone tails. The initial step appears to be rapidly followed by the spreading of silencing using linker DNA as a track.

Matrix formalism for site-specific binding of unstructured proteins to multicomponent lipid membranes

We describe a new approach to calculate the binding of flexible peptides and unfolded proteins to multicomponent lipid membranes. The method is based on the transfer matrix formalism of statistical mechanics recently described as a systematic tool to study DNA-protein-drug binding in gene regulation. Using the energies of interaction of the individual polymer segments with different membrane lipid species and the scaling corrections due to polymer looping, we calculate polymer adsorption characteristics and the degree of sequestration of specific membrane lipids. The method is applied to the effector domain of the MARCKS (myristoylated alanine rich C kinase substrate) protein known to be involved in signal transduction through membrane binding. The calculated binding constants of the MARCKS(151-175) peptide and a series of related peptides to mixed PC/PS/PIP2 membranes are in satisfactory agreement with in vitro experiments.