The local opening of DNA is an intriguing phenomenon from a statistical physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code can not take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular dynamics studies, were premature. This could either imply that the present PBD should be improved or that biological activity can only be predicted in a more complex frame work that involves interactions with proteins and super helical stresses. In this article, we give detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as function of position and bubble size and the so-called $l$-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.
We present a nonlinear dynamical model for DNA thermal denaturation, which is based on the finite stacking enthalpies used in thermodynamical nearest-neighbour calculations. Within this model, the finiteness of stacking enthalpies is shown to be responsible for the sharpness of calculated melting curves. Transfer-integral and molecular dynamics calculations are performed to demonstrate that the proposed model leads to good agreement with known experimental results for both homogeneous and inhomogeneous DNA.
In this Letter, we investigate the link between thermal denaturation and mechanical unzipping for two models of DNA, namely the Dauxois-Peyrard-Bishop model and a variant thereof we proposed recently. We show that the critical line that separates zipped from unzipped DNA sequences in mechanical unzipping experiments is a power-law in the temperature-force plane. We also prove that for the investigated models the corresponding critical exponent is proportional to the critical exponent alpha, which characterizes the behaviour of the specific heat in the neighbourhood of the critical temperature …
In this letter, we point out the inaccurate figures in a letter by Peyrard and Bishop, who investigated the statistical mechanics of a nonlinear model for DNA denaturation. We give the correct figures.
We theoretically investigated the temperature fluctuations of DNA close to denaturation and observed a strong enhancement of these fluctuations at the critical temperature. Although in a much lower frequency range, such a sharp increase was also reported in the recent experimental work of Nagapriya et al [Phys. Rev. Lett. 96, 038102 (2006)]. We showed that there is instead no enhancement of temperature fluctuations when the dissipation coefficient in Langevin equations is assumed to be larger than a few tens of ps-1, and pointed out the possible role of the solvent in real experiments. We soug…
We use the "magnetic tweezers" technique to reveal the structural transitions that DNA undergoes in the force-torsion space. In particular, we focus on regions corresponding to negative supercoiling. These regions are characterized by the formation of so-called denaturation bubbles, which have an essential role in the replication and transcription of DNA. We experimentally map the region of the force-torsion space where the denaturation takes place. We observe that large fluctuations in DNA extension occur at one of the boundaries of this region, i.e., when the formation of denaturation bubble…
In the demanding biosensing environment, improving selection efficiency strategies has become an issue of great significance. DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, are representative of the supercoiled DNA loops found in nature. Their short size makes them extremely susceptible to writhe and twist, which is known to play a central role in DNA denaturation. We investigate minicircle lengths and superhelical densities that induce DNA denaturation bubbles of nanometer size and control well-defined long-life. Mesoscopic modeling and accelerated dynamics si…
We recently proposed a dynamical mesoscopic model for DNA, which is based, like statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present article, 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 mod…
A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. We show that denaturation corresponds to a first-order phase transition from B-DNA to d-DNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling sigma. The denaturation free energy, the temperature dependence of the twist angle, the phase diagram in the T,Gamma plane and isotherms in the sigma, Gamma plane are…
The dynamics of the DNA denaturation is studied using the Peyrard-Bishop-Dauxois model. The denaturation rate of double stranded polymers decreases exponentially as function of length below the denaturation temperature. Above Tc, the rate shows a minimum, but then increases as function of length. We also examine the influence of sequence and solvent friction. Molecules having the same number of weak and strong base-pairs can have significantly different opening rates depending on the order of base-pairs.
DNA denaturation has long been a subject of intense study due to its relationship to DNA transcription and its fundamental importance as a nonlinear, structural transition. Many aspects of this phenomenon, however, remain poorly understood. Existing models fit quite well with experimental results on the fraction of unbound base pairs versus temperature. Yet, these same models give incorrect results for other essential quantities. For example, the predicted base pair fluctuation timescales - relevant to transcription - are orders of magnitude different from those observed experimentally. Here, …
The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double stranded helix, released by a loop denaturation, is absorbed by \emph{supercoils}. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent $c$. However the first order transition displayed by the PS model for $c>2$ in linear DNA is replaced by a continuous transition with arbitrarily high order as $c$ approaches 2…
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…
Unbinding of a double-stranded DNA reduces to an unscreened long range interaction and maps on various problems. Heterogeneity renormalizes interaction. Renormalization is temperature dependent. At an unbinding transition it approaches critical dimensionality. This implies giant non-universal critical indexes and invalidity of the Gibbs distribution sufficiently close to the critical temperature Tc. Fluctuations are macroscopically large below Tc. There are no fluctuations above it.
The melting transition of deoxyribonucleic acid (DNA), whereby the strands of the double helix structure completely separate at a certain temperature, has been characterized using neutron scattering. A Bragg peak from B-form fibre DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois (PBD) model with only one free parameter. The experiment is unique, as it gives spatial correlation along the molecule through the melting transition where other techniques cannot.
