We introduce a three-state model for a single DNA chain under tension that distinguishes between B-DNA, S-DNA and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ~ - c ln n for the entropy of a loop of length n. Force extension curves are derived exactly employing a generalized Poland-Scheraga approach and compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy, entering as a domain-wall energy between paired and unpaired bases, and the loop entropy are separated. Therefore we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.
We present a phenomenological dynamical model able to describe the stretching features of the curve of DNA length vs applied force. As concerns the chain, the model is based on the discrete wormlike chain model with elastic modifications, which properly describes the elongation features at low and intermediate forces. The dynamics is developed under a double-well potential with a linear term, which, at high forces, accounts for the narrow transition present in the DNA elongation (overstretching). A quite good agreement between simulation and experiment is obtained.
We present a perturbation theory to find the response of an anisotropic DNA to the external tension. It is shown that the anisotropy has a nonzero but small contribution to the force-extension curve of the DNA. Thus an anisotropic DNA behaves like an isotropic one with an effective bending constant equal to the harmonic average of its soft and hard bending constants.
DNA is structurally and mechanically altered by the binding of intercalator molecules. Intercalation strongly affects the force-extension behavior of DNA, in particular the overstretching transition. We present a statistical model that captures all relevant findings of recent force-extension experiments. Two predictions from our model are presented. The first suggests the existence of a novel hyper-stretching regime in the presence of intercalators and the second, a linear dependence of the overstretching force on intercalator concentration, is verified by re-analyzing available experimental d…
We show that the simple analytical model proposed by Zhang and Marko (Phys. Rev. E 77, 031916 (2008)) to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.
In order to interpret recent experimental studies of the dependence of conductance of ds-DNA as the DNA is pulled from the 3'end1-3'end2 ends, which find a sharp conductance jump for a very short (4.5 %) stretching length, we carried out multiscale modeling, to predict the conductance of dsDNA as it is mechanically stretched to promote various structural polymorphisms. We calculate the current along the stretched DNA using a combination of molecular dynamics simulations, non-equilibrium pulling simulations, quantum mechanics calculations, and kinetic Monte Carlo simulations. For 5'end1-5'end2 …
By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA…
A promising new method for measuring intramolecular distances in solution uses small-angle X-ray scattering interference between gold nanocrystal labels (Mathew-Fenn et al, Science, 322, 446 (2008)). When applied to double stranded DNA, it revealed that the DNA length fluctuations are strikingly strong and correlated over at least 80 base pair steps. In other words, the DNA behaves as accordion bellows, with distant fragments stretching and shrinking concertedly. This hypothesis, however, disagrees with earlier experimental and computational observations. This Letter shows that the discrepancy…
The complex mechanisms governing charge migration in DNA oligomers reflect the rich structural and electronic properties of the molecule of life. Controlling the mechanical stability of DNA nanowires in charge transport experiments is a requisite for identifying intrinsic issues responsible for long range charge transfers. By merging density-functional-theory-based calculations and model-Hamiltonian approaches, we have studied DNA quantum transport during the stretching-twisting process of poly(GC) DNA oligomers. During the stretching process, local maxima in the charge transfer integral t bet…
A three dimensional mesoscopic model is applied to study the properties of short DNA chains in a confining environment. The cylindrical channel is represented by a hard-wall repulsive potential incorporated in the system Hamiltonian. The macroscopic helical parameters are computed performing statistical averages over the ensemble of microscopic base pair fluctuations. The average molecule elongation, measured by the end-to-end distance, is derived as a function of the channel potential parameters both for a homogeneous and a heterogeneous chain. The overall results suggest that the mesoscopic …
We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality as the numerical evaluation of Marko's and Siggia's variational…
Mechanical properties of DNA, in particular their stretch dependent extension and their loop formation characteristics, have been recognized as an effective probe for understanding the possible biochemical role played by them in a living cell. Single stranded DNA (ssDNA), which, till recently was presumed to be an simple flexible polymer continues to spring surprises. Synthetic ssDNA, like polydA (polydeoxyadenosines) has revealed an intriguing force-extension (FX) behavior exhibiting two plateaus, absent in polydT (polydeoxythymidines) for example. Loop closing time in polydA had also been fo…
In order to improve the accuracy of molecular dynamics simulations, classical force fields are supplemented with a kernel-based machine learning method trained on quantum-mechanical fragment energies. As an example application, a potential-energy surface is generalised for a small DNA duplex, taking into account explicit solvation and long-range electron exchange--correlation effects. Study of the corrected potential energy versus extension shows that leading classical DNA models have excessive stiffness with respect to stretching. This discrepancy is found to be common across multiple forcefi…
Single molecule experiments on B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. It has been proposed that the first transition, at forces of 60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance f…
