Bubble lifetimes in DNA gene promoters and their mutations affecting transcription.

Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either increase or decrease transcriptional activity in the framework of the Peyrard-Bishop-Dauxois model. Extensive microcanonical simulations are used with energies corresponding to physiological temperature. The bubble lifetime profiles along the DNA sequences demonstrate a significant reduction of the average lifetime at the mutation sites when the mutated promoter decreases transcription, while a corresponding enhancement of the bubble lifetime is observed in the case of mutations leading to increased transcription. The relative difference in bubble lifetimes between the mutated and wild type promoters at the position of mutation varies from 20% to more than 30% as the bubble length decreases.

Chaotic dynamics of graphene and graphene nanoribbons.

We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically calculating the maximum Lyapunov exponent, we quantify the chaoticity for a spectrum of energies in both systems. We find that for all cases, the chaotic strength increases with the energy density and that the onset of chaos in graphene is slow, becoming evident after more than 104 natural oscillations of the system. For the GNRs, we also investigate the impact of the width and chirality (armchair or zigzag edges) on their chaotic behavior. Our results suggest that due to the free edges, the chaoticity of GNRs is stronger than the periodic graphene sheet and decreases by increasing width, tending asymptotically to the bulk value. In addition, the chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same width. Furthermore, we show that the composition of 12C and 13C carbon isotopes in graphene has a minor impact on its chaotic strength.

Distributions of bubble lifetimes and bubble lengths in DNA.

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelihoods for any GC content, but longer ones are substantially more likely to occur in AT-rich sequences. We also show that the ePBD model permits more, longer-lived, bubbles than the PBD system.

Heterogeneity and chaos in the Peyrard-Bishop-Dauxois DNA model.

We discuss the effect of heterogeneity on the chaotic properties of the Peyrard-Bishop-Dauxois nonlinear model of DNA. Results are presented for the maximum Lyapunov exponent and the deviation vector distribution. Different compositions of adenine-thymine (AT) and guanine-cytosine (GC) base pairs are examined for various energies up to the melting point of the corresponding sequence. We also consider the effect of the alternation index, which measures the heterogeneity of the DNA chain through the number of alternations between different types (AT or GC) of base pairs, on the chaotic behavior of the system. Biological gene promoter sequences have been also investigated, showing no distinct behavior of the maximum Lyapunov exponent.

Compressive response and buckling of graphene nanoribbons.

We examine the mechanical response of single layer graphene nanoribbons (GNR) under constant compressive loads through molecular dynamics simulations. Compressive stress-strain curves are presented for GNRs of various lengths and widths. The dependence of GNR's buckling resistance on its size, aspect ratio, and chiral angle is discussed and approximate corresponding relations are provided. A single master curve describing the dependence of the critical buckling stress of GNRs on their aspect ratio is presented. Our findings were compared to the continuum elasticity theories for wide plates and wide columns. In the large width limit, the response of the GNRs agrees with the predictions of the wide plates theory and thus, with that of wide graphenes. In the small width limit, the behavior of graphene nanoribbons deviates from that of periodic graphenes due to various edge related effects which govern the stiffness and the stability of the graphene membranes, but it qualitatively agrees with the theory of wide columns. In order to assess the effect of thermal fluctuations on the critical buckling stress a wide range of temperatures is examined. The findings of the current study could provide important insights regarding the feasibility and the evaluation of the performance of graphene-based devices.

Transforming graphene nanoribbons into nanotubes by use of point defects.

Using molecular dynamics simulations with semi-empirical potentials, we demonstrate a method to fabricate carbon nanotubes (CNTs) from graphene nanoribbons (GNRs), by periodically inserting appropriate structural defects into the GNR crystal structure. We have found that various defect types initiate the bending of GNRs and eventually lead to the formation of CNTs. All kinds of carbon nanotubes (armchair, zigzag, chiral) can be produced with this method. The structural characteristics of the resulting CNTs, and the dependence on the different type and distribution of the defects, were examined. The smallest (largest) CNT obtained had a diameter of ∼ 5 Å (∼ 39 Å). Proper manipulation of ribbon edges controls the chirality of the CNTs formed. Finally, the effect of randomly distributed defects on the ability of GNRs to transform into CNTs is considered.

