Sequence sensitivity of breathing dynamics in heteropolymer DNA

Equilibrium melting probabilities of a DNA molecule with a defect: An exact solution of the Poland-Scheraga model

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson-Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland-Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules.

Can one detect intermediate denaturation states of DNA sequences by following the equilibrium open-close dynamic fluctuations of a single base pair?

Melting of DNA sequences may occur through a few major intermediate states, whose influence on the melting curve has been discussed previously, while their effect on the kinetics has not been explored thoroughly. Here, we chose a simple DNA sequence, forming a hairpin in its native (zipped) state, and study it using molecular dynamic (MD) simulations and a model integrating the Gaussian network model with bond-binding energies-the Gaussian binding energy (GBE) model. We find two major partial denaturation states, a bubble state and a partial unzipping state. We demonstrate the influence of these two states on the closing-opening base pair dynamics, as probed by a tagged bond auto-correlation function (ACF). We argue that the latter is measured by fluorescence correlation spectroscopy experiments, in which one base of the pair is linked to a fluorescent dye, while the complementary base is linked to a quencher, similar to the experiment reported by Altan-Bonnet et al. [Phys. Rev. Lett. 90, 138101 (2003)]. We find that tagging certain base pairs at temperatures around the melting temperature results in a multi-step relaxation of the ACF, while tagging other base pairs leads to an effectively single-step relaxation, albeit non-exponential. Only the latter type of relaxation has been observed experimentally, and we suggest which of the other base pairs should be tagged in order to observe multi-step relaxation. We demonstrate that this behavior can be observed with other sequences and argue that the GBE can reliably predict these dynamics for very long sequences, where MD simulations might be limited.

Elasticity of a DNA chain dotted with bubbles under force

The flexibility and the extension along the direction of the force are shown to be related to the bubble number fluctuation and the average number of bubbles, respectively, when the strands of the DNA are subjected to a force along the same direction, here called a stretching force. The force-temperature phase diagram shows the existence of a tricritical point, where the first-order force-induced zipping transition becomes continuous. On the other hand, when the forces are being applied in opposite directions, here called an unzipping force, the transition remains first order, with the possibility of vanishing of the low-temperature reentrant phase for a semiflexible DNA. Moreover, we found that the bulk elasticity changes only if an external force penetrates the bound phase and affects the bubble states.

Manipulation of double-stranded DNA melting by force

By integrating elasticity-as described by the Gaussian network model-with bond binding energies that distinguish between different base-pair identities and stacking configurations, we study the force induced melting of a double-stranded DNA (dsDNA). Our approach is a generalization of our previous study of thermal dsDNA denaturation [J. Chem. Phys. 145, 144101 (2016)JCPSA60021-960610.1063/1.4964285] to that induced by force at finite temperatures. It allows us to obtain semimicroscopic information about the opening of the chain, such as whether the dsDNA opens from one of the ends or from the interior, forming an internal bubble. We study different types of force manipulation: (i) "end unzipping," with force acting at a single end base pair perpendicular to the helix, (ii) "midunzipping," with force acting at a middle base pair perpendicular to the helix, and (iii) "end shearing," where the force acts at opposite ends along the helix. By monitoring the free-energy landscape and probability distribution of intermediate denaturation states, we show that different dominant intermediate states are stabilized depending on the type of force manipulation used. In particular, the bubble state of the sequence L60B36, which we have previously found to be a stable state during thermal denaturation, is absent for end unzipping and end shearing, whereas very similar bubbles are stabilized by midunzipping, or when the force location is near the middle of the chain. Ours results offer a simple tool for stabilizing bubbles and loops using force manipulations at different temperatures, and may implicate on the mechanism in which DNA enzymes or motors open regions of the chain.

