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 florescence correlation spectroscopy.
The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Daxuois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles and the possibility of a two states transition are studied.
When pulled along the axis, double-strand DNA undergoes a large conformational change and elongates roughly twice its initial contour length at a pulling force about 70 pN. The transition to this highly overstretched form of DNA is very cooperative. Applying force perpendicular to the DNA axis (unzipping), double-strand DNA can also be separated into two single-stranded DNA which is a fundamental process in DNA replication. We study the DNA overstretching and unzipping transition using fully atomistic molecular dynamics (MD) simulations and argue that the conformational changes of double stran…
We develop a simple model to study the effects of an applied force on the melting of a double stranded DNA (dsDNA). Using this model, we could study the stretching, unzipping, rupture and slippage like transition in a dsDNA. We show that in absence of an applied force, the melting temperature and the melting profile of dsDNA strongly depend on the constrained imposed on the ends of dsDNA. The nature of the phase boundary which separates the zipped and the open state for the shearing like transition is remarkably different than the DNA unzipping
We study the melting of a double stranded DNA in the presence of stretching forces, via 3D Monte-Carlo simulations, exactly solvable models and heuristic arguments. The resulting force-temperature phase diagram is dramatically different for the cases where the force is applied to only one strand or to both. Different assumptions on the monomer size of single and double stranded DNA lead to opposite conclusions as to whether DNA melts or not as it overstretches.
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 investigate melting transition of DNA sequences embedded in a Langevin fluctuation-dissipation thermal bath. Torsional effects are considered by a twist angle $φ$ between neighboring base pairs stacked along the molecule backbone. Our simulation results show that the increase of twist angle translates linearly the melting temperature with a positive slope. After the so called equilibrium angle $φ_\mathrm{eq}$, the DNA chain becomes very rigid against opening and accordingly very high temperatures are required to initiate the melting process. In such cases however, the biofunctionality of DN…
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 study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We demonstrate that the associated Fokker-Planck equation is equivalent to a 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…
Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior loop melting. So far, in the modeling of DNA melting, the entropy of denaturated loops has been estimated from the number of configurations of a closed self-avoiding walk. It is well understood now that a loop embedded in a chain is characterized by a loop closure exponent c which is higher than that of an isolated loop. Here we report an analysis of DNA melti…
Thermal denaturation of DNA is often studied with coarse-grained models in which native sequential base pairing is mimicked by the existence of attractive interactions only between monomers at the same position along strands (Poland and Scheraga models). Within this framework, the existence of a three strand DNA bound state in conditions where a duplex DNA would be in the denaturated state was recently predicted from a study of three directed polymer models on simplified hierarchical lattices ($d>2$) and in $1+1$ dimensions. Such phenomenon which is similar to the Efimov effect in nuclear phys…
The melting behavior of long, heterogeneous DNA chains is examined within the framework of the nonlinear lattice dynamics based Peyrard-Bishop-Dauxois (PBD) model. Data for the pBR322 plasmid and the complete T7 phage have been used to obtain model fits and determine parameter dependence on salt content. Melting curves predicted for the complete fd phage and the Y1 and Y2 fragments of the $ϕ$X174 phage without any adjustable parameters are in good agreement with experiment. The calculated probabilities for single base-pair opening are consistent with values obtained from imino proton exchange …
Three, interrelated biologically-relevant examples of biased random walks are presented: (1) A model for DNA melting, modelled as DNA unzipping, which provides a way to illustrate the role of the Boltzmann factor in a venue well-known to biology and pre-medical students; (2) the activity of helicase motor proteins in unzipping double-stranded DNA, for example, at the replication fork, which is an example of a Brownian ratchet; (3) force generation by actin polymerization, which is another Brownian ratchet, and for which the force and actin-concentration dependence of the velocity of actin poly…
The distance distribution between complementary base pairs of the two strands of a DNA molecule is studied near the melting transition. Scaling arguments are presented for a generalized Poland-Scheraga type model which includes self-avoiding interactions. At the transition temperature and for a large distance r the distribution decays as 1/r^κwith κ=1+(c-2)/ ν. Here νis the self-avoiding walk correlation length exponent and c is the exponent associated with the entropy of an open loop in the chain. Results for the distribution function just below the melting point are also presented. Numerical…
There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular-closed plasmids, is less abrupt than that of linear molecules. This finding points to an intriguing role of topology in the physics of DNA denaturation, which is however poorly understood. Here, we shed light on this issue by combining large-scale Brownian Dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the sing…
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 temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of th…
Understanding the melting of short DNA sequences probes DNA at the scale of the genetic code and raises questions which are very different from those posed by very long sequences, which have been extensively studied. We investigate this problem by combining experiments and theory. A new experimental method allows us to make a mapping of the opening of the guanines along the sequence as a function of temperature. The results indicate that non-local effects may be important in DNA because an AT-rich region is able to influence the opening of a base pair which is about 10 base pairs away. An earl…
We investigate kinetic pathways of the DNA melting transition using variable-range versions of the Poland-Scheraga (PS) and Peyrard-Dauxois-Bishop (PDB) models of DNA. In the PS model, we construct a phi^4-field theory to calculate the critical droplet profile, the initial growth modes, and the exponent characterizing the divergence of the susceptibility near the spinodal. In the PDB model, we use a mean field analysis to calculate susceptibility exponent. We compare these theoretical results with Monte Carlo and Brownian dynamic simulations on the PS and PDB models, respectively. We find that…
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 r…
Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy pl…
The effect of heterogeneous sequence composition on the denaturation of double stranded DNA is investigated. The resulting pair-binding energy variation is found to have a negligible effect on the critical properties of the smooth second order melting transition in the simplest (Peyrard-Bishop) model. However, sequence heterogeneity is dramatically amplified upon adopting a more realistic treatment of the backbone stiffness. The model yields features of ``multi-step melting'' similar to those observed in experiments.
