Translational nucleosome positioning: A computational study.

About three-quarters of eukaryotic DNA is wrapped into nucleosomes; DNA spools with a protein core. The affinity of a given DNA stretch to be incorporated into a nucleosome is known to depend on the base-pair sequence-dependent geometry and elasticity of the DNA double helix. This causes the rotational and translational positioning of nucleosomes. In this study we ask the question whether the latter can be predicted by a simple coarse-grained DNA model with sequence-dependent elasticity, the rigid base-pair model. Whereas this model is known to be rather robust in predicting rotational nucleosome positioning, we show that the translational positioning is a rather subtle effect that is dominated by the guanine-cytosine content dependence of entropy rather than energy. A correct qualitative prediction within the rigid base-pair framework can only be achieved by assuming that DNA elasticity effectively changes on complexation into the nucleosome complex. With that extra assumption we arrive at a model which gives an excellent quantitative agreement to experimental in vitro nucleosome maps, under the additional assumption that nucleosomes equilibrate their positions only locally.

Performing SELEX experiments in silico.

Due to the sequence-dependent nature of the elasticity of DNA, many protein-DNA complexes and other systems in which DNA molecules must be deformed have preferences for the type of DNA sequence they interact with. SELEX (Systematic Evolution of Ligands by EXponential enrichment) experiments and similar sequence selection experiments have been used extensively to examine the (indirect readout) sequence preferences of, e.g., nucleosomes (protein spools around which DNA is wound for compactification) and DNA rings. We show how recently developed computational and theoretical tools can be used to emulate such experiments in silico. Opening up this possibility comes with several benefits. First, it allows us a better understanding of our models and systems, specifically about the roles played by the simulation temperature and the selection pressure on the sequences. Second, it allows us to compare the predictions made by the model of choice with experimental results. We find agreement on important features between predictions of the rigid base-pair model and experimental results for DNA rings and interesting differences that point out open questions in the field. Finally, our simulations allow application of the SELEX methodology to systems that are experimentally difficult to realize because they come with high energetic costs and are therefore unlikely to form spontaneously, such as very short or overwound DNA rings.

Designing nucleosomal force sensors.

About three quarters of our DNA is wrapped into nucleosomes: DNA spools with a protein core. It is well known that the affinity of a given DNA stretch to be incorporated into a nucleosome depends on the geometry and elasticity of the basepair sequence involved, causing the positioning of nucleosomes. Here we show that DNA elasticity can have a much deeper effect on nucleosomes than just their positioning: it affects their "identities". Employing a recently developed computational algorithm, the mutation Monte Carlo method, we design nucleosomes with surprising physical characteristics. Unlike any other nucleosomes studied so far, these nucleosomes are short-lived when put under mechanical tension whereas other physical properties are largely unaffected. This suggests that the nucleosome, the most abundant DNA-protein complex in our cells, might more properly be considered a class of complexes with a wide array of physical properties, and raises the possibility that evolution has shaped various nucleosome species according to their genomic context.

Stochastic model for nucleosome sliding under an external force.

Heat-induced diffusion of nucleosomes along DNA is an experimentally well-studied phenomenon, presumably induced by twist defects that propagate through the wrapped DNA portion. The diffusion constant depends dramatically on the local mechanical properties of the DNA and the presence of DNA-binding ligands. This has been quantitatively understood by a stochastic three-state model. Future experiments are expected to allow application of forces on the nucleosome that induce a directed sliding. By extending the three-state model, the present work studies theoretically the response of the nucleosome to such external forces and how it is affected by the mechanical properties of the DNA and the presence of DNA-binding ligands.

Kinetic proofreading of gene activation by chromatin remodeling.

Gene activation in eukaryotes involves the concerted action of histone tail modifiers, chromatin remodelers, and transcription factors, whose precise coordination is currently unknown. We demonstrate that the experimentally observed interactions of the molecules are in accord with a kinetic proofreading scheme. Our finding could provide a basis for the development of quantitative models for gene regulation in eukaryotes based on the combinatorical interactions of chromatin modifiers.

Rayleigh instability of charged aggregates: Role of the dimensionality, ionic strength, and dielectric contrast.

