Inhomogeneous DNA: Conducting exons and insulating introns Page: 1
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PHYSICAL REVIEW B 80, 085420 (2009)
Inhomogeneous DNA: Conducting exons and insulating introns
A. A. Krokhin,"'* V. M. K. Bagci,' F. M. Izrailev,2 0. V. Usatenko,3 and V. A. Yampol'skii3
'Department of Physics, University of North Texas, P.O. Box 311427, Denton, Texas 76203, USA
2Instituto de Fisica, Universidad Aut6noma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
3A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov, Ukraine
(Received 18 May 2009; revised manuscript received 8 July 2009; published 17 August 2009)
Parts of DNA sequences known as exons and introns play very different roles in coding and storage of
genetic information. Here we show that their conducting properties are also very different. Taking into account
long-range correlations among four basic nucleotides that form double-stranded DNA sequence, we calculate
electron localization length for exon and intron regions. Analyzing different DNA molecules, we obtain that the
exons have narrow bands of extended states, unlike the introns where all the states are well localized. The band
of extended states is due to a specific form of the binary correlation function of the sequence of basic DNA
nucleotides.DOI: 10.1103/PhysRevB.80.085420
I. INTRODUCTION
A DNA molecule is an exciting example of a natural com-
plex system with intriguing properties. Many of these prop-
erties remain unexplained and need new approaches for fur-
ther analysis. One of the fundamental questions is how
information is transferred along a sequence of nucleotides.
For example, if a mutation occurs in the sequence, it is usu-
ally healed. This means that some of physical parameters of
the DNA molecule are sufficiently sensitive to detect this
mutation. The length of a mutation is relatively short [- 10
base pairs (bps)] as compared to the length of a gene
(- 103-106 base pairs). Because of small statistical weight of
a mutation, the mechanical and thermodynamic characteris-
tics are not sensitive enough for its robust detection. Unlike
this, the electrical resistance of a DNA molecule strongly
fluctuates even if a single nucleotide in a long sequence is
replaced (or removed).1'2 This property is a signature of co-
herent transport that gives rise to universal fluctuations of
conductance in mesoscopic samples.3
In a DNA molecule the charge carriers move along a
double helix formed by two complementary sequences of
four basic nucleotides: A, T, G, and C. A conduction band
would form if the DNA texts would exhibit some
periodicity.4 However, many studies of the DNA texts have
revealed rich statistical properties but not the periodicity.
One of the suggestions is that a DNA molecule is a stochastic
sequence of nucleotides, the main feature of which is long-
range correlations.5 Therefore a popular method of detection
of correlations is mapping of a DNA sequence onto a random
walk. Long-range correlations are manifested then in an
anomalous scaling of the generated classical diffusion.6
Quantum transport through a DNA molecule is also
strongly affected by the correlations. An uncorrelated se-
quence of nucleotides localizes all quantum electron states,
as occurs in any one-dimensional (ID) white-noise potential,
making impossible charge transfer at distances longer than
the localization length l(E). However, since most of the mu-
tations in DNA are successfully healed, one may assume the
existence of charge transport7 through delocalized states that
are responsible for the transfer of information at much longerPACS number(s): 78.67.-n, 87.14.gk, 75.75.+a
distances. Such delocalized states are expected to exist
within exons-the coding regions where the genetic informa-
tion is stored. An important feature of charge transfer in car-
rying mutations exons was reported in Ref. 8. It was shown
that cancerous mutations usually produce much less variation
in the resistance than noncancerous ones. This apparent dis-
tinction shed light on the problem of survival of cancerous
mutations. The healing of a mutation occurs only if it is
detected by base excision repair enzymes. Since the detec-
tion of the mutation is most likely due to DNA-mediated
charge transport,9 it is clear that cancerous mutations, being
"electrically masked," are very unlikely to be detected and
then repaired.
On the other hand, the introns-the long segments of
DNA that apparently do not carry genetic code-may not
contain delocalized states in the energy spectrum, thus re-
maining insulators. In this paper we give evidence for the
validity of this hypothesis using a theoretical approach based
on the results of electron localization in correlated disordered
potentials. Our study of various DNA molecules shows that
the energy spectrum of the exons indeed contains practically
delocalized states. Unlike this, the electron wave functions
are well localized within the introns.
II. TWO-STRANDED MODEL OF DNA
Let us first consider the widely used model for electron
transport in DNA molecules, which is a discrete lattice with
random on-site potential en and site-independent nearest-
neighbor hopping amplitude t,(1)
The energies en are the ionization energies of the four nucle-
otides, EA= 8.24, ET= 9.14, EC= 8.87, and EG= 7.75 eV, and
the hopping amplitude t may vary from 0.1 to 1 eV.'l Al-
though the on-site energies in a sequence of coupled nucle-
otides do not coincide exactly with their ionization poten-
tials, one may neglect this difference as it plays a minor role
in our consideration. The regular periodic potential en= Vo in
Eq. (1) gives rise to Bloch functions n a exp(i/4n) with dis-
persion relation E- Vo=2t cos /1. The allowed energies of2009 The American Physical Society
t(4,n+1 + ~_1) = (En - E) n
1098-0121/2009/80(8)/085420(6)
085420-1
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Krokhin, Arkadii A.; Bagci, V. M. K.; Izrailev, Felix M.; Usatenko, O. V. & Yampol'skii, V. A. Inhomogeneous DNA: Conducting exons and insulating introns, article, August 17, 2009; [College Park, Maryland]. (https://digital.library.unt.edu/ark:/67531/metadc103272/m1/1/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.