Hole mobilities of periodic models of DNA double helices in the nucleosomes at different temperatures
ABSTRACT Using the Hartree-Fock crystal orbital method band structures of poly(G-C) and poly(A-T) were calculated (G, etc. means a nucleotide) including water molecules and Na+ ions. Due to the close packing of DNA in the ribosomes the motion of the double helix and the water molecules around it are strongly restricted, therefore the band picture can be used. The mobilities were calculated from the highest filled bands. The hole mobilities increase with decreasing temperatures. They are of the same order of magnitude as those of poly(A) and poly(T). For poly(G) the result is ∼5 times larger than in the poly(G-C) case.
- SourceAvailable from: Attila Bende[Show abstract] [Hide abstract]
ABSTRACT: Using the ab initio Hartree-Fock crystal orbital method in its linear combination of atomic orbital form, the energy band structure of the four homo-DNA-base stacks and those of poly(adenilic acid), polythymidine, and polycytidine were calculated both in the absence and presence of their surrounding water molecules. For these computations Clementi's double zeta basis set was applied. To facilitate the interpretation of the results, the calculations were supplemented by the calculations of the six narrow bands above the conduction band of poly(guanilic acid) with water. Further, the sugar-phosphate chain as well as the water structures around poly(adenilic acid) and polythymidine, respectively, were computed. Three important features have emerged from these calculations. (1) The nonbase-type or water-type bands in the fundamental gap are all close to the corresponding conduction bands. (2) The very broad conduction band (1.70 eV) of the guanine stack is split off to seven narrow bands in the case of poly(guanilic acid) (both without and with water) showing that in the energy range of the originally guanine-stack-type conduction band, states belonging to the sugar, to PO(4)(-), to Na(+), and to water mix with the guanine-type states. (3) It is apparent that at the homopolynucleotides with water in three cases the valence bands are very similar (polycytidine, because it has a very narrow valence band, does not fall into this category). We have supplemented these calculations by the computation of correlation effects on the band structures of the base stacks by solving the inverse Dyson equation in its diagonal approximation taken for the self-energy the MP2 many body perturbation theory expression. In all cases the too large fundamental gap decreased by 2-3 eV. In most cases the widths of the valence and conduction bands, respectively, decreased (but not in all cases). This unusual behavior is most probably due to the rather large complexity of the systems. From all this emerges the following picture for the charge transport in DNA: There is a possibility in short segments of the DNA helix of a Bloch-type conduction of holes through the nucleotide base stacks of DNA combined with hopping (and in a lesser degree with tunneling). The motivation of this large scale computation was that recently in Zurich (ETH) they have performed high resolution x-ray diffraction experiments on the structure of the nucleosomes. The 8 nucleohistones in them are wrapped around by a DNA superhelix of 147 base pairs in the DNA B form. The most recent investigations have shown that between the DNA superhelix (mostly from its PO(4) (-) groups) there is a charge transfer to the positively charged side chains (first of all arginines and lysines) of the histones at 120 sites of the superhelix. This would cause a hole conduction in DNA and an electronic one in the proteins.The Journal of Chemical Physics 04/2008; 128(10):105101. · 3.12 Impact Factor
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ABSTRACT: Attempts to infer DNA electron transfer from fluorescence quenching measurements on DNA strands doped with donor and acceptor molecules have spurred intense debate over the question of whether or not this important biomolecule is able to conduct electrical charges. More recently, first electrical transport measurements on micrometre-long DNA 'ropes', and also on large numbers of DNA molecules in films, have indicated that DNA behaves as a good linear conductor. Here we present measurements of electrical transport through individual 10.4-nm-long, double-stranded poly(G)-poly(C) DNA molecules connected to two metal nanoelectrodes, that indicate, by contrast, large-bandgap semiconducting behaviour. We obtain nonlinear current-voltage curves that exhibit a voltage gap at low applied bias. This is observed in air as well as in vacuum down to cryogenic temperatures. The voltage dependence of the differential conductance exhibits a peak structure, which is suggestive of the charge carrier transport being mediated by the molecular energy bands of DNA.Nature 03/2000; 403(6770):635-8. · 38.60 Impact Factor
