Theory of Nucleosome Corkscrew Sliding in the Presence of Synthetic DNA Ligands

Histone octamers show a heat-induced mobility along DNA. Recent theoretical studies have established two mechanisms that are qualitatively and quantitatively compatible with in vitro experiments on nucleosome sliding: octamer repositioning through one-base-pair twist defects and through ten-base-pair bulge defects. A recent experiment demonstrated that the repositioning is strongly suppressed in the presence of minor-groove binding DNA ligands. In the present study, we give a quantitative theory for nucleosome repositioning in the presence of such ligands. We show that the experimentally observed octamer mobilities are consistent with the picture of bound ligands blocking the passage of twist defects through the nucleosome. This strongly supports the model of twist defects inducing a corkscrew motion of the nucleosome as the underlying mechanism of nucleosome sliding. We provide a theoretical estimate of the nucleosomal mobility without adjustable parameters, as a function of ligand concentration, binding affinity, binding site orientation, temperature and DNA anisotropy. Having this mobility in hand, we speculate on the interaction between a nucleosome and a transcribing RNA polymerase, and suggest a novel mechanism that might account for polymerase-induced nucleosome repositioning on short DNA templates.

Elastic correlations in nucleosomal DNA structure

The structure of DNA in the nucleosome core particle is studied using an elastic model that incorporates anisotropy in the bending energetics and twist-bend coupling. Using the experimentally determined structure of nucleosomal DNA [T. J. Richmond and C. A. Davey, Nature (London) 423, 145 (2003)], it is shown that elastic correlations exist between twist, roll, tilt, and stretching of DNA, as well as the distance between phosphate groups. The twist-bend coupling term is shown to be able to capture these correlations to a large extent, and a fit to the experimental data yields a new estimate of G = 25 nm for the value of the twist-bend coupling constant.

Nucleosome dynamics between tension-induced states

We studied the dynamical behavior of a mononucleosome under tension using a theoretical model that takes into account the nucleosomal geometry, DNA elasticity, nonspecific DNA-protein binding, and effective repulsion between the two DNA turns. Using a dynamical Monte-Carlo simulation algorithm, we demonstrate that this model shows a behavior that for an appropriate set of parameters is in quantitative agreement with data from micromanipulation experiments on individual nucleosomes. All of the parameters of the model follow from the data obtained from two types of pulling experiments, namely, constant force and constant loading rate ensembles.

Effect of bending anisotropy on the 3D conformation of short DNA loops

The equilibrium three dimensional shape of relatively short loops of DNA is studied using an elastic model that takes into account anisotropy in bending rigidities. Using a reasonable estimate for the anisotropy, it is found that cyclized DNA with lengths that are not integer multiples of the pitch take on nontrivial shapes that involve bending out of planes and formation of kinks. The effect of sequence inhomogeneity on the shape of DNA is addressed, and shown to enhance the geometrical features. These findings could shed some light on the role of DNA conformation in protein-DNA interactions.

Active nucleosome displacement: a theoretical approach

Three-quarters of eukaryotic DNA are wrapped around protein cylinders forming so-called nucleosomes that block the access to the genetic information. Nucleosomes need therefore to be repositioned, either passively (by thermal fluctuations) or actively (by molecular motors). Here we introduce a theoretical model that allows us to study the interplay between a motor protein that moves along DNA (e.g., an RNA polymerase) and a nucleosome that it encounters on its way. We aim at describing the displacement mechanisms of the nucleosome and the motor protein on a microscopic level to understand better the intricate interplay between the active step of the motor and the nucleosome-repositioning step. Different motor types (Brownian ratchet versus power-stroke mechanism) that perform very similarly under a constant load are shown to have very different nucleosome repositioning capacities.

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.

