Toward DNA Conductivity: A Theoretical Perspective - American

PERSPECTIVE pubs.acs.org/JPCL

Toward DNA Conductivity: A Theoretical Perspective Sairam S. Mallajosyula and Swapan K. Pati* Theoretical Sciences Unit and New Chemistry Unit, Jawaharlal Nehru Center for Advanced Scientific Research, Jakkur Campus, Bangalore 560 064, India

ABSTRACT With most of the early experiments reporting a wide range of electronic properties for DNA, varying from insulating, semiconducting, and conducting to even induced superconductivity, the conductivity of DNA still remains a challenge. To this end, theoretical studies have greatly aided in explaining the observed conductance behavior of DNA. Theoretical charge-transfer studies of DNA can be divided into two broad categories, model calculations and ab initio calculations. In this Perspective, we discuss a few results from both categories and highlight the importance of both methods. The aim is to provide an overview of the theoretical methods that are used to study DNA conductivity, highlighting their strengths and deficiencies.

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he last two decades have seen an active interest in understanding the electronic structure and properties of DNA for applications in the field of molecular electronics and spintronics.1-4 The similar arrangement of the π orbitals in stacked metallic aromatic organic crystals, like Bechgaard salts,5 and the π orbitals of DNA bases encouraged researchers to believe that DNA could indeed act as a conducting material.6 This interest in studying DNA conductivity was further fueled by the initial studies on DNA charge transfer by Barton and co-workers, who observed evidence for distance-independent charge transfer between DNA-intercalated transition-metal complexes.7 These studies were followed by various other experiments by Henderson et al.,8 Lewis et al.,9 and Geise et al.,10 which established that superexchange (tunneling) occurs between guanines (or guanine dimers and trimers) separated by three or fewer A/T (adenine/thymine) base pairs, while for larger separations, diffusive hopping dominates the charge-transfer mechanism. This conclusion has also been supported by a large number of theoretical and experimental studies, which have been adequately reviewed earlier.11-17 While charge-transfer experiments seemed to converge on a general understanding of DNA chargetransfer properties, direct conductivity measurements yielded conflicting results. Direct conductivity measurements have attributed a range of electronic properties to DNA, varying from insulating, semiconducting, and conducting to even induced superconductivity. The aim of this Perspective is to provide an overview of the various theoretical methods, which have been used to study the phenomenon of DNA conductivity and highlight their strengths and deficiencies. We focus on concepts which have been found to govern DNA conductivity and may lead to improved DNA conductance for realizable molecular electronics applications. That being said, it is important to present a brief summary of the experiments that triggered off the interest in DNA conductivity.

r 2010 American Chemical Society

Direct conductivity measurements have attributed a range of electronic properties to DNA, varying from insulating, semiconducting, and conducting to even induced superconductivity. In 1998, Braun et al.18 reported insulating behavior for a μm long λ-DNA, whose 30 ends were chemically anchored to Au electrodes via Au-sulfur interactions. No measurable current was found across the DNA molecules for bias voltages ranging from -10 to 10 V. Later, Pablo et al.19 carried out experiments on a λ-DNA sitting on an insulating mica surface and connected by a gold electrode and a SFM (scanning force microscopy) tip, where they also found no trace of current. The schematic of the setup is shown in Figure 1a. Note that both experiments used λ-DNA, which is 48502 base pairs long and has a mixed sequence. Such a mixed sequence would lead to disorder-driven localized states preventing flow of current. Subsequent experiments by Storm et al.,20 with a varying DNA sequence (λ-DNA, as well as synthetic poly(G)-poly(C)), two types of electrodes (Pt and Au), and different insulating surfaces (SiO2, mica) also reported nonmeasurable conductance. However, an analysis of their AFM images revealed elongated DNA samples, which were no longer contained in a well-stacked orientation with a base Received Date: March 19, 2010 Accepted Date: May 20, 2010 Published on Web Date: June 04, 2010

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DOI: 10.1021/jz1003654 |J. Phys. Chem. Lett. 2010, 1, 1881–1894


Figure 1. (a) SFM image showing the DNA molecules in contact with the left gold electrode. The schematic shows the method in which the right electrode (SFM tip) contacts with the DNA molecules (reprinted with permission from ref 19, copyright 2000 by the American Physical Society). (b) Differential conductance for a ploy-GC sequence which shows a clear peak structure, suggesting electron transport mediated by molecular energy bands. The inset illustrates the semiconducting I-V profiles for the poly-GC sequence. The red curve in the inset illustrates an abrupt change in the I-V profile, which could be due to structural fluctuations (reprinted by permission from Macmillan Publishers Ltd: Nature (ref 22), copyright 2000). (c) Ohmic I-V profiles for 600 nm long λ-DNA ropes. The top panel illustrates the I-V curve when the probing tip is attached to one DNA rope. The bottom panel illustrates the I-V curve when the probing tip is attached to two ropes (reprinted by permission from Macmillan Publishers Ltd: Nature (ref 23), copyright 1999).

