Thermal denaturation of a helicoidal DNA model

A predictive model for the thermomechanical melting transition of double stranded DNA

By extending the classical Peyrard-Bishop model, we are able to obtain a fully analytical description for the mechanical response of DNA under stretching at variable values of temperature, number of base pairs and intrachains and interchains bonds stiffness. In order to compare elasticity and temperature effects, we first analyze the system in the zero temperature mechanical limit, important to describe several experimental effects including possible hysteresis. We then analyze temperature effects in the framework of equilibrium Statistical Mechanics. In particular, we obtain an analytical expression for the temperature-dependent melting force and unzipping assigned displacement in the thermodynamical limit, also depending on the relative stability of intra vs. inter molecular bonds. Such results coincide with the purely mechanical model in the limit of zero temperature and with the denaturation temperature that we obtain with the classical transfer integral method. Based on our analytical results, we obtain explicitly phase diagrams and cooperativity parameters, where also discreteness effect can be accounted for. The obtained results are successfully applied in reproducing the thermomechanical experimental melting of DNA and the response of DNA hairpins. Due to the generality of the model, exemplified in the proposed analysis of both overstretching and unzipping experiments, we argue that the proposed approach can be extended to other thermomechanically induced molecular melting phenomena. STATEMENT OF SIGNIFICANCE: We obtain a fully analytical description of the complex wiggly energy landscape of two stranded macromolecules under unzipping loading. Based on Equilibrium Statistical Mechanics, we describe the combined thermomechanical effects and the melting transition of double stranded molecules such as nucleic acids. This is proved by quantitatively predicting the experimental behavior of both melting of DNA and DNA hairpins opening. While analytical results have been previously attained under special conditions on the relative stiffness of the covalent vs. non-covalent bonds of the base pairs, our model is completely general in this respect, thus representing a tool in the perspective of the design at the molecular scale. We show that the obtained model can be fully inscribed in the theory of phase transitions giving a new interpretation of the thermomechanical behavior of double stranded molecules.

The incipient denaturation mechanism of DNA

DNA denaturation is related to many important biological phenomena, such as its replication, transcription and the interaction with some specific proteins for single-stranded DNA. Dimethyl sulfoxide (DMSO) is a common chemical agent for DNA denaturation. In the present study, we investigate quantitatively the effects of different concentrations of DMSO on plasmid and linear DNA denaturation by atomic force microscopy (AFM) and UV spectrophotometry. We found that persistent length of DNA decreases significantly by adding a small amount of DMSO before ensemble DNA denaturation occurs; the persistence length of DNA in 3% DMSO solution decreases to 12 nm from about 50 nm without DMSO in solution. And local DNA denaturation occurs even at very low DMSO concentration (such as 0.1%), which can be directly observed in AFM imaging. Meanwhile, we observed the forming process of DNA contacts between different parts for plasmid DNA with increasing DMSO concentration. We suggest the initial mechanism of DNA denaturation as follows: DNA becomes more flexible due to the partial hydrogen bond braking in the presence of DMSO before local separation of the two complementary nucleotide chains.

The persistent length of DNA decreases significantly by adding small amount of DMSO. Local DNA denaturation occurs even at very low DMSO concentration, which can be observed by atomic force microscopy directly.

Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12551-021-00801-0.

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

A fully analytical treatment of the base-pair and codon dynamics in double-stranded DNA molecules is introduced, by means of a realistic treatment that considers different mass values for G, A, T, and C nucleotides and takes into account the intrinsic three-dimensional, helicoidal geometry of DNA in terms of a Hamitonian in cylindrical coordinates. Within the framework of the Peyrard–Dauxois–Bishop model, we consider the coupling between stretching and stacking radial oscillations as well as the twisting motion of each base pair around the helix axis. By comparing the linearized dynamical equations for the angular and radial variables corresponding to the bp local scale with those of the longer triplet codon scale, we report an underlying hierarchical symmetry. The existence of synchronized collective oscillations of the base-pairs and their related codon triplet units are disclosed from the study of their coupled dynamical equations. The possible biological role of these correlated, long-range oscillation effects in double standed DNA molecules containing mirror-symmetric codons of the form XXX, XX’X, X’XX’, YXY, and XYX is discussed in terms of the dynamical equations solutions and their related dispersion relations.