We propose a new statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which mimic the geometrical constraints in the real molecule. This microscopic mechanism intrinsically accounts for the cooperativity related to the free energy penalty of bubble nucleation. The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves. Furthermore, the model explains the observed tempe…
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 explore the feasibility of using coarse-grained models to simulate the self-assembly of DNA nanostructures. We introduce a simple model of DNA where each nucleotide is represented by two interaction sites corresponding to the phosphate-sugar backbone and the base. Using this model, we are able to simulate the self-assembly of both DNA duplexes and Holliday junctions from single-stranded DNA. We find that assembly is most successful in the temperature window below the melting temperatures of the target structure and above the melting temperature of misbonded aggregates. Furthe…
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 …
The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from the genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights in the physical mechanisms underlying the evolution of genes.
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 …
We have studied the separation of a double stranded DNA (dsDNA), which is driven either by the temperature or force. By monitoring the probability of opening of entire base pairs along the chain, we show that the opening of a dsDNA depends not only on the sequence but also on the constraints on the chain in the experimental setups. Our results clearly demonstrate that the force induced melting of dsDNA, whose one of the ends is constrained, is significantly different from the thermal melting, when both ends free.
Experimental studies of the thermal denaturation of DNA yield a strong indication that the transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule are given by an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In this study we exploit recent results on scaling prope…
We study the melting of three-stranded DNA by using the real-space renormalization group and exact recursion relations. The prediction of an unusual Efimov-analog three-chain bound state, that appears at the critical melting of two-chain DNA, is corroborated by the zeros of the partition function. The distribution of the zeros has been studied in detail for various situations. We show that the Efimov DNA can occur even if the three-chain (i. e., three-monomer) interaction is repulsive in nature. In higher dimensions, a striking result that emerged in this repulsive zone is a continuous transit…
Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. A surprising result found here is that the entanglement entropy may become arbitrarily large and negative near the dissociation of a bound pair of quantum particles. Although apparently counter-intuitive, it is shown to be consistent and essential for the phase transition, by mapping to a classical problem of DNA melting. We associate the entanglement entropy to a subextensive part of the entropy of DN…
Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phas…
We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_…
The wormlike chain (WLC) model of DNA bending accurately reproduces single-molecule force-extension profiles of long (kilobase) chains. These bending statistics over large scales do not, however, establish a unique microscopic model for elasticity at the 1-10 bp scale, which holds particular interest in biological contexts. Here we examine a class of microscopic models which allow for disruption of base pairing (i.e., a `melt' or `kink', generically an `excitation') and consequently enhanced local flexibility. We first analyze the effect on the excitation free energy of integrating out the spa…
The effect of defects on the melting profile of short heterogeneous DNA chains are calculated using the Peyrard-Bishop Hamiltonian. The on-site potential on a defect site is represented by a potential which has only the short-range repulsion and the flat part without well of the Morse potential. The stacking energy between the two neigbouring pairs involving a defect site is also modified. The results are found to be in good agreement with the experiments.
