Torsional behavior of chromatin is modulated by rotational phasing of nucleosomes.

Torsionally stressed DNA plays a critical role in genome organization and regulation. While the effects of torsional stresses on naked DNA have been well studied, little is known about how these stresses propagate within chromatin and affect its organization. Here we investigate the torsional behavior of nucleosome arrays by means of Brownian dynamics simulations of a coarse-grained model of chromatin. Our simulations reveal a strong dependence of the torsional response on the rotational phase angle Ψ0 between adjacent nucleosomes. Extreme values of Ψ0 lead to asymmetric, bell-shaped extension-rotation profiles with sharp maxima shifted toward positive or negative rotations, depending on the sign of Ψ0, and to fast, irregular propagation of DNA twist. In contrast, moderate Ψ0 yield more symmetric profiles with broad maxima and slow, uniform propagation of twist. The observed behavior is shown to arise from an interplay between nucleosomal transitions into states with crossed and open linker DNAs and global supercoiling of arrays into left- and right-handed coils, where Ψ0 serves to modulate the energy landscape of nucleosomal states. Our results also explain the torsional resilience of chromatin, reconcile differences between experimentally measured extension-rotation profiles, and suggest a role of torsional stresses in regulating chromatin assembly and organization.

Scraping and stapling of end-grafted DNA chains by a bioadhesive spreading vesicle to reveal chain internal friction and topological complexity.

Stained end-grafted DNA molecules about 20 µm long are scraped away and stretched out by the spreading front of a bioadhesive vesicle. Tethered biotin ligands bind the vesicle bilayer to a streptavidin substrate, stapling the DNAs into frozen confinement paths. Image analysis of the stapled DNA gives access, within optical resolution, to the local stretching values of individual DNA molecules swept by the spreading front, and provides evidence of self-entanglements.

Reptation of a semiflexible polymer through porous media.

We study the motion of a single stiff semiflexible filament of length S through an array of topological obstacles. By means of scaling arguments and two-dimensional computer simulations, we show that the stiff chain kinetics follows the reptation picture, albeit with kinetic exponents (for the central monomer) different from those for flexible chain reptation. At early times when topological constraints are irrelevant, the chain kinetics is the anisotropic dynamics of a free filament. After the entanglement time tau(e) transverse modes are equilibrated under the topological constraints, but the chain is not yet correlated over its whole length. During the relaxation of longitudinal modes, both the longitudinal fluctuation of the central monomer and the longitudinal correlation length grow as approximately sqrt t. After time tau(r) approximately S(2) chain ends are correlated, the chain then diffuses globally along the tube and tube renewal takes place. In the reptation regime, the longitudinal fluctuation of the central monomer grows like approximately t(1). The opening of the intermediate approximately sqrt t regime, absent for a free filament, is a signature of the reptation process. Although the underlying physics is quite different, the intermediate regime is reminiscent of the internal Rouse mode relaxation found for reptating flexible chains. In most cases asymptotic power laws from scaling could be complemented by prefactors calculated analytically. Our results are supported by two-dimensional Langevin simulations with fixed obstacles via evaluation of the mean squared displacement of the central monomer. The scaling theory can be extended to long semiflexible polymers adopting random-walk equilibrium configurations and should also apply in three dimensions for porous media with pore diameter smaller than the persistence length of the filament.

Relaxation of a semiflexible grafted polymer.

The relaxation of single grafted semiflexible chains freely rotating around the grafting point is investigated by means of two dimensional computer simulations and scaling arguments. Both free chains and chains surrounded by topological obstacles are considered. We compute the autocorrelation of the end-to-end vector for the whole chain and for terminal sections of various lengths. Our results are relevant for the relaxation of star polymers with stiff arms or branched semiflexible polymers moving in an array of obstacles.

Free-energy landscape of mono- and dinucleosomes: Enhanced rotational flexibility of interconnected nucleosomes.