Distance dependence of hole transfer rates from G radical cations to GGG traps in DNA.

Relative reaction rates for hole transfer between G radical cations and GGG triplets in DNA, through different bridges of varying lengths, are numerically calculated and the obtained results are compared with corresponding experimental observations [Giese et al., 2001, Nature, 412, 318; Angew. Chem., Int. Ed., 1999, 38, 996]. Hole donors and acceptors are separated either by (T-A)n bridges or by N repeated barriers consisting of (T-A,T-A) double base-pairs which are connected through single G-C base-pairs. In the former case, hole transfer rates show a strong exponential decrease with the length of the bridge for short bridges, while a switching to weak distance dependence has been observed for longer bridges. In the latter case, a power law seems to better describe the distance dependence of charge transfer rates. All these experimental observations are qualitatively reproduced by our simulations without any adjustable parameter, considering only tunneling as the charge transfer mechanism. Physical insights into the mechanism providing the switching behavior in the case of (T-A)n bridges are presented through an analysis of the eigenfunctions of the system.

Charge transport in DNA: dependence of diffusion coefficient on temperature and electron-phonon coupling constant.

The diffusion coefficient is calculated for a charge propagating along a double-stranded DNA, while it interacts with the nonlinear fluctuational openings of base pairs. The latter structural dynamics of DNA is described by the Peyrard-Bishop-Dauxois model [T. Dauxois, M. Peyrard, and A. R. Bishop, Phys Rev. E 47 R44 (1993)], which represents essential anharmonicities of base-pair stretchings. The dependence of the diffusion coefficient on the temperature and the electron-phonon coupling constant is presented. The diffusion coefficient decreases when either the temperature or the electron-phonon coupling increases. Analytical expressions are provided that describe the temperature dependence of the diffusion coefficient. The variation of the parameters of these expressions with the electron-phonon coupling constant is also discussed. These results quantitatively demonstrate how DNA structural nonlinear dynamics affects macroscopic charge transport properties.

Electronic parameters for charge transfer along DNA.

We systematically examine all the tight-binding parameters pertinent to charge transfer along DNA. The pi molecular structure of the four DNA bases (adenine, thymine, cytosine, and guanine) is investigated by using the linear combination of atomic orbitals method with a recently introduced parametrization. The HOMO and LUMO wave functions and energies of DNA bases are discussed and then used for calculating the corresponding wave functions of the two B-DNA base-pairs (adenine-thymine and guanine-cytosine). The obtained HOMO and LUMO energies of the bases are in good agreement with available experimental values. Our results are then used for estimating the complete set of charge transfer parameters between neighboring bases and also between successive base-pairs, considering all possible combinations between them, for both electrons and holes. The calculated microscopic quantities can be used in mesoscopic theoretical models of electron or hole transfer along the DNA double helix, as they provide the necessary parameters for a tight-binding phenomenological description based on the pi molecular overlap. We find that usually the hopping parameters for holes are higher in magnitude compared to the ones for electrons. Our findings are also compared with existing calculations from first principles.

Dependence on temperature and guanine-cytosine content of bubble length distributions in DNA.

We present numerical results on the temperature dependence of the distribution of bubble lengths in DNA segments of various guanine-cytosine (GC) concentrations. Base-pair openings are described by the Peyrard-Bishop-Dauxois model and the corresponding thermal equilibrium distributions of bubbles are obtained through Monte Carlo calculations for bubble sizes up to the order of a hundred base pairs. The dependence of the parameters of bubble length distribution on temperature and the GC content is investigated. We provide simple expressions which approximately describe these relations. The variation of the average bubble length is also presented. We find a temperature dependence of the exponent c that appears in the distribution of bubble lengths. If an analogous dependence exists in the loop entropy exponent of real DNA, it may be relevant to understand overstretching in force-extension experiments.

