Insight into Quantum Mechanics of DNA Charge TransportJacek Matulewski, Sergei Baranovski, Peter Thomas

Faculty of Physics, Astronomy and InformaticsNicolaus Copernicus University in Toru, Poland

Departament of PhysicsPhillips-Universitat Marburg, Germany

Toru, 9 XI 2004Nucleobase sequence dependence

Motivation1. To clarify what mechanisms are involved in the transport2. To study dynamics of the process3. To check if incoherence is essential in the hopping process for longer bridges4. To check the importance of the dynamic disorder5. The charge-transport phenomenon is believed to be of high importance in protecting the information encoded in the DNA against the oxidative damage6. DNA is considered as a material for quantum wire

Outline1. Method2. Short DNA bridges3. Dynamic disorder4. Long-range transport in DNA5. Outlook

Outline1. Methoda) regimes: superexchange vs hoppingb) simplificationsc) solving of TDSEd) choosing the criterion of the electron relocation2. Short DNA bridges3. Dynamic disorder4. Long-range transport in DNA5. Outlook

Superexchange vs hoppingB. Gieses experiments (e.g. Current Opinion in Chemical Biology 2002, 6 612)Spreadingof wavefunction over overlaping A bases(p-orbitals, tunneling, driven tunneling, NNH)Direct couplingbetween G bases (A bases can be not populated)(SX, VRH)Hoppingbetween G bases in DNA

Qualitative explanationFor EG-EA 0.5eV, d 3.4, a 1.4 and kT 0.025eV we obtain n 4

Numerical simulations - simplifications1. Kronig-Penney model, one dimension2. Coherent mechanisms only, TDSE3. Initial state is described by the isolated well wavefunction4. 3-5 and other chem. details omitted5. Absorber instead of GGG trap

Solving time-dependent Schrdinger eq.Time-dependent Schrdinger equation for Kronig-Penney model:

Outline1. Methods2. Short DNA bridgesa) A/T dependence in two-base bridgeb) homogeneous bridge3. Dynamic disorder4. Long-range transport in DNA4. Outlook

Rabi-like oscillations

Criterion of electron transfer from G+ to Gabs: population of bases norm/prob. of absorbing cleavage ratio, ratio of population o donor and absorber stream, total stream prob. of finding hole/el. in area of absorberRabi-like oscillations

Criterion of electron transfer from G+ to Gabs: population of bases norm/prob. of absorbing cleavage ratio, ratio of population o donor and absorber stream, total stream prob. of finding hole/el. in area of absorberspacepotential, densitydonor (G+)absorber (Gabs)A/T basesStatic DNA system

reason: interplay of overlap of G and first A/T base wavefunctions and off-resonance energy difference (one can control both by choosing the energies of the bases)GTAGabsGATGabstimeprobability of being not absorbeda=8, pot. type IGTTGabsGAAGabswell knownnoveltyA/T nucleobase dependence of transfer rate

Width of initial state doesnt influence the rate ratio Base distance Different A and T energy differences was checked (rates ratio between 1.3 and 1.5)Rates ratio became equal to 1 as distance is increased(in fact rates are very close to 0 for distances 9 and 10) Ratio increases to about 2 for very deep potentialsA/T nucleobase dependence of transfer rateJ. Matulewski, S. Baranovskii, P. Thomas, phys. stat. sol. (b), 241 (2004), R46

Homogenous bridge length dependencebases numbernorm decay ratea=8, pot. type I Adding dynamic disorder will change this pictureRate of decay of probability (electron disappears after reaching the absorber area)

Homogenous bridge length dependencea=8, pot. type I, GAAGabstimea=8, pot. type I, GAAAAAAGabstimenorm, population

Homogenous bridge length dependence The same transport mechanism for short and long bridgesa=8, pot. type I, GAAGabs, G(A)6GabsProbabilityspaceinitial wavefunctionwavefunction in G(A)2Gabsafter 106 a.u.wavefunction in G(A)6Gabsafter 106 a.u. Futher increasing coupling strength do not change this picture (same result for a=6.426)

Outline1. Methods2. Short DNA bridges3. Dynamic disordera) Dynamic disorder supporting transportb) Strong dynamic disorder - jumping4. Long-range transport in DNA5. Outlook

spacepotential, densityabsorber (Gabs)A/T basesDynamic DNA systemdonor (G+)

Dynamic disorder in DNA systemRatebases numbera=8, pot. type I, dynamic disorder w 10-4a=8, pot. type I, G(A)6GabsspaceDensityDynamic disorder helps with transport of charge in DNA, but in longs bridges only. It allows to reproduce the crossover in Gieses experiments. 1e-009 1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0 1 2 3 4 5 6

Dynamic disorder in DNA systemNormNormtimetimea=8, pot. type I, GAAGabs, dyn. dis.a=8, pot. type I, G(A)6Gabs, dyn. dis.Dynamic disorder helps with transport of charge in DNA, but in longs bridges only. It allows to reproduce the crossover in Gieses experiments.

