Electronic Transport in DNA the disorder perspective

1
Electronic Transport in DNA the disorder
perspective
Quantum physics on biological nanostructures a
first attempt
Rudolf A Roemer Daphne Klotsa, Matthew
Turner Department of Physics and Centre for
Scientific Computing


2
Why nanostructures?
NanoStructures Laboratory, Princeton University

• New nanotechnologies will fabricate structures
  substantially smaller, better, and cheaper than
  current technology permits.
• Innovative nanoscale electronic, optoelectronic,
  and magnetic devices by combining cutting-edge
  nanotechnology with frontier knowledge from
  different disciplines.

3
Semiconductor nanostructuresQ-dots, -well, SETs
4
Why DNA?
A. Turberfield, PhysicsWorld 16, March 2003, 43-46

• DNA is a wonderful material with which to
  build. It can act as
• Molecular glue
• Fuel for molecular engines
• Parallel computer
• Self-assembled nanostructures
• E. Winfree , Nature 394, 539-544, Aug. 6, 1998
• scaffold in protein-crystallography
• Rigid tiles or girders J.H. Reif et al., (2003)

and many more
5
Why disorder?

• well-developed theory
• good computational algorithms
• DNA is in solution
• -gt there is disorder

Y2 of electron wave function in 1113 system
6
Combining DNA electronics

• Conductor
• Fink/Schoenenberger, Nature 398, 407 (1999)

Semiconductor Porath et al., Nature 403, 635 -
638 (10 Feb 2000)
Insulator Priyadarshy et al., J. Phys. Chem.,
100, 17678 (1996)
5 5
7
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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
electron
MutY
MutY
Broken DNA
MutY
MutY
8
DNA (Deoxyribonucleicacid)

• Linear bio-polymer, backbone of repeated
  sugar-phosphate units, attached with bases
• G uanine
• C ytosine
• A denine
• T hymine
• double helix structure
• AT, GC, not AC, AG, TC, TG

complementary
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DNA basics
ATCGATCGATGATGTCGA TAGCTAGCTACTACAGCT

• AT, GC pairs via attractive hybridization
• diameter 2nm, pitch 3.4 nm, base-pair separation
  0.34 nm, 3bn base-pairs/sequence
• 15 base-pairs stable at room T
• 3 base-pairs form a codon, unit of information,
  so 4364 words for 20 aminoacids and additional
  operations (stop/start).
• Samples with, say, AGCTAGTA code can be ordered
  with at least 1 accuracy
• Commercial suppliers ship within a few days

10
Huge amounts of genetic data

• H. sapiens 30,000 genes 3 ? 109 bp
• C. elegans 10,000 genes 108 bp
• E. coli 4,380 genes 4,639,221 bp
• SARS virus 14 genes 29,761 bp
• Paradox 105 proteins in H. sapiens
• ??One gene codes for more than one protein

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Biological function of DNA

• Replication
• Template for RNA coding for proteins polymerase
  of DNA -gt RNA -gt proteins (actin, cell rigidity)
• Self-assembly

12
Is DNA a quantum wire?

• Absence of dc-Conductivity in l-DNA
• De Pablo et al, PRL 86, 4992 (2000)
• Poly-GC strands have one-band of overlapping
  p-orbitals
• l-DNA overlap drops quickly
• 13 base-pairs, DFT calculation

LUMO/PolyGC
HOMO/PolyGC
LUMO/ l-DNA
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The fishbone model
Cuniberti et al., PRB 65, 24131(R) (2002)

• tight-binding model with a gap
• Poly-GC GCGCGCGC
• explains experiments in Poly-GC

Experiments vs. theory
14
The fishbone model

• Hopping amplitudes are 1 along chain and 2 onto
  backbone
• Onsite energies are zero, but could be used to
  model the ionization energies

15
Semiconducting gap in Poly-GC

• Transfer-matrix method
• Large DNA sequences possible
• Localization lengths l give possible extend of
  electron transfer -gt measurable via fluorescence
  experiments

Energy band
Energy band
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l-DNA
LOCUS NC_001416 48502 bp DNA linear PHG
08-JUL-2002 DEFINITION Bacteriophage lambda,
complete genome.

• Small differences between l-DNA and l(R)-DNA
• Computation for complete DNA strand

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Influence of backbone disorder
Klotsa, RAR, Turner, submitted (2004)

• Backbone (BB) disorder used to model
  environment/solution into which DNA is immersed
• BB disorder leads to a rescaling of the
  semi-conducting gap
• This might explain diversity of experimental
  observations

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Random adhesion of Na-Atoms at backbone
DNA is in solution, so there is disorder
Na
New states
Na
Na
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The ladder model

• Q-chemical calculations do not find HOMO/LUMO on
  both bases of a base pair
• Hopping amplitudes between chains is 1/2

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Na binary disorder at the BB
More disorder gives less localization! Contradict
ion to folklore!
less localized
highly localized
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Telomeric DNA with Na-BB disorder
TTAGGGTTAGGGTTAGGGDNA

• Differences in biologically different DNA
  sequences

less localized
highly localized
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The equivalent 1D chain

• Exact equivalence to 1D chain with modified
  onsite potential

• Physics of 1D localization is applicable
• Klotsa, RAR, Turner, submitted to Proceedings of
  ICPS27, (2004)

23
Centromeric DNA
813138 base pairs

• chromosome 2 of yeast
• meaningful DNA sequence
• highly repetitive according to biology

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Coding vs. non-coding regions

• Biologically there is a huge difference
• What about in transport?