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ABSTRACT: Electronic matrix elements for hole transfer between Watson–Crick pairs in desoxyribonucleic acid (DNA) of regular structure, calculated at the Hartree–Fock level, are compared with the corresponding intrastrand and interstrand matrix elements estimated for models comprised of just two nucleobases. The hole transfer matrix element of the GAG trimer duplex is calculated to be larger than that of the GTG duplex. “Through-space” interaction between two guanines in the trimer duplexes is comparable with the coupling through an intervening Watson–Crick pair. The gross features of bridge specificity and directional asymmetry of the electronic matrix elements for hole transfer between purine nucleobases in superstructures of dimer and trimer duplexes have been discussed on the basis of the quantum chemical calculations. These results have also been analyzed with a semiempirical superexchange model for the electronic coupling in DNA duplexes of donor (nuclobases)–acceptor, which incorporates adjacent base–base electronic couplings and empirical energy gaps corrected for solvation effects; this perturbation-theory-based model interpretation allows a theoretical evaluation of experimental observables, i.e., the absolute values of donor–acceptor electronic couplings, their distance dependence, and the reduction factors for the intrastrand hole hopping or trapping rates upon increasing the size of the nucleobases bridge. The quantum chemical results point towards some limitations of the perturbation-theory-based modeling. © 2001 American Institute of Physics.The Journal of Chemical Physics 03/2001; 114(13):5614-5620. · 3.12 Impact Factor
Hole mobilities of periodic models of DNA double helices in the nucleosomes
at different temperatures
Attila Bendea,c, Ferenc Bogárb,c, János Ladikc,⇑
aMolecular and Biomolecular Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, Str. Donath 65-103, C.P. 700,
Cluj Napoca RO-400293, Romania
bSupramolecular and Nanostructured Materials Research Group of the Hungarian Academy of Sciences, University of Szeged, Dóm tér 8, 6720 Szeged, Hungary
cChair for Theoretical Chemistry and Laboratory of the National Foundation for Cancer Research, Friedrich-Alexander-University-Erlangen-Närnberg,, Egerlandstr. 3,
91058 Erlangen, Germany
a r t i c l ei n f o
Received 4 December 2012
In final form 13 February 2013
Available online 20 February 2013
a b s t r a c t
Using the Hartree–Fock crystal orbital method band structures of poly(eG—eC) and poly(eA—eT) were calcu-
DNA in the ribosomes the motion of the double helix and the water molecules around it are strongly
restricted, therefore the band picture can be used. The mobilities were calculated from the highest filled
bands. The hole mobilities increase with decreasing temperatures. They are of the same order of magni-
tude as those of poly(eA) and poly(eT). For poly(eG) the result is ?5 times larger than in the poly(eG—eC) case.
lated (~G, etc. means a nucleotide) including water molecules and Na+ions. Due to the close packing of
? 2013 Elsevier B.V. All rights reserved.
We have performed large scale calculations on DNA because
according to many experiments carcinogens binding to DNA or
radiation hits do not act only locally but by different mechanisms
they can have also long range effects (see ). These long range ef-
fects can be strong if there is a hole conductivity in a DNA double
Recently, using the ab initio HF crystal orbital theory we have
calculated the band structures of the poly(eG—eC) and poly(eA—eT)
(S is the deoxyribose and P the phosphate group) .
Since in aqueous solution because of the structural distortions
of the DNA helix and especially of the fluctuation of the water
molecules around the DNA double helix, the band model is not
adequate. Therefore many authors have applied different forms
of hopping theories [3–5].
