Experimental and Theoretical investigation of electrical properties of DNA molecular structures

By Sefaattin Tongay21/10/2005

Introduction

DNA plays a pivotal role in biology as the carrier of genetic information in all living species. Recently, due to the effort in miniaturization of devices to nano-scale, physicists and chemists have become increasingly interested in the electronic properties of the "molecule of life". Nowadays, there are several research interest based on the DNA molecule, such as DNA as building blocks, transistors, nano-bots (nano robots) and electrical circuits etc. In this trend, problem of using DNA molecule as an electrical device raised much more than the others. In this respect, this work provides an extensive overview; analysis and discussion of DNA’s electronic states obtained both experimentally and computationally by the use of density functional theory.

Understanding Conductivity Properties of DNA molecule

After the discovery of Deoxyribose Nucleic Acid (DNA)’s double-helix character by Crick and Watson [1], two physicians Eley and Spivey theoretically proposed that the π- π interactions of the two nearest neighbor base pairs in double-helix DNA could lead to conducting behavior. [2]The physical interpretation behind this view was that: DNA double-strand structure is composed of many planar, benzene-type and unsaturated aromatic entities whose atomic orbitals, namely pz orbitals are perpendicular to the plane of the base. These pz orbitals can form π

bonding and π * antibonding orbitals. [3] It should be noted that the energy gap between these orbitals (it’s calculated to be approximately 4.2 eV in Ref. 3) can be reduced by increasing the coupling between the base pairs strong enough. If the coupling is strong enough, this will cause to extended states along the helix axis, with smaller energy gap between the orbitals. And if this coupling increased strong enough, then the energy gap will vanish and this will make the double-helix DNA structure conducting.

Figure 1. DNA from the point of physics. The solid lines at the edges indicate the double strand of DNA molecule. Intermediate structures between these double-strand structures are the base pairs, i.e. Adenine, Cytosine, Guanine, and Thymine. It should be noted that base pairs are in the same plane and the atomic orbital pz is perpendicular to the base pairs.

In summary in order to have metallic and extended states in DNA structure, π and π* which are formed by atomic pz orbitals those are perpendicular to the base pairs plane have to overlap sufficiently. And this depends on the distance between the two neighbor base-pairs and the twist angle. Endres also considered a simple Huckel model making use of these. [4]

After observing that the conducting behavior of DNA structure is correlated to the interaction between two successive base pairs, now I’ll attempt to write the coupling between these two bases. Treating the hybridization matrix elements will be very useful before going into the details. Actually, two pz orbitals from two different base pairs couple with each other by ppπ and ppσ hybridization. And this hybridization can be represented by Slater-Koster theory. [5] According to this theory, the hybridization matrix elements those are originated from the coupling between the pz orbitals can be expressed in terms of m electron mass, d distance between the nearest-neighbor base pairs, distance cutoff value Rc which is introduced in the equation for describing the tails of wavefunction at large separations and some parameter η which can be

determined by matching the results of ab-initio calculation results. As a result hybridization matrix elements take the following form;

After armed with this elegant theory, it will be suitable to construct the hybridization matrix elements (Electron transfer matrix elements) of two successive base pairs. Electron transfer matrix can be expressed as follows;

Figure 2. pz orbitals located on the perpendicular to the plane of neighbor base pairs. Base pair 1 and base pair 2 correspond to nearest base pairs between the two helical strands. Since there is an angle φ between the origins of p orbital, there will appear two terms in interaction matrix element, namely Vppπ and Vppσ.

In the last step, it has been make use of general form of hybridization matrix elements in Slater-Koster theory.

Now construction of V interaction matrix element caused by the interaction that exists between the pz orbitals of two successive base pairs allows us to write the coupling between nearest base pairs. For writing the electronic coupling, I approximate the molecular orbitals of

different base pairs to be orthogonal to each other. Within this approximation, the coupling written below;

In this equation, N1 and N2 correspond to the number of pz orbitals on the different base pairs indicated by 1 and 2. And c i1,n corresponds to the i th linear combination of atomic orbitals. Actually, detailed consideration states that the hybridization matrix element in the electronic coupling has only a small contribution to the inter-base-pair electronic coupling. As seen from the last two equation, the coupling is related to z and l, indicating that the coupling is related (in other words conductivity) to these two parameters. (These two parameters, namely twist angle and separation value are determined by the type of DNA structure.)