Dynamic disorder in DNA systemtimetimenorm, populationpopulationa=8, pot. type I, GAAGabsa=8, pot. type I, GAAAAAAGabsdynamic disorder

Outline1. Methods2. Short DNA bridges3. Dynamic disordera) Dynamic disorder supporting transportb) Strong dynamic disorder - jumping4. Long-range transport in DNA5. Outlook

Strong dynamic disorder - jumpingMotivation: find a regime in which dynamic disorder dominate tunneling what means that bases can be brought so close that coupling increase drastically frequencies are much smaller than thermally induced (w < 10-5 a.u. 1011 Hz)System: GAAAAAAGabsMethod: direct solving of TDSE in Kronig-Penney model

Strong dynamic disorder - jumping0600002000040000timespacespreading unbound part of initial statea=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type III0logarithm of probability density

Strong dynamic disorder - jumpingnormImpulses at acceptor - strong dynamic disorder (time dependent coupling) induces non exponential decay of normspreading unbound part of initial statea=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type IIItime

Strong dynamic disorder - jumpingnorm, populationlast A-base is almost not populated (still the same mechanism)timea=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type III

Outline1. Methods2. Short DNA bridges3. Dynamic disorder4. Long-range transport in DNA5. Outlook

Long range transportMotivation: to check if in fully coherent description one can obtain efficient long range transport in DNA via G bases examine the time dependent picture of transport in more realistic case (hops between G bases) investigate the importance of dynamic disorder in the long system, but with no long jumps between G basesSystem: GTTGTTGTTGTTGabsMethod: direct solving of TDSE in Kronig-Penney model

Long range transport between G basesGTTGTTGTTGTTK6E+62E+64E+60E+6logarithm of probability densitytimea=8, pot. type I, GTTGTTGTTGTTGabs, dyn. dis. type I

Long range transport between G bases 1G T T G T T G T T G T T Klogarithm of probability densitya=8, pot. type I, GTTGTTGTTGTTGabs, dyn. dis. type I

Long range transport between G basestimenorm, population

Long range transport between G basesConclusions: one can get long range transport (hopping through G bases) in fully coherent model dynamic disorder should cause time-dependent changes in observed intensities of intermediate G bases

Outlook Taking into account 3-5 and other chemical details, maybe two and three dimensions... Study the temperature dependence of the process Obtain quantitative results using stochastic perturbation to mimic the vibration of the helix molecules and variations of helix shape (other approach to dynamic disorder)

ten podzia sztuczny i wynika z uytego kryterium (w gammienie ma crossoveru

Czy 3'-5' moe by driving force, czy tylko dyfuzja???Urednianie moe by potrzebne tylko gdy pot. zaley od czasu(we focus on one step physics) - usprawdliwienie uproszczeUrednianie moe by potrzebne tylko gdy pot. zaley od czasustrumie oscyluje i to mocno na pocztku (dlaczego a tak, skoro jednostajny zanik - zaley od skali)(poza tym cakoiwty to to samo co norma)???

Dlaczego o tyle atwiej GAnK ni AGnK?????

Na pocztku oscylacje i zachowanie zaley od sprzenia G+ z pierwsz baz (A lub T), ale potem to ju tylko od struktury caoci (ustalenie balansu) (dobrze to wida w IIIg)Why there is no crossover? Obsadzenie w pierwszym A jest automatycznie??Mona ratio i wtedy crossover, ale na wykresach funkcji wida, e tunelowanie zanika exp i to samo w wykr gamma

Obsadzenia zmniejszaj si jednostajnie bez skokw

Na pocztku oscylacje = sprzenia, a potem detailed balance

Mechanizm:overlap przez sprzenie (pytkie studnie)zawsze tak samo bez wzgldu na ilo bazNawet w IIIg, ale dla 6.426 s takie same pocztkowe obsadzenia!!!

Plateau widziane jest tylko dla Pgabs/Pgdon

Ale to nie tylko ogon (w bazach A jest grka f.falowej)

suma nie jest jedynk bo overlap

perturbation theory of n-th order

doda jeszcze stream!!!!! - oscyluje - nie opaca si

Plateau jest, tylko w innej wielkoci (artefakt, czy inna wielko)Dynamic disorder ma wpyw tylko na skoki midzy dugimi bazami, czyli przy hoppingu z G do G nie ma znaczenia - ujawniaj si dopiero przy maych prdkociach (wic to DD, a nie TIH moe by przyczyn ........)

To wstawi przed longrange?????

zrobi wykres GAAAAAAGabs dla DD (eby potwierdzi, e obraz jest ten sam)

pokaza dla krtkiego bridga jak DD zwiksza lub zmniejsza przepyw

Dla 6 gaaaaaak_IIIg DD3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!i bez DD

u Koharego DD przeszkadza??? a u nas pomaga

Inny stosunek beta do DD (jaki parametr to opisuje)

ale dlaczego taki duy ubytek na pocztku (por. ga/tk w IIIg z i bez DD3)

Jak sprzenie za dugo, to populacja robi peny cykl i wraca

Static position disorder, ale zmienny w czasie (nie ma fononw (przesuni energii, s tylko zmiany sprze)

ale dlaczego taki duy ubytek na pocztku (por. ga/tk w IIIg z i bez DD3)

Jak sprzenie za dugo, to populacja robi peny cykl i wraca

Static position disorder, ale zmienny w czasie (nie ma fononw (przesuni energii, s tylko zmiany sprze)

pytkie studnie - couplingTylko G s znaczco obsadzoneDD powoduje pywanie pikw, bez DD jest cay czas rwno??? - zobaczy f.falowe. bez DD

szybkie ale mae oscylacje - nierez. sprzenie GAwolne due osc - sprzenia GG

Ale bez DD z a=6.426 nie wida tych duych oscylacji!!!!