On the other hand according to high resolution X-ray investiga-
tions of DNA in the nucleosome is very closely packed [6,7]. This
strongly diminishes the possibilities both of structural distortions
of the DNA molecule and the fluctuations of the water molecules
around it. In our study we have applied the ab initio Hartree–Fock
(HF) crystal orbital method [8–11] taking into account also the 36?
rotation of each base pair perpendicular to the main axis of the he-
lix  to obtain the band structures for different periodic DNA
models. In the calculations the LCAO approximation was used
periodic double helices. Here,~G stands for the nucleotide G–S–P
. One should observe that the HOMO levels of the double
stranded DNA lie by about 5 eV higher than those of the single
chains  (in both cases with the sugar and phosphate groups
and in the presence of water). This is caused by the fact that there
is a charge transfer of about 0.2e from deoxyribose to the nucleo-
tide base to which it is bound and these excess charges repel each
other in the double stranded cases .
On the basis of the obtained band structure we have computed
the mobilities of the holes (at different temperatures) belonging to
the contraction–dilatation motion of the double helix (we did not
take into account the mobilities belonging to the torsional motion
of the helix, because in our earlier studies we have found that the
effect of carcinogens or radiation hits on DNA happens not only lo-
cally, but they can have also long-range effects (see )). For this
reason the contraction–dilatation movement of the double helix
is the only important one. Therefore we have computed only the
mobility along the main axes of the DNA.
The band structure of poly(eG—eC) and poly(eA—eT) systems were
form [8–11] by applying the helical symmetry operation . For
the HF calculations Clementi’s double n basis set was used .
The unit cell was built taking the G–C and A–T nucleotides from
the experimental geometrical structure of double-stranded DNA
B reported by Olson et al. . The negatively charged PO?
of the nucleotides were neutralized by two Na+ions, which posi-
tions were optimized using the GAUSSIAN 03 program package 
using the HF method together with the same Clementi’s basis set.
obtained using the ab initio HF crystal orbital method in its LCAO
0009-2614/$ - see front matter ? 2013 Elsevier B.V. All rights reserved.
⇑Corresponding author. Fax: +49 9131 406958.
(F. Bogár), Janos.Ladik@chemie.uni-erlangen.de (J. Ladik).
Chemical Physics Letters 565 (2013) 128–131
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
To determine the water structure around the nucleotides, first, a
triple stack ofeG—eC andeA—eT in the DNA B geometry were gener-
were randomly placed using the PACKMOL program  and after
that, their geometries were optimized using molecular mechanics
(Amber force field from the GAUSSIAN 03 ), while the nucleotide
sequences were kept frozen. As next step the two outer (highest
and lowest) base pairs as well as their surrounding water mole-
cules were eliminated. Finally, we kept only 15 water molecules
around the remaining nucleotides in both of theeG—eC andeA—eT
nucleotide pairs + 2 Na+ions + 15 water molecules (for details see
Refs. [17,18]). The number of k-points in the half Brillouin zone
was 12 in both cases and the number of contracted basis functions
per unit cell was 766 in the poly(eG—eC) case and 754 for
ergy per unit cell) we needed about 20 iterations.
It is well-known that the HF method gives too large band gaps
and wrong energy positions for the conduction bands. In our previ-
ous work  we have shown that the electron correlation can de-
crease the too large HF gaps with about 2 eV as well as it moves
down the conduction bands. Since, we are interested in the hole
conductivity which occurs at the upper region of the valence band,
the electron correlations would not change significantly the HF pic-
ture. One should point out that the DFT method  in its first
form gives a too small gap, which could be increased during the
further development of this method.
