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.     

Comment on the paper “Comparison of the measured phase diagrams in the force-temperature plane for the unzipping of two different natural DNA sequences” by C.H. Lee, C. Danilowicz, V.W Coljee, and M. Prentiss

The paper by Lee et al. describes the experiments on the unzipping of λ DNA sequences as a function of force and temperature. This comment aims to stress that the unzipping takes place out of equilibrium due to high sequence-dependent free-energy barriers. The force at which a heterogeneous sequence is unzipped therefore depends on the experimental waiting time.     

Loops in DNA: An overview of experimental and theoretical approaches

DNA loop formation plays a central role in many cellular processes. The aim of this paper is to present the state of the art and open problems regarding the experimental and theoretical approaches to DNA looping. A particular attention is devoted to the effects of the protein bridge size and of protein induced sharp DNA bending on DNA loop formation enhancement.     

Dynamics of intramolecular recognition: Base-pairing in DNA/RNA near and far from equilibrium

The physics of the base-pairing interaction in DNA and RNA molecules plays a fundamental role in biology. Past experimental and theoretical research has led to a fairly complete and quantitative understanding of the equilibrium properties such as the different phases, the melting behavior, and the response to slow stretching. The non-equilibrium behavior is even richer than might be expected on the basis of thermodynamics. However, the non-equilibrium behavior is also far less understood. Here, we review different theoretical approaches to the study of base-pairing thermodynamics and kinetics, and illustrate the rich phenomenology with several examples that use these approaches.     

Counterion vibrations in the DNA low-frequency spectra

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na⁺ , K⁺ , Rb⁺ and Cs⁺ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na⁺ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs⁺ have effect on the internal vibrations of the DNA structural elements.     

Chromatin physics: Replacing multiple, representation-centered descriptions at discrete scales by a continuous, function-dependent self-scaled model

This commentary on the inspiring works and ideas by Langowski, Mangeol et al., Lee et al., Bundschuh and Gerland, Schiessel, Vaillant et al., Lesne and Victor, Claudet and Bednar, Fuks, Allemand et al., and Blossey, all appearing in this issue (Eur. Phys. J. E 19 (2006)), expresses our felt need of novel approaches to chromatin modeling.     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

Chromatin code, local non-equilibrium dynamics, and the emergence of transcription regulatory programs

Chromatin is a, if not the, hallmark of eukaryotic life. Any molecular process entailing genomic DNA or the nucleus by default provokes or depends on chromatin structural dynamics on various space and time scales. Chromatin dynamics are result of changes in the physico-chemical properties of the chromatin constituents themselves or the nuclear environment. Chromatin has been found in the former case to undergo many different covalent enzyme-mediated chemical modifications. Their identification sheds light on the molecular mechanisms and the physico-chemical properties underlying chromatin dynamics, and allows the development of quantitative models for the chromatin fiber. The abundance of the different modifications, their dynamics, and short- as well as long-range correlation phenomena between different modifications also point to a second layer of genomic coding implemented at the level of chromatin. Especially, gene regulatory coding seems to depend on such a second-level code. The information-theoretical properties of chromatin in the context of gene regulatory coding are discussed. A model for the emergence of cellular differentiation from the intricate interplay between genomic and chromatin code is presented and discussed in light of recent experimental insights.     

Conformational transitions in single polymer molecules modeled with a complete energy landscape: continuous two-state model

An extension of the two-state Freely Jointed Chain model is presented in which the discrete energies of the two conformers are replaced by continuous functions of the conformer length. The statistical mechanics is initially developed in the Gibbs ensemble and leads to a conformational multi-state model. This is used to fit the equilibrium force-extension curve for Dextran. The continuous model also allows the use of Transfer Matrix methods to calculate all statistical properties in the Helmholtz ensemble, including thermal fluctuations. The latter are obtained with near perfect agreement to experiment.     

Stretching dynamics of semiflexible polymers

We analyze the nonequilibrium dynamics of single inextensible semiflexible biopolymers as stretching forces are applied at the ends. Based on different (contradicting) heuristic arguments, various scaling laws have been proposed for the propagation speed of the backbone tension which is induced in response to stretching. Here, we employ a newly developed unified theory to systematically substantiate, restrict, and extend these approaches. Introducing the practically relevant scenario of a chain equilibrated under some prestretching force f _pre that is suddenly exposed to a different external force f _ext at the ends, we give a concise physical explanation of the underlying relaxation processes by means of an intuitive blob picture. We discuss the corresponding intermediate asymptotics, derive results for experimentally relevant observables, and support our conclusions by numerical solutions of the coarse-grained equations of motion for the tension.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

Kinetics of protein-release by an aptamer-based DNA nanodevice

A recently introduced DNA nanodevice can be used to selectively bind or release the protein thrombin triggered by DNA effector strands. The release process is not well described by simple first or second order reaction kinetics. Here, fluorescence resonance energy transfer and fluorescence correlation spectroscopy experiments are used to explore the kinetics of the release process in detail. To this end the influence of concentration variations and also of temperature is determined. The relevant kinetic parameters are extracted from these experiments and the kinetic behavior of the system is simulated numerically using a set of rate equations. The hydrodynamic radii of the aptamer device alone and bound to thrombin are determined as well as the dissociation constant for the aptamer device-thrombin complex. The results from the experiments and a numerical simulation support the view that the DNA effector strand first binds to the aptamer device followed by the displacement of the protein.     

Unfolding designable structures

Among an infinite number of possible folds, nature has chosen only about 1000 distinct folds to form protein structures. Theoretical studies suggest that selected folds are intrinsically more designable than others; these selected folds are unusually stable, a property called the designability principle. In this paper we use the 2D hydrophobic-polar lattice model to classify structures according to their designability, and Langevin dynamics to account for their time evolution in the presence of shear flow. We demonstrate that, among all possible folds, the more designable ones are easier to unfold due to their large number of surface-core bonds.     

Activated dynamics of semiflexible polymers on structured substrates

We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.