In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts, Rathore, Schwartz and de Pablo (J. Chem. Phys. 126, 084901 (2007)), can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical…
In this paper we report direct measurement of large low frequency temperature fluctuations in double stranded (ds) DNA when it undergoes thermal denaturation transition. The fluctuation, which occurs only in the temperature range where the denaturation occurs, is several orders more than the expected equilibrium fluctuation. It is absent in single stranded (ss) DNA of the same sequence. The fluctuation at a given temperature also depends on the wait time and vanishes in a scale of few hours. It is suggested that the large fluctuation occurs due to coexisting denaturated and closed base pairs t…
The equilibrium statistical properties of DNA denaturation bubbles are examined in detail within the framework of the Peyrard-Bishop-Dauxois model. Bubble formation in homogeneous DNA is found to depend crucially on the presence of nonlinear base-stacking interactions. Small bubbles extending over less than 10 base pairs are associated with much larger free energies of formation per site than larger bubbles. As the critical temperature is approached, the free energy associated with further bubble growth becomes vanishingly small. An analysis of average displacement profiles of bubbles of varyi…
We used the Transfer-Integral method to compute, with an uncertainty smaller than 5%, the six fundamental characteristic exponents of two dynamical models for DNA thermal denaturation and investigate the validity of the scaling laws. Doubts concerning this point arise because the investigated systems (i) have a divergent internal length, (ii) are described by a divergent order parameter, (iii) are of dimension 1. We found that the assumption that the free energy can be described by a single homogeneous function is robust, despite the divergence of the order parameter, so that Rushbrooke's and …
The denaturation transition of circular DNA is studied within a Poland-Scheraga type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant $κ$ associated with the overtwisting energy for any g…
The phase transition of $(PolyA/PolyT)_{100}$ duplex into the denaturated state is studied in the Peyrard-Bishop-Dauxois model by the method of direct molecular-dynamical modeling. The temperature dependencies of the total energy and heat capacity of the duplex are calculated. The approach applied can be used to calculate the statistical properties of the duplexes of any length and nucleotide composition.
We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations.
The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.
The Peyrard-Bishop DNA model describes the molecular interactions with simple potentials which allow efficient calculations of melting temperatures. However, it is based on a Hamiltonian that does not consider the helical twist or any other relevant molecular dimensions. Here, we start from a more realistic 3D model and work out several approximations to arrive at a new non-linear 1D Hamiltonian with a twist angle dependence. Our approximations were numerically compared to full 3D calculations, and established its validity in the regime of small angles. For long DNA sequences we obtain sharp, …
As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the …
DNA has a well-defined structural transition -- the denaturation of its double-stranded form into two single strands -- that strongly affects its thermal transport properties. We show that, according to a widely implemented model for DNA denaturation, one can engineer DNA "heattronic" devices that have a rapidly increasing thermal conductance over a narrow temperature range across the denaturation transition (~350 K). The origin of this rapid increase of conductance, or "switching", is the softening of the lattice and suppression of nonlinear effects as the temperature crosses the transition t…
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_…
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 …
The issue of the nucleation and slow closure mechanisms of non superhelical stress-induced denaturation bubbles in DNA is tackled using coarse-grained MetaDynamics and Brownian simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring rotating strands with a prescribed torsional modulus in the duplex state. We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pair bubble, in agreement with experiments, are associated with the crossing of a free-energy barrier of $22~k_{\rm B}T$ (resp. $13~k_{\rm B}T$) …
The impact of various types of external potentials to the Peyrard-Bishop DNA denaturation is investigated through statistical mechanics approach. The partition function is obtained using transfer integral method, and further the stretching of hydrogen bond is calculated using time independent perturbation method. It is shown that all types of external potentials accelerate the denaturation processes at lower temperature. In particular, it is argued that the Gaussian potential with infinitesimal width reproduces a constant force at one end of DNA sequence as already done in some previous works.
Biological information is not only stored in the digital chemical sequence of double helical DNA, but is also encoded in the mechanical properties of the DNA strands, which can influence biochemical processes involving its readout. For example, loop formation in the Lac operon can regulate the expression of key genes, and DNA supercoiling is closely correlated to rhythmic circardian gene expression in cyanobacteria. Supercoiling is also important for large scale organisation of the genome in both eukaryotic and prokaryotic cells. DNA can respond to torsional stress by writhing to form looped s…
We consider a model for strand separation in negatively supercoiled dna, and study the effect of supercoiling on the localization of denaturation, using notions from statistical mechanics. The model is based on on mean field Ising system, coupled with a random field one dimensional ISing model. The effect of the word in AT and Gc associated with the DNA on localization of denaturation is studied under the hypothesis of small perimeter.