To the calculation of the mobilities of poly(eG—eC) and
tures. The valence band widths are ?0.7 eV in the poly(eG—eC) case
substantially broader that the thermal energy at body temperature
(kBT ¼ 8:617 ? 10?5? 310 ¼ 2:67 ? 10?2eV). Therefore the defor-
mation potential approximation for the mobility calculations can
be applied. One should point out that to perform a simultaneous
translation and rotation one can proceed in the same way as in
the case of simple translation because in both cases their symme-
try groups have the same multiplication table (isomorphous
groups). Therefore for the helix operation we have to put the nuclei
in the right positions and rotate the basis functions (unless they are
s functions) with the relevant rotation angle . For more details
For the calculation of the mobilities the deformation potential
method was used . In the case of 1D systems (as a single
DNA double helix) the original expression for a 3D systems had
to be modified. This has been done in a previous paper . The re-
sult for 1D system in the case of hole mobilities is
ated. Around these systems a huge number of water molecules
cases. Accordingly, the unit cell is built by singleeG—eC andeA—eT
poly(eA—eT). To reach self-consistency (7–8 decimals in the total en-
poly(eA—eT) systems we have started from their ab initio band struc-
and ?0.3 eV in the poly(eA—eT) case (see Table 1a and 1b) which are
Here c?is the elastic constant for the contraction and dilatation
of the chain. e1his the deformation potential at the G or A-type
upper limits of the valence bands of the poly(eG—eC) and poly(eA—eT)
systems, respectively. The deformation potential for holes is de-
l0¼ 3:32 Å;
Dl ¼ ?0:2 Å
of the corresponding valence band
Finally, the elastic constant c?was calculated from the contrac-
Dl ¼ ?0:02Å
expression, where l is the length of the DNA double helix, E its total
energy per unit cell and l0the stacking distance in equilibrium.
One should mention that we have taken as the equilibrium
stacking distance 3:32 Å instead of 3:36 Å (the Watson–Crick va-
lue), due to the very tight packing of the DNA molecule in the
The condition of the applicability of the deformation potential
approximation is that the width of the bands for which it is applied
should be at least four times larger than the thermal energy
(2:67 ? 10?2eV). On the other hand the valence band widths for
poly(eG—eC) + H2O + Naþare 0.69 eV and 0.21 eV for poly(eA—eT) +
tion potential method can be safely used because the thermal en-
ergy is at least by one order of magnitude smaller than the widths
of the valence bands for which we intend to calculate the
his the effective mass calculated from the dispersion curve
of the two stacks
l0¼ 3:32 Å
H2O + Naþsystems , respectively. This means that the deforma-
In Table 1 we present the conduction and valence bands of the
poly(eG—eC) and poly(eA—eT) systems in the presence of water and
Though the known d.c. conductivity measurements on DNA
provided d.c. hole conductivities, it may happen in the future that
due to the action of electron donors also d.c. electronic conduction
takes place through the base stacks of DNA. This is the reason that
we have included in Table 1 also the description of the first empty
band of poly(eG—eC) and poly(eA—eT), respectively, which are domi-
Naþions at three different stacking distances. See our previous pa-
nated by base stacks.
The band structures of poly(eG—eC) and poly(eG—eCÞ + Naþ+ 15 water molecules at
different stacking distances. (u.l. = upper limit, l.l. = lower limit, w. = width)
3:30 Å3:32 Å3:34 Å
Cond. band (C-type) – 16 impurity bands
u.l.6.81 (k = 12)
l.l.6.51 (k = 0)
6.79 (k = 12)
6.49 (k = 0)
6.77 (k = 12)
6.47 (k = 0)
Valence bands (G-type)
?2.41 (k = 12)
?3.16 (k = 0)
?2.53 (k = 12)
?3.27 (k = 0)
?2.58 (k = 12)
?3.29 (k = 0)
The band structures of poly(eA—eT) and poly(eA—eT) + Naþ+ 15 water molecules at
different stacking distances. (u.l. = upper limit, l.l. = lower limit, w. = width)
3:30 Å3:32 Å3:34 Å
Cond. band (T-type) – 13 impurity bands
u.l. 6.35 (k = 12)
l.l.5.90 (k = 0)
6.32 (k = 12)
5.89 (k = 0)
6.29 (k = 12)
5.88 (k = 0)
Valence bands (A-type)
?4.27 (k = 12)
?4.57 (k = 0)
?4.30 (k = 12)
?4.60 (k = 0)
?4.34 (k = 12)
?4.63 (k = 0)
A. Bende et al./Chemical Physics Letters 565 (2013) 128–131
In Table 2 we give the effective masses, the elastic constants
and the deformation potentials which occur in Eq. (1).
