Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting 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 consist of 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 the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

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 the two strands grows as in both phases. Received 8 May 2002 Published online 13 August 2002     

Roles of stiffness and excluded volume in DNA denaturation

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 approximately 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 inclusion of specific base-pair sequence heterogeneities.     

The invariance of order parameter and temperature redefinition in helix-coil transition theory of circular closed DNA

The order-disorder (helix-coil) transition in circular closed DNA (ccDNA) is described on the basis of the open chain DNA (ocDNA) model, proposed earlier, which considers the transition as loop formation. The Hamiltonian of the ccDNA model is constructed on the basis of the open chain model taking into account topological restrictions. These restrictions are taken into account through hydrogen bond reduced energy dependence on the fraction of broken hydrogen bonds in the macromolecule. The invariance of the order parameter (helicity degree) has been shown for ocDNA and ccDNA. This invariance results in the interdependence between temperatures of ocDNA and ccDNA with the same value of helicity degree. The dependence can be obtained with the help of the derivative of reduced energy of hydrogen bonding dependence on instantaneous denaturation degree. Thus, it has been shown that the melting curve of ccDNA can be obtained from the consequent curve of ocDNA through the redefinition of temperature scale. The calculated and experimentally measured melting curves have been compared under inversion conditions and qualitative agreement between them is found.     

Bubble nucleation and cooperativity in DNA melting

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Dauxois 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-state transition are studied.     

Spontaneous breaking of one-dimensional chains investigated with scanning tunneling microscopy

Landau (1937) [1] had an argument that one-dimensional long chains are not stable at finite temperature, and will break into short sections due to thermal fluctuation. However, until recently, fragmentation of one-dimensional chains by formation of thermal vacancies was first discovered in Bagatskii et al. (2014) [6] for the Xenon that physically adsorbed in the grooves of single-walled carbon nanotube bundles. In this work, scanning tunneling microscopy (STM) was first used to observe the influence of thermal fluctuations on the length of one-dimensional chains of the amino acids systems chemically adsorbed on metal surfaces. One-dimensional chains of amino acids formed on noble metal surfaces are spontaneously broken into chain segments with an average length of ～46 Å at room temperature. Very amazingly, the chain phase shows a unique self-adaptability in that it can always keep the length of chain segments unchanged at a fixed value, which is fulfilled through their flexible orientations, even though there is space limitation. While thermal fluctuation is a stochastic process, breaking of chains does not occur randomly along the chains. Breaking points are equidistantly distributed along the chain with a density (i.e., ratio of breaking points to adsorbates in a chain) of ～1/9 at room temperature. After heated to 400 K, the chain segments are shortened to ～31 Å. And thus, the breaking point density is increased to ～1/6. The activation energy for forming a breaking point is ～0.04 eV, being within the range of energy for a common hydrogen bond, implying that the amino acid chain is formed by intermolecular hydrogen bonds between adsorbates. The stable spatial distribution of broken points in a chain is resulted from the loss of one-dimensional translational symmetry at the two ends of a chain. This research experimentally first time substantiated both Landau's argument as well as prediction in some recent theoretical simulations.     

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).     

New results on the melting thermodynamics of a circular DNA chain

We investigate the impact of supercoil period and nonzero supercoil formation energy on the thermal denaturation of a circular DNA. Our analysis is based on a recently proposed generalization of the Poland-Scheraga model that allows the DNA melting to be studied for plasmids with circular topology, where denaturation is accompanied by formation of supercoils. We find that the previously obtained first-order melting transition persists under the generalization discussed. The dependence of the size of the order-parameter jump at the transition point and the associated melting temperature are obtained analytically.     

Influence of multiplicative noise on properties of first order dynamical phase transition

Critical phenomena in distributed dynamical two-dimensional nonlinear system near the point of the Turing instability are discussed. The system is considered in the presence of thermal fluctuations and multiplicative noise (MN) representing fluctuations of the bifurcation parameter. Since such a noise of the control parameter can have macroscopic (not thermal) nature, the intensity is considered as sufficiently large in comparison with the amplitude of thermal fluctuations, and it is shown that in the system the first order phase transition occurs with the characteristics which are independent on the thermal noise. Hence the discontinuous transtion could be observable in experimental situations where this would not be possible in the absence of MN (like the Rayleigh-Benard problem). When the correlation length of MN is small, the transition results in the formation of a complex state possessing only short-range order, and when MN is spatially uniform, a quasi-one-dimensional structure will be formed.     

Baryogenesis via density fluctuations with a second-order electroweak phase transition

We consider the presence of cosmic string-induced density fluctuations in the early universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time-scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second-order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs doublet model (with appropriate CP violation), we show that one can get the required baryon asymmetry if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production, though it is still 3–4 orders of magnitude larger than the conventional case of second-order transition.     

Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls, interpolating between bound and unbound segments of the chain. Their free energy is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g., DNA unzipping and/or thermal denaturation) can be understood in terms of domain wall formation.     

Infrared spectroscopy and ultrasonic velocimetry as a tool for probing conformational flexibility of proteins

Abstract

Because of the crucial importance of structural fluctuations for function and stability of proteins, there is a strong interest for the relationships between structural fluctuations, the parameters of protein denaturation and the kinetics of H/D-exchange. Structural fluctuations can be described by volume and entropy fluctuations and these quantities are accessible via the isothermal compressibility, the thermal expansion and the isobaric heat capacity.

Our aim is to present the principal problem concerning the experimental procedures to answer those questions using lysozyme and α-lactalbumin. Whereas the transition parameters and the kinetics of the H/D-exchange were obtained using FTIR spectroscopy, the adiabatic compressibility was obtained by a combination of ultrasonic velocimetry and densitometry. It could be shown that the stability of the investigated proteins is correlated with reduced volume fluctuations. The expected direct correlation between H/D exchange rates and structural fluctuations could not be seen and it is assumed that the interactions are more complex than from the intuitive point of view.     

Thermomechanics of DNA: theory of thermal stability under load

A theory for thermomechanical behavior of homogeneous DNA at thermal equilibrium predicts critical temperatures for denaturation under torque and stretch, phase diagrams for stable B-DNA, supercoiling, optimally stable torque, and the overstretching transition as force-induced DNA melting. Agreement with available single molecule manipulation experiments is excellent.     

DENATURATION AND PROPAGATION OF THE LOCALIZED EXCITATION IN DNA

The thermal denaturation and propagation of the localized excitation in desoxyribonucleic acid (DNA) molecules are studied in the unified way under a new Hamiltonian proposed in this work and the large amplitude motion of the DNA molecules is investigated during the propagation of the localized excitation. We discussed the nonlinear effect on the formation of the localized excitation, and showed that our model not only can reproduce the experimental results of the DNA thermal denaturation, but also can describe the process of the nonlinear localized excitation of fluctuational opening in DNA molecules.     

Diffusion and segmental dynamics of double-stranded DNA

Diffusion and segmental dynamics of the double-stranded lambda-phage DNA polymer are quantitatively studied over the transition range from stiff to semiflexible chains. Spectroscopy of fluorescence fluctuations of single-end fluorescently labeled monodisperse DNA fragments unambiguously shows that double-stranded DNA in the length range of 10(2) - 2 x 10(4) base pairs behaves as a semiflexible polymer with segmental dynamics controlled by hydrodynamic interactions.     

Melting of columnar hexagonal DNA liquid crystals

The persistence length DNA hexagonal-cholesteric phase transition upon dilution and/or increase in solvent ionic strength is investigated with polarized light microscopy. The ionic strength dependence of the transition follows Lindemann criterion , i.e., the hexagonal lattice melts when the root-mean-square fluctuations in transverse order exceed 10% of the interaxial spacing. The spacings are derived from density and the fluctuations are estimated with a theory of undulation enhanced electrostatic interactions. Additional support for this theory is given by the DNA equation of state and anisotropic neutron radiation scattering from magnetically aligned cholesteric samples just below the phase transition. Received: 17 November 1997 / Revised: 21 January 1998 / Accepted: 25 February 1998     

Theoretical Study on Effects of Salt and Temperature on Denaturation Transition of Double-stranded DNA

We investigate the statistical mechanics properties of a nonlinear dynamics model of the denaturation of the DNA double-helix and study the effects of salt concentration and temperature on denaturation transition of DNA. The specific heat, entropy, and denaturation temperature of the system versus salt concentration are obtained. These results show that the denaturation of DNA not only depends on the temperature but also is influenced by the salt concentration in the solution of DNA, which are in agreement with experimental measurement.     

Competitive and non-competitive interaction of solvent with biopolymers at the helix-coil transition

On the basis of generalized model of polypeptide chain (GMPC) as a microscopic theory of the helix-coil transition applicable to both polypeptides and DNA, the Hamiltonian of the model of solvent, which interacts with a biopolymer in both competitive and non-competitive ways, is introduced. It is shown that the partition function of this model is reduced to multipliers to the model without solvent. In this case thermal and entropic parameters of the theory are redefined. Based on calculation of the helicity degree and correlation length different cases of relation between parameters of competitive and non-competitive interaction are discussed.     

Statistical mechanics of thermal denaturation of DNA oligomers

Double stranded DNA chain is known to have non-trivial 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 of defect sites located at different parts of the chain.     

Polymers in a vacuum

In a variety of situations, isolated polymer molecules are found in a vacuum, and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken slowly by thermal radiation. For an ideal chain, the time autocorrelation for monomer position oscillates with a period proportional to chain length. The oscillations and damping are analyzed in detail. Short-range repulsive interactions suppress oscillations and speed up relaxation, but stretched chains still show damped oscillatory correlations.