Electronic Transport in DNA – the disorder perspective

Electronic Transport in DNA – the disorder perspective

Rudolf A Roemer

Daphne Klotsa, Matthew Turner

Department of Physics and Centre for Scientific Computing

Quantum physics on biological nanostructures – a first attempt

04/21/23Electronic Transport in Disordered Systems and DNA

Why nanostructures?

• 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.

[NanoStructures Laboratory, Princeton University]


Semiconductor nanostructures:Q-dots, -well, SET’s


“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)]

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

and many more …


Why disorder?

• well-developed theory

• good computational algorithms

• DNA is in solution

there is “disorder”

of electron wave function in 1113 system


Combining DNA & electronicsConductor:[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


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).

MutY MutY

MutY MutY

Healthy DNA

Broken DNA

electron


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, TGcom

plementary


• 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

DNA basics:…ATCGATCGATGATGTCGA……TAGCTAGCTACTACAGCT…


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 virus14 genes 29,761 bp

Paradox : ~ 105 proteins in H. sapiens

▬►One gene codes for more than one protein


Biological function of DNA• Replication:

• Template for RNA coding for proteins: polymerase of DNA RNA proteins (actin, cell rigidity)

• Self-assembly

AGCTGATCAGCTGATC

AG

TCGACTAG

TCGACTAGTCGAC

CTGATC

TAGAGCTGATC


Is DNA a quantum wire?

• “Absence of dc-Conductivity in -DNA”

De Pablo et al, PRL 86, 4992 (2000):

– Poly-GC strands have one-band of overlapping -orbitals

-DNA overlap drops quickly

• 13 base-pairs, DFT calculation

LUMO/PolyGC

HOMO/PolyGC

LUMO/ -DNA


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:


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

1 1 ,

.1 .L L

i i qi i

qi

qit i i t iq ii iH h ciq i


Semiconducting gap in Poly-GC

•Transfer-matrix method:

•Large DNA sequences possible

•Localization lengths give possible extend of electron transfer measurable via fluorescence experiments

111 )( nnnnnn tEt

Ene

rgy

band

Ene

rgy

band


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

•Small differences between -DNA and (R)-DNA

•Computation for complete DNA strand

gap fills


Influence of backbone disorder

• 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

[Klotsa, RAR, Turner, submitted (2004)]


Random adhesion of Na-Atoms at backbone

Na

Na Na

New states

DNA is in solution, so there is “disorder”


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

, 1,21 2

,1, ,

1 . .,1 ,2L

iii

iq

qi

qH t i i t i iq iq h ci ii q t ii


Na: binary disorder at the BB

More disorder gives less localization!

Contradiction to folklore!

highly localized

less localized

0E

0E


Telomeric DNA with Na-BB disorder

Differences in biologically different DNA sequences

highly localized

less localized

TTAGGGTTAGGGTTAGGG…DNA

0E


The equivalent 1D chain• Exact equivalence to 1D chain with

modified onsite potential:

E

t

E

t

i

i

i

iii

22

~

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


Centromeric DNA

• chromosome 2 of yeast

• meaningful DNA sequence

• highly repetitive according to biology

813138 base pairs


Coding vs. non-coding regions

• Biologically there is a huge difference

• What about in transport?

3E


Outlook:

• 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

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.”


Music from 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

http://www.visionlearning.com/library/x_linker.php?moid=2034


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.


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


A MIT due to disorder-induced quantum interference:

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

metal insulator

multifractal

disorder


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)]


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


The excitonic AB effect for nano-rings

Nano-sized

rings with

radius of

30-50nm exist:

[R. A. Römer and M. E. Raikh, Phys. Rev. B 62, 7045-7049 (2000)]

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?


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]

x

V


(R)-DNA:•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

LOCALIZATION!

[10000 base-pairs, random ATCG-DNA sequence]

gap fills


(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


“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]


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

and many more …


Telomeric DNA with 6000 base pairs

Buffer sequences at beginning or end of meaningful DNA gene sequences

TTAGGGTTAGGGTTAGGG…DNA


Telomeric DNA with BB disorder

Large localization lengths even in presence of disorder


Outlook 2:• What about a two-rung model?

• Results qualitatively similar, but

2rung 1rung

(Quantum chemistry calculations)

2 4 6 8 10BBSiteDis

5

10

15

20

25

30

1gamma 00006000. raw


Transport in and Physics with DNA

• Molecular glue

• Fuel for molecular engines

• Parallel computer

• Self-assembled nanostructures [E. Winfree , Nature 394, 539-544, Aug. 6, 1998]


A. Turberfield, PhysicsWorld 16, March 2003, 43-46


Energy-Dependence for ladder model

Documents

Electronic Transport in DNA – the disorder perspective