Sequencing-independent delocalization in a DNA-like double chain with base pairing

Tight-Binding Modeling of Nucleic Acid Sequences: Interplay between Various Types of Order or Disorder and Charge Transport

This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB and a discussion of its various submodels [wire, ladder, extended ladder, fishbone (wire), fishbone ladder] and of the process of renormalization. We proceed to a discussion of aperiodicity, quasicrystals and the mathematics of aperiodic substitutional sequences: primitive substitutions, Perron–Frobenius eigenvalue, induced substitutions, and Pisot property. We discuss the energy structure of nucleic acid wires, the coupling to the leads, the transmission coefficients and the current–voltage curves. We also summarize efforts aiming to examine the potentiality to utilize the charge transport characteristics of nucleic acids as a tool to probe several diseases or disorders.

Quasi-Periodic and Fractal Polymers: Energy Structure and Carrier Transfer

We study the energy structure and the coherent transfer of an extra electron or hole along aperiodic polymers made of N monomers, with fixed boundaries, using B-DNA as our prototype system. We use a Tight-Binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We consider quasi-periodic (Fibonacci, Thue-Morse, Double-Period, Rudin-Shapiro) and fractal (Cantor Set, Asymmetric Cantor Set) polymers made of the same monomer (I polymers) or made of different monomers (D polymers). For all types of such polymers, we calculate the highest occupied molecular orbital (HOMO) eigenspectrum and the lowest unoccupied molecular orbital (LUMO) eigenspectrum, the HOMO-LUMO gap and the density of states. We examine the mean over time probability to find the carrier at each monomer, the frequency content of carrier transfer (Fourier spectra, weighted mean frequency of each monomer, total weighted mean frequency of the polymer), and the pure mean transfer rate k. Our results reveal that there is a correspondence between the degree of structural complexity and the transfer properties. I polymers are more favorable for charge transfer than D polymers. We compare k ( N ) of quasi-periodic and fractal sequences with that of periodic sequences (including homopolymers) as well as with randomly shuffled sequences. Finally, we discuss aspects of experimental results on charge transfer rates in DNA with respect to our coherent pure mean transfer rates.

Periodic, quasiperiodic, fractal, Kolakoski, and random binary polymers: Energy structure and carrier transport

We study periodic, quasiperiodic (Thue-Morse, Fibonacci, period doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski, and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A), on the same strand, i.e., our prototype binary alphabet is {G,A}. Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization, and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients, and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.

Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of a wire model versus an extended ladder model

We employ two tight-binding (TB) approaches to systematically study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of N monomers (base pairs): (I) at the base-pair level, using the onsite energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the onsite energies of the bases and the hopping integrals between neighboring bases, i.e., an extended ladder model since we also include diagonal hoppings. We solve a system of M (matrix dimension) coupled equations [(I) M=N, (II) M=2N] for the time-independent problem, and a system of M coupled first order differential equations for the time-dependent problem. We perform a comparative study of stationary and time-dependent aspects of the two TB variants, using realistic sets of parameters. The studied properties include HOMO and LUMO eigenspectra, occupation probabilities, density of states and HOMO-LUMO gaps as well as mean over time probabilities to find the carrier at each site [(I) base pair or (II) base], Fourier spectra, which reflect the frequency content of charge transfer, and pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.

(De)localization and the mobility edges in a disordered double chain with long-range intrachain correlation and short-range interchain correlation

Correlation effects and phase transitions are central issues in current studies on disordered systems. In this paper, we study the electronic properties of a disordered double chain with long-range intrachain correlation and short-range interchain correlation. Based on detailed numerical calculations, finite size scaling analysis and empirical analytical calculations, we obtain a phase diagram containing rich physics due to the interplay among the disorder, short-range and long-range correlations. Besides the long-range correlation induced localization-delocalization transitions, we find both first-order and second-order quantum phase transitions on changing the short-range correlation. Interestingly, the localization may be suppressed by increasing the disorder strength in some parameter regime and the 'anti-correlation' leads to the most delocalized state. Our studies shine some light on the mechanism of the charge transport in DNA molecules, where both types of correlated disorders are present.

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t̃. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t̃/2 and ± t̃. We find that the anomalies at E = ± t̃ are associated with the π-coupling occurring within one energy band and those at E = ± t̃/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.

Localization on a two-channel model with cross-correlated disorder

We study the wavepacket dynamics in a two-channel Anderson model with correlated diagonal disorder. To impose correlations in the disorder distribution we construct the on-site energy landscape following both symmetric and antisymmetric rules. Our numerical data show that symmetric cross-correlations have a small impact on the degree of localization of the one-particle eigenstates. In contrast, antisymmetric correlations lead to a reduction of the effective degree of disorder, thus resulting in a substantial increase of the wavepacket spread. A finite-size scaling analysis shows that the antisymmetric cross-correlations, in spite of weakening the localization, do not promote ballistic transport. The present results shed light on recent findings concerning an apparent delocalization transition in a correlated DNA-like ladder model.

