The denaturation dynamics of a long double-stranded DNA is studied by means of a model of the Poland-Scheraga type. We note that the linking of the two strands is a locally conserved quantity, hence we introduce local updates that respect this symmetry. Linking dissipation via untwist is allowed only at the two ends of the double strand. The result is a slow denaturation characterized by two time scales that depend on the chain length $L$. In a regime up to a first characteristic time $τ_1\sim L^{2.15}$ the chain embodies an increasing number of small bubbles. Then, in a second regime, bubbles coalesce and form entropic barriers that effectively trap residual double-stranded segments within the chain, slowing down the relaxation to fully molten configurations, which takes place at $τ_2\sim L^3$. This scenario is different from the picture in which the helical constraints are neglected.
We report on the nature of the thermal denaturation transition of homogeneous DNA as determined from a renormalisation group analysis of the Peyrard-Bishop-Dauxois model. Our approach is based on an analogy with the phenomenon of critical wetting that goes further than previous qualitative comparisons, and shows that the transition is continuous for the average base-pair separation. However, since the range of universal critical behaviour appears to be very narrow, numerically observed denaturation transitions may look first-order, as it has been reported in the literature.
We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent $c$ for which we find the new value $c=4ν-1/2$ such that the transition is second order with $c=1.85<2$ in $d=3$. We show that a finite stretching force $F$ destabilizes DNA, corresponding to a lower melting temperature $T(F)$, in agreement with single-molecule DNA stretching experiments.
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 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 …
The thermodynamical properties of heterogeneous DNA sequences are computed by path integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds between complementary strands. The portion of configuration space contributing to the partition function is determined, at any temperature, by selecting the ensemble of paths which fulfill the second law of thermodynamics. For a short DNA fragment, the denaturation is signaled by a succession of …
We study the static and dynamical properties of DNA in the vicinity of its melting transition, i.e. the separation of the two strands upon heating. The investigation is based on a simple mechanical model which includes the helicoidal geometry of the molecule and allows an exact numerical evaluation of its thermodynamical properties. Dynamical simulations of long-enough molecular segments allow the study of the structure factors and of the properties of the denaturated regions. Simulations of finite chains display the hallmarks of a first order transition for sufficiently long-ranged stacking f…
We study DNA denaturation by integrating elasticity -- as described by the Gaussian network model -- with bond binding energies, distinguishing between different base-pair and stacking energies. We use exact calculation, within the model, of the Helmholtz free-energy of any partial denaturation state, which implies that the entropy of all formed bubbles ("loops") is accounted for. Considering base-pair bond removal single events, the bond designated for opening is chosen by minimizing the free-energy difference for the process, over all remaining base-pair bonds. Despite of its great simplicit…
We briefly review some of the models used to describe DNA denaturation dynamics, focusing on the value of the dynamical exponent $z$, which governs the scaling of the characteristic time $τ\sim L^z$ as a function of the sequence length $L$. The models contain different degrees of simplifications, in particular sometimes they do not include a description for helical entanglement: we discuss how this aspect influences the value of $z$, which ranges from $z=0$ to $z \approx 3.3$. Connections with experiments are also mentioned.
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.
Recent theoretical predictions on DNA mechanical separation induced by pulling forces are numerically tested within a model in which self-avoidance for DNA strands is fully taken into account. DNA strands are described by interacting pairs of self avoiding walks (SAW) which are pulled apart by a force applied at the two extremities. The whole phase diagram is spanned by extensive Monte Carlo (MC) simulations and the existence of a low temperature denaturation is confirmed. The basic features of the phase diagram and the re-entrant phase boundary are also obtained with a simple heuristic argume…
The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.
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 study the effect of the composition of the genetic sequence on the melting temperature of double stranded DNA, using some simple analytically solvable models proposed in the framework of the wetting problem. We review previous work on disordered versions of these models and solve them when there were not preexistent solutions. We check the solutions with Monte Carlo simulations and transfer matrix numerical calculations. We present numerical evidence that suggests that the logarithmic corrections to the critical temperature due to disorder, previously found in RSOS models, apply more genera…
We present a precise equivalence of the Lifson-Poland-Scheraga model with wetting models. Making use of a representation of the former model in terms of random matrices, we obtain, in the limit of weak disorder, a mean--field approximation, that shows a change of the critical behavior due to disorder.
Double stranded DNA chain is known to have nontrivial elasticity. We study the effect of this elasticity on the denaturation profile of DNA oligomer by constraining one base pair at one end of the oligomer to remain in unstretched (or intact) state. The effect of this constraint on the denaturation profile of the oligomer has been calculated using the Peyrard-Bishop Hamiltonian. The denaturation profile is found to be very different from the free (i.e. without the constraint) oligomer. We have also examined how this constraint affects the denaturation profile of the oligomer having a segment o…
The hypothesis that phase transitions originate from some topological change of the critical level hypersurface of the potential energy receives direct evident support by our study of the Bishop--Peyrard model of DNA thermal denaturation.
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 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.
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 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 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 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…
It is shown that the scaling analysis presented in Phys. Rev. Lett. 85, 4988 (2000) is valid for finite chains of lengths relevant to experiments, in contrast to a recent claim made by A. Hanke and R. Metzler in cond-mat/0110164.
The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of …
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 replacment of mutual avoidance of polymers by a long-range interaction of the type proposed by Garel etal (Europhys. Lett. 55, 132 (2001), cond-mat/0101058) is inconsistent with the prevalent renormalization group arguments.
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…
It is shown that the scaling analysis presented in Phys. Rev. Lett. 85, 4988 (2000) (cond-mat/0007141) is valid for finite chains of lengths relevant to experiments, in contrast to a recent claim made by A. Hanke and R. Metzler in cond-mat/0108323.