pair separation of about 3.4 Å. This result was also confirmed by Cai et al.,21 who found increased helical periodicity for DNA samples on a mica substrate elongated with the free-flowing method. On the other hand, wide band gap semiconducting behavior was reported in the case of short DNA sequences by Porath et al.22 Using the ``electrostatic trapping'' method, they studied the conductance of a short (30 base pairs) DNA molecule with a homogeneous sequence [poly(G)-poly(C)]. In this method, an electric field between the two electrodes polarizes the molecule, which is then attracted to the gap between the electrodes, owing to the field gradient (Figure 1b). In fact, the authors were able to analyze the conductance properties of the short DNA in terms of the alignment of the molecular orbitals of guanine and cytosine with respect to the Fermi level (EF) of the electrodes, which was simpler than the case of λ-DNA, where a heterogeneous disordered DNA sequence led to the mixing and thereby localization of the molecular orbitals. A direct tunneling mechanism was ruled out due to the large tunneling distance (about 8 nm) between the electrodes and correspondingly large currents which


were observed. Since they used high electric field and found large electron-transfer rates, a diffusive transfer mechanism was also ruled out. From this, the authors concluded that the most probable model of DNA conduction is through the molecular bands which are delocalized over the entire length of the molecule. In this picture, the electron transport is then facilitated by the alignment of the EF of the electrode with the band edge upon the application of bias voltage. This conclusion was also supported by a clear peak structure in the differential conductance (Figure 1b), which suggests that electron transport is mediated by the DNA molecular energy bands. Contrary to the single molecules used in the semiconducting or insulating studies, in 1999, Fink et al.23 reported Ohmic conductance for λ-DNA bundles. In their experiment, these bundles were laid across 2 μm holes in Au-coated carbon foil (Figure 1c). The conductance was measured between a metalcoated mechanical tip that touched the bundle and the Aucoated carbon foil. The whole setup was then imaged with a low-energy electron point source (LEEPS) microscope. Interestingly, Pablo et al.19 argued that doping effects through the

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migration in DNA.11-13,28 In these models, the main pathways of charge migration along the DNA molecular stack are analyzed in terms of on-site energies and hopping strengths. With an appropriate selection of on-site energies and hopping strengths, much larger system sizes can be studied in comparison to ab initio methods. For a complete description of the energetics of a double-stranded DNA chain, one should take into account contributions coming from (i) the nucleobase system, (ii) the backbone system, and (iii) the environment. Since the experimental studies indicate that the charge transfer essentially occurs via nucleobases, in many of the TB models, the contributions from the backbone system and environment are parametrized into the nucleobase system, thereby reducing the number of parameters. Two of these models have found prominence in DNA research, onedimensional model and the two-channel model. (a) One-Dimensional Model. In this simplest TB model for the DNA stack, every individual site represents a base pair, and every link between the sites implies hopping amplitude. The Hamiltonian for this model is given as L X ½ð Ji aiþ ai þ 1 þ hcÞ þ εi aiþ ai H ¼

imaging electrons might have induced the observed conductance. However, Tran et al.24 were able to measure the contactless ac conductivity of λ-DNA from the absorption in a microwave cavity, which also predicted Ohmic behavior. In this experiment, which was performed in a buffer solution, it was found that the conductance in solution was an order of magnitude higher than the conductance in the dry state. This, in principle, is consistent with the better base pair stacking in B-DNA (prevalent in wet conditions) compared to that in A-DNA (prevalent in dry conditions). Similar Ohmic conductance was also measured by Yoo et al.25 for μm long poly(G)poly(C) and poly(A)-poly(T) DNA molecules trapped between Au/Ti nanoelectrodes separated by 20 nm. There exists only one report of superconducting behavior for a 16 μm long λ-DNA by Kasumov et al.26 However, this remains largely a controversial result that has not been reproduced by others working in the field of DNA conductivity. The experiments discussed above are only to highlight the variances in the experimental results, which form the basis of numerous theoretical calculations. For a more critical analysis of the experimental results, the readers are referred to excellent reviews by Porath et al.,2 Endres et al.,3 and Taniguchi et al.4 These experimental results highlight pertinent questions like, why do DNA bundles show Ohmic behavior? Is it due to the trapping of water and counterions between the DNA strands leading to a different channel for conduction? Why does the observed conductance increase by an order of magnitude in solution? While this could be due to the formation of an ordered DNA structure (B-DNAversus A-DNA), there has also been crystallographic evidence of the formation of well-ordered water structures around DNA which could be involved in alternative pathways for conductance.27 What is the affect of the DNA sequence on conductivity? With a lot of experimental data available, theoretical studies provide an avenue to capture the essential mechanisms that dictate DNA charge transfer. Theoretical approaches to study DNA conductivity can be broadly divided into two classes, model Hamiltonian calculations and ab initio calculations. Ab-initio methods are very powerful and can capture the overall energetics of the DNA system; however, they come with a very high computational cost. To this end, model calculations (tightbinding (TB) models) for DNA present themselves as simpler, effective models to capture the local parameters affecting DNA conductivity with very low computational costs.

i¼1

where Ji is the hopping amplitude between nearest-neighbor sites i, i þ 1 along the central branch, and εi denotes the onsite energy at each site along the central branch. L is the number of sites/bases in the sequence (Figure 2a). Roche studied the impact of leads and torsional fluctuations on transmission using this simple model.29 He showed that for a periodic DNA system (poly-GC) with comparable intrinsic DNA hopping amplitude, it was possible to achieve high transmission within well-defined DNA bands. However, the introduction of quasirandom biological sequences (λ-DNA) reduced the transmission coefficient at all energies (Figure 2b). In this study, the site energies were modeled as the ionization potential (IP) of the nucleobases.30 Interestingly, the hopping amplitude had an angular component which introduced the intrinsic twist of DNA. Thus, even with this simple model, it was realized that the structural parameters of DNAwere important to capture the essentials of its conductance phenomenon. (b) Two-Channel Model. In a two-channel model, there are two central branches linked with one another, where each site represents a complete base. This model overcomes the deficiency of the one-dimensional model by considering each DNA base as an independent site. The hydrogen bonding between the base pair now becomes an additional hopping parameter perpendicular to the DNA stack. The Hamiltonian for this model is given as

Theoretical approaches to study DNA conductivity can be broadly divided into two classes, model Hamiltonian calculations and ab initio calculations.

H ¼

þ J1, 2 aiþ, 1 ai, 2 þ hc where Ji,τ is the hopping amplitude between sites along each branch τ = 1, 2 and εi,τ is the corresponding on-site energy. The new parameter J1,2 represents the hopping between the two central branches, that is, perpendicular to the direction of conduction (Figure 3a).

