arXiv subjects

Marco Zoli

Publications and source records attributed to Marco Zoli.

At least 37 records · Page 2Linked to original sources

arXiv2014

Entropic Penalties in Circular DNA Assembly

The thermodynamic properties of DNA circular molecules are investigated by a new path integral computational method which treats in the real space the fundamental forces stabilizing the molecule. The base pair and stacking contributions to the classical action are evaluated separately by simulating a broad ensemble of twisted conformations. We obtain, for two short sequences, a free energy landscape with multiple wells corresponding to the most convenient values of helical repeat. Our results point to a intrinsic flexibility of the circular structures in which the base pair fluctuations move the system from one well to the next thus causing the local unwinding of the helix. The latter is more pronounced in the shorter sequence whose cyclization causes a higher bending stress. The entropic reductions associated to the formation of the ordered helicoidal structure are estimated.

cond-mat.soft↗

arXiv2014

Twist versus Nonlinear Stacking in Short DNA Molecules

The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous short sequences of DNA, i.e. $\sim 100$ base pairs, in the framework of a mesoscopic Hamiltonian model which accounts for the helicoidal geometry of the molecule. The theoretical background for the application of the path integral formalism to predictive analysis of the molecule thermodynamical properties is discussed. The base pair displacements with respect to the ground state are treated as paths whose temperature dependent amplitudes are governed by the thermal wavelength. The ensemble of base pairs paths is selected, at any temperature, consistently with both the model potential and the second law of thermodynamics. The partition function incorporates the effects of the base pair thermal fluctuations which become stronger close to the denaturation. The transition appears as a gradual phenomenon starting from the molecule segments rich in adenine-thymine base pairs. Computing the equilibrium thermodynamics, we focus on the interplay between twisting of the complementary strands around the molecule axis and nonlinear stacking potential: it is shown that the latter affects the melting profiles only if the rotational degrees of freedom are included in the Hamiltonian. The use of ladder Hamiltonian models for the DNA complementary strands in the pre-melting regime is questioned.

q-bio.BM↗

arXiv2014

Twisting and Bending Stress in DNA Minicircles

The interplay between bending of the molecule axis and appearance of disruptions in circular DNA molecules, with $\sim 100$ base pairs, is addressed. Three minicircles with different radii and almost equal content of AT and GC pairs are investigated. The DNA sequences are modeled by a mesoscopic Hamiltonian which describes the essential interactions in the helix at the level of the base pair and incorporates twisting and bending degrees of freedom. Helix unwinding and bubble formation patterns are consistently computed by a path integral method that sums over a large number of molecule configurations compatible with the model potential. The path ensembles are determined, as a function of temperature, by minimizing the free energy of the system. Fluctuational openings appear along the helix to release the stress due to the bending of the molecule backbone. In agreement with the experimental findings, base pair disruptions are found with larger probability in the smallest minicircle of \textit{66-bps} whose bending angle is $\sim 6^{o} $. For this minicircle, a sizeable untwisting is obtained with the helical repeat showing a step-like increase at $τ=\,315K$. The method can be generalized to determine the bubble probability profiles of open ends linear sequences.

cond-mat.soft↗

arXiv2013

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.

q-bio.BM↗

arXiv2013

Modeling DNA Dynamics by Path Integrals

Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (\emph{bps}). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The \emph{bps} displacements with respect to the ground state are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds. The portion of the paths configuration space contributing to the partition function is determined by selecting the ensemble of paths which fulfill the second law of thermodynamics. Computations of the thermodynamics in the denaturation range show the energetic advantage for the equilibrium helicoidal geometry peculiar of B-DNA. I discuss the interplay between twisting of the double helix and anharmonic stacking along the molecule backbone suggesting an interesting relation between intrinsic nonlinear character of the microscopic interactions and molecular topology.

physics.bio-ph↗

arXiv2012

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.

cond-mat.soft↗

arXiv2011

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 $\sim 10^7 - 10^8$ 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.

q-bio.BM↗

arXiv2011

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 \emph{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.

cond-mat.soft↗

arXiv2010

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 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.