Base-Pairs' Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules

By introducing a suitable renormalization process, the charge carrier and phonon dynamics of a double-stranded helical DNA molecule are expressed in terms of an effective Hamiltonian describing a linear chain, where the renormalized transfer integrals explicitly depend on the relative orientations of the Watson-Crick base pairs, and the renormalized on-site energies are related to the electronic parameters of consecutive base pairs along the helix axis, as well as to the low-frequency phonons' dispersion relation. The existence of synchronized collective oscillations enhancing the π-π orbital overlapping among different base pairs is disclosed from the study of the obtained analytical dynamical equations. The role of these phonon-correlated, long-range oscillation effects on the charge transfer properties of double-stranded DNA homopolymers is discussed in terms of the resulting band structure.

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

Dynamical control of denaturation bubble nucleation in supercoiled DNA minicircles

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending- or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

Investigation of changes in the arrangement of water molecules and salt ions surrounding different atoms of the DNA molecule during the melting process: a molecular dynamics simulation study

A molecular dynamics simulation was performed on a B-DNA duplex (CGCGAATTGCGC) at different temperatures. The DNA was immerged in a saltwater medium with 1 mol/L NaCl concentration. The arrangements of water molecules and cations around the different atoms of DNA on the melting pathway were investigated. Almost for all atoms of the DNA by double helix → single-stranded transition, the water molecules released from the DNA duplex and cations were close to single-stranded DNA, but this behavior was not clearly seen at melting temperatures. Therefore, release of water molecules and cations approaching the DNA by the increase of temperature does not have any effect on the sharpness of the transition curve. Most of the water molecules and cations were found to be around the negatively charged phosphate oxygen atoms. The number of water molecules released from the first shell hydration upon melting in the minor groove was higher than in the major groove, and intrusion of cations into the minor groove after melting was higher than into the major groove. The hydrations of imino protons were different from each other and were dependent on DNA bases.

An effective mesoscopic model of double-stranded DNA

Watson and Crick's epochal presentation of the double helix structure in 1953 has paved the way to intense exploration of DNA's vital functions in cells. Also, recent advances of single molecule techniques have made it possible to probe structures and mechanics of constrained DNA at length scales ranging from nanometers to microns. There have been a number of atomistic scale quantum chemical calculations or molecular level simulations, but they are too computationally demanding or analytically unfeasible to describe the DNA conformation and mechanics at mesoscopic levels. At micron scales, on the other hand, the wormlike chain model has been very instrumental in describing analytically the DNA mechanics but lacks certain molecular details that are essential in describing the hybridization, nano-scale confinement, and local denaturation. To fill this fundamental gap, we present a workable and predictive mesoscopic model of double-stranded DNA where the nucleotides beads constitute the basic degrees of freedom. With the inter-strand stacking given by an interaction between diagonally opposed monomers, the model explains with analytical simplicity the helix formation and produces a generalized wormlike chain model with the concomitant large bending modulus given in terms of the helical structure and stiffness. It also explains how the helical conformation undergoes overstretch transition to the ladder-like conformation at a force plateau, in agreement with the experiment.

Anharmonic stacking in supercoiled DNA

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

Hysteresis in pressure-driven DNA denaturation

In the past, a great deal of attention has been drawn to thermal driven denaturation processes. In recent years, however, the discovery of stress-induced denaturation, observed at the one-molecule level, has revealed new insights into the complex phenomena involved in the thermo-mechanics of DNA function. Understanding the effect of local pressure variations in DNA stability is thus an appealing topic. Such processes as cellular stress, dehydration, and changes in the ionic strength of the medium could explain local pressure changes that will affect the molecular mechanics of DNA and hence its stability. In this work, a theory that accounts for hysteresis in pressure-driven DNA denaturation is proposed. We here combine an irreversible thermodynamic approach with an equation of state based on the Poisson-Boltzmann cell model. The latter one provides a good description of the osmotic pressure over a wide range of DNA concentrations. The resulting theoretical framework predicts, in general, the process of denaturation and, in particular, hysteresis curves for a DNA sequence in terms of system parameters such as salt concentration, density of DNA molecules and temperature in addition to structural and configurational states of DNA. Furthermore, this formalism can be naturally extended to more complex situations, for example, in cases where the host medium is made up of asymmetric salts or in the description of the (helical-like) charge distribution along the DNA molecule. Moreover, since this study incorporates the effect of pressure through a thermodynamic analysis, much of what is known from temperature-driven experiments will shed light on the pressure-induced melting issue.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [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 forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Modeling DNA response to terahertz radiation