The Transfer-Integral (TI) operator is a powerful method to investigate the statistical physics of 1-dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be reduced to a Pseudo-Schrödinger Equation (PSE), according to which the DNA sequence is equivalent to a point particle moving in a potential well. In this paper, I check the validity of the standard PSE approximation for two different 1-dimensional DNA models, and show that it fails to provide correct results for both of them. I then propose a generalized PS…
The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous short sequences of DNA, i.e. $\sim 100$ base pairs, in the framework of a mesoscopic Hamiltonian model which accounts for the helicoidal geometry of the molecule. The theoretical background for the application of the path integral formalism to predictive analysis of the molecule thermodynamical properties is discussed. The base pair displacements with respec…
The damping effect to the DNA bubble is investigated within the Peyrard-Bishop model. In the continuum limit, the dynamics of the bubble of DNA is described by the damped nonlinear Schrodinger equation and studied by means of variational method. It is shown that the propagation of solitary wave pattern is not vanishing in a non-viscous system. Inversely, the solitary wave vanishes soon as the viscous force is introduced.
We propose a nonlinear model derived from first principles, to describe bubble dynamics of DNA. Our model equations include a term derived from the dissipative effect of intermolecular vibrational modes. Such modes are excited by the propagating bubble, and we term it "curvature dissipation". The equations we derive allow for stable pinned localized kinks which form the bubble. We perform the stability analysis and specify the energy requirements for the motion of the localized solutions. Our findings are consistent with properties of DNA dynamics, and can be used in models for denaturation bu…
Standard DNA melting curves record the separation of the two strands versus temperature, but they do not provide any information on the location of the opening. We introduce an experimental method which adds a new dimension to the melting curves of short DNA sequences by allowing us to record the degree of opening in several positions along the molecule all at once. This adds the spatial dimension to the melting curves and allows a precise investigation of the role of the base-pair sequence on the fluctuations and denaturation of the DNA double helix. We illustrate the power of the method by i…
We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length ($10^6-10^9$ base pairs). We show that, at physiological c…
Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process …
It appears that thermally activated DNA bubbles of different sizes play central roles in important genetic processes. Here we show that the probability for the formation of such bubbles is regulated by the number of soft AT pairs in specific regions with lengths which at physiological temperatures are of the order of (but not equal to) the size of the bubble. The analysis is based on the Peyrard- Bishop-Dauxois model, whose equilibrium statistical properties have been accurately calculated here with a transfer integral approach.
It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.
We study the thermal and mechanical behavior of DNA denaturation in the frame of the mesoscopic Peyrard- Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of the P5 promoter sequence and use the Principal Component Analysis of the trajectories to extract the main information on the dynamical behavior of the system. We find that this analysis method gives an ex…
We propose a new simple model for DNA denaturation bases on the pendulum model of Englander\cite{A1} and the microscopic model of Peyrard {\it et al.},\cite{A3} so called "combined model". The main parameters of our model are: the coupling constant $k$ along each strand, the mean stretching $y^\ast$ of the hydrogen bonds, the ratio of the damping constant and driven force $γ/F$. We show that both the length $L$ of unpaired bases and the velocity $v$ of kinks depend on not only the coupling constant $k$ but also the temperature $T$. Our results are in good agreement with previous works.
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 conforma…
We present numerical results on the temperature dependence of the distribution of bubble lengths in DNA segments of various guanine-cytosine (GC) concentrations. Base-pair openings are described by the Peyrard-Bishop-Dauxois model and the corresponding thermal equilibrium distributions of bubbles are obtained through Monte Carlo calculations for bubble sizes up to the order of a hundred base pairs. The dependence of the parameters of bubble length distribution on temperature and the GC content is investigated. We provide simple expressions which approximately describe these relations. The vari…
We propose a statistical mechanics model for DNA melting in which base stacking and pairing are explicitly introduced as distinct degrees of freedom. Unlike previous approaches, this model describes thermal denaturation of DNA secondary structure in the whole experimentally accessible temperature range. Base pairing is described through a zipper model, base stacking through an Ising model. We present experimental data on the unstacking transition, obtained exploiting the observation that at moderately low pH this transition is moved down to experimentally accessible temperatures. These measure…
We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the meltin…
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…
The distribution of bubble lengths in double-stranded DNA is presented for segments of varying guanine-cytosine (GC) content, obtained with Monte Carlo simulations using the Peyrard-Bishop-Dauxois model at 310 K. An analytical description of the obtained distribution in the whole regime investigated, i.e., up to bubble widths of the order of tens of nanometers, is available. We find that the decay lengths and characteristic exponents of this distribution show two distinct regimes as a function of GC content. The observed distribution is attributed to the anharmonic interactions within base pai…
A double-stranded DNA unravels thermally through intermediate denatured bubble segments. Intrinsically, fluctuations ensue at the bubble boundaries from non-equilibrium (NE) energy exchanges with the environment. However, such details gets obscured by large population kinetics at the macroscale, associating equilibrium pathway to the unravelling landscape. In this work, we capture evidence of fluctuation energetics with picoliter samples in a microfluidic cantilever. We exploit nanomechanical resonance to measure the NE energy exchanges through dissipation, revealing a crucial pre-melting tran…
Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (\emph{bps}). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The \emph{bps} displacements with respect to the ground state …
