The model of the deformation of DNA macromolecule is developed with the accounting of two types of components of deformation: external and internal. External components describe the bend, twist and stretch of the double helix. The internal component - the conformational mobility inside of the double helix. In the work the deformation of DNA macromolecule is considered taking into account the coupling of the external component (of deformation) with the internal component (of conformational change). Under the task consideration the macromolecule twist-stretch coupling and coupling between twist and internal component are taken into account. The solution obtained in these conditions for the deformation components allows changing the character of respond in stretch component on unwind (overwind) in dependence on the applied force to twist component. The changing of the character of deformation from compression to tension achieving of critical untwisting force (and vise versa the changing of the character of deformation from overwind to unwind at critical tension force)is known from the single molecular experiments. The nature of such unexpected behavior of double helix have clarified in the present work by including in consideration the internal component. The obtained solutions and their conformity to experimental results show the essential role of coupling between internal and external components in the double helix conformational mechanics under action force in pN range.
The mechanism of threshold elongation (overstretching) of DNA macromolecules under the action of external force is studied within the framework of phenomenological approach. When considering the task it is taken into account that double-stranded DNA is a polymorphic macromolecule with a set of metastable states. Accordingly to proposed mechanism, DNA threshold elongation can take place as a cooperative structural transition of macromolecule to metastable form, which is stabilized by the external force. For the description of DNA overstretching, the model included external (stretching) and inte…
We present experimental results regarding the electrotransfer of plasmid DNA into phosphatidylcholine giant unilamellar vesicles (GUVs). Our observations indicate that a direct entry is the predominant mechanism of electrotransfer. A quantitative analysis of the DNA concentration increments inside the GUVs is also performed, and we find that our experimental data are very well described by a simple theoretical model in which DNA entry is mostly driven by electrophoresis. Our theoretical framework allows for the prediction of the amount of transfered DNA as a function of the electric field para…
In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the fractal dimension $D_f\ge 2$ in the three-dimensional space, which are analyzed both numerically and \textit{via} the mean-field Flory approach. Our study is motivated by an attempt to mimic the conformational statistics of collapsed unknotted polymer rings, which are known to form compact hierarchical crumpled globules (CG) with $D_f=3$ at large scales. Re…
Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modelled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of conformational change in the model have been investigated and several reduced order models developed, the conformational dynamics as a function of the length of the oscillator chain is relatively less clear. To address this, we used a modified Lindstedt-Poincare method and numerical computations. We calculate a perturbation expansion of the frequency of the m…
I consider a generic coarse-grained model suitable for the study of bulk self-assembly of liquid crystal (LC) macromolecules. The cases include LC dendrimers, gold nanoparticles modified by polymer chains with terminating LC groups and others. The study is focused on the relation between a number of grafted chains, $N_{\rm ch}$, and the symmetry of the self-assembled bulk phases. Simple space-filling arguments are used first to estimate stability intervals for a rod-like, disc-like and spherulitic conformations in terms of $N_{\rm ch}$. These are followed by coarse-grained molecular dynamics s…
From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-loopi…
We have adsorbed plasmid PuC19 DNA on a supported bilayer. The mobility of the lipids within the bilayer ensured a 2D equilibrium of the DNA molecule. By varying the fraction of cationic lipids in the membrane, we have tuned the surface charge. Plasmids conformations were imaged by Atomic Force Microscopy (AFM).We performed two sets of experiments: deposition from salt free solution on charged bilayers and deposition from salty solutions on neutral bilayers. Plasmids can be seen as rings, completely opened structures, or tightly supercoiled plectonemes, depending on the experimental conditions…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structur…
In the present Comment we show that, contrary to the recent findings of Reisner et al. [Phys. Rev. Lett. 99, 058302 (2007)], the excluded volume effect does not play an important role in determining DNA behavior in nanochannels at low ionic strength. We argue that the DNA extension data are described very well without the notion of an effective polymer width using the entropic depletion theory due to Odijk.