We extended a previous analysis of the classical Rayleigh instability of spherical charged droplets in the presence of neutralizing monovalent counterions [M. Deserno, Eur. Phys. J. E 6, 163 (2001)], by generalizing the problem for suspensions of aggregates with D-dimensional symmetry, corresponding for D = 2 to infinite (rodlike) cylindrical charged bundles and for D = 3 to spherical charged droplets. In addition, we include the effects of added monovalent salt and of dielectric contrast between the charged aggregate and the surrounding solvent. The electrostatic energy taking the microion screening into account is estimated using uniform profiles within the framework of the cell model. We verify the robustness of these results by also considering Debye-Hückel-type microion profiles that are obtained by the minimization of a linearized Poisson-Boltzmann free-energy functional. In the case when the microions can enter inside the charged aggregates, we confirm the occurrence of a discontinuous phase change between aggregates of finite size and an infinite aggregate, which takes place at a collapse temperature that depends on their volume fraction phi and on the salt content. Decrease of phi shifts the phase-change temperature toward higher values, while salt addition has an opposite effect. We obtain analytical expressions for the phase-separation line in the asymptotic limit of infinite dilution (phi-->0), showing that the collapse temperature depends logarithmically on phi . As an application for D = 3 we discuss the stability of the pearl-necklace structures of flexible polyelectrolytes in poor solvents. The case D = 2 is applied to the problem of finite bundle sizes of stiff polyelectrolytes that attract each other-via, e.g., multivalent counterions-leading to an effective surface tension.

Tail-induced attraction between nucleosome core particles.

We study a possible electrostatic mechanism underlying the compaction of DNA inside the nuclei of eucaryotes: the tail-bridging effect between nucleosomes, the fundamental DNA packaging units of the chromatin complex. As a simple model of the nucleosome we introduce the eight-tail colloid, a charged sphere with eight oppositely charged, flexible, grafted chains that represent the terminal histone tails. We show that our complexes attract each other via the formation of chain bridges and contrast this to the effect of attraction via charge patches. We demonstrate that the attraction between eight-tail colloids can be tuned by changing the fraction of charged monomers on the tails. This suggests a physical mechanism of chromatin compaction where the degree of DNA condensation is controlled via biochemical means, namely the acetylation and deacetylation of lysines in the histone tails.

Comment on "Chromatin fiber functional organization: some plausible models" by A. Lesne and J.-M. Victor.

In this comment on the contribution of A. Lesne and J.-M. Victor I provide some additional ideas on the hypothesis that higher-order chromatin structures stamp their marks on their small subunits.

The nucleosome: a transparent, slippery, sticky and yet stable DNA-protein complex.

Roughly three quarters of eucaryotic DNA are tightly wrapped onto protein cylinders organized in so-called nucleosomes. Despite this fact, the wrapped DNA cannot be inert since DNA is at the heart of many crucial life processes. We focus here on physical mechanisms that might allow nucleosomes to perform a great deal of such processes, specifically 1) on unwrapping fluctuations that give DNA-binding proteins access to the wrapped DNA portions without disrupting the nucleosome as a whole, 2) on corkscrew sliding along DNA and some implications and on 3) tail-bridging-induced attraction between nucleosomes as a means of controlling higher-order folding.

Statics and dynamics of polymer-wrapped colloids.

We study the complex between a colloidal particle and a semiflexible polymer chain that "wraps" around it. Via molecular dynamics simulation we investigate statistical and dynamical properties of this system. First we establish the dependence of wrapped chain length on absorption energy and chain persistence length and obtain the distribution of wrapped-sphere positions. Then we study the length and position distributions of thermally excited loop defects. Finally we consider the repositioning dynamics of the colloid, focusing on the case where the chain stays wrapped onto the complex. Specifically we determine the mean square displacement of the central monomer of the wrapped chain and the resulting diffusion coefficient of the chain as a function of its persistence length, absorption energy, chain length, and size of the sphere. We argue that both statics and dynamics of these complexes can be mainly understood by energetic arguments, whereas entropic contributions from the chain configurations play only a minor role.

DNA spools under tension.

DNA spools, structures in which DNA is wrapped and helically coiled onto itself or onto a protein core, are ubiquitous in nature. We develop a general theory describing the nonequilibrium behavior of DNA spools under linear tension. Two puzzling and seemingly unrelated recent experimental findings, the sudden quantized unwrapping of nucleosomes and that of DNA toroidal condensates under tension, are theoretically explained and shown to be of the same origin. The study provides new insights into nucleosome and chromatin fiber stability and dynamics.

Chromatin dynamics: nucleosomes go mobile through twist defects.