Tight Binding Models. TB models for DNA have been used extensively in the literature to capture the essentials of charge


L X X ½ ð Ji, τ aiþ, τ ai þ 1, τ þ εi, τ aiþ, τ ai, τ Þ i ¼ 1 τ ¼ 1, 2

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Figure 2. (a) One-dimensional TB model. (b) Energy-dependent transmission coefficient (T(E)) for a 60 base pair long periodic poly-GC DNA and random λ-DNA. Clear reduction in the T(E) at all energies is observed for the random λ-DNA sequence. The Fermi level (EF) is at 7.75 eV (reprinted with permission from ref 29, copyright 2003 by the American Physical Society).

stilbenedicarboxamide-linked DNA hairpins.33-36 Using the same model, they also studied the selective oxidation of guanines in DNA. They found that the site energy of guanine is strongly influenced by the neighboring flanking bases, with the site energy of the central G increasing in the order -AGG< -CGG- < -TGG- < -GGA-, -GGT- < -GGC-. In fact, the site energy of the central G in a -GGG- triplet was found to be 7.89 eV, 1.84 eV lower than that of an isolated G (9.73 eV).32 These results highlighted the strengths of the fragment orbital scheme and the two-channel model. It was immediately realized that this scheme could be used to study the influence of structural fluctuations on charge transfer. Influence of Structural Dynamics on Charge Transfer. Structural fluctuations in DNA are described at two distinct levels, the base step level and the base pair level.37 Other than a structural basis, these fluctuations are also energetically different from each other. While the base step is stabilized by the interbase π-π interactions, the base pair is stabilized through interbase hydrogen bonding (H bond). By convention, these fluctuations are described by six degrees of freedom (three translational and three rotational) in both cases. At the base step level, the translational degrees of freedom are shift (Dx), slide (Dy), and rise (Dz), while the same at the base pair level are stagger (Sz), stretch (Sy), and shear (Sx). Similarly, the rotational degrees of freedom for the base step level are tilt (τ), roll (F), and twist (Ω), while the same for the base pair level are propeller twist (ω), buckle (κ), and open (σ) (see Figure 3b and d for illustrations). Using the fragment orbital scheme, we studied the influence of base pair fluctuations on the charge-transfer properties of DNA.38 It was shown that intra base pair charge transfer, in both the A/Tand G/C base pairs, was strongly influenced by the hard vibrational modes, namely, open (σ) and stretch (Sy) (Figure 3c). From an analysis of local fluctuations for the A/T and G/C base pairs in AT-GC and GC-AT dinucleotide steps, we were able to show that local fluctuations in the G/C base pair

This model has been very successful in describing charge transfer as well as charge transport in DNA.11-13,28 In many of the early studies using this model, the site energies were modeled as the ionization potential (IP) of the bases, and the hopping amplitudes were adjusted to reproduce the experimental results. However, the drawbacks of the two models lie in the choice of parameters. It has been shown that the IPs of the bases are strongly influenced by the environment and the DNA sequence, as is discussed later. Hence, using a single value of the IP for the bases derived from gas-phase data is an over approximation which is inherent to these models. It is also to be emphasized that the hopping amplitudes have generally been varied over a large range to match the experimental results. This adjustment of the hopping amplitudes does not reflect well when discussing key issues such as DNAelectrode interactions, which are very important in the overall conductivity phenomenon. To this end, Ratner and co-workers have very recently developed a protocol wherein the site energies and hopping amplitudes are directly evaluated by using the fragment orbital scheme implemented in the Amsterdam density functional (ADF) code.31-36 This method allows the wave function of the hole to be expressed as a linear superposition of the highest occupied molecular orbitals (HOMOs) of the individual nucleobases in a fragment orbital basis, where a fragment consists of all of the atoms in a nucleobase. The advantage of this method is that the overlap matrix can now be evaluated as the overlap between molecular orbitals of individual nucleobases, thus allowing a direct evaluation of the site energies and the hopping amplitudes as the diagonal and off-diagonal elements of the Kohn-Sham Hamiltonian. By mapping the directly evaluated site energies and the hopping amplitudes onto a two-dimensional model, Ratner and co-workers were able to reproduce the experimentally observed absolute rates of hole transfer between guanine nucleobases separated by one and two A/T base pairs in