Studies of circular DNA confined to nanofluidic channels are relevant both from a fundamental polymer-physics perspective and due to the importance of circular DNA molecules in vivo. We here observe the unfolding of DNA from the circular to linear configuration as a light-induced double strand break occurs, characterize the dynamics, and compare the equilibrium conformational statistics of linear and circular configurations. This is important because it allows us to determine to which extent existing statistical theories describe the extension of confined circular DNA. We find that the ratio o…
Chain-like macromolecules in solution, whether biological or synthetic, transform from a spatially extended conformation to a compact one upon change of temperature or solvent qualities. This sharp transition plays a key role in various phenomena, including DNA condensation, protein folding, and the behaviour of polymer solutions. In biological processes such as DNA condensation the collapse is sensitively induced by a small amount of added molecules. Here we derive a general criterion for the effect of such agents on conformational transitions. We find two different scenarios depending on cha…
Linear polymers with dendrons of first and second generations based on L-aspargic acid are studied by the methods of flow birefringence and electric birefringence. Optical, dipole, dynamic, and conformational properties of the macromolecules, as well as contributions to their optical anisotropy due to macroform and microform effects, are investigated. The polymers are found to possess permanent electric dipole moments and undergo reorientation in external electric and hydrodynamic fields according to large-scale rotation mechanism. A significant growth in equilibrium rigidity, optical anisotro…
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…
We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substanti…
We examine the elastic model of short circular DNA. We obtain analytic expressions for configurations, elastic energy, twist and linking number of our solutions. We find the onset of the plectonemic transition. We suggest ways to use our formalism to describe other elastic models, and to improve the current finite-element-analysis methods. We estimate the effect of thermodynamic fluctuations.
It had been proposed that overstretching double stranded DNA from the 5-5 ends will produce a new fiber form of dsDNA that is narrower than the S form that has been suggested to result when the dsDNA is overstretched from the 3-3 ends. We present the first comparison of the structures that result when dsDNA is overstretched from the 5-5, 3-3, and 3-5 ends and show that the stability of the overstretched form depends on the ends to which the force is applied. The stability also depends strongly on the ionic environment as well as the presence of reagents that bind to ssDNA.
We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal…
It is discussed that the kinetics observed by Shusterman et al. [Phys. Rev. Lett. 92, 048303] for long dsDNA is not the Rouse one and, in fact, the macromolecule behaves (approximately) as the Zimm polymer.
We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri J, Manghi M and Destainville N 2007 Phys. Rev. Lett. 99 088103). Our Discrete Helical Wormlike Chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in …
We suggested a geometric approach to address the external field influence on the DNA molecules, described by the WLC model via geometric coupling. It consists in the introduction of the effective metrics depending on the potential of the external field, with further re-definition of the arc-length parameter and of the extrinsic curvatures of the DNA molecules. It yields the nontrivial impact of the external field in the internal energy of macromolecules. We give the Hamiltonian formulation of this model and perform its preliminary analysis in the redefinition of the initial energy density.
The ubiquitous biomacromolecule DNA has an axial rigidity persistence length of ~50 nm, driven by its elegant double helical structure. While double and multiple helix structures appear widely in nature, only rarely are these found in synthetic non-chiral macromolecules. Here we describe a double helical conformation in the densely charged aromatic polyamide poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) or PBDT. This double helix macromolecule represents one of the most rigid simple molecular structures known, exhibiting an extremely high axial persistence length (~1 micrometer). We pre…
A detailed description of the conformational plasticity of double stranded DNA (ds) is a necessary framework for understanding protein-DNA interactions. Until now, however structure and kinetics of the transition from the basic conformation of ds-DNA (B state) to the 1.7 times longer and partially unwound conformation (S state) have not been defined. The force-extension relation of the ds-DNA of lambda-phage is measured here with unprecedented resolution using a dual laser optical tweezers that can impose millisecond force steps of 0.5-2 pN (25 C). This approach reveals the kinetics of the tra…
Effects of the size and concentration of depleting agents on the stabilization of the double-helix structure and DNA condensation: a single molecule force spectroscopy study
We investigate the translocation of a single stranded DNA through a pore which fluctuates between two conformations, using coupled master equations. The probability density function of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono peaked behavior, depending on the interconversion rates between the conformations, the applied electric field, and the initial conditions. The cumulative probability function of the FPT, in a field-free environment, is shown to have two regimes, characterized by fast and slow timescales. An analytical ex…