The effects of base pair separation and torsional modes on the electronic coupling are also an important subject. The effect of change in the base pair separation is previously discussed by Endres et.al. [4] and it has been indicated that the base pair separation is less dramatic comparing the torsional effects. Returning back to torsional effects, Fig. 3 depicts the electronic coupling computed from DFT as a function of twist angle about the helical axis. According to Fig.3, there appear some sign changes in electronic coupling. In fact, the linear combination of atomic orbital coefficients remains approximately constant during the rotation. Thus it’s expected to sign changes must caused from the interaction matrix terms. After this, interesting discussion, it should also be noted that the separately at angle -360 the base pairs are aligned and paralleled each other. Thus this will lead to optimal sigma overlap and to a maximal electronic coupling.

Experimental Point of ViewThe most challenging thing in measuring the conductance value of DNA is the attachment of a DNA bundle or single molecule to two electrodes. This process can be handled in various ways by the use of recent developments in nanotechnology such as electron-beam lithography, atomic force microscopy, electron point source microscopy, scanning tunneling microscope and etc. Electron-beam lithography is used to fabricate nanoelectrodes, atomic force microscopy (AFM) and low energy electron point source (LEEPS) microscopy are used to image the sample, and scanning tunneling microscopes (STM) can be utilized to induce a tunneling current. For the last and the most cruel step, attaching DNA molecules to metal electrodes, attaching technique named DNA oligomer-based1 ‘‘gluing’’ was first developed by Braun et al. [11] In this approach sticky ends of DNA (single-stranded ‘‘overhang’’ regions) are hybridized to short surface-bound oligomers. After this novel work some other similar experimental work have been done by Zhang et al. and Hartzell et al. [12,23] Similarly, DNA modified with thiol (SH) groups at the 58 ends can directly hybridize on gold or platinum electrodes (Storm et al., 2001). In addition to these methods, another method -aligning DNA molecules between the leads has been presented by Porath et al. In this method, an applied electric field between two electrodes polarizes a nearby molecule in a droplet of DNA solution, which is then attracted to the gap between the electrodes owing to the field gradient called. Since there exist an applied field between the two electrodes, this method is often named by ‘‘electrostatic trapping.’’ [9,21]

Although there have been performed considerable amount of experimental work, these have been performed using the methods presented previously, the electrical properties of DNA molecule are still

not well established yet. Experimental efforts on this subject do not clarify the electrical nature of the DNA structure since different group of results points out different electrical properties. Before going into the details of the experimental results, it will be suitable to focus on the possible reasons of such extremely different results. The possible reasons can be grouped in two main categories. One of these two is the contact problem. It’s now well known that type of contact between the electrode and the DNA molecule dominates the electrical behavior of the finite DNA molecule. [25] The physical reason behind this is the less known work functions of the metal electrodes. The contact is characterized by the work function f of the electrode, as well as the tunneling barrier. But since the work functions of electrodes are not well defined, this situation states the first difference between experimental efforts.

Second group is differences in experimental values due to the structural difference in the DNA and their environment. (i.e. length of DNA molecule, character of DNA, stretched DNA, DNA sequence, environment of DNA etc.) Most possibly the most problematic thing is not to have amount controllable parameter over these properties. In the previous presented experimental works, it have been point out that some of the above-mentioned variables are hard to control, e.g., the nature of the actual structure of the DNA and the contact. However, most recently some success has been achieved by Hartzell et.al. In his work, dependence of DNA conductance on the nature of the contact to the electrode and whether the DNA is repaired or nicked has been understood. In the scope of these works, some of the experimental efforts are summarized in table with their findings. [7-11]

Truly metallic Wide bandgap semiconductor

Insulator at room temperature

Ohmic at room temperature

Kasumov et.al Porath et.al. Rakitin et.al.

Storm et.al. Braun et.al. Zhang et.al.

Rakitin et.alYoo et.al Cai et.al. Tran et.al. Schonenberger et.al.

Table 1. Overview of the results of experimental works with different approaches presented above. As discussed some environmental and contact effects influence the obtained results resulting in different electrical properties.