Finally, in Table 3 the mobilities are presented at different
For the HF band structures of poly(eG—eC) and poly(eA—eT) the
 the gap is 8.95 eV for the first system and 9.30 eV in the second
one, respectively, while in the present one they are 9.02 eV and
10.19 eV, respectively, (see Table 1). This is caused by the different
stacking distances used: in Ref.  we have taken 3:36 Å for it,
while in the present Letter considering the close packing in DNA
in the nucleosomes we have used for its equilibrium value 3:32 Å
in the deformation potential calculation.
The small differences in the widths of the valence bands and the
base-dominant conduction bands as well in their upper and lower
limits are most probably due to the same reason (compare Tables 1
and 2 of Ref.  with Table 1 of the present Letter). Further, if one
compares the upper and lower limits of the valence band of the
poly(eA—eT) in Ref.  and the values obtained in the present calcu-
sequent analysis of these results showed us that there are errors
in Ref.  caused by a steric hindrance due to a H2O molecule
which becomes too close to the deoxyribose binding to adenine
during the helix operation (translation–rotation). Another source
of this discrepancy (but with much less influence on the valence
band shift) could be the number of the water molecules around
the nucleotide base in the unit cell as well as the slightly different
stacking distance between the bases. In the present calculation we
have considered 15 water molecules and 3:32 Å as the stacking dis-
tance, while in Ref.  we used 18 water molecules and 3:36 Å for
the stacking distance.
The calculation of the band structures of poly(eG—eC) and
tances were necessary for the calculation of the deformation po-
tential. The upper and lower limits as well as the band widths of
valence and base-dominant conduction bands for poly(eG—eC) and
the three different stacking distances (3:30 Å; 3:32 Å and 3:34 Å)
the band widths of both the valence and conduction bands either
remain unchanged or become slightly smaller at increasing stack-
ing distances. At the same time, the upper and lower limits of the
valence bands and of the conduction bands in both systems slightly
decrease with increasing stacking distances. In each case the bands
show monotonic behavior in the first Brillouin zone (without any
singularity) their edges fit with the limits of the first Brillouin zone
(k = 0 or k = 12).
Performing a detailed analysis of the eigenvectors we found
that the crystal orbitals belonging to the so-called base-type lowest
unfilled bands (which we call conduction bands), contain only
about 60% contributions from those AO-s which belong to C or T,
respectively. The remaining 40% has sugar-phosphate backbone
or Naþcharacter. This analysis shows also that in the case of
same methods were used as in Ref. . In our previous calculation
lation we observe a significant discrepancy between them. A sub-
poly(eA—eT) at smaller (3:30 Å) and larger (3:34 Å) stacking dis-
poly(eA—eT) systems are presented in Table 1a and 1b. Considering
conduction bands there are significant overlaps between the base-
and non-base-type AO-s and these conduction bands are spread
both on base- and non-base-type molecular fragments. Finally, it
should be mentioned that between the valence band and the
base-dominant conduction bands there are (as in the previous
calculation ) in the case of poly(eG—eC) 16 bands which have
bands for poly(eA—eT) where the AO-s do not belong to T.
poly(eA—eT) were calculated from the dispersion curves of the va-
technique taking a seventh order polynomial function (three k-
points both at the left and the right sides of the edge of the Brillou-
in zone) and taking the expression of the effective mass given by
Eq. (3). Since hole conduction is the more probable in DNA, we
have calculated the quantities necessary for the computation of
the deformation potentials of the poly(eG—eC) and poly(eA—eT) sys-
G- or A-type. We obtain an effective hole mass of m?
for the poly(eG—eC) and m?