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.
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.
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…
Poland-Scheraga models were introduced to describe the DNA denaturation transition. We give a rigorous and refined discussion of a family of these models. We derive possible scaling functions in the neighborhood of the phase transition point and review common examples. We introduce a self-avoiding Poland-Scheraga model displaying a first order phase transition in two and three dimensions. We also discuss exactly solvable directed examples. This complements recent suggestions as to how the Poland-Scheraga class might be extended in order to display a first order transition, which is observed ex…
In this comment we argue that while the conclusions in the original paper (Y. Kafri, D. Mukamel and L. Peliti, Phys. Rev. Lett. 85, 4988 (2000)) are correct for asymptotically long DNA chains, they do not apply to the chains used in typical experiments. In the added last paragraph, we point out that for real DNA the average distance between denatured loops is not of the order of the persistence length of a single-stranded chain but much larger. This corroborates our reasoning that the double helix between loops is quite rigid, and thereby our conclusion.
Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, i…
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.
Following Poland and Scheraga, we consider a simplified model for the denaturation transition of DNA. The two strands are modeled as interacting polymer chains. The attractive interactions, which mimic the pairing between the four bases, are reduced to a single short range binding term. Furthermore, base-pair misalignments are forbidden, implying that this binding term exists only for corresponding (same curvilinear abscissae) monomers of the two chains. We take into account the excluded volume repulsion between monomers of the two chains, but neglect intra-chain repulsion. We find that the ex…
The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, $P \sim l^{-c}$. If excluded volume effects are fully taken into account, c= 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclu…
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.
We study a model for the denaturation transition of DNA in which the molecules are considered as composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d=2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops w…
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 …
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 …
In the framework of the Poland Scheraga model of DNA denaturation, we derive a recursion relation for the partition function of double stranded DNA, allowing for mismatches between the two strands. This relation is studied numerically using standard parameters for the stacking energies and loop entropies. For complementary strands (of length 1000), we find that mismatches are significant only when the cooperativity parameter $σ$ is of order one. Since $σ\sim O(10^{-5})$ in DNA, entropic gains from mismatches are overwhelmed by the energetic cost of opening a loop: mismatches are therefore irre…
The closure dynamics of a pre-equilibrated DNA denaturation bubble is studied using both Brownian dynamics simulations and an analytical approach. The numerical model consists of two semi-flexible interacting single strands (ssDNA) and a bending modulus which depends on the base-pair state, with double-strand DNA (dsDNA) segments being 50 times stiffer than ssDNA ones. For DNA lengths from N=20 to 100 base-pairs (bp) and initial bubble sizes of N-6 bp, long closure times of 0.1 to 4 microseconds are found, following a scaling law in N^2.4. The bubble starts to close by a fast zipping which sto…
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…
We compare results of previous simulations of a simple model of DNA denaturation to the predictions of the Poland-Scheraga model. Concentrating on the critical region of the latter model we calculate both thermodynamic quantities and the distribution functions measured in the simulations. We find that the Poland-Scheraga model yields an excellent fit to the data, provided (i) we include a (singular) factor weighting the open ends of the doubly stranded chain, and (ii) we keep the leading corrections to the finite size scaling limit. The exponent c_1, which governs the end-weighting factor, is …
We present detailed molecular dynamics results for the displacement autocorrelation spectra of the Peyrard-Bishop model of thermal DNA denaturation. As the phase transition is approached, the spectra depend on whether the wavelength is smaller than, or exceeds the correlation length. In the first case, the spectra are dominated by a single peak, whose frequency approaches the bare acoustic frequency of the harmonic chain, and whose linewidth approaches zero as $T_c-T$. In the second case, a central peak (CP) feature is dominant, accounting for most of the weight; the linewidth of the CP appear…
The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appear…
In this paper, we investigate DNA denaturation through Statistical Mechanics and show that exceptional polynomials lead to DNA mutation. We consider a DNA model with two chains connected by Morse potential representing the H bonds, and then we calculate the partition function for this model. The partition function is converted into a Schrödinger like an equation. We exploit the techniques of SUSY quantum mechanics to model DNA mutation. We also compute the thermal denaturation of DNA for each mutated state.
We study the fluctuation dynamics of localized denaturation bubbles in heteropolymer DNA with a master equation and complementary stochastic simulation based on novel DNA stability data. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a biological sequence of the T7 bacteriophage. Quantitative agreement with data from fluorescence correlation spectroscopy (FCS) is demonstrated.
We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the $d = 3$ case, the…
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.
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 present a study on the role of defects on the stability of short DNA molecules. We consider short DNA molecules (16 base pairs) and investigate the thermal as well as mechanical denaturation of these molecules in the presence of defects that occurs anywhere in the molecule. For the investigation, we consider four different kinds of chains. Not only the ratio of AT to GC different in these molecules but also the distributions of AT and GC along the molecule are different. With suitable modifications in the statistical model to show the defect in a pair, we investigate the denaturation of sho…
By exploring a recent model [Palmeri, J., M. Manghi, and N. Destainville. 2007. Phys. Rev. Lett. 99:088103] where DNA bending elasticity, described by the wormlike chain model, is coupled to base-pair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic force microscopy (AFM) experiments [Wiggins, P. A., et al. 2006. Nature Nanotech. 1:137-141]. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally…
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…
Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Pal…
We suggest that the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles). On the basis of the reconstructed bubble size distribution, this is achieved through stochastic optimization of the free energies in terms of Simulated Annealing. In particular, it is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy. This method will be useful to obtain…
The 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…
For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end-segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first order thermal denaturation in both cases. Results for end-segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, ar…
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…