The local mechanical properties of DNA are believed to play an important role in their biological functions and DNA-based nanomechanical devices. Using a simple sphere-tip compression system, the local radial mechanical properties of DNA are systematically studied by changing the tip size. The compression simulation results for the 16 nm diameter sphere tip are well consistent with the experimental results. With the diameter of the tip decreasing, the radial compressive elastic properties under external loads become sensitive to the tip size and the local DNA conformation. There appears a sudd…
The Tethered Particle Motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dy…
Single molecule force spectroscopy of DNA strands adsorbed at surfaces is a powerful technique used in air or liquid environments to quantify their mechanical properties. Although the force responses are limited to unfolding events so far, single base detection might be possible in more drastic cleanliness conditions such as ultra high vacuum. Here, we report on high resolution imaging and pulling attempts at low temperature (5K) of a single strand DNA (ssDNA) molecules composed of 20 cytosine bases adsorbed on Au(111) by scanning probe microscopy and numerical calculations. Using electrospray…
If a semiflexible polymer confined to a narrow channel bends around by 180 degrees, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte Carlo simulations of co…
The in vivo free energy of looping double-stranded DNA by the lac repressor has a remarkable behavior whose origins are not fully understood. In addition to the intrinsic periodicity of the DNA double helix, the in vivo free energy has an oscillatory component of about half the helical period and oscillates asymmetrically with an amplitude significantly smaller than predicted by current theories. Here, we show that the in vivo behavior is accurately accounted for by the simultaneous presence of two distinct conformations of looped DNA. Our analysis reveals that these two conformations have dif…
Structural changes in giant DNA induced by the addition of the flexible polymer PEG were examined by the method of single-DNA observation. In dilute DNA conditions, individual DNA assumes a compact state via a discrete coil-globule transition, whereas in concentrated solution, DNA molecules exhibit an extended conformation via macroscopic phase segregation. The long axis length of the stretched state in DNA is about 1000 times larger than that of the compact state. Phase segregation at high DNA concentrations occurs at lower PEG concentrations than the compaction at low DNA concentrations. The…
Macromolecular crowding plays a principal role in a wide range of biological processes including gene expression, chromosomal compaction, and viral infection. However, the impact that crowding has on the dynamics of nucleic acids remains a topic of debate. To address this problem, we use single-molecule fluorescence microscopy and custom particle-tracking algorithms to investigate the impact of varying macromolecular crowding conditions on the transport and conformational dynamics of large DNA molecules. Specifically, we measure the mean-squared center-of-mass displacements, as well as the con…
All-atom simulations have become increasingly popular to study conformational and dynamical properties of nucleic acids as they are accurate and provide high spatial and time resolutions. This high resolution however comes at a heavy computational cost and within the time scales of simulations nucleic acids weakly fluctuate around their ideal structure exploring a limited set of conformations. We introduce the RBB-NA algorithm which is capable of controlling rigid base parameters in all-atom simulations of Nucleic Acids. With suitable biasing potentials this algorithm can "force" a DNA or RNA …
Using analytical approach and Monte-Carlo (MC) simulations, we study the elastic behaviour of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than 3D conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in 2D, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-be…
Single-molecule stretching experiments on DNA, RNA, and other biological macromolecules opened up the possibility of an impressive progress in many fields of Life and Medical sciences. The reliability of such experiments may be crucially limited by the possibility of determining the influence of the apparatus on the experimental outputs. Here we deduce an analytical model that we show to be coherent with previous numerical results and that quantitively reproduce AFM experimental tests on titin macromolecules and P-selectin AFM experiments with variable probe stiffnesses. We believe that the ob…
During the last decade, the laser trapping technique has been actively applied to elucidate the property of macromolecules, DNA, RNA, cytoskeleton fibres, etc. Due to the inherent difficulty in the direct trapping of single molecules at approximately 300 K, most of the current studies on laser trapping utilize the experimental technique to grasp microbeads that are attached to a single macromolecule, instead of using direct trapping. A few studies have demonstrated the applicability of laser trapping for highly packed compact DNA under a `poor' solvent condition without any beads. The present …