We study the spontaneous "sliding" of histone spools (nucleosomes) along DNA as a result of thermally activated single base pair twist defects. To this end we map the system onto a suitably extended Frenkel-Kontorova model. Combining results from several recent experiments we are able to estimate the nucleosome mobility without adjustable parameters. Our model shows also how the local mobility is intimately linked to the underlying base pair sequence.

Nucleosome repositioning via loop formation.

Active (catalyzed) and passive (intrinsic) nucleosome repositioning is known to be a crucial event during the transcriptional activation of certain eukaryotic genes. Here we consider theoretically the intrinsic mechanism and study in detail the energetics and dynamics of DNA-loop-mediated nucleosome repositioning, as previously proposed by earlier works. The surprising outcome of the present study is the inherent nonlocality of nucleosome motion within this model-being a direct physical consequence of the loop mechanism. On long enough DNA templates the longer jumps dominate over the previously predicted local motion, a fact that contrasts simple diffusive mechanisms considered before. The possible experimental outcome resulting from the considered mechanism is predicted, discussed, and compared to existing experimental findings.

Where the linearized Poisson-Boltzmann cell model fails: the planar case as a prototype study.

The linearized Poisson-Boltzmann (PB) approximation is investigated for the classical problem of two infinite, uniformly charged planes in electrochemical equilibrium with an infinite monovalent salt reservoir. At the nonlinear level, we obtain an explicit expression of the associated electrostatic contribution to the semi-grand-canonical potential. The linearized osmotic-pressure difference between the interplane region and the salt reservoir becomes negative in the low-temperature, large-separation, or high-surface charge limits, in disagreement with the exact (at mean-field level) nonlinear PB solution. We show that these artifacts--although thermodynamically consistent with quadratic expansions of the nonlinear functional--can be traced back to the nonfulfillment of the underlying assumptions of the linearization. Explicit comparison between the analytical expressions of the exact nonlinear solution and the corresponding linearized equations allows us to show that the linearized results are asymptotically exact in the weak-coupling and counterionic ideal-gas limits, but always fail otherwise, predicting negative osmotic-pressure differences. By taking appropriate limits of the full nonlinear PB solution, we provide asymptotic expressions for the semi-grand-canonical potential and the osmotic-pressure difference that involve only elementary functions, which cover the complementary region where the linearized theory breaks down.

Defect-induced perturbations of atomic monolayers on solid surfaces.

We study long-range morphological changes in atomic monolayers on solid substrates induced by different types of defects; e.g., by monoatomic steps in the surface, or by the tip of an atomic force microscope (AFM), placed at some distance above the substrate. Representing the monolayer in terms of a suitably extended Frenkel-Kontorova-type model, we calculate the defect-induced density profiles for several possible geometries. In case of an AFM tip, we also determine the extra force exerted on the tip due to the tip-induced dehomogenization of the monolayer.

Polymer reptation and nucleosome repositioning.

We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem arises in the case of globular aggregates of proteins (histones) that are wound by DNA in the chromosomes of plants and animals; these beads (nucleosomes) are multiply wrapped and yet are able to reposition themselves over long distances, while remaining bound by the DNA chain.

DNA folding: structural and mechanical properties of the two-angle model for chromatin.

We present a theoretical analysis of the structural and mechanical properties of the 30-nm chromatin fiber. Our study is based on the two-angle model introduced by Woodcock et al. (Woodcock, C. L., S. A. Grigoryev, R. A. Horowitz, and N. Whitaker. 1993. Proc. Natl. Acad. Sci. USA. 90:9021-9025) that describes the chromatin fiber geometry in terms of the entry-exit angle of the nucleosomal DNA and the rotational setting of the neighboring nucleosomes with respect to each other. We analytically explore the different structures that arise from this building principle, and demonstrate that the geometry with the highest density is close to the one found in native chromatin fibers under physiological conditions. On the basis of this model we calculate mechanical properties of the fiber under stretching. We obtain expressions for the stress-strain characteristics that show good agreement with the results of recent stretching experiments (Cui, Y., and C. Bustamante. 2000. Proc. Natl. Acad. Sci. USA. 97:127-132) and computer simulations (Katritch, V., C. Bustamante, and W. K. Olson. 2000. J. Mol. Biol. 295:29-40), and which provide simple physical insights into correlations between the structural and elastic properties of chromatin.