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charge-transfer integrals were strongly influenced by the fluctuations at the base pair level. Among the rotational degrees of freedom, the propeller twist (ω) and open (σ) were found to influence the overall charge-transfer processes, while for the translational degrees of freedom, the shear (Sx) strongly influenced the overall charge-transfer process. Similar studies at the base step level have highlighted the importance of twist angle (ω) and rise (Dz) in governing the charge-transfer properties. From both the fragment orbital approach and Koopman's theorm approach, it has been found that the charge transfer between neighboring base pairs is highest when the twist angle is ∼36°, which is the twist angle for a B-DNA conformation (Figure 3e).33,39,40 Similarly, it has been found that the rise (Dz) affects the value of the charge-transfer integral, which decreases rapidly upon increasing the separation between the two base pairs. In a recent study, Elstner and co-workers used the fragment orbital approach to evaluate the charge-transfer parameters for a molecular dynamics (MD) trajectory in which the environmental effects were captured using a quantum mechanicsmolecular mechanics (QM/MM) coupling scheme.40 Using this methodology, they were able to capture the variations in the site energies as well as the charge-transfer integrals (hopping amplitude) for a 100 fs trajectory (Figure 3f). This study emphasized the importance of the environment (solvent and the counterions) in governing the IP and in turn the charge-transfer properties of DNA. Thus, while the simple TB models can capture the physics behind DNA charge transfer, it is important to account for the effect of environment for a complete understanding of DNA conductance. Effect of Environment (Solvent and Counterions) on Electronic Properties of DNA. The influence of solvent on the chargetransfer properties of DNA has been captured by ab initio methods in conjunction with MD simulations. In many of these studies, classical MD simulations have been used to dynamically generate configurations, which have then been studied using electronic structure methods. Barnett et al. performed one of the first of such ab initio studies, analyzing charge migration in DNA.41 In their study, the authors used classical MD simulations in conjunction with large-scale firstprinciples electronic structure calculations to reveal that quantum transport of an injected charge was gated in a correlated manner by the thermal motions of the hydrated counterions. They found that counterion configurations around DNA led to the formation of states which could be characterized by varying degrees of charge localization. From their MD trajectories, the authors identified three important configurations of a four base pair B-DNA duplex d(50 -G1A2G3G4-30 ), which were subsequently analyzed by first-principles electronic structure calculations. The main difference between these configurations was the location of a hydrated Naþ counterion. In configuration (I), all of the Naþ ions were near the phosphates, thus forming what the authors called a “coaxial double-layer” about the helix of the DNA together with the backbone phosphates. In configuration (II), one of the Naþ ions was displaced to the major groove with the Naþ located near N7 of G3, while configuration (III) was another “groove configuration” with the Naþ located near N7 of G1. It was found that the vertical IP energy required to remove an electron from the

Figure 3. (a) Two-channel TB model. (b) Translational and rotational degrees of freedom at the base pair level (reprinted from ref 39). (c) Variations in the site energies of the DNA bases as a function of translational and rotational degrees of freedom at the base pair level (reprinted from ref 38). (d) Translational and rotational degrees of freedom at the base step level (reprinted from ref 39). (e) Charge-transfer integrals as a function of twist angle between neighboring base pairs in the same strand (reprinted from ref 33). (f) Variations in the IPs of guanine and adenine in a poly-GA system for a 100 fs MD trajectory (reprinted from ref 40).

strongly influenced the site energies of the neighboring base step when compared to fluctuations in the A/T base pair. However, for both dinucleotide steps, we found that the


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Figure 4. (a) Left panel: HOMO of the neutral 50 -G1A2G3G4-30 localized on G3G4. Right panel: Orbital plot of one of the degenerate, highest singly occupied spin-orbitals for the ionized duplex. The orbital is delocalized over G1A2G3G4. (b) Isosurface of the total electron charge density difference between the neutral and ionized duplexes for the three different configurations. Notice that, for configuration (III), the displacement of one Naþ into the groove causes a noticeable change in the charge density distribution, which becomes localized over G3G4 (reprinted with permission from ref 41, copyright 2001 by AAAS). (c) Spin density distribution for the quantum subsystem studied in ref 42. The left panel illustrates the spin density distribution for the initial unconstrained runs. The right panel is the spin density distribution after the charge was initially localized on the end base. (d) Radial distribution functions (gN7-HW(r)) for the neutral (delocalized) and charged (localized) models. Notice the loss of the first peak structure for the charged models, indicating solvent reorganization (reprinted with permission from ref 42, copyright 2007 by the American Physical Society).

molecular mechanical (SIC-QM/MM) simulations on two ionized A/T bridge models in explicit water at finite temperature.42 The simulations were performed on the ideal (B-DNA) and distorted conformations of d(50 -AA8A-30 ). In their calculations, the central five A/T base pairs were included into the quantum subsystem. Their calculations showed that the initial charge was delocalized over all of the adenines, similar to the findings by Barnett et al.41 From these conformations, the authors then performed two additional SIC-QM/MM calculations wherein the charge was localized onto adenine 5 or adenine 8 in the quantum subsystem. The quantum subsystem was then frozen, and the solvent was allowed to reorganize in the presence of localized charges. It was found that the charge did not redistribute over the bridge and remained localized on adenine 5 or 8 (Figure 4c). It was also found that the ions did not migrate from their original positions, thereby negating the IGT mechanism. The authors concluded that this localization of the charge was due to the restructuring of the first solvation shell. This conclusion was

system increased by 0.24 and 0.47 eV upon going from configuration (I) to configurations (II) and (III), respectively, illustrating the influence of counterions on charge injection. An analyses of the HOMO and the total electron charge density difference between the neutral and ionized duplexes also highlighted features of ionization energetics. It was found that the HOMO, which was localized on G3G4, becomes delocalized over the entire purine strand upon ionization, indicating that the ionization process delocalizes the hole, which was also apparent from the total charge difference (Figure 4a and b). On the basis of their results, the authors postulated the “ion-gated transport” (IGT) mechanism, wherein only a small fraction of the thermally accessible ionic configurations contribute to the spatial movement of the hole. However, more recent data suggests that conformational changes and solvent rearrangement play a more prominent role when compared to the IGT mechanism. This issue was addressed by Parrinello and co-workers by performing selfinteraction-corrected density functional quantum mechanical-


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Figure 5. (a) Left panel: Energy level diagram for the Z-DNA crystal. EF is set to 0 eV and positioned to be in the middle of the HOMO-LUMO gap. Right panel: (i) Averaged optical conductivity (Ω-1cm-1) versus frequency (eV). (ii) Optical conductivity in the strand direction. (iii) Optical conductivity perpendicular to the strand direction. The orange histograms represent the contributions to the total conductivity (gray histograms) from excitations ending on Naþ electron-transfer virtual states. The continuous black line in (ii) and (iii) represents the average conductivity (reprinted with permission from ref 45, copyright 2002 by the American Physical Society). (b) Left panel: Partial density of states (PDOS) for the 50 -GAAT-30 B-DNA sequence with Mg2þ counterions. (i) PDOS projected onto the DNA bases. (ii) PDOS projected onto water molecules. The contributions from water molecules located near DNA ends have been plotted with the red line. EF is set to 0 eV and positioned to be in the middle of the HOMO-LUMO gap. Right panel: Optical conductivity for the 50 -GAAT-30 B-DNA sequence with Naþ counterions. (i) Low-energy features originating from occupied water states. (ii) High-energy range, illustrating the π-π* direct band gap (reprinted with permission from ref 46, copyright 2005 by the American Physical Society).