Distribution of bubble lengths in DNA.

The distribution of bubble lengths in double-stranded DNA is presented for segments of varying guanine-cytosine (GC) content, obtained with Monte Carlo simulations using the Peyrard-Bishop-Dauxois model at 310 K. An analytical description of the obtained distribution in the whole regime investigated, i.e., up to bubble widths of the order of tens of nanometers, is available. We find that the decay lengths and characteristic exponents of this distribution show two distinct regimes as a function of GC content. The observed distribution is attributed to the anharmonic interactions within base pairs. The results are discussed in the framework of the Poland-Scheraga and the Peyrard-Bishop (with linear instead of nonlinear stacking interaction) models.

ac conductivity in a DNA charge transport model.

We present the ac response of a DNA charge transport model, where the charge in the pi-stack interacts with the base-pair opening dynamics of the double strand. The calculated ac conductivity exhibits prominent peaks at polaron normal modes with electronic character, while weaker response appears at lower frequencies in the vibrational part of the polaron normal mode spectrum. Examples of the former, strong peaks, show redshifts as the amplitude of the ac field increases.

Breather-induced anomalous charge diffusion.

We present results on the diffusive motion of a charge interacting with the nonlinear dynamics of a thermalized underlying lattice. Signatures of anomalous diffusive properties are found at relatively high temperatures, where highly nonlinear excitations are present. A sublinear diffusion and a plateau appear before the standard long-time diffusion during the evolution of the mean-squared displacement and a significant degree of heterogeneity is exhibited among individual trajectories. Both properties are connected with the existence of vibrational hot spots (breather or multibreather excitations). Transport parameters of the charge are strongly affected in this case, as can be exemplified by the significant suppression of the diffusion coefficient D. The variation of D with temperature follows a stretched exponential law. The results are contrasted with those of the linearized case, in the absence of breathers. Such anomalous diffusion of a charge coupled to a thermalized lattice may be relevant in low-dimensional soft materials with strong anharmonicities, such as biomolecules, conducting polymers, etc.

Multipeaked polarons in soft potentials.

We consider a minimal coupled charge / excitation-lattice model capturing a competition between linear polaronic self-trapping and the self-focusing effects of a soft nonlinear on-site potential. The standard single-humped polaron ceases to exist above a critical value of the coupling strength, closely related to the inflection point in the nonlinear potential. For couplings beyond this critical value, we find that successive multihumped polaronic solutions correspond to the lowest-energy stationary states of the system, which may admit interesting quantum resonance behavior.

Localization in physical systems described by discrete nonlinear Schrodinger-type equations.

Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.

Effects of intrinsic base-pair fluctuations on charge transport in DNA.

We investigate propagation of a charge carrier along intrinsically dynamically disordered double-stranded DNA. This is realized by the semiclassical coupling of the charge with a nonlinear lattice model that can accurately describe the statistical mechanics of the large amplitude fluctuations of the base pairs leading to the thermal denaturation transition of DNA. We find that the fluctuating intrinsic disorder can trap the charge and inhibit polaronic charge transport. The dependence of the mean distance covered by the charge carrier until its trapping, as a function of the energy of the fluctuations of the base pairs is also presented.

Delocalizing transition of Bose-Einstein condensates in optical lattices.

A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.

Reactive dynamics on two-dimensional supports: Monte Carlo simulations and mean-field theory.

Monte Carlo simulations and mean-field models are used for the study of nonequilibrium reactions taking place on the surface of a catalyst. The model represents the catalytic reduction of NO with H2 on a Pt surface. Both Monte Carlo simulations and mean-field results predict the existence of a critical surface in the parameter space where the catalyst remains active for long times. Outside this critical region the catalyst remains active for finite times only. A discrete version of the mean-field model is proposed that takes into account the discrete, two-dimensional nature of the catalyst. For homogeneous initial conditions this improved model provides better quantitative agreement with the Monte Carlo results.