25
Outlook
Kelley et al., Science 283, 375 (1999) ..
Paradigms must now be developed to describe these
properties of the DNA p-stack, which can range
from insulator- to wire-like.

• Can electronic transport measurement be used to
  access biological function?
• Investigate sub-sequences of DNA with well-known
  biological functions
• Investigate trigger sequences. Is process
  transport specific?
• Relate to fluorescence experiments

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Music from l-DNA

• Music from DNA
• The Shamen, S2 Translation - An instrumental
  piece of music based on the DNA code for the S2
• S2 receptor protein for 5-hydroxy tryptamine
  (Serotonin) and others. One of the most important
  molecules in the mediation of both ordinary and
  non-ordinary (or "Shamanic") states of
  consciousness, which is why the molecule was
  chosen for this piece.

Serotonin
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Conclusions

• The electronic properties of DNA are an important
  challenge for both experiment and theory.
• Applications are manifold if linking of
  biological with electronic function can be made.
• Present research offers a route into DNA physics
  via the pathway of disordered systems.

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Disordered Quantum Systems

• DNA D. Klotsa, M. Turner
• Localization M. Ndawana, J. Stephany, A. Croy,
  H. Schulz-Baldes (Berlin)
• Nano-rings J. He, M. Raikh (Utah)
• Quantum Hall C. Sohrmann, B. Muzykantskii, P.
  Cain (Chemnitz)
• Bio-diffusion D. Skirvin (HRI Warwick)
• Numerical methods C. Sohrmann, O. Schenk (Basel)
• Funding EPSRC, Warwick, DFG

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A MIT due to disorder-induced quantum
interference

• Adding disorder to a quantum model of
  non-interacting electrons gives a transition

disorder
metal
insulator
multifractal
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Challenges at the MIT

• Is there universality?
• Ndawana, RAR, Schreiber, EPJB 27, 399-407
  (2002)
• What about correlations in the disorder?
• Ndawana, RAR, Schreiber, accepted in EPL (2004)
• What about many-body interactions?
• Schuster, RAR, Schreiber, Phys. Rev. B 65,
  115114-7 (2002)
• What about other transport quantities such as
  thermoelectric power?
• RAR, MacKinnon, Villagonzalo, J. Phys. Soc. Jpn.
  72 Suppl. A, 167-168 (2003)

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The Anderson model as a challenge to modern
eigenvalue methods

• Indefinite matrix problematic for iterative
  solvers, convergence accelerators,
  preconditioners
• Improving

Colloboration with numerical mathematicians
(Basel) PARDISO is faster for large matrices
32
The excitonic AB effect for nano-rings
R. A. Römer and M. E. Raikh, Phys. Rev. B 62,
7045-7049 (2000)

• Nano-sized
• rings with
• radius of
• 30-50nm exist

A. Lorke et al., Microelectronic Engineering 47,
95 (1999).
Excitons are being generated via
photoluminescence. What about Aharonov-Bohm
effect for this nano-geometry and neutral
(quasi-)particle?
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Challenges

• Trions and other charged excitons
• R. A. Römer, M. E. Raikh, phys. stat. sol. (b)
  227, 381-385 (2001)
• Experimental verification
• thus far only for trions
• Bayer, et al., Phys. Rev. Lett. 90, 186801
  (2003)
• AB effect in an electric field
• a current project

V
x
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l(R)-DNA
10000 base-pairs, random ATCG-DNA sequence

• Hopping strengths according to DNA content
• AT-AT -gt 1t
• GC-GC -gt 1t
• DNA-BB -gt 2t
• AT-GC -gt ½ t
• Physics of a random hopping chain
• LOCALIZATION!

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l(R)-DNA
10000 base-pairs, random ATCG-DNA sequence

• Hopping strengths according to DNA content
• AT-AT -gt 1t
• GC-GC -gt 1t
• DNA-BB -gt 2t
• AT-GC -gt 1/10 t

36
Why DNA?
A. Turberfield, PhysicsWorld 16, March 2003, 43-46

• DNA is a wonderful material with which to
  build. It can act as
• Molecular glue
• Fuel for molecular engines
• Parallel computer
• Self-assembled nanostructures
• E. Winfree , Nature 394, 539-544, Aug. 6, 1998
• scaffold in protein-crystallography
• Rigid tiles or girders J.H. Reif et al., (2003)

and many more
37
Telomeric DNA with 6000 base pairs
TTAGGGTTAGGGTTAGGGDNA

• Buffer sequences at beginning or end of
  meaningful DNA gene sequences

38
Telomeric DNA with BB disorder

• Large localization lengths even in presence of
  disorder

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Outlook 2

• What about a two-rung model?

(Quantum chemistry calculations)

• Results qualitatively similar, but

40
Transport in and Physics with DNA
A. Turberfield, PhysicsWorld 16, March 2003, 43-46

• Molecular glue
• Fuel for molecular engines
• Parallel computer
• Self-assembled nanostructures
• E. Winfree , Nature 394, 539-544, Aug. 6, 1998
• scaffold in protein-crystallography
• Rigid tiles or girders J.H. Reif et al., (2003)

41
Energy-Dependence for ladder model