Identification of a prototypical single-stranded uracil DNA glycosylase from Listeria innocua

A recent phylogenetic study on UDG superfamily estimated a new clade of family 3 enzymes (SMUG1-like), which shares a lower homology with canonic SMUG1 enzymes. The enzymatic properties of the newly found putative DNA glycosylase are unknown. To test the potential UDG activity and evaluate phylogenetic classification, we isolated one SMUG1-like glycosylase representative from Listeria innocua (Lin). A biochemical screening of DNA glycosylase activity in vitro indicates that Lin SMUG1-like glycosylase is a single-strand selective uracil DNA glycosylase. The UDG activity on DNA bubble structures provides clue to its physiological significance in vivo. Mutagenesis and molecular modeling analyses reveal that Lin SMUG1-like glycosylase has similar functional motifs with SMUG1 enzymes; however, it contains a distinct catalytic doublet S67-S68 in motif 1 that is not found in any families in the UDG superfamily. Experimental investigation shows that the S67M-S68N double mutant is catalytically more active than either S67M or S68N single mutant. Coupled with mutual information analysis, the results indicate a high degree of correlation in the evolution of SMUG1-like enzymes. This study underscores the functional and catalytic diversity in the evolution of enzymes in UDG superfamily.

Sufficient minimal model for DNA denaturation: Integration of harmonic scalar elasticity and bond energies

We study DNA denaturation by integrating elasticity - as described by the Gaussian network model - with bond binding energies, distinguishing between different base pairs and stacking energies. We use exact calculation, within the model, of the Helmholtz free-energy of any partial denaturation state, which implies that the entropy of all formed "bubbles" ("loops") is accounted for. Considering base pair bond removal single events, the bond designated for opening is chosen by minimizing the free-energy difference for the process, over all remaining base pair bonds. Despite of its great simplicity, for several known DNA sequences our results are in accord with available theoretical and experimental studies. Moreover, we report free-energy profiles along the denaturation pathway, which allow to detect stable or meta-stable partial denaturation states, composed of bubble, as local free-energy minima separated by barriers. Our approach allows to study very long DNA strands with commonly available computational power, as we demonstrate for a few random sequences in the range 200-800 base-pairs. For the latter, we also elucidate the self-averaging property of the system. Implications for the well known breathing dynamics of DNA are elucidated.

Coherence and resonance effects in the ultra-intense laser-induced ultrafast response of complex atoms

Both coherent pumping and energy relaxation play important roles in understanding physical processes of ultra-intense coherent light-matter interactions. Here, using a large-scale quantum master equation approach, we describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions. As examples, two typical cases of light-matter interactions are studied. First, we investigate coherent dynamics of inner-shell electrons of a neon gas irradiated by a high-intensity X-ray laser along with vast number of decaying channels. In these single-photon dominated processes, we find that, due to coherence-induced Rabi oscillations and power broadening effects, the photon absorptions of a neon gas can be suppressed resulting in differences in ionization processes and final ion-stage distributions. Second, we take helium as an example of multiphoton and multichannel interference dominated electron dynamics, by investigating the transient absorption of an isolated attosecond pulse in the presence of a femtosecond infrared laser pulse.

Efimov-like phase of a three-stranded DNA and the renormalization-group limit cycle

A three-stranded DNA with short range base pairings only is known to exhibit a classical analog of the quantum Efimov effect, viz., a three-chain bound state at the two-chain melting point where no two are bound. By using a nonperturbative renormalization-group method for a rigid duplex DNA and a flexible third strand, with base pairings and strand exchange, we show that the Efimov-DNA is associated with a limit cycle type behavior of the flow of an effective three-chain interaction. The analysis also shows that thermally generated bubbles play an essential role in producing the effect. A toy model for the flow equations shows the limit cycle in an extended three-dimensional parameter space of the two-chain coupling and a complex three-chain interaction.

Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA

We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction ε(hb)(AT) for an AT base pair and the ring factor ξ turn out to be the most sensitive parameters. In addition, the stacking interaction ε(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization.

Binding of nucleoid-associated protein fis to DNA is regulated by DNA breathing dynamics