terion states. Interestingly, for the DNA system with Mg counterions, it was found that occupied water states are also very close to the unoccupied π* orbital of the bases. The authors inferred that this proximity of the occupied Mg, water states, and the unoccupied π* states of the bases could lead to doping of DNA by water or Mg states. Signatures of this phenomenon were captured by optical conductivity calculations, which serve as a soft probe to identify signatures of band gap doping. While discussing results based on DFT, it is important to highlight two of the common pitfalls of DFT that are of prime relevance when discussing the conductivity of DNA. (a) DFTas a method is known to systematically underestimate the band gap (in the case of DNA, the π-π* gap). Thus, the results discussed above have to be analyzed with this knowledge in mind. The claims that there could be charge transfer between unoccupied π* orbital of the bases and the occupied states of water and counterions remains somewhat ambiguous as the relative position of the unoccupied orbital is subject to uncertainty. To be more generic, DFT is more applicable as an excellent guide to describe a number of ground-state properties systematically for a large range of systems. (b) Another important pitfall of using DFT for DNA systems is the poor description of the dispersion interactions (which, in the case of DNA, are involved in the base stacking), which are crucial to the stability of DNA. Thus, studies in which the DNA geometries

also supported by comparing the radial distribution functions between N7 of adenine in the ideal and disordered models and the water hydrogen atoms (Figure 4d). It was found that for neutral adenine, there existed a strong nitrogen-water hydrogen bond, which was lost upon ionization. These studies highlighted the influence of solvent on the electronic structure of DNA. Cox and co-workers performed first-principles-based DFT calculations to study the influence of different counterions on the band structure of DNA.3 From their calculations for the four base pair long B-DNA sequence 50 -GAAT-30 , they analyzed contributions from water molecules which were clustered around various DNA regions (base pairs; phosphates and ions) to identify possible charge-transfer pathways involving water. These large-scale calculations (with nearly 25 water molecules per nucleotide) were performed using the DFT code SIESTA that makes use of local orbitals (the SankeyNiiklewski approach), pseudopotentials, and linear scaling algorithms to facilitate ab initio calculations for large systems like DNA.43 They found that the energy states associated with water and counterions appear in the π-π* gap, which corresponds to the gap between the HOMO of guanine and LUMO of thymine. They also found that the contributions from the water states nearly overlap with the contributions from the counterion (Na and Mg) states, leading to the possibility of hopping conductivity between water and coun-


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are optimized using DFT are again subject to doubt. The advantage of using MD snapshots for single-point DFT calculations is that the DNA system is described well by the molecular mechanics force fields, which take into account the dispersion corrections. However, the interactions between the charged phosphates and the surrounding counterions and water molecules are largely approximated. To this end, empirical corrections to DFT methods that account for the dispersion forces (DFT-D) are a suitable alternative to study DNA.44 Optical Conductivity Studies on Wet DNA. Parinello and coworkers used DFT Car-Parrinello calculations to study the optical conductivity profile of a poly-GC Z-DNA crystal.45 They found that the bonding patterns for water molecules in close proximity to DNA were different from that of bulk water, which led to a wide distribution of dipole moments ranging from 1.7 D (close to the dipole moment of gas-phase clusters of water) to 3.8 D (close to dipole moment for five-fold coordinated water molecules). This highlighted the different character of the water molecules in close proximity of the nucleic acids. This effect was also captured by the optical conductivity profile. The direct gap in DNA from the π-π* orbitals of guanine was identified by the sharp peak in the optical conductivity profile at 4 eV. Other than the direct band gap, many low-intensity excitations were identified below 4 eV (Figure 5a). Upon inspection, it was found that these states arose due to guanine f Naþ transitions. The low intensity of these transitions was attributed to the dynamical fluctuations in the ion distribution. Using a combination of MD simulations and DFT calculations, Cox and co-workers were able to capture the low-energy signatures in the optical conductivity profile of B-DNA.46 Their results showed that the thermally activated doping of DNA by water states led to electronic contributions to low-frequency absorption. It was found that the main contributions to the low-frequency absorption were from water clusters located near DNA ends, breaks or nicks, thus being associated with structural defects in DNA. From their DFT calculations, they were able to identify contributions from occupied water states and unoccupied π* orbitals near EF, which led to the observed low-energy excitations at about 150 meV (Figure 5b). These differences in the low-frequency regions of optical conductivity spectrum of B-DNA and Z-DNA are directly related to the secondary structure of B-DNA and Z-DNA. While B-DNA has a well-defined major and minor groove wherein the DNA bases are exposed to water interactions, Z-DNA lacks such a welldefined groove structure, thereby hindering DNA base-water interactions and favoring interactions between the DNA backbone (phosphates) and the environment (water and counterions). These calculations establish the influence of the environment on DNAconductivity. They also highlighted the importance of statistical averaging to describe DNA energetics, which are strongly influenced by structural fluctuations. Direct Conductance Measurement of DNA in Aqueous Solution. As overviewed earlier, many of the early experiments on direct DNA conductivity were performed using dried DNA samples, which caused a reduction in conductance due to inefficient interbase π-π coupling (A-DNA structure). To this end, in 2004, Tao and co-workers performed direct conductance measurements of single DNA molecules in aqueous solution.47 They studied two series of DNA sequences, 50 -(GC)n-30 -thiol