Collective response of DNA to terahertz electric fields is studied in a simple pair bond model. We confirm, with some caveats, a previous observation of destabilizing DNA breather modes and explore the parameter dependence of these modes. It is shown that breather modes are eliminated under reasonable physical conditions and that thermal effects are significant.

Thermal fluctuation spectroscopy of DNA thermal denaturation

We have developed the technique of thermal fluctuation spectroscopy to measure the thermal fluctuations in a system. This technique is particularly useful to study the denaturation dynamics of biomolecules like DNA. Here we present a study of the thermal fluctuations during the thermal denaturation (or melting) of double-stranded DNA. We find that the thermal denaturation of heteropolymeric DNA is accompanied by large, non-Gaussian thermal fluctuations. The thermal fluctuations show a two-peak structure as a function of temperature. Calculations of enthalpy exchanged show that the first peak comes from the denaturation of AT rich regions and the second peak from denaturation of GC rich regions. The large fluctuations are almost absent in homopolymeric DNA. We suggest that bubble formation and cooperative opening and closing dynamics of basepairs causes the additional fluctuation at the first peak and a large cooperative transition from a partially molten DNA to a completely denatured state causes the additional fluctuation at the second peak.

Energy localization in an anharmonic twist-opening model of DNA dynamics

Energy localization is investigated in the framework of the anharmonic twist-opening model proposed by Cocco and Monasson. This model includes the coupling between opening and twist that result from the helicoidal geometry of B-DNA. I first reduce the corresponding two-component model to its amplitude equations, which have the form of coupled discrete nonlinear Schrödinger (DNLS) equations, and I perform the linear stability analysis of the plane waves, solutions of the coupled DNLS equations. It is shown that the stability criterion deeply depends on the stiffness of the molecule. Numerical simulations are carried out in order to verify analytical predictions. It results that increasing the value of the molecule stiffness makes the energy patterns long-lived and highly localized. This can be used to explain the way enzymes concentrate energy on specific sequences of DNA for the base-pairs to be broken. The role of those enzymes could therefore be to increase the stiffness of closed regions of DNA at the boundaries of an open state.

Melting of genomic DNA: Predictive modeling by nonlinear lattice dynamics

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 ϕX174 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 experiments.

Stationary solutions for a modified Peyrard-Bishop DNA model with up to third-neighbor interactions

We investigate a DNA model that takes into account stacking interactions with neighbors up to three bases away. The model is a generalization of the well-known Peyrard-Bishop (PB) model and is motivated by studies that suggest that nearest-neighbor models for base-pair interaction in a DNA chain might not be enough to capture the mechanism and dynamics of DNA base-pair opening. We study stationary solutions of the modified model and investigate their stability. A comparison with the PB model reveals that under a wide range of parameter values the main characteristics of the original model --such as the hyperbolicity of the equilibrium at the origin-- are preserved, but new types of stationary solutions emerge.

Supercoil formation in DNA denaturation

We generalize the Poland-Scheraga 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 the 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<or=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 place in the actual system, as in the case with no supercoils. These results are in contrast with other treatments of circular DNA melting where denaturation is assumed to be accompanied by an increase in twist rather than writhe on the bound segments.

Single DNA denaturation and bubble dynamics

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

Dynamical versus statistical mesoscopic models for DNA denaturation

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

Thermal equivalence of DNA duplexes for probe design

We present the theory of thermal equivalence in the framework of the Peyrard-Bishop model and some of its anharmonic variants. The thermal equivalence gives rise to a melting index τ which maps closely the experimental DNA melting temperatures for short DNA sequences. We show that the efficient calculation of the melting index can be used to analyse the parameters of the Peyrard-Bishop model and propose an improved set of Morse potential parameters. With this new set we are able to calculate some of the experimental melting temperatures to ± 1.2 °C. We review some of the concepts of sequencing probe design and show how to use the melting index to explore the possibilities of gene coverage by tuning the model parameters.

