DNA denaturation bubbles at criticality

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 varying sizes at different temperatures reveals almost identical scaled shapes in the absence of nonlinear stacking; nonlinear stacking leads to distinct scaled shapes of large and small bubbles.Comment: 8 pages, 8 figure

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 (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs 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 DW formation.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

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 $\phi$X174 phage without any adjustable parameters are in good agreement with experiment. The calculated probabilities for single base-pair opening are consistent with values obtained from imino proton exchange experiments.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Phase transitions in one dimension: are they all driven by domain walls?

Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B) the ferromagnetic, spin 1/2 Ising model with long-range pair interactions varying as the inverse square of the distance between pairs. In both cases it can be shown that the domain wall configurations become entropically stable at, or very near, the critical temperature. This might provide a "positive" criterion for the occurrence of a phase transition in one-dimensional systems.Comment: 9 pages, 3 figures. To appear in a special volume of Physica D (Serge Aubry 60th birthday symposium

Base Pair Openings and Temperature Dependence of DNA Flexibility

The relationship of base pair openings to DNA flexibility is examined. Published experimental data on the temperature dependence of the persistence length by two different groups are well described in terms of an inhomogeneous Kratky-Porot model with soft and hard joints, corresponding to open and closed base pairs, and sequence-dependent statistical information about the state of each pair provided by a Peyrard-Bishop-Dauxois (PBD) model calculation with no freely adjustable parameters

On 4-point correlation functions in simple polymer models

We derive an exact formula for the covariance of cartesian distances in two simple polymer models, the freely-jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case correlations exist as long as the two distances at least partially share the same segments. For the interacting case, we demonstrate that the naive expectation of increasing correlations with increasing interaction strength only holds in a finite range of values. Some suggestions for future single-molecule experiments are made

Structural correlations and melting of B-DNA fibres

Despite numerous attempts, the understanding of the thermal denaturation of DNA is still a challenge due to the lack of structural data at the transition since standard experimental approaches to DNA melting are made in solution and do not provide spatial information. We report a measurement using neutron scattering from oriented DNA fibres to determine the size of the regions that stay in the double-helix conformation as the melting temperature is approached from below. A Bragg peak from the B-form of DNA has been observed as a function of temperature and its width and integrated intensity have bean measured. These results, complemented by a differential calorimetry study of the melting of B DNA fibres as well as electrophoresis and optical observation data, are analysed in terms of a one-dimensional mesoscopic model of DNA

The thermal denaturation of DNA studied with neutron scattering

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.Comment: accepted for publication in Physical Review Letter