Resonant states and wavepacket super-diffusion in intra-chain correlated ladders with diluted disorder

In this work, we study a tight-binding Hamiltonian model system of a binary correlated ladder with diluted disorder. We introduce intra-chain correlations between the on-site potentials by imposing that ϵ(i, s) = - ϵ(i, - s) where s = ± 1 indexes the two ladder chains. Further, we consider each ladder chain as composed of inter-penetrating ordered and random sub-chains. We show that the presence of a random on-site distribution in one of the inter-penetrating chains leads to Anderson localization except at a specific symmetric pair of energy eigenmodes. Further, by integrating the time-dependent Schroedinger equation, we follow the time-evolution of an initially localized one-electron wavepacket. We report that the remaining delocalized resonant modes are responsible for a super-diffusive spread of the wavepacket dispersion while the wavepacket participation function remains finite. A scaling analysis of the wavepacket distribution shows that it obeys a universal scaling form with the development of a power-law tail followed by a super-diffusively evolving cutoff. We obtain three exponents characterizing this super-diffusive dynamics and show that they satisfy a simple scaling relation.

Transverse electric field modulated tunneling magnetoresistance in a DNA molecular device

Quantum spin-dependent transport in a ferromagnetic(FM)/DNA/ferromagnetic(FM) device is theoretically investigated based on the lattice Green function method and the Landauer-Büttiker theory. The effect of a transverse electric field on magnetoresistance (MR) of the device is investigated. It is predicted that either the direction or strength of the transverse electric field can change the MR of the device. We suggest a possible application of modulating MR of the FM/DNA/FM device by a transverse electric field.

Charge transport in DNA molecules: Cooperative interplay between the disordered base-pair channel and the ordered backbone

Charge transport in DNA molecules has raised considerable interest because of its importance in biological processes and potential applications in nanoscale devices. A DNA molecule can be viewed as a quasi-one-dimensional system composed of stacked base pairs (AT , CG) together with backbones of sugar phosphates. Motivated by recent experimental observations on the importance of the backbone integrity, we investigate the interplay between charge transport through the ordered backbone and disordered base stacks with random sequences. By analytical and numerical calculations, we find that the coupling between the backbone and base-pair channels plays an important role in charge transport. The backbone can generate effective hopping constants well beyond the adjacent base pairs, enhancing charge transport through the base-pair channel. The corresponding enhancement of the localization length is nearly independent of the length of the DNA and increases with increasing coupling between backbone and base pair. Our model can explain qualitatively several experimental observations.

Charge transfer in DNA: effective Hamiltonian approaches

Aperiodic order plays a very significant role in biology, as it determines most informative content of genomes. Amongst the various physical, chemical or biological phenomena that might be inferred from sequence correlations, charge transfer properties deserve particular attention. Indeed, the nature of DNA-mediated charge migration has been related to the understanding of damage recognition process, protein binding, or with the task of engineering biological processes (e.g. designing nanoscale sensing of genomic mutations), opening new challenges for emerging nanobiotechnologies. Nevertheless, the solution of Schrödinger´s equation with a potential that is given by a one-dimensional array of the double-stranded DNA remains as a main open theme in solid state physics of biological macromolecules. In this contribution, I will shortly review several approaches introduced during the last few years in order to describe charge transfer migration in DNA in terms of tight-binding effective Hamiltonians.

Generation of correlated binary sequences from white noise

We suggest a method for generation of random binary sequences of elements 0 and 1, with prescribed correlation properties. It is based on a modification of the widely used convolution method of constructing continuous random processes. Using this method, a binary sequence with a power-law decaying pair correlator can be easily generated.

Long-range correlation and charge transfer efficiency in substitutional sequences of DNA molecules

We address the relation between long-range correlations and coherent charge transfer in substitutional DNA sequences using the transfer matrix approach. The substitutional sequences exhibit long-range correlations and show good transmittivity in comparison with uncorrelated random ones. It is found that the charge transfer efficiency varies for different substitutional sequences and many will present electronic delocalization in the system. Further, the resistivity for substitutional sequences may range from decreasing with the length, length independence, or increasing with the length. The conduction mechanisms of various behaviors observed for these sequences are analyzed.

Characteristic length scale of electric transport properties of genomes

A tight-binding model together with a statistical method are used to investigate the relation between the sequence-dependent electric transport properties and the sequences of protein-coding regions of complete genomes. A correlation parameter Omega is defined to analyze the relation. For some particular propagation length w max, the transport behaviors of the coding and noncoding sequences are very different and the correlation reaches its maximal value Omega max. w max and Omega max are characteristic values for each species. A possible reason for the difference between the features of transport properties in the coding and noncoding regions is the mechanism of DNA damage repair processes together with natural selection.