Figure 6. (a) Conductance histograms constructed from multiple measurements for the 50 -CGCGCGCG-30 -thiol linker and 50 -CGCGAATTCGCG30 -thiol linker. The peak positions change upon the incorporation of AT domains in a poly-GC sequence, with an associated decrease in the observed conductance. (b) Formation of molecular junctions monitored by the appearance of discrete steps in the conductance profile. I-V curves for the eight base pair 50 -CGCGCGCG-30 -thiol linker sequence, where the lines with different colors are I-V curves obtained from measurement on three individual molecular junctions. The open squares are the current values obtained from the peak positions of the conductance histograms at different bias voltages (reprinted from ref 47). (c) PDOS for the sequences 50 -GCGCGC-30 , 50 -GCATGC-30 , 50 -GGATGG-30 , and 50 -ATATAT-30 . Contributions from the various bases are color coded: guanine, black line; cytosine, red; adenine, green; thymine, blue. In each panel, the inset shows the T(E) of the associated HOMO guanine band. The Fermi level (EF) determined by the Au clusters is scaled to lie at 0. (d) HOMO plots for (i) 50 -GCGCGC-30 , (ii) 50 -GCATGC-30 , and (iii) 50 -GGATGG-30 (reprinted with permission from ref 48, copyright 2008 by the American Physical Society).

linker with n=4, 5, 6, and 7 and 50 -CGCG(AT)mCGCG-30 -thiol linker with m = 0, 1, and 2, which are known to form B-DNA

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structures in aqueous solutions. The CH2CH2CH2-SH (thiol linker) groups at its 30 ends were incorporated to bind to the Au electrodes via strong Au-S bonds. In the experimental setup, individual molecular junctions were created by repeatedly moving a STM (scanning tunneling microscope) tip into and out of contact with a flat Au electrode in the buffer containing DNA. The formation of a molecular junction was identified by the appearance of steps in the conductance profile. It was observed that conductance steps did not always appear at the same conductance values, reflecting variations in the molecule electrode contacts due to the structural fluctuations in DNA. Thus, the conductance histograms were constructed from more than 500 individual measurements to average out the influence of structural deformations (Figure 6a). The histograms revealed peaks near integer multiples of 1.3 10-3G0, which corresponded to the conductance of a single eight-bp DNA duplex. To avoid the influence of ionic conduction, the STM tip electrode was coated with Apiezon wax to keep the ionic leakage current between the two electrodes below 1 pA. The highlight of the experiment was that the currentvoltage (I-V) curves were evaluated using two different methods. In the first method, the I-V curve was obtained by monitoring the peak positions in the conductance histograms obtained at different bias voltages. This gave a I-V curve averaged over many DNA junctions. At the same time, the I-V profile was also measured for individual molecular junctions using a second complementary method. In this method, the tip position was frozen upon the formation of a single DNA junction (identified by the appearance of the lowest conduction plateau), and the current was recorded while sweeping the bias voltage (Figure 6b). Both methods gave I-V curves that were in good agreement with one another. Interestingly, the authors found that the I-V was linear up to 0.5 V for a eight base pair poly-GC sequence. They also found that the conductance for the (GC)n sequences deceased with increasing length (L) and was proportional to 1/L, while the decrease in conductance for the 50 -CGCG(AT)mCGCG-30 sequence with an increase in length could be described by an exponential. These results highlighted the sequence-dependent conductivity of DNA. Sequence-Dependent Electron Transport. The experimental report by Tao and co-workers provided an excellent reference for first-principles theoretical analysis of DNA conduction in solution. We modeled the experiment setup by studying four hexamer sequences 50 -GCGCGC-30 , 50 -GCATGC-30 , 50 -GGATGG30 , and 50 -ATATAT-30 .48 The initial structures of the DNA hexamers surrounded by 3000 TIP3P water molecules and counterions (14 Naþ) were obtained from classical MD simulations of the DNA octamers. An important part of our model was the explicit incorporation of Au electrodes into the ab initio calculations. We found that the role of electrodes influencing the transport properties of DNA had not been discussed in earlier first-principles studies, while for explaining the observed conductance trends, it was important to know the exact alignment of the molecular orbitals of DNA with the EF of the electrodes. The gold electrodes used in the experimental study were modeled by placing two 48 atom gold clusters obtained from relaxed surface calculations at either end of the


