Experimental and Theoretical investigation of electrical
properties of DNA molecular structures
By Sefaattin Tongay
21/10/2005
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 doublehelix 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 p z
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
structures
DNA
molecule.
Intermediate
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;
V ppX   ppX
h2
exp( d / Rc )
md 2
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 V ppπ and
Vppσ.
V  sin 2 V pp  cos 2 V pp
 2 e d / Rc
V
md 2


z2
(



)


pp
pp 
 pp
2
2
l

z


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;
t
n,m
N1
  j 2 Vij12 ci1,n c 2j .m
N
i
In this equation, N1 and N2 correspond to the number of pz orbitals on the
different base pairs indicated by 1 and 2. And ci1,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 View
The 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.al
Yoo 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 lambdaDNA 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 lambdaDNA 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 View
In 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 Mechanisms
From 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,
k cs  k 0 e R
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-tobase 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 densityfunctional 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 (ZDNA). 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. The
gap 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.
Conclusion
In 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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