Solitonlike base pair opening in a helicoidal DNA: an analogy with a helimagnet and a cholesteric liquid crystal

We propose a model for DNA dynamics by introducing the helical structure through twist deformation in analogy with the structure of a helimagnet and a cholesteric liquid-crystal system. The dynamics in this case is found to be governed by the completely integrable sine Gordon equation, which admits kink-antikink solitons with increased width, representing a wide base-pair opening configuration in DNA. The results show that the helicity introduces a length-scale variation and thus provides a better representation of the base-pair opening in DNA.

The pathway of oligomeric DNA melting investigated by molecular dynamics simulations

Details of the reaction coordinate for DNA melting are fundamental to much of biology and biotechnology. Recently, it has been shown experimentally that there are at least three states involved. To clarify the reaction mechanism of the melting transition of DNA, we perform 100-ns molecular dynamics simulations of a homo-oligomeric, 12-basepair DNA duplex, d(A(12)).d(T(12)), with explicit salt water at 400 K. Analysis of the trajectory reveals the various biochemically important processes that occur on different timescales. Peeling (including fraying from the ends), searching for Watson-Crick complements, and dissociation are recognizable processes. However, we find that basepair searching for Watson-Crick complements along a strand is not mechanistically tied to or directly accessible from the dissociation steps of strand melting. A three-step melting mechanism is proposed where the untwisting of the duplex is determined to be the major component of the reaction coordinate at the barrier. Though the observations are limited to the characteristics of the system being studied, they provide important insight into the mechanism of melting of other more biologically relevant forms of DNA, which will certainly differ in details from those here.

How topological constraints facilitate growth and stability of bubbles in DNA

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

A breathing wormlike chain model on DNA denaturation and bubble: effects of stacking interactions

DNA stably exists as a double-stranded structure due to hydrogen-bonding and stacking interactions between bases. The stacking interactions are strengthened when DNA is paired, which results in great enhancement of bending rigidity. We study the effects of this stacking-induced stiffness difference on DNA denaturation and bubble formations. To this end, we model double-stranded DNA as a duplex of two semiflexible chains whose persistence length varies depending on the base-pair distance. Using this model, we perform the Langevin dynamics simulation to examine the characteristics of the denaturation transition and the statistics of the bubbles. We find that the inclusion of the stacking interactions causes the denaturation transition to be much sharper than otherwise. At physiological temperature, the stacking interactions prohibit the initiation of bubble formation but promote bubbles, once grown, to retain the large size.

Stability domains of actin genes and genomic evolution

In eukaryotic genes, the protein coding sequence is split into several fragments, the exons, separated by noncoding DNA stretches, the introns. Prokaryotes do not have introns in their genomes. We report calculations of the stability domains of actin genes for various organisms in the animal, plant, and fungi kingdoms. Actin genes have been chosen because they have been highly conserved during evolution. In these genes, all introns were removed so as to mimic ancient genes at the time of the early eukaryotic development, i.e., before intron insertion. Common stability boundaries are found in evolutionarily distant organisms, which implies that these boundaries date from the early origin of eukaryotes. In general, the boundaries correspond with intron positions in the actins of vertebrates and other animals, but not much for plants and fungi. The sharpest boundary is found in a locus where fungi, algae, and animals have introns in positions separated by one nucleotide only, which identifies a hot spot for insertion. These results suggest that some introns may have been incorporated into the genomes through a thermodynamically driven mechanism, in agreement with previous observations on human genes. They also suggest a different mechanism for intron insertion in plants and animals.

Theoretical investigation of finite size effects at DNA melting

We investigated how the finiteness of the length of a sequence affects the phase transition that takes place at the DNA melting temperature. For this purpose, we modified the transfer integral method to adapt it to the calculation of both extensive (partition function, entropy, specific heat, etc.) and nonextensive (order parameter and average separation between paired bases) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We characterized in some detail the three effects that take place when the length of the sequence is decreased, namely, (i) the decrease of the critical temperature, (ii) the decrease of the peak values of all quantities that diverge at the thermodynamic limit but remain finite for finite sequences, like the specific heat and the correlation length, and (iii) the broadening of the temperature range over which the transition affects the dynamics of the system. We also performed a finite size scaling analysis of the two models and showed that the singular part of the free energy can indeed be expressed in terms of a homogeneous function. However, Josephson's identity is satisfied for none of the investigated models, so that the derivation of the characteristic exponents which appear, for example, in the expression of the specific heat requires some care.