Electrostatic contribution to twist rigidity of DNA

The electrostatic contribution to the twist rigidity of DNA is studied, and it is shown that the Coulomb self-energy of the double-helical sugar-phosphate backbone makes a considerable contribution-the electrostatic twist rigidity of DNA is found to be C(elec) approximately 5 nm, which makes up about 7% of its total twist rigidity ( C(DNA) approximately 75 nm). The electrostatic twist rigidity is found, however, to depend only weakly on the salt concentration, because of a competition between two different screening mechanisms: (1) Debye screening by the salt ions in the bulk, and (2) structural screening by the periodic charge distribution along the backbone of the helical polyelectrolyte. It is found that, depending on the parameters, the electrostatic contribution to the twist rigidity could stabilize or destabilize the structure of a helical polyelectrolyte.

Geometrical correlations in the nucleosomal DNA conformation and the role of the covalent bonds rigidity

We develop a simple elastic model to study the conformation of DNA in the nucleosome core particle. In this model, the changes in the energy of the covalent bonds that connect the base pairs of each strand of the DNA double helix, as well as the lateral displacements and the rotation of adjacent base pairs are considered. We show that because of the rigidity of the covalent bonds in the sugar-phosphate backbones, the base pair parameters are highly correlated, especially, strong twist-roll-slide correlation in the conformation of the nucleosomal DNA is vividly observed in the calculated results. This simple model succeeds to account for the detailed features of the structure of the nucleosomal DNA, particularly, its more important base pair parameters, roll and slide, in good agreement with the experimental results.

Regulation of the membrane wrapping transition of a cylindrical target by cytoskeleton adhesion

The adsorption of external objects to the cell membrane often triggers cellular responses involving large deformations. In phagocytosis, upon contact with the target, the cell creates large extensions that wrap around the target and ultimately lead to its engulfment. Although active force generation, in particular by actin polymerization, is required for completion of this process, the elastic deformation of the cell membrane upon adhesion to an external object might play an important part in its initiation. In this paper, the elastic deformation of a bilayer owing to the binding of a cylindrical object is studied, taking into account the membrane bending rigidity and the surface tension, the membrane adhesion to both the external target and inner cytoskeleton. The problem is studied within the framework of the Helfrich-Hamiltonian and using force balance relations and the proper boundary conditions that are related to the adhesion energy coefficients. It is shown that membrane wrapping around the target may be a continuous or abrupt transition upon increasing the target binding energy, depending on the value of the parameter. The degree of wrapping and the shape of the membrane in the vicinity of the object are computed numerically, and analytical expressions are given for the boundaries separating the different wrapping regimes in the parameter space.

Wrapping of a nanowire by a supported lipid membrane

Internalization of particles by cells plays a crucial role for adsorbing nutrients and fighting infection. Endocytosis is one of the most important mechanisms of particle uptake, which encompasses multiple pathways. Although endocytosis is a complex mechanism involving biochemical signaling and active force generation, the energetic cost associated with the large deformations of the cell membrane wrapping around a foreign particle is an important factor controlling this process, which can be studied using quantitative physical models. Of particular interest is the competition between membrane-cytoskeleton and membrane-target adhesion. This competitive adhesion mechanism can be reproduced to some extent by studying particle wrapping by a membrane adhered to a substrate. We propose a theoretical analysis of this process. Here, we explore the wrapping of a lipid membrane around a long cylindrical object in the presence of a substrate mimicking the cytoskeleton. Using discretization of the Helfrich elastic energy, which accounts for the membrane bending rigidity and surface tension, we obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy, which includes unwrapped, partially wrapped and fully wrapped states. We provide an analytical expression for the boundary between the different regimes. While the transition to partial wrapping is independent of the membrane tension, the transition to full wrapping is very much influenced by the membrane tension. We also show that target wrapping may proceed in an asymmetric fashion in the full wrapping regime.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

DNA conformation and energy in nucleosome core: a theoretical approach

DNA conformation in complex with proteins is far from its canonical B-form. The affinity of complex formation and structure of DNA depend on its attachment configuration and sequence. In this article, we develop a mechanical model to address the problem of DNA structure and energy under deformation. DNA in nucleosome core particle is described as an example. The structure and energy of nucleosomal DNA is calculated based on its sequence and positioning state. The inferred structure has remarkable similarity with X-ray data. Although there is no sequence-specific interaction of bases and the histone core, we found considerable sequence dependency for the nucleosomal DNA positioning. The affinity of nucleosome formation for several sequences is examined and the differences are compatible with observations. We argue that structural energy determines the natural state of nucleosomal DNA and is the main reason for affinity differences in vitro. This theory can be utilized for the DNA structure and energy determination in protein-DNA complexes in general. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:17.