The nature of electrostatic interactions involving polyanions modulate the properties of both synthetic and biological macromolecules. Although intensely studied for decades the interplay of many length scales has prevented a complete resolution of some of the basic questions such as how the electrostatic persistence length ($l_e$) varies with ionic strength ($I$). In this review we describe certain characteristics of polyelectrolytes (PAs) and polyampholytes (PAs), which are polymers whose monomers have a random distribution of opposite charges. After reviewing the current theoretical underst…
Recent work indicates that twist-bend coupling plays an important role in DNA micromechanics. Here we investigate its effect on bent DNA. We provide an analytical solution of the minimum-energy shape of circular DNA, showing that twist-bend coupling induces sinusoidal twist waves. This solution is in excellent agreement with both coarse-grained simulations of minicircles and nucleosomal DNA data, which is bent and wrapped around histone proteins in a superhelical conformation. Our analysis shows that the observed twist oscillation in nucleosomal DNA, so far attributed to the interaction with t…
A polarizable environment, prominently the solvent, responds to electronic changes in biomolecules rapidly. The knowledge of conformational relaxation of the biomolecule itself, however, may be scarce or missing. In this work, we describe in detail the structural changes in DNA undergoing electron transfer between two adjacent nucleobases. We employ an approach based on averaging of tens to hundreds of thousands of nonequilibrium trajectories generated with molecular dynamics simulation, and a reduction of dimensionality suitable for DNA. We show that the conformational response of the DNA pro…
When pulled along the axis, double-strand DNA undergoes a large conformational change and elongates roughly twice its initial contour length at a pulling force about 70 pN. The transition to this highly overstretched form of DNA is very cooperative. Applying force perpendicular to the DNA axis (unzipping), double-strand DNA can also be separated into two single-stranded DNA which is a fundamental process in DNA replication. We study the DNA overstretching and unzipping transition using fully atomistic molecular dynamics (MD) simulations and argue that the conformational changes of double stran…
The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find theoreticlly and by a simple blob picture that the extension scales as fr_D where r_D is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like confor…
This study reveals that, in strong coulomb coupling regime, bending a straight and fully overcharged DNA (up to its maximal acceptance by multivalent counterions) to a circle releases some of the adsorbed (correlated)counterions but still remains fully overcharged. This phenomenon seems to be inherent to the minimum energy state of a DNA. By definition, the total electrostatic potential energy of a macroion-counterion system reaches to its lowest point at maximal acceptance of overcharging counterions that ensures the most stable conformation. This intermediate phenomenon of release of cations…
We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between neighboring base-pairs. The sugar-phosphate backbones are taken into account by semi-rigid harmonic springs with a non-zero spring length. The competition of these two interactions and the introduction of a simple geometrical constraint leads to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the Stack-of-Plates model enables us to optimize the free model parameters so as to reproduce the exper…
We study numerically the mechanical stability and elasticity properties of duplex DNA molecules within the frame of a network model incorporating microscopic degrees of freedom related with the arrangement of the base pairs. We pay special attention to the opening-closing dynamics of double-stranded DNA molecules which are forced into non-equilibrium conformations. Mechanical stress imposed at one terminal end of the DNA molecule brings it into a partially opened configuration. We examine the subsequent relaxation dynamics connected with energy exchange processes between the various degrees of…
We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dünweg [J. Chem. Phys. {\bf 111}, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio $\frac…
Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable worm-like chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40 $\pm$ 10 nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago (Marko and Siggia, …
Relying on symmetry considerations appropriate for helical biopolymers such as DNA and filamentous actin, we argue that crystalline packings of mutually repulsive helical macromolecules fall principally into two categories: unfrustrated (hexagonal) and frustrated (rhombohedral). For both cases, we construct the Landau-Ginzburg free energy for the 2D columnar-hexagonal to 3D crystalline phase transition, including the coupling between molecular displacements {\it along} biopolymer backbone to displacements in the plane of hexagonal order. We focus on the distinct elastic properties that emerge …
The base pair fluctuations and helix untwisting are examined for a circular molecule. A realistic mesoscopic model including twisting degrees of freedom and bending of the molecular axis is proposed. The computational method, based on path integral techniques, simulates a distribution of topoisomers with various twist numbers and finds the energetically most favorable molecular conformation as a function of temperature. The method can predict helical repeat, openings loci and bubble sizes for specific sequences in a broad temperature range. Some results are presented for a short DNA circle rec…