Simple combined model for nonlinear excitations in DNA

We propose a simple model for DNA denaturation bases on the pendulum model of Englander [Proc. Natl. Acad. Sci. U.S.A. 77, 7222 (1980)] and the microscopic model of Peyrard and Bishop [Phys. Rev. Lett. 62, 2755 (1989)], so-called "combined model." The main parameters of our model are the coupling constant k along each strand, the mean stretching y* of the hydrogen bonds, the ratio of the damping constant and driven force gamma/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.

Stacking heterogeneity: a model for the sequence dependent melting cooperativity of duplex DNA

A microscopic Potts-like one-dimensional model with many particle interactions [referred as the generalized model of polypeptide chains (GMPCs)] is developed to investigate cooperativity of DNA sequence dependent melting. For modeling sequence, regular homogeneous sequences were arranged in heterogeneous blocks of various lengths. Within the framework of the GMPC the authors show that the inclusion of stacking interaction heterogeneity relative to homogeneous hydrogen bond interactions leads to an unexpected and quite remarkable increase in melting cooperativity for small blocks. In some cases this tendency persists for long blocks having sharp sequence heterogeneity.

Composite model for DNA torsion dynamics

DNA torsion dynamics is essential in the transcription process; a simple model for it, in reasonable agreement with experimental observations, has been proposed by Yakushevich (Y) and developed by several authors; in this, the nucleotides (the DNA subunits made of a sugar-phosphate group and the attached nitrogen base) are described by a single degree of freedom. In this paper we propose and investigate, both analytically and numerically, a "composite" version of the Y model, in which the sugar-phosphate group and the base are described by separate degrees of freedom. The model proposed here contains as a particular case the Y model and shares with it many features and results, but represents an improvement from both the conceptual and the phenomenological point of view. It provides a more realistic description of DNA and possibly a justification for the use of models which consider the DNA chain as uniform. It shows that the existence of solitons is a generic feature of the underlying nonlinear dynamics and is to a large extent independent of the detailed modeling of DNA. The model we consider supports solitonic solutions, qualitatively and quantitatively very similar to the Y solitons, in a fully realistic range of all the physical parameters characterizing the DNA.

The effect of sequence correlation on bubble statistics in double-stranded DNA

DNA exists stably in the double-stranded structure at physiological temperatures, but base pairs are observed to unbind locally, giving way to bubbles (i.e., locally denatured states) due to thermal fluctuation. In this study, we consider the effect of sequence on the bubble statistics. On the basis of the Edwards equation description [W. Sung and J.-H. Jeons, Phys. Rev. E 69, 031902 (2004) ], we develop a stochastic model incorporating the sequence randomness as a dichotomic noise, where the bubble and its size are identified as a returning random walk and its first passage time, respectively. By simulating the model Langevin equation, we obtain the bubble size distribution and show how it is affected by the sequence correlation. We find that the bubble size distribution of DNA with finite sequence correlation deviates from the Poland-Scheraga-type distribution. In particular, the formation of large bubbles is dramatically enhanced as sequence correlation length gets longer.

Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation l0 --> 0, where l0 is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without l0 --> 0. The model still supports soliton solutions indexed by two winding numbers (n,m); we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively.

A semiflexible chain model of local denaturation in double-stranded DNA

Double-stranded DNA (dsDNA) is known to form a locally denatured structure ("bubble") below its denaturation temperature (T(c)). We have investigated the physical behavior of the bubbles using a model of dsDNA as two wormlike chains containing interacting complementary base pairs. The model incorporates two biologically relevant features, i.e., semiflexibility of the strand and overdamping nature of aqueous background. Computer simulations using the Langevin equation are performed to examine the size distribution and dynamics of bubbles. The results show that the entropy associated with semiflexibility of DNA sensitively affects the size distribution and lifetime of bubble. In particular, the lifetime grows with bubble size m as m(2.7) at temperature close to T(c), which is consistent with our analysis based on a stochastic model of bubble size dynamics.