Distribution of counterions and interaction between two similarly charged dielectric slabs: roles of charge discreteness and dielectric inhomogeneity

The distribution of counterions and the electrostatic interaction between two similarly charged dielectric slabs is studied in the strong coupling limit. Dielectric inhomogeneities and discreteness of charge on the slabs have been taken into account. It is found that the amount of dielectric constant difference between the slabs and the environment, and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions. At small interslab separations, increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the intersurface space between the slabs and the discreteness of charge pushes them to the surfaces of the slabs. In the limit of point charges, independent of the strength of dielectric inhomogeneity, counterions distribute near the surfaces of the slabs. The interaction between the slabs is attractive at low temperatures and its strength increases with the dielectric constant difference. At room temperature, the slabs may completely attract each other, reach to an equilibrium separation, or have two equilibrium separations with a barrier in between, depending on the system parameters.

Nonlinear mechanical response of DNA due to anisotropic bending elasticity

The response of a short DNA segment to bending is studied, taking into account the anisotropy in the bending rigidities caused by the double-helical structure. It is shown that the anisotropy introduces an effective nonlinear twist-bend coupling that can lead to the formation of kinks and modulations in the curvature and/or in the twist, depending on the values of the elastic constants and the imposed deflection angle. The typical wavelength for the modulations, or the distance between the neighboring kinks is found to be set by half of the DNA pitch.

Elastic model for dinucleosome structure and energy

The equilibrium structure of a dinucleosome is studied using an elastic model that takes into account the force and torque balance conditions. Using the proper boundary conditions, it is found that the conformational energy of the problem does not depend on the length of the linker DNA. In addition it is shown that the two histone octamers are almost perpendicular to each other, and the linker DNA in short lengths is almost straight. These findings could shed some light on the role of DNA elasticity in the chromatin structure.

The characteristics of nuclear membrane fluctuations in stem cells

We analyse the stem cell nucleus shape fluctuation spectrum obtained from optical confocal microscopy on an hour time scale with 10 s resolution. In particular, we investigate the angular and time dependencies of these fluctuations, define appropriate correlation functions that reveal the fundamentally out of equilibrium nature of the observed fluctuations as well as their global anisotropy. Langevin equations respecting the symmetry of the system allow us to model the damped oscillatory behaviour of the time correlations.

Role of particle local curvature in cellular wrapping

Cellular uptake through membranes plays an important role in adsorbing nutrients and fighting infection and can be used for nanomedicine developments. Endocytosis is one of the pathways of cellular uptake which associate with elastic deformation of the membrane wrapping around the foreign particle. The deformability of the membrane is strongly regulated by the presence of a cortical cytoskeleton placed underneath the membrane. It is shown that shape and orientation of the particles influence on their internalization. Here, we study the role of particle local curvature in cellular uptake by investigating the wrapping of an elastic membrane around a long cylindrical object with an elliptical cross-section. The membrane itself is adhered to a substrate mimicking the cytoskeleton. Membrane wrapping proceeds differently whether the initial contact occurs at the target's highly curved part (vertical) or along its long side (horizontal). We obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy, which includes three distinct regimes (unwrapped, partially wrapped and fully wrapped), separated by two phase transitions. We also provide analytical expressions for the boundaries between the different regimes which confirm that the transitions strongly depend on the orientation and aspect ratio of the nanowire.