In the first column, a single experiment by Kasumov et.al [7] showed resistance data consistent with induced superconductivity in DNA. In their experiment, they used mica method with Rheium and Carbon electrodes with 16- mmlong lambda-DNA structure. Initially the DNA was combed by the buffer flow and touched the insulating but charged mica between the electrodes. This experiment differs from all others in that a buffer with predominantly divalent magnesium counter ions was used was metallic down to extremely low temperatures requiring true extended states. By using this this method Kasumov obtained a result indicating that the lambda-DNA between the two electrodes induced superconductivity (T<1K)

In the second column, there exist two independent works pointing out the similar results. In the experiment of Porath et.al [9] short length DNA molecule used between the Pt electrodes. In this work DNA structure was only 30 base pairs long. This was the most important point, since the persistence length of the DNA was about 100 base pairs at room temperature. Since the DNA molecule between the Platinium electrodes is

short relative to the persistence length of the DNA at room temperature, some defects may occur in the molecule and these defects would lead to extra uncertainty and interruption of π-π interactions. By referring to the effect of the π-π interactions in the transport properties of DNA molecule discussed previously, it is expected to have a semiconducting behavior. This was actually what one might expect since short DNA molecule’s bases have rather large Highest Occupied Molecular Orbital (HOMO) and Lowest Occupied Molecular Orbital (LUMO) gap with value of 4 eV. In result it has been obtained that the bias voltage gap is of order 1-2 eV energy difference between the Pt work function and either Guanine (HOMO) or Cytosine (LUMO). In addition to this work Rakitin [8] obtained very similar bias voltage gap, although they placed the short DNA molecule between the Gold (Au) electrodes. [Fig.3]

Figure 3. [8] A semiconductor like plateau (conductance gap) of about 200 meV is observed for B-DNA(-black spots- B-DNA in standard buffer at pH 7.5 was dropped across the electrode gap and then dried in vacuo.), whereas this plateau disappears (or, at least, shrinks to a value which cannot be resolved at room temperature) in the case of M-DNA (white spots). Typical I-V curves for samples of B-DNA with “glue” oligomers are shown in the inset of Fig. 3. As shown there exist 1-2 eV semiconducting gap.

Some experimentalists focus their attention onto single stranded lambda-DNA and PolyG, PolyC DNA molecules with some different methods. In this experimental part, Braun et.al [11] used gluing technique which is discussed previously with Au electrodes and Na+ ions. In his experiment, he found out that the single stranded lambda-DNA possess

insulating behavior at room temperature. There years later in 2001 Storm et.al [10] worked with single stranded lambda-DNA and PolyG, PolyC DNA with Pt and Au electrodes with the method of “mica” and similar trend obtained this time including PolyG, PolyC DNA. Lastly, in 2002 Zhang et.al [12] revealed out that these molecules also possess conducting behavior, when these structures are doped.

Figure 4. [12] Investigated the electrical conductivity of lambda-DNA using DNA covalently bonded to Au electrodes. The two-probe current vs. voltage (I-V) curve for a sample of lambda-DNA bridging two parallel Au electrodes separated by 4 micrometer (the sample comprises nearly 1000 molecules). As seen from the graph current at any driving voltage equals to zero indicating that the lambda-DNA is insulating. Dashed spots state for the linear fit of the obtained result.

For the last part, in their experiments Rakitin et.al Yoo et.al, Cai et.al. , Tran et.al. revealed out that the bundles of DNA, networks of bundles of DNA exhibits ohmic behavior using defend approach such as microwave absorption, SFM on mica and gluing method.

Figure 5. [14] Conductivity of dry lambda-DNA and lambda-DNA in buffer versus inverse temperature as measured at 12 and at 100 GHz. The magnitude of the conductivity was determined at 12 GHz, and the 100 GHz data were normalized to the 12 GHz results at room temperature. The conductivity is strongly temperature dependent around room temperature with a crossover to a weakly temperature dependent conductivity at low temperatures. Removal of the water mantle around the double helix leads to reduced conductivity.

Theoretical Point of ViewIn understanding the electrical properties of DNA molecule,

theoretical approaches divide into two parts namely model calculations and ab-initio calculations for the existing limitations uncertainty about which degree of freedom for the model calculations and computational cost due to large supercells and huge number of atoms presented in the unitcell for the ab-initio based calculations.

