Marco Zoli

Thermodynamics of twisted DNA with solvent interaction

The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over ~10(7)-10(8) base pair paths, a large number of double helix configurations is taken into account consistently with the physical requirements of the model potential. The partition function is computed as a function of the twist. It is found that the equilibrium twist angle, peculiar of B-DNA at room temperature, yields the stablest helicoidal geometry against thermal disruption of the base pair hydrogen bonds. This result is corroborated by the computation of thermodynamical properties such as fractions of open base pairs and specific heat.

Denaturation patterns in heterogeneous DNA.

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 peaks in the specific-heat plots while the entropy grows continuously versus T. Thus, the opening of the double strand with bubble formation appears as a smooth crossover due to base pair fluctuation effects which are accounted for by the path-integral method. The multistep transition is driven by the adenine-thymine- (AT) rich regions of the DNA fragment. The base pairs path ensemble shows an enhanced degree of cooperativity at about the same temperatures for which the specific-heat peaks occur. These findings establish a link between microscopic and macroscopic signatures of the transition. The fractions of mean base pair stretchings are computed by varying the AT base pairs content and taking some threshold values for the occurrence of the molecule denaturation.

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.

Stacking interactions in denaturation of DNA fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time-dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine-rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble, we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.

Helix untwisting and bubble formation in circular DNA.

The base pair fluctuations and helix untwisting are examined for a circular molecule. A realistic mesoscopic model including twisting degrees of freedom and bending of the molecular axis is proposed. The computational method, based on path integral techniques, simulates a distribution of topoisomers with various twist numbers and finds the energetically most favorable molecular conformation as a function of temperature. The method can predict helical repeat, openings loci, and bubble sizes for specific sequences in a broad temperature range. Some results are presented for a short DNA circle recently identified in mammalian cells.

Lattice Dynamics Effects on Small Polaron Properties

This study details the conditions under which strong-coupling perturbation theory can be applied to the molecular crystal model, a fundamental theoretical tool for analysis of the polaron properties. I show that lattice dimensionality and intermolecular forces play a key role in imposing constraints on the applicability of the perturbative approach. The polaron effective mass has been computed in different regimes ranging from the fully antiadiabatic to the fully adiabatic. The polaron masses become essentially dimension independent for sufficiently strong intermolecular coupling strengths and converge to much lower values than those tradition-ally obtained in small-polaron theory. I find evidence for a self-trapping transition in a moderately adiabatic regime at an electron-phonon coupling value of .3. Our results point to a substantial independence of the self-trapping event on dimensionality.

Path Integral Method for DNA denaturation

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 fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc*, whereas the fraction of unbound base pairs grows continuously around and above Tc*. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc*. The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

Polaron Crossover in Molecular Solids

An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behaviour of the effective mass as a function of the electron–phonon coupling. By increasing the strength of the intermolecular forces the crossover becomes smoother and occurs at higher e–ph couplings. These effects are more evident in three dimensions. We show that our modified Lang–Firsov method starts to capture the occurrence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order times the bare band mass according to the dimensionality and the value of the adiabatic parameter. Modified Lang–Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.

Path integral of the two-dimensional Su-Schrieffer-Heeger model

The equilibrium thermodynamics of the two-dimensional Su-Schrieffer-Heeger model is derived by means of a path integral method that accounts for the variable range of the electronic hopping processes. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The free energy of the system and its temperature derivatives are computed by summing at any

Mass renormalization in the Su-Schrieffer-Heeger model

T