Short-range interactions and size of ligands bound to DNA strongly influence adsorptive phase transition caused by long-range interactions

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.

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.

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.

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.

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

The transfer matrix methodology is proposed as a systematic tool for the statistical-mechanical description of DNA-protein-drug binding involved in gene regulation. We show that a genetic system of several cis-regulatory modules is calculable using this method, considering explicitly the site-overlapping, competitive, cooperative binding of regulatory proteins, their multilayer assembly and DNA looping. In the methodological section, the matrix models are solved for the basic types of short- and long-range interactions between DNA-bound proteins, drugs and nucleosomes. We apply the matrix method to gene regulation at the O(R) operator of phage lambda. The transfer matrix formalism allowed the description of the lambda-switch at a single-nucleotide resolution, taking into account the effects of a range of inter-protein distances. Our calculations confirm previously established roles of the contact CI-Cro-RNAP interactions. Concerning long-range interactions, we show that while the DNA loop between the O(R) and O(L) operators is important at the lysogenic CI concentrations, the interference between the adjacent promoters P(R) and P(RM) becomes more important at small CI concentrations. A large change in the expression pattern may arise in this regime due to anticooperative interactions between DNA-bound RNA polymerases. The applicability of the matrix method to more complex systems is discussed.

SCN- binding to the charged lysines of histones end domains mimics acetylation and shows the major histone-DNA interactions involved in eu and heterochromatin stabilization

SCN- binds to the charged amino group of lysines, inducing local changes in the electrostatic free energy of histones. We exploited this property to selectively perturb the histone-DNA interactions involved in the stabilization of eu and heterochromatin. Differential scanning calorimetry (DSC) was used as leading technique in combination with trypsin digestion that selectively cleaves the histone end domains. Euchromatin undergoes progressive destabilization with increasing KSCN concentration from 0 to 0.3 M. Trypsin digestion in the presence of 0.2 M KSCN show that the stability of the linker decreases as a consequence of the competitive binding of SCN- to the amino groups located in the C and N-terminal domain of H1 and H3, respectively; likewise, the release of the N-terminal domain of H4 induces an appreciable depression in both the temperature and enthalpy of melting of core particle DNA. Unfolding of heterochromatin requires, in addition to further cleavage of H4, extensive digestion of H2A and H2B, strongly suggesting that these histones stabilize the higher order structure by forming a protein network which extends throughout the heterochromatin domain.

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.