Nikos Theodorakopoulos

Order of the phase transition in models of DNA thermal denaturation.

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(||) = 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( perpendicular) = -beta = 1/2,nu(||) = gamma/2 = 1.

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.

Thermal denaturation of DNA studied with neutron scattering.

The melting transition of 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 fiber DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois 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.

Thermodynamic Instabilities in One Dimension: Correlations, Scaling and Solitons

Many thermodynamic instabilities in one dimension (e.g., DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential with a repulsive core, a stable minimum and a flat top. The paper deals with the case of the Morse on-site potential, which can be treated exactly in the continuum limit. Analytical expressions for correlation functions are derived; they are shown to obey scaling; numerical transfer-integral values obtained for a discrete version of the model exhibit the same critical behavior. Furthermore, it is shown in detail that the onset of the transition can be characterized by an entropic stabilization of an—otherwise unstable—nonlinear field configuration, a soliton-like domain wall (DW) with macroscopic energy content. The statistical mechanics of the DW provides an exact estimate of the critical temperature for a wide range of the discretization parameter; this suggests that the transition can be accurately viewed as being “driven” by a nonlinear entity.

Temperature Dependence of the DNA Double Helix at the Nanoscale: Structure, Elasticity, and Fluctuations

Biological organisms exist over a broad temperature range of -15°C to +120°C, where many molecular processes involving DNA depend on the nanoscale properties of the double helix. Here, we present results of extensive molecular dynamics simulations of DNA oligomers at different temperatures. We show that internal basepair conformations are strongly temperature-dependent, particularly in the stretch and opening degrees of freedom whose harmonic fluctuations can be considered the initial steps of the DNA melting pathway. The basepair step elasticity contains a weaker, but detectable, entropic contribution in the roll, tilt, and rise degrees of freedom. To extend the validity of our results to the temperature interval beyond the standard melting transition relevant to extremophiles, we estimate the effects of superhelical stress on the stability of the basepair steps, as computed from the Benham model. We predict that although the average twist decreases with temperature in vitro, the stabilizing external torque in vivo results in an increase of ∼1°/bp (or a superhelical density of Δσ ≃ +0.03) in the interval 0-100°C. In the final step, we show that the experimentally observed apparent bending persistence length of torsionally unconstrained DNA can be calculated from a hybrid model that accounts for the softening of the double helix and the presence of transient denaturation bubbles. Although the latter dominate the behavior close to the melting transition, the inclusion of helix softening is important around standard physiological temperatures.

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.

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.

Competing mechanisms for the transport of energy in the α-helix

Abstract The Davydov model for a molecular chain of hydrogen-bonded peptide groups admits lattice acoustic as well as intramolecular solitons when the anharmonicity of the H-bond is explicitly taken into account. On the basis of a numerical simulation we suggest that such (supersonic) lattice solitons may present a more efficient alternative than the original (subsonic) selftrapped Davydov soliton for transporting energies under realistic conditions.

Solitary excitations in the α-helix: Viscous and thermal effects

Abstract We report a molecular dynamics study of the propagation of a solitary excitation in a one-dimensional Lennard-Jones lattice when thermal and frictional effects are included. We give to the parameters that characterize the system the values of a typical chain of hydrogen-bonded peptide groups in the α-helix and observe that at temperatures and energies of biological interest and with water as a solvent, potential energies can be transported over long distances.

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 fewer than ten 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.