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 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.
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…
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…
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.
We propose a dynamical model for the secondary structure of DNA, which is based on the finite stacking enthalpies used in thermodynamics calculations. In this model, the two strands can separate and the bases are allowed to rotate perpendicular to the sequence axis. We show, through molecular dynamics simulations, that the model has the correct behaviour at the denaturation transition.
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…
Can Specific THz Fields Induce Collective Base-Flipping in DNA? A Stochastic Averaging and Resonant Enhancement Investigation Based on a New Mesoscopic Model
The thermal conductivity of B-form double-stranded DNA (dsDNA) of the Drew-Dickerson sequence d(CGCGAATTCGCG) is computed using classical Molecular Dynamics (MD) simulations. In contrast to previous studies, which focus on a simplified 1D model or a coarse-grained model of DNA to improve simulation times, full atomistic simulations are employed to understand the thermal conduction in B-DNA. Thermal conductivity at different temperatures from 100 to 400 K are investigated using the Einstein Green-Kubo equilibrium and Müller-Plathe non-equilibrium formalisms. The thermal conductivity of B-DNA at…
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…
A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites…
I present a Hamiltonian model and a computational method suitable to evaluate structural and thermodynamic properties of helical molecules embedded in crowded environments which may confine the space available to the base pair fluctuations. It is shown that, for the specific case of a short DNA fragment in a nanochannel, the molecule is markedly over-twisted and stretched by narrowing the width of the channel.
Despite numerous attempts, the understanding of the thermal denaturation of DNA is still a challenge due to the lack of structural data at the transition since standard experimental approaches to DNA melting are made in solution and do not provide spatial information. We report a measurement using neutron scattering from oriented DNA fibres to determine the size of the regions that stay in the double-helix conformation as the melting temperature is approached from below. A Bragg peak from the B-form of DNA has been observed as a function of temperature and its width and integrated intensity ha…
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.
Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Li…
Genomes contain rare guanine-rich sequences capable of assembling into four-stranded helical structures, termed G-quadruplexes, with potential roles in gene regulation and chromosome stability. Their mechanical unfolding has only been reported to date by all-atom simulations, which cannot dissect the major physical interactions responsible for their cohesion. Here, we propose a mesoscopic model to describe both the mechanical and thermal stability of DNA G-quadruplexes, where each nucleotide of the structure, as well as each central cation located at the inner channel, is mapped onto a single …
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…
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…
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…
The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available to base pair fluctuations and derive the partition function. The apparent persistence lengths of a set of short chains have been computed as a function of the twist conformation both in the over-twisted and the untwisted regimes, whereby the equilibrium twist is selected by free energy minimization. The obtained values are significantly lower than those gene…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free energy landscape. Melting profiles, dependence …
Nucleic acids physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse grained models, e.g. the worm-like-chain, taken from polymer physics. In this article, I present an intermediate (mesoscopic) approach and show how to build a three dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical a…
Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases …
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 …
DNA supercoiling, the under or overwinding of DNA, is a key physical mechanism both participating to compaction of bacterial genomes and making genomic sequences adopt various structural forms. DNA supercoiling may lead to the formation of braided superstructures (plectonemes), or it may locally destabilize canonical B-DNA to generate denaturation bubbles, left-handed Z-DNA and other functional alternative forms. Prediction of the relative fraction of these structures has been limited because of a lack of predictive polymer models that can capture the multiscale properties of long DNA molecule…
The effects of ionic ordering in DNA water solutions are studied by conductivity experiments. The conductivity measurements are performed for the solutions of DNA with KCl salt in the temperature range from 28 to 70 C. Salt concentration vary from 0 to 2 M. The conductivity of solutions without DNA but with the same concentration of KCl salt are also performed. The results show that in case of salt free solution of DNA the melting process of the double helix is observed, while in case of DNA solution with added salt the macromolecule denaturation is not featured. For salt concentrations lower …
The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over $\sim 10^7 - 10^8$ base pair paths, a large number of double helix configurations is taken into account consistently …
The homochirality of the molecules of life has been a vexing problem with no generally accepted solution to date. Since a racemic mixture of chiral nucleotides frustrates the extension and replication of RNA and DNA, understanding the origin of homochirality has important implications to the investigation of the origin of life. Here we suggest a novel solution to the homochirality problem based on a recently proposed thermodynamic dissipation theory for the origin of life. Homochirality is suggested to have been incorporated gradually into the emerging life as a result of asymmetric right- ove…