Direct observation of large temperature fluctuations during DNA thermal denaturation

In this Letter, we report direct measurement of large low frequency temperature fluctuations in double stranded DNA when it undergoes a 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 DNA of the same sequence. The fluctuation at a given temperature also depends on the wait time and vanishes in a scale of a few hours. It is suggested that the large fluctuation occurs due to coexisting denaturated and closed base pairs that are in dynamic equilibrium due to the transition through a potential barrier in the scale of 25-30kBT0 (T0=300 K).

Thermal denaturation of double-stranded DNA: effect of base stacking

We study the thermal denaturation of double-stranded DNA, i.e., separation of its two strands upon heating. A simple homo-polymer model is used to account for the effect of base stacking on the thermal stability of DNA. We find that stacking influences the stability in a nontrivial way: It not only enhances the stability but also makes the denaturation transition sharp. While stacking between bound monomers stabilizes DNA as does base pairing, stacking in unbound parts (or loops) rather destabilizes DNA--the overall stability is, however, enhanced by stacking.

Helicoidal transfer matrix model for inhomogeneous DNA melting

An inhomogeneous helicoidal nearest-neighbor model with continuous degrees of freedom is shown to predict the same DNA melting properties as traditional long-range Ising models, for free DNA molecules in solution, as well as superhelically stressed DNA with a fixed linking number constraint. Without loss of accuracy, the continuous degrees of freedom can be discretized using a minimal number of discretization points, yielding an effective transfer matrix model of modest dimension (d=36). The resulting algorithms to compute DNA melting profiles are both simple and efficient.

The helix-coil transition in heterogeneous double stranded DNA: Microcanonical method

A microscopic Potts-like one-dimensional model with many-particle interactions is developed to construct a statistical mechanical description of the melting of heterogeneous sequence duplex DNA. For this model, referred as the generalized model of polypeptide chains (GMPC), a closed-form expression for the free energy is derived. The characteristic equation of the model enables estimates on the melting temperature and transition interval, consistent with results obtained from more classical approaches. From the characteristic equation of the model, the temperature-dependent statistical weight parameter for helical states is evaluated. This parameter is shown to change throughout the transition from a harmonic form in early regions of the transition to an arithmetic form in later stages. The GMPC is extended to consider the influence of sequence heterogeneity in the melting of duplex DNA.

Statistical theory of force-induced unzipping of DNA

The unzipping transition under the influence of external force of a dsDNA molecule has been studied using the Peyrard-Bishop Hamiltonian. The critical force F(c)(T) for unzipping calculated in the constant force ensemble is found to depend on the potential parameter k which measures the stiffness associated with a single strand of DNA and on D, the well depth of the on-site potential representing the strength of hydrogen bonds in a base pair. The dependence on temperature of F(c)(T) is found to be (T(D) - T)(1/2) (T(D) being the thermal denaturation temperature) with F(c)(T(D)) = 0 and F(c)(0) = [Formula: see text]. We used the constant extension ensemble to calculate the average force F(y) required to stretch a base pair a y distance apart. The value of F(y) needed to stretch a base pair located far away from the ends of a dsDNA molecule is found twice the value of the force needed to stretch a base pair located at one of the ends to the same distance for y >/= 1.0 A. The force F(y) in both cases is found to have a very large value for y approximately 0.2 A compared to the critical force found from the constant force ensemble to which F(y) approaches for large values of y. It is shown that the value of F(y) at the peak depends on the value of krho which measures the energy barrier associated with the reduction in DNA strand rigidity as one passes from dsDNA to ssDNA and on the value of the depth of the on-site potential. The effect of defects on the position and height of the peak in the F(y) curve is investigated by replacing some of the base pairs including the one being stretched by defect base pairs. The formation and behaviour of a loop of Y shape when one of the ends base pair is stretched and a bubble of ssDNA with the shape of "an eye" when a base pair far from ends is stretched are investigated.

Model for DNA hairpin denaturation

We investigate the thermal denaturation of DNA hairpins using molecular dynamics simulations of a simple model describing the molecule at a scale of a nucleotide. The model allows us to analyze the different interacting features that determine how an hairpin opens, such as therole of the loop and the properties intrinsic to the stem.