The nucleosome represents the basic unit of eukaryotic genome organization, and its conformational fluctuations play a crucial role in various cellular processes. Here we provide insights into the flipping transition of a nucleosome by computing its free-energy landscape as a function of the linking number and nucleosome orientation using the density-of-states Monte Carlo approach. To investigate how the energy landscape is affected by the presence of neighboring nucleosomes in a chromatin fiber, we also compute the free-energy landscape for a dinucleosome array. We find that the mononucleosome is bistable between conformations with negatively and positively crossed linkers while the conformation with open linkers appears as a transition state. The dinucleosome exhibits a markedly different energy landscape in which the conformation with open linkers populates not only the transition state but also the global minimum. This enhanced stability of the open state is attributed to increased rotational flexibility of nucleosomes arising from their mechanical coupling with neighboring nucleosomes. Our results provide a possible mechanism by which chromatin may enhance the accessibility of its DNA and facilitate the propagation and mitigation of DNA torsional stresses.

Extracting intrinsic dynamic parameters of biomolecular folding from single-molecule force spectroscopy experiments.

Single-molecule studies in which a mechanical force is transmitted to the molecule of interest and the molecular extension or position is monitored as a function of time are versatile tools for probing the dynamics of protein folding, stepping of molecular motors, and other biomolecular processes involving activated barrier crossing. One complication in interpreting such studies, however, is the fact that the typical size of a force probe (e.g., a dielectric bead in optical tweezers or the atomic force microscope tip/cantilever assembly) is much larger than the molecule itself, and so the observed molecular motion is affected by the hydrodynamic drag on the probe. This presents the experimenter with a nontrivial task of deconvolving the intrinsic molecular parameters, such as the intrinsic free energy barrier and the effective diffusion coefficient exhibited while crossing the barrier from the experimental signal. Here we focus on the dynamical aspect of this task and show how the intrinsic diffusion coefficient along the molecular reaction coordinate can be inferred from single-molecule measurements of the rates of biomolecular folding and unfolding. We show that the feasibility of accomplishing this task is strongly dependent on the relationship between the intrinsic molecular elasticity and that of the linker connecting the molecule to the force probe and identify the optimal range of instrumental parameters allowing determination of instrument-free molecular dynamics.

Competition between B-Z and B-L transitions in a single DNA molecule: Computational studies.

Under negative torsion, DNA adopts left-handed helical forms, such as Z-DNA and L-DNA. Using the random copolymer model developed for a wormlike chain, we represent a single DNA molecule with structural heterogeneity as a helical chain consisting of monomers which can be characterized by different helical senses and pitches. By Monte Carlo simulation, where we take into account bending and twist fluctuations explicitly, we study sequence dependence of B-Z transitions under torsional stress and tension focusing on the interaction with B-L transitions. We consider core sequences, (GC)_{n} repeats or (TG)_{n} repeats, which can interconvert between the right-handed B form and the left-handed Z form, imbedded in a random sequence, which can convert to left-handed L form with different (tension dependent) helical pitch. We show that Z-DNA formation from the (GC)_{n} sequence is always supported by unwinding torsional stress but Z-DNA formation from the (TG)_{n} sequence, which are more costly to convert but numerous, can be strongly influenced by the quenched disorder in the surrounding random sequence.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond.

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Kinetics of a semiflexible chain under external force.

The kinetic properties of a semiflexible chain subject to an external force are investigated using scaling arguments and computer simulations. By monitoring the mean square displacements in principal axes, the authors found that the anisotropic dynamic fluctuations go through several distinct kinetic regimes characterized by two different exponents corresponding to transverse and longitudinal fluctuations. When a force is applied at one chain end, the tension propagates gradually to the other end, leading to nonuniform tension profiles. At short times, they observe sublinear relaxation of the mean square fluctuations in both longitudinal and transverse directions. At intermediate times, the kinetics is dominated by tension driven straightening with smaller kinetic exponents. Nonuniform tension profiles lead to the superlinear dependence of the longitudinal mean square displacement. In contrast, the late stage relaxation is diffusive again once the tension profile becomes uniform. The detailed tension profiles are reported for constant force measurement as well as constant pulling speed measurement.