Physicochemical properties of DNA, such as shape, affect protein-DNA recognition. However, the properties of DNA that are most relevant for predicting the binding sites of particular transcription factors (TFs) or classes of TFs have yet to be fully understood. Here, using a model that accurately captures the melting behavior and breathing dynamics (spontaneous local openings of the double helix) of double-stranded DNA, we simulated the dynamics of known binding sites of the TF and nucleoid-associated protein Fis in Escherichia coli. Our study involves simulations of breathing dynamics, analysis of large published in vitro and genomic datasets, and targeted experimental tests of our predictions. Our simulation results and available in vitro binding data indicate a strong correlation between DNA breathing dynamics and Fis binding. Indeed, we can define an average DNA breathing profile that is characteristic of Fis binding sites. This profile is significantly enriched among the identified in vivo E. coli Fis binding sites. To test our understanding of how Fis binding is influenced by DNA breathing dynamics, we designed base-pair substitutions, mismatch, and methylation modifications of DNA regions that are known to interact (or not interact) with Fis. The goal in each case was to make the local DNA breathing dynamics either closer to or farther from the breathing profile characteristic of a strong Fis binding site. For the modified DNA segments, we found that Fis-DNA binding, as assessed by gel-shift assay, changed in accordance with our expectations. We conclude that Fis binding is associated with DNA breathing dynamics, which in turn may be regulated by various nucleotide modifications.

Cellular transcription factors (TFs) are proteins that regulate gene expression, and thereby cellular activity and fate, by binding to specific DNA segments. The physicochemical determinants of protein-DNA binding specificity are not completely understood. Here, we report that the propensity of transient opening and re-closing of the double helix, resulting from thermal fluctuations, aka “DNA breathing” or “DNA bubbles,” can be associated with binding affinity in the case of Fis, a well-studied nucleoid-associated protein in Escherichia coli. We found that a particular breathing profile is characteristic of high-affinity Fis binding sites and that DNA fragments known to bind Fis in vivo are statistically enriched for this profile. Furthermore, we used simulations of DNA breathing dynamics to guide design of gel-shift experiments aimed at testing the idea that local breathing influences Fis binding. As a result, we show that via nucleotide modifications but without modifying nucleotides that directly contact Fis, we were able to transform a low-affinity Fis binding site into a high-affinity site and vice versa. The nucleotide modifications were designed only based on DNA breathing simulations. Our study suggests that strong Fis-DNA binding depends on DNA breathing - a novel physicochemical characteristic that could be used for prediction and rational design of TF binding sites.

DNA breathing dynamics distinguish binding from nonbinding consensus sites for transcription factor YY1 in cells

The genome-wide mapping of the major gene expression regulators, the transcription factors (TFs) and their DNA binding sites, is of great importance for describing cellular behavior and phenotypic diversity. Presently, the methods for prediction of genomic TF binding produce a large number of false positives, most likely due to insufficient description of the physiochemical mechanisms of protein–DNA binding. Growing evidence suggests that, in the cell, the double-stranded DNA (dsDNA) is subject to local transient strands separations (breathing) that contribute to genomic functions. By using site-specific chromatin immunopecipitations, gel shifts, BIOBASE data, and our model that accurately describes the melting behavior and breathing dynamics of dsDNA we report a specific DNA breathing profile found at YY1 binding sites in cells. We find that the genomic flanking sequence variations and SNPs, may exert long-range effects on DNA dynamics and predetermine YY1 binding. The ubiquitous TF YY1 has a fundamental role in essential biological processes by activating, initiating or repressing transcription depending upon the sequence context it binds. We anticipate that consensus binding sequences together with the related DNA dynamics profile may significantly improve the accuracy of genomic TF binding sites and TF binding-related functional SNPs.

Anharmonic stacking in supercoiled DNA

Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.

Determining the DNA stability parameters for the breathing dynamics of heterogeneous DNA by stochastic optimization

We suggest that the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles). On the basis of the reconstructed bubble size distribution, this is achieved through stochastic optimization of the free energies in terms of simulated annealing. In particular, it is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy. This method will be useful to obtain the DNA stacking and hydrogen bonding free energies from single bubble breathing assays rather than equilibrium data.

Stacking interactions in denaturation of DNA fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time-dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine-rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble, we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.

DNA breathing dynamics: analytic results for distribution functions of relevant Brownian functionals

We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

Supercoiling induces denaturation bubbles in circular DNA

We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.