cond-mat.stat-mech↗

arXiv2009

Instantonic Methods for Quantum Tunneling in Finite Size

The instantonic approach for a $ϕ^4$ model potential is reexamined in the asymptotic limit. The path integral of the system is derived in semiclassical approximation expanding the action around the classical background. It is shown that the singularity in the path integral, arising from the zero mode in the quantum fluctuation spectrum, can be tackled only assuming a {\it finite} (although large) system size. On the other hand the standard instantonic method assumes the (anti)kink as classical background. But the (anti)kink is the solution of the Euler-Lagrange equation for the {\it infinite} size system. This formal contradiction can be consistently overcome by the finite size instantonic theory based on the Jacobi elliptic functions formalism. In terms of the latter I derive in detail the classical background which solves the finite size Euler-Lagrange equation and obtain the general path integral in finite size. Both problem and solution offer an instructive example of fruitful interaction between mathematics and physics. {\bf Keywords: Path Integral Methods, Finite Size Systems, Instantons}

quant-ph↗

arXiv2009

Polaron Mass and Electron-Phonon Correlations in the Holstein Model

The Holstein Molecular Crystal Model is investigated by a strong coupling perturbative method which, unlike the standard Lang-Firsov approach, accounts for retardation effects due to the spreading of the polaron size. The effective mass is calculated to the second perturbative order in any lattice dimensionality for a broad range of (anti)adiabatic regimes and electron-phonon couplings. The crossover from a large to a small polaron state is found in all dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon dispersion largely smooths such crossover which is signalled by polaron mass enhancement and on site localization of the correlation function. The notion of self-trapping together with the conditions for the existence of light polarons, mainly in two- and three-dimensions, are discussed. By the imaginary time path integral formalism I show how non local electron-phonon correlations, due to dispersive phonons, renormalize downwards the {\it e-ph} coupling justifying the possibility for light and essentially small 2D Holstein polarons.

cond-mat.supr-con↗

arXiv2009

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 fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. 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 continuosly versus $T$ while the specific heat displays a remarkable peak at $T^*_c$. 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.

cond-mat.stat-mech↗

arXiv2008

Finite Temperature Theory of Metastable Anharmonic Potentials

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low $T$ up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lamè equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.

cond-mat.stat-mech↗

arXiv2008

Metastability Driven by Soft Quantum Fluctuation Modes

The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which makes a saddle for the action, is derived in terms of Jacobian elliptic functions whose periodicity establishes the one-to-one correspondence between energy of the classical motion and temperature (inverse imaginary time) of the system. The quantum fluctuation contribution has been computed through the theory of the functional determinants for periodic boundary conditions. The decay rate shows a peculiar temperature dependence mainly due to the softening of the low lying quantum fluctuation eigenvalues. The latter are determined by solving the Lamè equation which governs the fluctuation spectrum around the time dependent classical bounce.

quant-ph↗

arXiv2008

On the Decay Rate of the False Vacuum

The finite size theory of metastability in a quartic potential is developed by the semiclassical path integral method. In the quantum regime, the relation between temperature and classical particle energy is found in terms of the first complete elliptic integral. At the sphaleron energy, the criterion which defines the extension of the quantum regime is recovered. Within the latter, the temperature effects on the fluctuation spectrum are evaluated by the functional determinants method and computed. The eigenvalue which causes metastability is determined as a function of size/temperature by solving a Lamè equation. The ground state lifetime shows remarkable deviations with respect to the result of the infinite size theory.

cond-mat.stat-mech↗

arXiv2008

Instanton Solution of a Nonlinear Potential in Finite Size

The Euclidean path integral method is applied to a quantum tunneling model which accounts for finite size ($L$) effects. The general solution of the Euler Lagrange equation for the double well potential is found in terms of Jacobi elliptic functions. The antiperiodic instanton interpolates between the potential minima at any finite $L$ inside the quantum regime and generalizes the well known (anti)kink solution of the infinite size case. The derivation of the functional determinant, stemming from the quantum fluctuation contribution, is given in detail. The explicit formula for the finite size semiclassical path integral is presented.

cond-mat.stat-mech↗

arXiv2007

Path Integral Methods in the Su-Schrieffer-Heeger Polaron Problem

I propose a path integral description of the Su-Schrieffer-Heeger Hamiltonian, both in one and two dimensions, after mapping the real space model onto the time scale. 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 method accounts for the variable range of the electronic hopping processes. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un upturn peculiar to a glass-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality. The effects of the electron-phonon anharmonic interactions on the phonon subsystem are studied by the path integral cumulant expansion method.

cond-mat.mtrl-sci↗

arXiv2005

Path Integral of the Holstein Model with a $ϕ^4$ on site potential

We derive the path integral of the semiclassical, one dimensional anharmonic Holstein model assuming that the electron motion takes place in a bath of non linear oscillators with quartic on site hard (and soft) potentials. The interplay between {\it e-ph} coupling and anharmonic force constant is analysed both in the adiabatic and antiadiabatic regime. In the latter we find much larger anharmonic features on the thermodynamic properties of low energy oscillators. Soft on site potentials generate attractive centres at large amplitude oscillator paths and contribute to the anomalous shape of the {\it heat capacity over temperature} ratio in the intermediate to low $T$ range. This anharmonic lattice effect is superimposed to the purely electronic contribution associated to a temperature dependent hopping with variable range inducing local disorder in the system.

cond-mat.mtrl-sci↗