Single molecule experiments on single- and double stranded DNA have sparked a renewed interest in the force-extension of polymers. The extensible Freely Jointed Chain (FJC) model is frequently invoked to explain the observed behavior of single-stranded DNA. We demonstrate that this model does not satisfactorily describe recent high-force stretching data. We instead propose a model (the Discrete Persistent Chain, or ``DPC'') that borrows features from both the FJC and the Wormlike Chain, and show that it resembles the data more closely. We find that most of the high-force behavior previously at…
The flexibility of short DNA fragments is studied by a Hamiltonian model which treats the inter-strand and intra-strand forces at the level of the base pair. The elastic response of a set of homogeneous helices to externally applied forces is obtained by computing the average bending angles between adjacent base pairs along the molecule axis. The ensemble averages are performed over a room temperature equilibrium distribution of base pair separations and bending fluctuations. The analysis of the end-to-end distances and persistence lengths shows that even short sequences with less than $100$ b…
We report a structural polymorphism of the S-DNA when a canonical B-DNA is stretched under different pulling protocols and provide a fundamental molecular understanding of the DNA stretching mechanism. Extensive all atom molecular dynamics simulations reveal a clear formation of S-DNA when the B-DNA is stretched along the 3' directions of the opposite strands (OS3) and is characterized by the changes in the number of H-bonds, entropy and free energy. Stretching along 5' directions of the opposite strands (OS5) leads to force induced melting form of the DNA. Interestingly, stretching along the …
We have performed single molecule stretching experiments and dynamic light scattering (DLS) in order to characterize the interaction between the DNA molecule and the fluorescent stain GelRed. The results from single molecule stretching show that the persistence length of the DNA-GelRed complexes increases as the ligand concentration increases up to some critical concentration, then decreasing for higher concentrations. The contour length of the complexes, on the other hand, increases monotonically as a function of GelRed concentration, suggesting that intercalation is the main binding mechanis…
The quite recent technological rise in molecular biology allowed single molecule manipulation experiments, where molecule stretching plays a primary role. In order to understand the experimental data, it is felt the urge of some physical and mathematical models to quantitatively express the mechanical properties of the observed molecules. In this paper we reconsider a simple phenomenological model which reproduces the behaviour of single and double stranded DNA under tension. The problem is easily solved via the cavity method both in the small forces range and in presence of overstretching tra…
Combining two-color infared pump-probe spectroscopy and anharmonic force field calculations we characterize the anharmonic coupling patterns between fingerprint modes and the hydrogen-bonded symmetric NH$_2$ stretching vibration in adenine-thymine dA$_{20}$-dT$_{20}$ DNA oligomers. Specifically, it is shown that the anharmonic coupling between the NH$_2$ bending and the CO stretching vibration, both absorbing around 1665 cm-1, can be used to assign the NH$_2$ fundamental transition at 3215 cm-1 despite the broad background absorption of water.
DNA and Carbon nanotubes (CNTs) have unique physical, mechanical and electronic properties that make them revolutionary materials for advances in technology. In state-of-the-art applications, these physical properties can be exploited to design a type of bio-nanorobot. In this paper, we present the behaviors of DNA-based nanotweezers and show the capabilities of controlling the robotic device. The theoretical calculations are based on the Englander-Peyrard-Bishop model for DNA. Furthermore, the influence of the Casimir force between on the opening and closing of nanotweezers is studied in comp…
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force--elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double--stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experi…
A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-s…
At present, there have been suggested two types of physical mechanism that may facilitate preferential pairing between DNA molecules, with identical or similar base pair texts, without separation of base pairs. One solely relies on base pair specific patterns of helix distortion being the same on the two molecules, discussed extensively in the past. The other mechanism proposes that there are preferential interactions between base pairs of the same composition. We introduce a model, built on this second mechanism, where both thermal stretching and twisting fluctuations are included, as well as…
While stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with a distinct plateau region. Here we propose a unified theory that connects force-extension characteristics of the polymer chain with the convexity properties of the extension energy profile of its individual monomer subunits. Namely, if the effective monomer deformation energy as a function of its extension has a non-convex (concave up) region, the stretched polymer chain separates into two phases: the weakly and strongly stretched monomers. Simplifi…
Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy pl…
We propose an Ashkin-Teller like model for elastic response of DNA molecule to external force and torque. The base-stacking interaction is described in a simple and uniform way. We obtain the phase diagram of dsDNA, and in particular, the transition from B form to the S state induced by stretching and twisting. The elastic response of the ssDNA is presented also in a unified formalism. The close relation of dsDNA molecule structure with elastic response is shown clearly. The calculated folding angle of the dsDNA molecule is $59.2^o$.
Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. This paper presents calculations of a lattice-gas model of charge inversion for the adsorption of charged dimers on DNA. Each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. The entropy and charge distributions of these three species are calculated including the lowest order fluctuation corrections to mean-field theory. We find that the in…
Plectonemes are intertwined helically looped domains which form when a DNA molecule is supercoiled, i.e. over- or under-wounded. They are ubiquitous in cellular DNA and their physical properties have attracted significant interest both from the experimental and modeling side. In this work, we investigate fluctuations of the end-point distance z of supercoiled linear DNA molecules subject to external stretching forces. Our analysis is based on a two-phase model, which describes the supercoiled DNA as composed of a stretched and of a plectonemic phase. Several different mechanisms are found to c…
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…
In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field approximation can be described analytically via a mapping to a restricted random-graph ensemble having local degree constraints and global constraints on the number of connected components. It shows the emergence of protein clusters co…
Metropolis Monte Carlo simulation is used to investigate the elasticity of torsionally stressed double-stranded DNA, in which twist and supercoiling are incorporated as a natural result of base-stacking interaction and backbone bending constrained by hydrogen bonds formed between DNA complementary nucleotide bases. Three evident regimes are found in extension versus torsion and/or force versus extension plots: a low-force regime in which over- and underwound molecules behave similarly under stretching; an intermediate-force regime in which chirality appears for negatively and positively superc…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. We introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibri…
We use optical tweezers to perform stretching experiments on DNA molecules when interacting with the drugs daunomycin and ethidium bromide, which intercalate the DNA molecule. These experiments are performed in the low-force regime from zero up to 2 pN. Our results show that the persistence length of the DNA-drug complexes increases strongly as the drug concentration increases up to some critical value. Above this critical value, the persistence length decreases abruptly and remains practically constant for larger drug concentrations. The contour length of the molecules increases monotonically…
Overstretching of B-DNA is currently understood as force-induced melting. Depending on the geometry of the stretching experiment, the force threshold for the overstretching transition is around 65 or 110 pN. Although the mechanisms behind force-induced melting have been correctly described by Rouzina and Bloomfield \cite{RouzinaBloomfield2001a}, neither force threshold has been exactly calculated by theory. In this work, a detailed analysis of the force-extension curve is presented, based on a description of single-stranded DNA in terms of the discrete Kratky-Porod model, consistent with (i) t…
DNA is an astonishing material that can be used as a molecular building block to construct periodic arrays and devices with nanoscale accuracy and precision. Here, we present simple bead-spring model of DNA nanostars having three, four and five arms and study their self-assembly using molecular dynamics simulations. Our simulations show that the DNA nanostars form thermodynamically stable fully bonded gel phase from an unstructured liquid phase with the lowering of temperature. We characterize the phase transition by calculating several structural features such as radial distribution function …
Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs con…
Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived base pairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression -c ln m, where m is the length…
By using single-DNA observation with fluorescence microscopy, we observed the effects of divalent and trivalent cations on the higher-order structure of giant DNA (T4 DNA with 166 kbp). It was found that divalent cations, such as Mg(2+) and Ca(2+), inhibit DNA compaction induced by a trivalent cation, spermidine (SPD(3+)). On the other hand, in the absence of SPD(3+), divalent cations cause the shrinkage of DNA. These experimental observations are inconsistent with the well-established Debye-Huckel scheme regarding the shielding effect of counter ions, which is given as the additivity of contr…
We propose a new statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which mimic the geometrical constraints in the real molecule. This microscopic mechanism intrinsically accounts for the cooperativity related to the free energy penalty of bubble nucleation. The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves. Furthermore, the model explains the observed tempe…
In various chemical systems enthalpy-entropy compensation (EEC) is a well-known rule of behavior, although the physical roots of it are still not completely understood. It has been frequently questioned whether EEC is a truly physical phenomenon or a coincidence due to trivial mathematical connections between statistical-mechanical parameters - or even simpler: A phantom effect resulting from the misinterpretation of experimental data. Here, we review EEC from a new standpoint using the notion of correlation which is essential for the method of factor analysis, but is not conventional in physi…
When double-stranded DNA molecules are heated, or exposed to denaturing agents, the two strands get separated. The statistical physics of this process has a long history, and is commonly described in term of the Poland-Scheraga (PS) model. Crucial to this model is the configurational entropy for a melted region (compared to the entropy of an intact region of the same size), quantified by the loop factor. In this study we investigate how confinement affects the DNA melting transition, by using the loop factor for an ideal Gaussian chain. By subsequent numerical solutions of the PS model, we dem…
Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phas…
We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_…
From the crystal structure data and using the concept of equilbrium statistical mechanics we show how to calculate the thermodynamics of protein/DNA complexes. We apply the method to the TATA-box binding protein (TBP)/TATA sequence complex. We have estimated the change in free energy and entropy for each of the base pair (bp). The local rigidity of the DNA is estimated from the curvature of the free energy. We also estimate the free energy gain of the protein due to bond formation with a particular bp. We thus figure out the bps responsible for specific binding.
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…
Loop formation in long molecules occurs many places in nature, from solutions of carbon nanotubes to polymers inside a cell. In this article, we review theoretical studies of the static and dynamic properties of polymer loops. For example, long polymers must search many configurations to find a "target" binding site, while short polymers are stiff and resist bending. In between, there is an optimal loop size, which balances the entropy of long loops against the energetic cost of short loops. We show that such simple pictures of loop formation can explain several long-standing observations in D…
