Electric Transport and Coding
Sequences of DNA Molecules
C. T. Shih
Dept. Phys., Tunghai University
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Outline
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Introduction and Motivation
Experimental Results
The Coarse-Grained Tight-Binding
Model
Sequence-Dependent Conductance and
the Gene-Coding Sequences
Summary
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What is DNA? A Schematic View
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Coding/Noncoding region
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Not all DNA codes correspond to genes
(proteins)
There are “junk” segments between
genes
There are introns and exons in genes
Only exons related to genetic codes
In human genome, more than 98%
codes are junk and introns
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Motivation: Is DNA a good
conductor?
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Interbase hybridization of pz orbitals
→ Conductor? (Eley and Spivey,
Trans. Faraday Soc. 58, 411, 1962)
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Is DNA a molecular wire in
biological system?
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Distance-independent charge transfer
between DNA-intercalated transition-metal
complexes (Murphy et al., Science 262, 1025,
1993)
The conductance of DNA may related to the
mechanism of healing of a thymine dimer
defect (Hall et al., Nature 382, 731, 1996;
Dandliker et al., Science 275, 1465, 1997)
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Thymine Dimer
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How proteins (involved
in repairing DNA
defects) sense these
defects?
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Do enzymes scan DNA using
electric pulses?
"DNA-mediated charge transport for DNA repair" E.M. Boon, A.L.
Livingston, N.H. Chmiel, S.S. David, and J.K. Barton, Proc. Nat.
Acad. Sci. 100, 12543-12547 (2003).
Healthy DNA
MutY
electron
MutY
Broken DNA
MutY
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MutY
Courtesy: R. A. Römer, Univ. Warwick
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Is DNA a building block in
molecular electronics?
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Sequence dependent
Self-assembly
Can be build as nanowires with complex
geometries and topologies
As template of nanoelectronic devices
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Chen, J. and Seeman, N.C. (1991),
Nature (London) 350, 631-633.
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Zhang, Y. and Seeman, N.C. (1994), J. Am.
Chem. Soc. 116, 1661-1669.
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Experimental Results
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The results are controversial – almost cover all
possibilities (Endres et al., Rev. Mod. Phys. 76,
195, 2004)
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Anderson insulator (Zhang et al., PRL 89, 198102,
2002)
Band-gap insulator (Porath et al., Nature 403, 635,
2000)
Activated hopping conductor (Tran et al., PRL 85,
1564, 2000)
Induced superconductor (Kasumov et al., Science
291, 280, 2000)
Score Now – Superconductor: Conductor: Semiconductor: Insulator = 1:5:5:7
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Experiment 1: Semiconductor
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D. Porath et al. Nature 403, 635
(2000)
I-V curves
Poly(G)-Poly(C) seq. (GC)15
Length: 10.4 nm
Put the DNA between the
electrodes (space = 8nm) by
electrostatic trapping
Several check to confirm that “1”
DNA molecule between the
electrodes
Measurement under air, vacuum,
and several temperature
Maximum current ~ 100 nA ~
1012 electrons/sec
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Gap
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Higher T, larger gap
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○: Sample #1
＋: Sample #2
● and △:
Sample #3,
cooling and
heating
measurements
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Experiment 2:
Superconductivity?
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Yu. Kasumov et al. Science 291, 280 (2000)
Sample: l-DNA (bacteria phage), length=16mm
Substrate: Mica
Electrode: Rhenium/Carbon (Re/C) → SC with Tc~ 1K, normal R ~
100 W
Slit R ~ 1 GW, with DNA R ~ several KWs
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Results:
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Measurement: 1 nA, 30 Hz
Ohmic behavior over the
temperature range
Power-law fit for the R-T curve
for T>1K (Luttinger liquid
behavior)
Exponent: -0.05, -0.03, -0.08
for DNA1, 2, and 3 respectively
At T~1K, R drops for DNA1, 2
Critical field: ~ 1Tesla
Magnetoresistance: positive for
DNA1 and 2, negative for 3
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Endres et al., Rev. Mod. Phys. 76, 195, 2004
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Reasons for Diversified Results
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Contacts between electrode and DNA
Differences in the DNA molecules
(length, sequence, number of chains…)
Effects of the environments
(temperature, number of H2O,
preparation and detection…)
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Effective Hamiltonian of the
hole propagation
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S. Roche, PRL 91, 108101 (2003)
εn : hole energy for diff. base=8.24eV, 9.14eV, 8.87eV,
and 7.75eV for n=A,T,C,G, respectively
Zero temperature, t0=tm=1.eV, εm= εG
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Transmission Coefficient:
Transfer Matrix Method
E: Energy of injected hole; T(E): Transmission coefficent
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GCGCGC…… (60bps)
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Transmission Coefficient for Human
Chromosome and Random Sequence
Main: Human Ch22
Chromosome
Inset: Random Seq.
S. Roche et al., PRL 91,
228101 (2003)
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Transmission Analysis of
Genomes
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The lengths of complete genomic sequences are too
long (in comparison with the electric propagation
length) -> analyze subsequences instead
W: length (window size) of the subsequence which T(E)
will be calculated
T(E,W,i): transmission coefficient of the subsequence
from i-th to i+W-1-th base, with incident energy E
Integrate T(E,W,i) in the range E0→E0+DE to get
T(E0,E0+DE,W,i)
Moving the window along the sequences and calculate
T(E0,E0+DE,W,i) for all i
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Yeast 3
tDNA=1.0
Fitted by
e  w / w0
Y3
R3
tDNA=0.4
Randomized
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Comparison between the Coding region and the
Integrated Transmission
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t=0.4 eV
t=1 eV
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Overlap of T(W,i) and G(i)
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For particular W, both transmission and
coding (G(i)=1 if i is in the coding
region, and =0 otherwise) are vectors
in L-dimension (L: length of the seq.)
Normalize the two vectors
Calculating the scalar product of the
two normalized vectors
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Overlap between T(W,i) and G(i)
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T(W,i)=(t1, t2....ti,....tN)
The averaged transmission:
1
t 
N
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t
i 1 i
Let t’i=ti-<t>, and norm of t’:
t' 
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N
2
t
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i1 i
N
t”i=t’i/|t’|, T”(W,i)=(t1”, t2”....ti”,.... t”N)
Similarly, normalize G(i) → G”(i)
Calc. the scalar product:
W(W )  i T " (W , i)G" (i)
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Yeast ChIII (310kbps), tDNA=1eV
(WMAX,wG)=(0.1,240)
W
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tDNA=1eV
tDNA=0.8eV
tDNA=0.6eV
tDNA=0.4eV
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Yeast Ch VIII (526kbps)
(WMAX,wG)=(0.08,200)
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(WMAX,wG)=(-0.13,80)
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(WMAX,wG)=(-0.08,50)
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Summary
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There are two parameters WMax and wG which are
characteristic values for different species
The possible applications:
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To locate the genes
To understand the relation between transport properties and coding
Relation to evolution and taxonomy
DNA defect and repair
Future Works:
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Analysis for more genomes
Finite-temperature effects – flexibility of the DNA chain, interaction
with phonons
Ionization potential for bases is sequence-dependent
More realistic (finer-grained) Hamiltonian
Interaction of carriers – Hubbard U?
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