The first theories were mostly based on the model calculation due to computation problem on the ab-initio calculations. With this model calculation single charge transfer mechanism in DNA molecules are better understood comparing to the knowledge about conductance in DNA obtained by the model calculations. For this reason in this section, first I’ll focus on the charge transfer mechanisms and then focus on ab-initio based calculations in understanding the electrical properties of DNA molecule, and lastly point out the theoretical efforts by the use of model calculations.

a. Charge Transfer MechanismsFrom above theoretical effort, three possible mechanisms of charge transfer have emerged: (i) DNA as a molecular wire, (ii) charge transfer by hole hopping, and (iii) phonon-assisted polaron hopping.i. DNA as a molecular wire

Double stranded DNA contains two polyanionic strands that connect with each other by base pair formation. The base pairs stack one top another and, it is speculated that this stack may conduct charge along the axis of the double helix.[26] Charge can then be transferred through a super-exchange process, in which an excited state acceptor and donor are separated through a conjugated base pair bridge [Fig.6].[27]

Figure 6. Super-exchange process occurring in DNA where charge is delocalized between the donor and acceptor through the DNA.

The super-exchange process is described by the simplified Marcus equation (Marcus-Levich-Jortner Theorem) as shown below for non-adiabatic electron transfer,

where the rate constant for charge separation, kcs, in a donor-bridge-acceptor system is dependent upon a pre-exponential factor ko,

the donor-acceptor center-to-center distance R, and b, which is dependent upon the nature of the bridge and its coupling with the donor and acceptor.[28] The rates of charge transfer (CT) processes are dependent upon the integrity of the aromatic base stack, with small imperfections affecting the value of b. Because of the fluid-like motion of DNA [29], random imperfections within the stack tend to occur, and, as a consequence, super-exchange becomes inefficient over long distances. For DNA to act as a molecular wire, a system of highly ordered, stacked aromatic base pairs must be present.

ii. Charge transfer by hole hopping

In this model, it is required that the DNA molecule must exist as a collection of discrete base pairs, but not in a conjugated aromatic stack. [27] Under this point of view, because of the lack of conjugation by stacking, charge will be localized at the base which is Guanine (G) with the lowest oxidation potential [28] Charge transfer is proposed to occur through a process of tunneling from low energy base to low energy base, since charge will not be able to migrate to adjacent bases with higher oxidation potential. [Fig.7] In this, a radical cation hole can “hop” from guanine to guanine, in an individual superexchange. The modified Marcus equation indicates that the hop with the largest R (G to G distance) will be the rate-determining step. Charge transfer efficiency (E) is described simply by the equation ln E • ln N, where N is equal to the number of hopping steps that take place. A high efficiency of charge transfer and low b can be expected from a hole hopping model.

Figure 7. Illustration of Hole hopping model. In this model charge tunnels from low energy state to low energy state as shown above.

iii. phonon-assisted polaron hopping (PAPH)Phonon-assisted polaron hopping (PAPH) is a hybrid of the two

extreme models, namely the molecular wire and hole hopping models. A DNA polaron is a radical cation or anion that is extended over 5-7 base pairs. The DNA unwinds, increasing molecular orbital overlap between bases while decreasing the base-to-base distance. The distortion results in a minimization of the radical cation energy in the DNA.

Phonons are internal motions such as changes in winding or inclination angle. These motions may encourage hopping of the polaron. When charge is introduced into DNA in the PAPH model, a polaron is formed in the helix, stabilizing the charge. By interaction with a phonon, the polaron will undergo a hopping mechanism where small groups of base pairs with similar energy will enter and leave, thereby moving the polaron super-exchange occurs inside of the polaron transferring charge as described by the Marcus equation for electron transfer with equation presented previously giving almost instantaneous exchange of an electron through the polaron. However, long-range migration of the polaron itself must occur through PAPH, as a long-range superexchange would be unlikely. By incorporating

polarons and phonons into the mechanistic model, PAPH takes into account the dynamic nature of DNA.

Figure 8. Illustrated phonon assisted polaron hopping through DNA molecule.

The two extreme mechanistic models proposed for charge transfer in DNA are not realistic for charge transfer through DNA. DNA as a molecular wire assumes complete conjugation of the base airs, highly unlikely over any reasonable distance. Charge transfer demonstrates a distance dependence hat would not be expected in the molecular wire model. Hole hopping, on the other hand, relies upon electrons hopping through discrete molecular orbital of low oxidation guanine base pairs. The phonon-assisted polaron hopping model describes delocalization of charge through a polaron, while movement of the charge occurs by hopping. phonon-assisted polaron hopping currently best describes charge transfer in DNA.

b. Electrical Properties of DNA (Theoretical approach)After discussing three models of charge transfer mechanism, from now on electrical properties of DNA molecule will be handled by referring to

the previous works by use of density functional theory and molecular orbital theory.