DNA-Destabilizing Agents as an Alternative Approach for Targeting DNA: Mechanisms of Action and Cellular Consequences

DNA targeting drugs represent a large proportion of the actual anticancer drug pharmacopeia, both in terms of drug brands and prescription volumes. Small DNA-interacting molecules share the ability of certain proteins to change the DNA helix's overall organization and geometrical orientation via tilt, roll, twist, slip, and flip effects. In this ocean of DNA-interacting compounds, most stabilize both DNA strands and very few display helix-destabilizing properties. These types of DNA-destabilizing effect are observed with certain mono- or bis-intercalators and DNA alkylating agents (some of which have been or are being developed as cancer drugs). The formation of locally destabilized DNA portions could interfere with protein/DNA recognition and potentially affect several crucial cellular processes, such as DNA repair, replication, and transcription. The present paper describes the molecular basis of DNA destabilization, the cellular impact on protein recognition, and DNA repair processes and the latter's relationships with antitumour efficacy.

Statistical properties of metastable intermediates in DNA unzipping

We unzip DNA molecules using optical tweezers and determine the sizes of the cooperatively unzipping and zipping regions separating consecutive metastable intermediates along the unzipping pathway. Sizes are found to be distributed following a power law, ranging from one base pair up to more than a hundred base pairs. We find that a large fraction of unzipping regions smaller than 10 bp are seldom detected because of the high compliance of the released single stranded DNA. We show how the compliance of a single nucleotide sets a limit value around 0.1 N/m for the stiffness of any local force probe aiming to discriminate one base pair at a time in DNA unzipping experiments.

Nonlinear breathing modes at a defect site in DNA

Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the "rogue" base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations. The mesoscopic model is calibrated to data from the all-atom molecular dynamics package AMBER for a variety of twist angles of the DNA duplex. Defects are considered in the interchain interactions as well as in the along-chain interactions. This paper also discusses the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices, and how breathing can be viewed as competition between the along-chain elastic energy and the interchain binding energy.

Backtracking and proofreading in DNA transcription

Biological cell function crucially relies on the accuracy of RNA sequences, transcribed from the DNA genetic code. To ensure sufficiently high fidelity in the face of high spontaneous error rates during transcription, error correction mechanisms must play an important role. A particular mechanism of transcriptional error correction involves backtracking of the RNA polymerase and RNA cleavage. Motivated by recent single molecule experiments characterizing the dynamics of backtracking, we present a microscopic model of this editing process. We show that such a mechanism can yield error frequencies that are in agreement with in vivo observations.

Localization and delocalization of energy in a Peyrard-Bishop chain

This paper studies energy localization conditions in lattices of the type proposed by Peyrard and Bishop. Homogeneous and inhomogeneous lattices are analyzed and the role of interfaces in the latter is emphasized. Simulations allowed us to identify critical energy values for the existence of localization. After a certain energy value, it is possible to observe the loss of energy localization along the chain.

Bubble merging in breathing DNA as a vicious walker problem in opposite potentials

We investigate the coalescence of two DNA bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of double-stranded DNA. In a continuum Fokker-Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behavior, while at high temperatures, the bubble corners perform drift diffusion toward coalescence. In the calculations, we map the bubble dynamics on the problem of two vicious walkers in opposite potentials. We also present a discrete master equation approach to the bubble coalescence problem. Numerical evaluation and stochastic simulation of the master equation show excellent agreement with the results from the continuum approach. Given that the coalesced state is thermodynamically stabilized against a state where only one or a few of the base pairs of the barrier region are re-established, it appears likely that this type of setup could be useful for the quantitative investigation of thermodynamic DNA stability data as well as the rate constants involved in the unzipping and zipping dynamics of DNA in single molecule fluorescence experiments.

Path integral method for DNA denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc*, whereas the fraction of unbound base pairs grows continuously around and above Tc*. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc*. The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

Stretching chimeric DNA: a test for the putative S-form

Double-stranded DNA "overstretches" at a pulling force of about 65 pN, increasing in length by a factor of 1.7. The nature of the overstretched state is unknown, despite its considerable importance for DNA's biological function and technological application. Overstretching is thought by some to be a force-induced denaturation and by others to consist of a transition to an elongated, hybridized state called S-DNA. Within a statistical mechanical model, we consider the effect upon overstretching of extreme sequence heterogeneity. "Chimeric" sequences possessing halves of markedly different AT composition elongate under fixed external conditions via distinct, spatially segregated transitions. The corresponding force-extension data vary with pulling rate in a manner that depends qualitatively and strikingly upon whether the hybridized S-form is accessible. This observation implies a test for S-DNA that could be performed in experiment.