The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by P.J. Flory in 1956. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition, and compute exact values of critical…
The paper deals with the two-state (opening-closing of base pairs) model used to describe the fluctuation dynamics of a single bubble formation. We present an exact solution for the discrete and finite size version of the model that includes end effects and derive analytic expressions of the correlation function, survival probability and lifetimes for the bubble relaxation dynamics. It is shown that the continuous and semi-infinite limit of the model becomes a good approximation to exact result when a^N << 1, where N is bubble size and a, the ratio of opening to closing rates of base pairs, is…
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…
The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of the unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed in expense of 1) overtwist, 2) supercoils. Recent work has shown that the supercoiling mechanism results in a BEC-like picture where a macroscopic loop appears at Tc and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show …
We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri J, Manghi M and Destainville N 2007 Phys. Rev. Lett. 99 088103). Our Discrete Helical Wormlike Chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in …
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…
We generalize the Poland-Scheraga (PS) model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent single-molecule experiments on DNA strands, we assume that the torsional stress induced by denaturation enforces formation of supercoils whose writhe absorbs the linking number expelled by the loops. Our model predicts that, when the entropy parameter of a loop satisfies $c \le 2$, denaturation transition does not take place. On the other hand for $c>2$ a first-order denaturation transition is consistent with our model and may take …
We report studies of the equilibrium and the dynamics of a general set of lattice models which capture the essence of the force-induced or mechanical DNA unzipping transition. Besides yielding the whole equilibrium phase diagram in the force vs temperature plane, which reveals the presence of an interesting re-entrant unzipping transition for low T, these models enable us to characterize the dynamics of the process starting from a non-equilibrium initial condition. The thermal melting of the DNA strands displays a model dependent time evolution. On the contrary, our results suggest that the dy…
This paper explores the use of a cumulant method to determine the zeros of partition functions for continuous phase transitions. Unlike a first-order transition, with a uniform density of zeros near the transition point, a continuous transition is expected to show a power law dependence of the density with a nontrivial slope for the line of zeros. Different types of models and methods of generating cumulants are used as a testing ground for the method. These include exactly solvable DNA melting problem on hierarchical lattices, heterogeneous DNA melting with randomness in sequence, Monte Carlo…
When pulled along its axis, double-stranded DNA elongates abruptly at a force of about 65 pN. Two physical pictures have been developed to describe this overstretched state. The first proposes that strong forces induce a phase transition to a molten state consisting of unhybridized single strands. The second picture instead introduces an elongated hybridized phase, called S-DNA, structurally and thermodynamically distinct from standard B-DNA. Little thermodynamic evidence exists to discriminate directly between these competing pictures. Here we show that within a microscopic model of DNA we ca…
The possibility of prescribing local interactions between nano- and microscopic components that direct them to assemble in a predictable fashion is a central goal of nanotechnology research. In this article we advance a new paradigm in which self-assembly of DNA-functionalized colloidal particles is programmed using linker oligonucleotides dispersed in solution. We find a phase diagram that is surprisingly rich compared to phase diagrams typical of other DNA-functionalized colloidal particles that interact by direct hybridization, including a re-entrant melting transition upon increasing linke…
The following properties are in the present literature associated with the behavior of super-cooled glass-forming liquids: faster than exponential growth of the relaxation time, dynamical heterogeneities, growing point-to-set correlation length, crossover from mean field behavior to activated dynamics. In this paper we argue that these properties are also present in a much simpler situation, namely the melting of the bulk of an ordered phase beyond a first order phase transition point. This is a promising path towards a better theoretical, numerical and experimental understanding of the above …
There are deep analogies between the melting dynamics in systems with a first order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first order transition - namely p-spin models on the so-called Nishimori line - it can be shown that the melting dynamics can be exactly mapped to the equilibrium dynamics. In this mapping the dynamical -or mode-coupling- glass transition corresponds to the spinodal point, while the Kauzmann transition corresponds to the first order phase transition itself. Both in mean field and finite dime…
The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power law (IPL) potential, most notably the superpositioning of relaxation data as a function of the variable TVγ, where T is temperature, V the specific volume, and γ a material constant. A related scaling law, TmVmΓ, with the same exponent Γ=γ, links the melting temperature Tm and volume Vm of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid cry…
We present molecular dynamics simulations of the thermodynamic melting transition of a bcc metal, vanadium using the Finnis-Sinclair potential. We studied the structural, transport and energetic properties of slabs made of 27 atomic layers with a free surface. We investigated premelting phenomena at the low-index surfaces of vanadium; V(111), V(001), and V(011), finding that as the temperature increases, the V(111) surface disorders first, then the V(100) surface, while the V(110) surface remains stable up to the melting temperature. Also, as the temperature increases, the disorder spreads fro…
We present molecular dynamics simulations of the homogeneous (mechanical) melting transition of a bcc metal, vanadium. We study both the nominally perfect crystal as well as one that includes point defects. According to the Born criterion, a solid cannot be expanded above a critical volume, at which a 'rigidity catastrophe' occurs. This catastrophe is caused by the vanishing of the elastic shear modulus. We found that this critical volume is independent of the route by which it is reached whether by heating the crystal, or by adding interstitials at a constant temperature which expand the latt…
We study the size fluctuations of a local denaturation zone in a DNA molecule in the presence of proteins that selectively bind to single-stranded DNA, based on a (2+1)-dimensional master equation. By tuning the physical parameters we can drive the system from undisturbed bubble fluctuations to full, binding protein-induced denaturation. We determine the effective free energy landscape of the DNA-bubble and explore its relaxation modes.
The long time dynamics of the conformational transition from B-DNA to Z-DNA is shown to undergo a dynamic phase transition. We obtained the dynamic phase diagram for the stability of the front separating B and Z. The instability in this front results in two split fronts moving with different velocities. Hence, depending on the system parameters a denatured state may develop dynamically eventhough it is thermodynamically forbidden. This resolves the current controversies on the transition mechanism of the B-DNA to Z-DNA.
We study DNA self-assembly and DNA computation using a coarse-grained DNA model within the directional dynamic bonding framework {[}C. Svaneborg, Comp. Phys. Comm. 183, 1793 (2012){]}. In our model, a single nucleotide or domain is represented by a single interaction site. Complementary sites can reversibly hybridize and dehybridize during a simulation. This bond dynamics induces a dynamics of the angular and dihedral bonds, that model the collective effects of chemical structure on the hybridization dynamics. We use the DNA model to perform simulations of the self-assembly kinetics of DNA tet…