Twist-stretch correlation of DNA

We present an elastic model for B-form DNA with variable radius to study the elastic twist-stretch coupling of stretched DNA. In this model, only two strain variables as well as the changes in the energy of the hydrogen and covalent bonds of DNA during the deformation are considered. It is found that, depending on the elastic constants, the correlation between twisting and stretching of a helical molecule can be positive or negative. It is shown that for the suitable elastic constants in the model, the twist-stretch coupling of DNA behaves nonmonotonically, and contrary to intuition, the DNA twisting and stretching are positively correlated for small distortions. This result is entirely consistent with recent experimental results.

Modeling of ribosome dynamics on a ds-mRNA under an external load

Protein molecules in cells are synthesized by macromolecular machines called ribosomes. According to the recent experimental data, we reduce the complexity of the ribosome and propose a model to express its activity in six main states. Using our model, we study the translation rate in different biological relevant situations in the presence of external force and the translation through the RNA double stranded region in the absence or presence of the external force. In the present study, we give a quantitative theory for translation rate and show that the ribosome behaves more like a Brownian Ratchet motor. Our findings could shed some light on understanding behaviors of the ribosome in biological conditions.

Effects of dielectric inhomogeneity on electrostatic twist rigidity of a helical biomolecule in Debye-Hückel regime

The electrostatic interactions play a crucial role in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Hückel regime using the analytical Green function that is calculated in the paper. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as a DNA and an actin filament. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters, and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.

Theoretical study of RNA-polymerase behavior considering the backtracking state

The dynamical behavior of the RNA polymerase in the transcription process is vital to gene expression. During the transcription process, the 3' end of the transcribed RNA can be dislocated from the active site of the enzyme and as a result, the RNA polymerase goes to the backtracked state. Here, we develop a theoretical model to study the transcription process considering the backtracking state. We aim at describing the behavior of the enzyme in the backtracking state in the presence of an external force, which leads to two possibilities: (i) rescuing from the backtracking state and, (ii) the arresting of the enzyme. We study the probability and the rate of the mentioned processes. In addition, we find that entering the backtracking state behaves like the Brownian ratchet mechanism. This model could shed some light on the modeling of the transcription process and further studies on the energy landscape of the backtracking channel and the gene regulation.

Growth of nonmotile stress-responsive bacteria in 3D colonies under confining pressure

We numerically study three-dimensional colonies of nonmotile stress-responsive bacteria growing under confining isotropic pressure in a nutrient-rich environment. We develop a novel simulation method to demonstrate how imposing an external pressure leads to a denser aggregate and strengthens the mechanical interactions between bacteria. Unlike rigid confinements that prevent bacterial growth, confining pressure acts as a soft constraint and allows colony expansion with a nearly linear long-term population growth and colony size. Enhancing the mechanosensitivity reduces instantaneous bacterial growth rates and the overall colony size, though its impact is modest compared to pressure for our studied set of biologically relevant parameter values. The doubling time grows exponentially at low mechanosensitivity or pressure in our bacterial growth model. We provide an analytical estimate of the doubling time and develop a population dynamics model consistent with our simulations. Our findings align with previous experimental results for E. coli colonies under pressure. Understanding the growth dynamics of stress-responsive bacteria under mechanical stresses provides insight into their adaptive response to varying environmental conditions.

Insight into the unwrapping of the dinucleosome

Dynamics of nucleosomes, the building blocks of chromatin, has crucial effects on the expression, replication and repair of genomes in eukaryotes. Beside the constant movements of nucleosomes by thermal fluctuations, ATP-dependent chromatin remodelling complexes cause their active displacements. Here we propose a theoretical analysis of dinucleosome wrapping and unwrapping dynamics in the presence of an external force. We explore the energy landscape and configurations of a dinucleosome in different unwrapped states. Moreover, using a dynamical Monte-Carlo simulation algorithm, we demonstrate the dynamical features of the system such as the unwrapping force for partial and full wrapping processes. Furthermore, we show that in the short length of linker DNA (∼10-90 bp), asymmetric unwrapping occurs. These findings could shed some light on chromatin dynamics and gene accessibility.