The deformation potentials were determined from the valence
band upper limits, according to Eq. (2). The elastic constants were
calculated from Eq. (4) assuming a parabolic dependence of the
total electronic energy along the z axis (the long axis of the DNA
double helix). In the poly(eG—eC) case we have obtained for the
stant 7:38 ? 10?2dyn. The corresponding values for the poly(eA—eT)
Finally, in Table 3 we show the hole mobilities (in cm2=V s
units) computed from Eq. (1) at three different temperatures:
310 K (the human body temperature), 300 K (room temperature)
and 273 (water freezing temperature) using the previously com-
puted values for the effective masses, deformation potentials and
elastic constants. The hole mobilities increase with decreasing
temperatures as expected for both investigated systems. One
should point out that the obtained values refer only to the contrac-
tion–dilatation motion of the DNA helix.
The hole mobilities obtained in the present calculation are of
the same order of magnitude as those obtained for the previous
single stranded DNA calculations  for poly(eA) and poly(eT). Only
sult by a factor of 5 larger than the one found in the present work
for poly(eG—eC). The reason of this discrepancy can lie in the differ-
stranded DNA helices. To clear up this problem we are going to
perform further calculations. On the other hand, our mobility value
obtained for the poly(eG—eC) system is in a good agreement with
Hamiltonian, where the motion of holes is coupled to structural
fluctuations of the poly(G–C). In the ‘frozen’ twist motion case they
obtained for the mobility a value of 22 cm2=V s, which has the
same order of magnitude as our mobility result based on the band
The first d.c. conductivity measurements on native DNA were
performed back in 1962 by Eley and Spivey . From the temper-
ature dependence of the specific conductivity, they have found for
no contributions from the AO-s belonging to the C bases and 13
Turning to Table 2 the effective masses for both poly(eG—eC) and
lence bands. For this we have used the polynomial interpolation
tems, respectively, only for their valence bands which are purely
h¼ ?3:69me for the poly(eA—eT) system,
deformation potential a value of 9.36 eV and for the elastic con-
system are 5.97 eV and 2:82 ? 10?2dyn, respectively.
in the case of poly(eG) was obtained in the previous work  a re-
ence of the band structures of the single stranded and double
that obtained by Grozema et al.  using a tight-binding model
The deformation potentials for holes (in eV-s), the elastic constants (in dyns) and the
effective masses (in me-s) for poly(eG—eC) and poly(eA—eT) in the presence of water and
7.38 ? 10?2
2.82 ? 10?2
The hole mobilities of poly(eG—eC) and poly(eA—eT) in the presence of water molecules
and a Na+ion at different temperatures (in cm2=V ? s units).
A. Bende et al./Chemical Physics Letters 565 (2013) 128–131
the activation energy of conductivities 4.8 eV. This value lies not
very far from our HF + MP2 gap value calculated by the extended
basis set for a C stack (6.6 eV). In an subsequent paper Porath
et al.  have performed a two point d.c. measurement of a
10.4 nm (30 base pairs) long poly(eG—eC) double helix. In their the-
techniques) the charge transfer is mediated by energy bands. In re-
cent papers [26,27] of the Barton group they have found charge
transport in DNA of 34 nm (over 100 base pairs) lengths. They
point out that such a long distance CT cannot be explained by hop-
ping or superexchange mechanisms. They suppose a coherent CT
mechanism if the double helix is intact (not a distortion or mis-
match is present). Coherent mechanism means in other words
the existence of energy bands.
oretical analysis, they conclude that at least in such a compara-
We should like to express our gratitude to Professor Ferenc Bel-
eznay for the very useful discussions about the deformation poten-
tial approximation method. The numerical work has been carried
out using the facilities at the High Performance Computing Group
of the University of Szeged and the DataCenter of INCDTIM Cluj-
Napoca. We gratefully acknowledge their support.
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