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Insight into Quantum Mechanics of DNA Charge Transport

Insight into Quantum Mechanics of DNA Charge Transport. Nucleobase sequence dependence. Jacek Matulewski, Sergei Baranovski, Peter Thomas Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University in Toruń, Poland Departament of Physics

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Insight into Quantum Mechanics of DNA Charge Transport

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  1. Insight into Quantum Mechanics of DNA Charge Transport Nucleobase sequence dependence Jacek Matulewski, Sergei Baranovski, Peter Thomas Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University in Toruń, Poland Departament of Physics Phillips-Universitat Marburg, Germany Toruń, 9 XI 2004

  2. Motivation 1. To clarify what mechanisms are involved in the transport 2. To study dynamics of the process 3. To check if incoherence is essential in the hopping process for longer bridges 4. To check the importance of the dynamic disorder 5. The charge-transport phenomenon is believed to be of high importance in protecting the information encoded in theDNA against the oxidative damage 6. DNA is considered as a material for quantum wire

  3. Outline 1. Method 2. Short DNA bridges 3. Dynamic disorder 4. Long-range transport in DNA 5. Outlook

  4. Outline 1. Method a) regimes: superexchange vs hopping b) simplifications c) solving of TDSE d) choosing the criterion of the electron relocation 2. Short DNA bridges 3. Dynamic disorder 4. Long-range transport in DNA 5. Outlook

  5. Superexchange vs hopping B. Giese’s experiments (e.g. Current Opinion in Chemical Biology 2002, 6 612) Hopping between G bases in DNA Direct coupling between G bases (A bases can be not populated) (SX, VRH) Spreading of wavefunction over overlaping A bases (p-orbitals, tunneling,driven tunneling, NNH)

  6. Miller-Abrahams formula for rate: Direct tunneling between Gs: Activated hopping through the bridge: Model: A A A EG -EA G R = n d G Qualitative explanation For EG-EA0.5eV, d 3.4Å, a1.4Åand kT 0.025eV we obtain n  4

  7. Time-dependent Schrödinger equation potential, density space Numerical simulations - simplifications 1. Kronig-Penney model, one dimension 2. Coherent mechanisms only, TDSE 3. Initial state is described by the isolated well wavefunction 4. 3’-5’ and other chem. details omitted 5. Absorber instead of GGG trap

  8. Numerical method: Crank-Nicholson = Cayley’s formula • Advantages: • all couplings included • couplings and energies are time-dependent implicite • possibility of studying hops through short bridges in details • Disadvantages: • time consuming simulations - important in averaging, T-dependence - no bridges longer than 20 bases • difficulties in defining the criterion of reaching the absorber Solving time-dependent Schrödinger eq. Time-dependent Schrödinger equation for Kronig-Penney model:

  9. Outline 1. Methods 2. Short DNA bridges a) A/T dependence in two-base bridge b) homogeneous bridge 3. Dynamic disorder 4. Long-range transport in DNA 4. Outlook

  10. Static DNA system • 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 absorber • 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 absorber potential, density space absorber (Gabs) donor (G+) A/T bases

  11. A/T nucleobase dependence of transfer rate 1 0.1 0.01 0.001 0.0001 0 2E5 4E5 6E5 8E5 1E6 a=8, pot. type I well known probability of being not absorbed GTTGabs GATGabs novelty GTAGabs time GAAGabs 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)

  12. A/T nucleobase dependence of transfer rateJ. Matulewski, S. Baranovskii, P. Thomas, phys. stat. sol. (b), 241 (2004), R46 bases distance • Base distance • Width of initial state doesn’t influence the rate ratio • Different A and T energy differences was checked (rates ratio between 1.3 and 1.5) • Ratio increases to about 2 for very deep potentials Rates ratio became equal to 1 as distance is increased (in fact rates are very close to 0 for distances 9 and 10)

  13. Å-1 0.01 0.001 0.0001 • Experimental value of b is 0.6Å-1 to 0.7Å-1 1e-005 1e-006 1e-007 1e-008 1e-009 0 1 2 3 4 5 6 Exponential decay without plateau! Homogenous bridge length dependence Rate of decay of probability(electron disappears after reaching the absorber area) a=8, pot. type I norm decay rate • Adding dynamic disorder will change this picture bases number