In the understanding of electrical properties of the DNA molecule, ab initio method is one of the best methods. But as discussed previously one problematic difficulty arising here is the computational cost due to existence of large number of atoms (approximately 1000 atoms). Because of this difficulty, the calculation of band structure of DNA molecule waited by considerable time for the development in silicon-based technology.

Figure 9. DNA segment consists of ten guanine-cytosine basepairs. Each basepair is just an nx36° and an nx3.3728 Å translation of the first. This structure was fully relaxed to the nearest local minimum, and the electronic and vibrational DOS’s were calculated.

.

The first band-structure calculation was done on the canonical B-DNA (a DNA segment composed of ten guanine-cytosine base-pairs) structure [Fig.9] by Lewis et.al. [20] In this model the structure was considered without solvent surrounding around it. In this novel work Lewis and coworkers have performed a quantum-molecular dynamics calculation of a deoxyribonucleic acid (DNA) double helix, using a 0.2-

femtosecond (fm) time step. The relaxation was accomplished via a method known as dynamical quenching, where the velocities are set to zero as the kinetic energy reaches a maximum; thus the system’s geometry seeks the nearest minimum-energy configuration. [Fig.10] Obtained results are depicted below.

Figure 10. The calculated electronic DOS for (a) an isolated GC basepair and (b) the poly(dG).poly(dC) structure. In this figure Fermi level of the system is set at 0 eV by convention. Since there is a gap near the Fermi level this structure is semiconducting as supported by experimentalist, discussed in previous section[Tab.1]. The band gap is found to be 1.40 eV for the poly(dG).poly(dC) structure, and 3.37 eV for the isolated basepair.

Three years later Pablo et.al also find out similar results for A-DNA, this time by using a DFT [30] code with similar features, namely SIESTA. SIESTA code was also applied to calculate the band structure of a fully relaxed structure. Results indicated that there appears an extremely small HOMO/LUMO bandwidth. [21]

After this novel theoretical efforts, effect of solvent and counterions in electrical properties of DNA molecule left as a problem. Very recently, Lewis et.al, Gervasio et.al, handled this problem with different ab-initio based methods. [20,22] In Gervasio’s novel work, the electronic properties of a Z-DNA [Fig.11] which is synthesized in the laboratory are investigated by means of density-functional theory Car-Parrinello calculations. From their well-cared calculations DFT gap

between empty and occupied states was particularly small, being only 1.28 eV. This very small value heralds the rather novel nature of the states at the

Figure 10. View of the three-dimensional structure of the Gua:Cyt dodecamer (Z-DNA). Water molecules, counterions, and hydrogens have been removed for clarity. The sugar-phosphate backbone is represented as ribbons.

bottom of the conduction band, which is a charge transfer state where one electron has been moved outside the helix mostly on the Na_ counterions and on the PO_4 groups. To assess the effect of water molecules on this state and on the value of the gap, authors repeated the calculation by removing the water molecules but otherwise leaving the geometry of the DNA and counterions unchanged. Thegap is much reduced. This reveals the electrostatic nature of the charge transfer states and the fundamental role of water in shielding the DNA from the electrostatic field of counterions. If we left the details aside, within this work, it emerged clearly that for a proper understanding of DNA electronic properties it is imperative to include solvation effects.

Before conclusion, it will be suitable to talk about the homogeneous sequences of DNA molecules. For homogeneous sequences the unit cell can be reduced to a single base pair by using the following

procedure. Bloch’s theorem for periodic systems can be extended to helical systems by replacing a simple translation by a translation plus a rotation. For canonical B-DNA the values corresponding to this screw operation

are 3.4 Å and 36°, respectively. This was first used for helical chain polymers, was applied to helical carbon nanotubes, and was then used to calculate the electronic structure of homogeneous DNA (Zhang et al., 1999). However, the screw symmetry cannot be rigorously employed when solvent and counterions are present.

ConclusionIn this work, I have presented and discussed the theoretical and

experimental approach in understanding the conduction in different DNA molecules. In the first part, I focused on some important properties of the DNA and physics behind these molecules, making these structures very suitable for molecular electronic devices, and allowing them giving quantum mechanically conductance. In the next part, experimental works have been understood and clarified by giving full details. For the last part, I summarized the theoretical findings.

Acknowledgment I’m very thankful to Prof. Dr. Hagen for all of his discussions in class,

I really find Biophysics course very informative…

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