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
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.
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Semiconductor nanostructures:
Q-dots, -well, SET’s
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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 …
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Why disorder?
• well-developed
theory
• good computational
algorithms
• DNA is in solution
-> there is “disorder”
|Y|2 of electron wave
function in 1113 system
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Combining DNA & electronics
Conductor:
Semiconductor:
[Fink/Schoenenberger,
Nature 398, 407 (1999)]
5
Insulator:
[Priyadarshy et al., J. Phys.
Chem., 100, 17678 (1996)]
[Porath et al., Nature 403,
635 - 638 (10 Feb 2000)]
:
5
Electronic Transport in
Disordered Systems and DNA
:
7
17/07/2016
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
MutY
Electronic Transport in
Disordered Systems and DNA
17/07/2016
DNA (Deoxyribonucleicacid)
Linear bio-polymer,
backbone of repeated
sugar-phosphate units,
attached with “bases”
•C ytosine
•A denine
•T hymine
complementary
•G uanine
double helix structure
AT, GC, not AC, AG, TC, TG
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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 43=64 “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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Huge amounts of genetic data:
•
•
•
•
H. sapiens
C. elegans
E. coli
SARS virus
30,000 genes
10,000 genes
4,380 genes
14 genes
3  109 bp
108 bp
4,639,221 bp
29,761 bp
Paradox : ~ 105 proteins in H. sapiens
▬►One gene codes for more than one protein
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Biological function of DNA
• Replication:
AGCTGATC
AGCTGATC 

TCGACTAG
AGCTGATC

 TCGACTAG
TCGACTAG
AGCTGATC
• Template for RNA coding for proteins:
polymerase of DNA -> RNA ->
proteins (actin, cell rigidity)
• Self-assembly
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Is DNA a quantum wire?
•
“Absence of dc-Conductivity in l-DNA”
De Pablo et al, PRL 86, 4992 (2000):
LUMO/
PolyGC
– Poly-GC strands have
one-band of
overlapping p-orbitals
- l-DNA overlap drops HOMO/
PolyGC
quickly
• 13 base-pairs, DFT
calculation
LUMO/
l-DNA
Electronic Transport in
Disordered Systems and DNA
17/07/2016
The fishbone model
•tight-binding model with a gap
Cuniberti et al., PRB 65, 24131(R) (2002)
Experiments vs. theory:
•Poly-GC: GCGCGCGC…
•explains experiments in Poly-GC
Electronic Transport in
Disordered Systems and DNA
17/07/2016
The fishbone model
L
L
H   ti i i  1   i i i 
i 1

i 1 q  ,
tiq iq i   iq iq i  h.c.
• Hopping amplitudes are 1
along chain and 2 onto
backbone
• Onsite energies are zero,
but could be used to model
the ionization energies
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Semiconducting gap in
Poly-GC
•Large DNA sequences
possible
•Localization lengths l give
possible extend of electron
transfer -> measurable via
fluorescence experiments
Electronic Transport in
Disordered Systems and DNA
Energy band
tn1 n1 ( E -  n ) n - tn n-1
Energy band
•Transfer-matrix method:
17/07/2016
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
gap fills
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Random adhesion of Na-Atoms
at backbone
DNA is in solution,
so there is “disorder”
Na
New states
Na
Na
Electronic Transport in
Disordered Systems and DNA
17/07/2016
The ladder model

H     ti , i
i 1   1, 2
L

i  1    i , i

i 
t
q  ,
q
i
i iq   iq iq  t1,2
q
i

i,1 i, 2   h.c.

• Q-chemical calculations do
not find HOMO/LUMO on
both bases of a base pair
• Hopping amplitudes
between chains is 1/2
Electronic Transport in
Disordered Systems and DNA
17/07/2016
E 0
Na: binary disorder at the BB
More
disorder
gives less
localization!
Contradiction
to folklore!
E 0
less localized
highly localized
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Telomeric DNA with Na-BB
disorder
TTAGGGTTAGGGTTAGGG…DNA
less localized
Differences
in
biologically
different
DNA
sequences
highly localized
Electronic Transport in
Disordered Systems and DNA
E 0
17/07/2016
The equivalent 1D chain
• Exact equivalence to 1D chain with
modified onsite potential:
 
t
~
i  i - 
2

i
i - E
-
t 
2

i
 -E

i
• Physics of 1D localization is applicable
[Klotsa, RAR, Turner, submitted to Proceedings of ICPS27, (2004)
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Centromeric DNA
•
•
•
813138 base pairs
chromosome
2 of yeast
meaningful
DNA
sequence
highly
repetitive
according to
biology
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Coding vs. non-coding regions
• Biologically
there is a
huge
difference
• What
about in
transport?
E 3
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Outlook:
Kelley et al., Science 283, 375 (1999):
“.. Paradigms must now be developed to
describe these properties of the DNA pstack, 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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Music from l-DNA
• Music from DNA
Serotonin
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 nonordinary (or "Shamanic") states of consciousness,
which is why the molecule was chosen for this piece.
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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.
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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)]
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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 nanogeometry and neutral (quasi-)particle?
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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
V
[Bayer, et al., Phys. Rev. Lett. 90, 186801 (2003)]
• AB effect in an electric field
[a current project]
x
Electronic Transport in
Disordered Systems and DNA
17/07/2016
l(R)-DNA:
[10000 base-pairs, random
ATCG-DNA sequence]
•Hopping strengths
according to DNA
content:
•AT-AT -> 1t
•GC-GC -> 1t
•DNA-BB -> 2t
•AT-GC -> ½ t
•Physics of a random
hopping chain
gap fills
LOCALIZATION!
Electronic Transport in
Disordered Systems and DNA
17/07/2016
l(R)-DNA:
[10000 base-pairs, random
ATCG-DNA sequence]
•Hopping strengths
according to DNA
content:
•AT-AT -> 1t
•GC-GC -> 1t
•DNA-BB -> 2t
•AT-GC -> 1/10 t
Electronic Transport in
Disordered Systems and DNA
17/07/2016
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 …
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Telomeric DNA with 6000 base
TTAGGGTTAGGGTTAGGG…DNA
pairs
Buffer
sequences at
beginning or
end of
meaningful
DNA gene
sequences
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Telomeric DNA with BB disorder
Large
localization
lengths
even in
presence of
disorder
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Outlook 2:
1 gamma
00006000. raw
• What about a two-rung
model?
30
25
20
15
(Quantum
chemistry calculations)
10
5
2
4
6
8
• Results qualitatively similar, but
l2rung  l1rung
Electronic Transport in
Disordered Systems and DNA
17/07/2016
10
BBSiteDis
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)]
Electronic Transport in
Disordered Systems and DNA
17/07/2016
Energy-Dependence for ladder model
Electronic Transport in
Disordered Systems and DNA
17/07/2016