Single DNA denaturation and bubble dynamics

While the Watson-Crick double-strand is the thermodynamically stable state of DNA in a wide range of temperature and salt conditions, even at physiological conditions local denaturation bubbles may open up spontaneously due to thermal activation. By raising the ambient temperature, titration, or by external forces in single molecule setups bubbles proliferate until full denaturation of the DNA occurs. Based on the Poland-Scheraga model we investigate both the equilibrium transition of DNA denaturation and the dynamics of the denaturation bubbles with respect to recent single DNA chain experiments for situations below, at, and above the denaturation transition. We also propose a new single molecule setup based on DNA constructs with two bubble zones to measure the bubble coalescence and extract the physical parameters relevant to DNA breathing. Finally we consider the interplay between denaturation bubbles and selectively single-stranded DNA binding proteins.

Force induced DNA melting

When pulled along the axis, double-strand DNA undergoes a large conformational change and elongates by roughly twice its initial contour length at a pulling force of about 70 pN. The transition to this highly overstretched form of DNA is very cooperative. Applying a force perpendicular to the DNA axis (unzipping), double-strand DNA can also be separated into two single-stranded DNA, this being 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-strand DNA associated with either of the above mentioned processes can be viewed as force induced DNA melting. As the force at one end of the DNA is increased the DNA starts melting abruptly/smoothly above a critical force depending on the pulling direction. The critical force f(m), at which DNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the DNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base pairs. The fraction of Watson-Crick base pair hydrogen bond breaking as a function of force does not show smooth and continuous behavior and consists of plateaus followed by sharp jumps.

Dynamical versus statistical mesoscopic models for DNA denaturation

We recently proposed a dynamical mesoscopic model for DNA, which is based, like the statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present paper, we first describe how the parameters of this model are varied to get predictions in better agreement with experimental results that were not addressed up to now, like mechanical unzipping, the evolution of the critical temperature with sequence length and temperature resolution. We show that the model with the new parameters provides results that are in quantitative agreement with those obtained from statistical models. Investigation of the critical properties of the dynamical model suggests that DNA denaturation looks like a first-order phase transition in a broad temperature interval, but that there necessarily exists, very close to the critical temperature, a crossover to another regime. The exact nature of the melting dynamics in this second regime still has to be elucidated. We finally point out that the descriptions of the physics of the melting transition inferred from statistical and dynamical models are not completely identical and discuss the relevance of our model from the biological point of view.

Dynamics of DNA melting

The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as fluorescence correlation spectroscopy.

How topological constraints facilitate growth and stability of bubbles in DNA

The bubbles in double-stranded DNA, essential for gene transcription and replication, occur in mechanically constrained situations. Through an elastic model incorporating topological constraint, we show that, when a stretched double helix is underwound above a critical value of twist, a bubble can spontaneously form, yielding extension and torque behaviors quantitatively in agreement with magnetic tweezers experiments. We find that, unlike thermal bubble in an unconstrained DNA, the bubbles in these constrained states can grow and stabilize, provided that tension and length of DNA are above critical values.

A model coupling vibrational and rotational motion for the DNA molecule

We investigate a mechanical model for the DNA molecule using an extension of the Peyrard and Bishop model. In the present model, there are two chains of oscillators linked by a Morse potential, which represent the hydrogen bonds. The rotational and vibrational motions of each base pair are considered and the coupling for these motions are introduced by a nonlinear combination of them in the Morse potential. In this context, thermodynamics and structural properties are discussed.

Statistical physics of the melting of inhomogeneous DNA

We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused on precise sequences and investigated the succession of local openings that lead to their dissociation. For this purpose, we performed transfer-integral-type calculations with two different dynamical models: namely, the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite stacking enthalpies we recently proposed. It appears that, for both models, the essential effect of heterogeneity is to let different portions of the investigated sequences open at slightly different temperatures. Besides this macroscopic effect, the local aperture of each portion indeed turns out to be very similar to that of a homogeneous sequence with the same length. Rounding of each local opening transition is therefore merely a size effect. For the Dauxois-Peyrard-Bishop model, sequences with a few thousand base pairs are still far from the thermodynamic limit, so that it is inappropriate, for this model, to discuss the order of the transition associated with each local opening. In contrast, sequences with several hundred to a few thousand base pairs are pretty close to the thermodynamic limit for the model we proposed. The temperature interval where a power law holds is consequently broad enough to enable the estimation of critical exponents. On the basis of the few examples we investigated, it seems that, for our model, disorder does not necessarily induce a decrease of the order of the transition.