DNA molecule. These clusters were then attached to the DNA molecule via the thiol linker (-CH2CH2CH2S) attached to the 30 ends of the DNA strands, where the sulfur head group was aligned on the fcc hollow site of the Au(111) surface using previously reported S-Au distances.49 From our calculations, we found that for all sequences containing guanine, the HOMO was formed from the contributions of guanine orbitals. Interestingly, it was found that the EF of the electrodes for these sequences was pinned to the HOMO band (EF was determined by the presence of the Au clusters) (Figure 6c). The contributions from other DNA bases (adenine, thymine, and cytosine) were not close to EF, and their contributions to the HOMO were found to be negligible. This was clear for the 50 -ATATAT-30 sequence wherein the HOMO level was found to be 0.4 eV below EF. To study the influence of sequence dependence, we calculated the gap (Δ) defined as EF - Emax, where Emax is the energy of the peak maximum of the guanine HOMO band closest to EF. We found that the Δ value increased upon going from 50 -GCGCGC-30 to 50 -GCATGC-30 (0.06-50.9 meV), indicating a widening of the gap upon the incorporation of A/T base pairs. Similarly, it was found that Δ reduced upon going from 50 -GCATGC-30 to 50 -GGATGG-30 (5031.5 meV), indicating that intrastrand guanine coupling reduces Δ. For a qualitative description, we calculated the zero bias transmission function, T(E), for the energy range spanning the HOMO band using the Green's function method. We found that the T(E) for 50 -GGATGG-30 was 3 orders of magnitude greater than that for 50 -GCATGC-30 , suggesting that an intrastrand coupling is more efficient when compared to interstrand coupling. We also found that the T(E) maximum magnitude at 0.056 eV for 50 -GCGCGC-30 (1.8 10-5) was an order of magnitude higher than the same for 50 -GCATGC-30 (8.54 10-6), indicating that the incorporation of the A/T base pair into G/C-rich domains acts as a tunneling barrier. This became clear upon inspecting the HOMO plots of 50 -GCGCGC-30 , 50 -GCATGC-30 , and 50 -GGATGG-30 (Figure 6d). While 50 -GCGCGC-30 favors delocalization over the entire length, 50 -GCATGC-30 , and 50 -GGATGG-30 form localized domains on guanines at either end. Additionally, our calculations were also supported by the close agreement of the theoretically calculated decay factor, β = 0.53 Å-1, with the experimentally obtained value (βexpt = 0.43 Å-1)47 for the 50 -GCATGC-30 sequence using the super exchange model and theoretically calculated band gaps. We were able to show that the sequence dependence of conductance was indeed due to inherent electronic coupling between the DNA bases, which is strongly dependent on the secondary structure of DNA (B-DNA versus A-DNA or Z-DNA). Recently, Elstner, Cuniberti, and co-workers used a hybrid method based on a combination of classical MD simulations, quantum chemical calculations, and a model Hamiltonian approach to describe charge transport through biomolecular wires with variable lengths in the presence of a solvent.50,51 Using this approach, they were able to show that correlated fluctuations of the base pair dynamics were crucial in determining the transport properties of DNA and that the effect of fluctuations can be quite different for sequences with low and high static disorders, that is, differences in base IP. Metal-Ion-Modified DNA Scaffold. Finally, we give an overview of the electronic properties of metal-ion-modified DNA

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Figure 7. (a) Base-pairing schemes for M-DNA. The imino proton is replaced by the divalent metal ion. (b) Asymmetric I-V curve for a B-DNA sample. Inset: Symmetric I-V curve upon formation of M-DNA (reprinted with permission from ref 52, copyright 2001 by the American Physical Society). (c) Hydroxylpyridone metal base pair. (d) Formation of the extended Cu-O network in hydroxylpyridone-incorporated M-DNA. (reprinted with permission from ref 61. Copyright 2009 by Wiley-VCH Verlag GmbH & Co. KGaA). (e) Optical conductivity profile for the hydroxylpyridone-incorporated M-DNA oligomers. Code: black, monomer; red, dimer; blue, trimer; green, tetramer (reprinted with permission from ref 61, copyright 2009 by Wiley-VCH Verlag GmbH & Co. KGaA).

(M-DNA) structures, which exhibit stable conduction properties when compared to native DNA structures. Two methods have found predominance for incorporating metal ions into the DNA scaffold to create M-DNA structures, (a) exchange of hydrogen atoms (imino proton) that are part of the WatsonCrick base pairing by divalent metal ions at high pH and (b) incorporation of metallo base pairs into the DNA sequence, that is, noncanonical base pairs that chelate metal ions and incorporate them into the DNA duplex structure (Figure 7a and c). Rakitin and co-workers observed metallic behavior for μm long M-DNA structures, wherein the imino proton of each base pair was replaced by Zn2þ at a pH of 9.0 (Figure 7b).52 Soler and co-workers performed electronic structure calculations for this type of M-DNA structure by replacing the imino proton by three divalent metal ions, Zn2þ, Co2þ, and Fe2þ.53 From their calculations, they found that Co2þ and Fe2þ contribute to the HOMO and LUMO of DNA, while the contributions from Zn2þ were not significant. This feature is synonymous with the doping of the π-π* gap by occupied water and


counterion states. While the replacement of the imino proton is highly pH-sensitive and thus prone to defects, the incorporation of artificial metal base pairs into the DNA sequence overcomes these limitations. Artificial metal base pairs have been used to incorporate a number of metal ions into the DNA structure, namely, Cu2þ, Mn2þ, Ni2þ, Hg2þ, Agþ, and so forth. For more information on M-DNA structures, we refer the reader to excellent reviews in this field.54-57 Shionoya and co-workers reported self-assembly of up to five Cu2þ ions within the DNA structure using hydroxylpyridone metal base pairs (Figure 7c).58,59 We and a few other groups performed electronic structure calculations to model their experiments.60-63 We found that the Cu2þ centers were ferromagnetically coupled to each other via the formation of an extended Cu-O network, which leads to a ferromagnetic domain formation. We also found that the metallic states dope the π-π* energy gap, which was evident from the appearance of low-frequency peaks in the optical conductivity spectrum, which could also be used as a guide to probe

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magnetic interactions (odd-even fluctuations common to spin 1/2 systems) (Figure 7d).64-67 In another experiment, the groups led by Shionoya and Carell were able to selfassemble Cu2þ and Hg2þ into the same DNA scaffold.59 Our calculations for their experimentally realized structures revealed that such controlled assembly led to the formation of decoupled magnetic domains. We also found that the incorporation of a nonmagnetic ion (Hg2þ) was not essential for decoupling and that the magnetic domains could be decoupled upon the incorporation of a natural base pair between the magnetic domains.61 It has been difficult to resolve the X-ray structure for the M-DNA systems, with only one crystal structure and one solution structure having been reported so far for these type of M-DNA systems.68,69 To this end, electronic structure calculations have presented themselves as valuable tools to probe the structural and electronic properties of this novel class of DNA systems which could truly exhibit stable conductance properties.