Stochastic dynamics and denaturation of thermalized DNA

In the first part of the paper, the stochastic dynamics of the Peyrard-Bishop-Dauxois (PBD) DNA model is studied. A one-dimensional averaged Itô stochastic differential equation governing the total energy of the system and the associated Fokker-Planck equation governing the transition probability density function of the total energy are derived from the Langevin equations for the base-pair (bp) separation of the PBD DNA model by using the stochastic averaging method for quasinonintegrable Hamiltonian systems. The stationary probability density function of the average energy and the mean square of the bp separation are obtained by solving the reduced Fokker-Planck equation. In the second part of the paper, the local denaturation of the thermalized PBD DNA model is studied as a first-passage-time problem in the energy. A backward Kolmogorov equation and a Pontryagin equation are derived from the averaged Itô equation and solved to yield the waiting-time distribution and the mean bp opening time. All the analytical results are confirmed with those from Monte Carlo simulation. It is pointed out that the proposed method may yield a reasonable mean bp opening time if the friction coefficient is fixed using experimental results.

Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a one-dimensional Ising model, which describes the internal base-pair states, coupled to a discrete wormlike chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of poly(dA)-poly(dT) and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square radius as a function of temperature leads to a coherent explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulas, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square radius, all as a function of temperature and DNA length.

Dynamics of DNA breathing: weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature, the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature, the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

DNA bubble dynamics as a quantum Coulomb problem

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution W(t). Below Tm, W(t) is associated with the continuum of scattering states of the repulsive Coulomb potential. At Tm, the Coulomb potential vanishes and W(t) assumes a power-law tail with nontrivial dynamic exponents: the critical exponent of the entropy loss factor may cause a finite mean lifetime. Above Tm (attractive potential), the long-time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Master equation approach to DNA breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies up to a few k(B)T. Thermal motion within the DNA double strand therefore causes the opening of intermittent single-stranded denaturation zones, the DNA bubbles. The unzipping and zipping dynamics of bps at the two zipper forks of a bubble, where the single strand of the denatured zone joins the still intact double strand, can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA breathing in a heteropolymer DNA with given sequence in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.

Breathing dynamics in heteropolymer DNA

While the statistical mechanical description of DNA has a long tradition, renewed interest in DNA melting from a physics perspective is nourished by measurements of the fluctuation dynamics of local denaturation bubbles by single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA breathing) is supposedly crucial for biological functioning during, for instance, transcription initiation and DNA's interaction with selectively single-stranded DNA binding proteins. Motivated by this, we consider the bubble breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master equation and complementary stochastic Gillespie simulations, providing the bubble size and the position of the bubble along the sequence as a function of time. We utilize new experimental data that independently obtain stacking and hydrogen bonding contributions to DNA stability. We calculate the spectrum of relaxation times and the experimentally measurable autocorrelation function of a fluorophore-quencher tagged basepair, and demonstrate good agreement with fluorescence correlation experiments. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a promoter sequence of the T7 phage. The strong dependence on sequence, temperature and salt concentration for the breathing dynamics of DNA found here points at a good potential for nanosensing applications by utilizing short fluorophore-quencher dressed DNA constructs.

DNA confined in nanochannels: Hairpin tightening by entropic depletion

A theory is presented of the elongation of double-stranded DNA confined in a nanochannel based on a study of the formation of hairpins. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The DNA in the hairpin remains double-stranded. The free energy of the hairpin is significantly larger than what one would expect if this entropic effect were unimportant. As a result, the distance between hairpins or the global persistence length is often tens of micrometer long and may even reach millimeter sizes for 10 nm thin channels. The hairpin shape and size and the DNA elongation are computed for nanoslits and circular and square nanochannels. A comparison with experiment is given.