To summarize, theoretical calculations greatly aid in rationalizing the experimental results on DNA conductivity. Electronic structure calculations of DNA have shown that native DNA acts as a wide band gap semiconductor, with a band gap of approximately 1-2 eV, depending upon the DNA sequence. It has been found that the HOMO is generally localized on the purine bases (guanine if present in the sequence or adenine), while the LUMO is generally localized on the pyridine bases (thymine if present in the sequence or cytosine). The observed band gap is strongly influenced by structural fluctuations in DNA or in the corresponding environment comprised of water and counterions. Theoretical studies have also shown that the direct gap in DNA can be doped by water or counterions states. Specifically, it has been shown that water clusters around DNA ends and nicks could dope DNA. This doping could be responsible for the enhanced conductance observed in experimental studies of DNA under humid conditions. For the direct conductance measurements, theoretical calculations have shown that the HOMO of DNA (when comprised of contributions from guanine) is pinned to the EF of the Au electrode, thereby creating a direct tunneling pathway between the two electrodes, leading to the observed metallic behavior for short poly-GC DNA sequences. It is to be noted that, even though the direct gap still remains at 1-2 eV, the alignment of the EF and the HOMO leads to the observed I-V behavior. Recent progress in the use of hybrid methods based on a combination of classical MD simulations, quantum chemical calculations, and model Hamiltonians greatly aids in the predictive power of the theorists. Theoretical studies have also been instrumental in exploring modifications of DNA (M-DNA structures and alternate nucleotide components), which could lead to stable conductance properties.70-73 However, it is to be emphasized that theoretical calculations have, in most cases, always followed experimental finding and that the predictive power of theory has greatly been under utilized by experimentalists. It is of importance to highlight that a collaborative approach would be beneficial to the field of DNA conductivity. This fact can be illustrated by the recent finding of efficient long-range charge transport in DNA by replacing adenine (A) with diaminopurine (D).74 In this study, the authors chose to replace the A/T base pair with a D/T base pair as the HOMO of the D/T base pair was shown to be closer to that of G/C by earlier theoretical calculations.75 Thus, we note that a synergetic collaborative approach between theoretical and experimental groups would help in working toward the goal of realizable biomolecular electronics.76,77

Metal-ion-modified DNA (M-DNA) structures exhibit stable conduction properties when compared to native DNA structures.

Before summarizing, we present a critical overview of the theoretical methodologies used to study DNA systems. As already mentioned, model Hamiltonians are a powerful tool to study DNA charge transport. However, they are plagued with an oversimplification of the parameters used. It would be greatly beneficial to use parameters derived from a fragment orbital basis to improve the performance of model Hamiltonian calculations. While studying DNA systems coupled to electrodes, it is important to obtain appropriate site energies (for electrodes) and hopping parameters (molecule-electrode) rather than adjusting them to reproduce the experimental results. To this end, the recent developments made by Elstner, Cuniberti, and co-workers could greatly improve the performance of model Hamiltonian-based calculations.50,51 In regard to ab intio methodologies, it is important to note that DFT has been one of the more successful methods to study large systems; however, it is plagued with its own deficiencies. Two of the major concerns, as already mentioned, are the dispersion corrections and treatment of excited states (leading to band gap underestimation). While progress has been made to treat the former by the inclusion of empirical dispersion corrections to DFT (DFT-D),44 the latter is still a cause of concern as the description of excited states requires the incorporation of correlations, a matter that is more fundamental to DFT. Thus, in our opinion, the currently available set of results must be used more as a guide to predict trends in DNA conductivity rather than to quantify DNA conductivity, good examples being the works by Ratner et. al32-35 and Elstner, Cuniberti, and co-workers.40,50,51


A synergetic collaborative approach between theoretical and experimental groups would help in working towards the goal of realizable biomolecular electronics.

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AUTHOR INFORMATION Corresponding Author:

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*To whom correspondence should be addressed. E-mail: pati@ jncasr.ac.in.

Biographies

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Sairam S. Mallajosyula received his doctoral degree from Jawaharlal Nehru Centre for Advanced Scientific Research (JNACSR), Bangalore, India, in 2009 for theoretical investigations of electronic structure and charge-transfer properties of DNA and modified DNA. He was a recipient of the International Institute for Complex Adaptive Matter (I2CAM) Junior Exchange Award in the year 2007. He is currently a postdoctoral fellow at the Computer Aided Drug Design Center at the University of Maryland, Baltimore, U.S.A. His current research interests include electronic structure theory, molecular electronics, and force field development for biological systems. Swapan K. Pati obtained his Ph.D. from the Indian Institute of Science, Bangalore, followed by postdoctoral work in the department of Physics at the University of California, Davis, and in the Chemistry Department at Northwestern University. He is currently a Professor at the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore. He has been a Visiting Faculty Member to a number of universities in the United States, Europe, and Japan. He has been a Young Affiliate of the Academy of Sciences for the Developing World since 2007. He is a recipient of the Material Research Society of India medal (2006) and Chemical Research Society of India bronze medal (2007). He was selected for the Swarnajayanthi Fellowship by the Department of Science and Technology, Government of India, in 2007. He has recently been elected as a fellow of the Indian Academy of Sciences. His research interests include quantum many-body theory, molecular electronics, nonlinear optical phenomena, quantum magnetism, generalized charge-transfer mechanisms, and hydrogen storage. He is also actively involved in developing new theoretical tools for a holistic understanding of structure-property correlations in a whole range of systems from molecules to materials, including biological and biomimetic systems (see http://www.jncasr.ac.in/pati/ for more information).

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ACKNOWLEDGMENT This work was supported by the Depart-

ment of Science and Technology (DST) and the Council for Scientific and Industrial Research (CSIR), Government of India. We would like to acknowledge D. L. Cox, R. R. P. Singh, J. C. Lin, and K. Senthilkumar for their contributions to our DNA-based research.

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Toward DNA Conductivity: A Theoretical Perspective - American

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