  14. 1 1 norm 0.2 donor 0.8 0.04 1st A-base 0.008 2nd A-base 0.6 1.6E-3 3.2E-4 0.4 6.4E-5 0.2 1.28E-5 2.56E-6 0 0 2E5 4E5 0 2E5 4E5 6E5 8E5 1E6 • The delay in populating the A bases is no longer then 104 a.u. • because of wavefunctions overlap Homogenous bridge length dependence a=8, pot. type I, GAAGabs a=8, pot. type I, GAAAAAAGabs norm, population time time

  15. Homogenous bridge length dependence a=8, pot. type I, GAAGabs, G(A)6Gabs wavefunction in G(A)6Gabs after 106 a.u. Probability wavefunction in G(A)2Gabs after 106 a.u. initial wavefunction space • The same transport mechanism for short and long bridges • Futher increasing coupling strength do not change this picture (same result for a=6.426)

  16. Outline 1. Methods 2. Short DNA bridges 3. Dynamic disorder a)Dynamic disorder supporting transport b) Strong dynamic disorder - “jumping” 4. Long-range transport in DNA 5. Outlook

  17. Dynamic DNA system In our model:dynamic disorder is unordered motion of coupled bases (coupled oscillators) G/A Energy difference: 0.0205a.u. = 0.558 eV Dynamic disorder meanfrequency: 0.001a.u. ≈ 1013 Hz Kinetic energy ≈ 300K potential, density space absorber (Gabs) donor (G+) A/T bases

  18. Dynamic disorder in DNA system 1 average over realisation! 0.01 0.0001 1e-006 1e-008 1e-010 no dynamic disorder no dynamic disorder 1e-012 dynamic disorder dynamic disorder 1e-014 -40 -20 0 20 40 60 80 100 a=8, pot. type I, dynamic disorder w ≈ 10-4 a=8, pot. type I, G(A)6Gabs 0.01 0.001 0.0001 Rate Density 1e-005 1e-006 1e-007 1e-008 1e-009 0 1 2 3 4 5 6 space bases number Dynamic disorder helps with transport of charge in DNA, but in longs bridges only.It allows to reproduce the crossover in Giese’s experiments.

  19. Dynamic disorder in DNA system 1 1 0.9 no dynamic disorder no dynamic disorder 0.8 0.95 dynamic disorder 0.7 0.6 0.9 0.5 0.4 0.85 0.3 0.2 0.8 dynamic disorder 0.1 0 0.75 0 1E5 2E5 3E5 4E5 5E5 0 1E5 2E5 3E5 4E5 5E5 a=8, pot. type I, GAAGabs, dyn. dis. a=8, pot. type I, G(A)6Gabs, dyn. dis. Norm Norm time time Dynamic disorder helps with transport of charge in DNA, but in longs bridges only.It allows to reproduce the crossover in Giese’s experiments.

  20. Dynamic disorder in DNA system 1 0.1 1 norm 0.01 0.9 donor 0.8 0.001 1st A-base 0.7 0.6 2nd A-base 0.0001 0.5 1e-005 0.4 0.3 1 0.2 0.1 0.1 1 0.01 norm 0.9 donor 0.8 0.001 1st A-base 0.7 0.0001 2nd A-base 0.6 0.5 1e-005 0.4 0.3 1e-006 4E5 0 2E5 0.2 0.1 0 0 2E5 4E5 a=8, pot. type I, GAAGabs a=8, pot. type I, GAAAAAAGabs population norm, population dynamic disorder time time

  21. Outline 1. Methods 2. Short DNA bridges 3. Dynamic disorder a)Dynamic disorder supporting transport b) Strong dynamic disorder - “jumping” 4. Long-range transport in DNA 5. Outlook

  22. Strong dynamic disorder - “jumping“ • Motivation: • 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: GAAAAAAGabs Method: direct solving of TDSE in Kronig-Penney model

  23. Strong dynamic disorder - “jumping“ spreading unbound part of initial state a=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type III space 0 logarithm of probability density 0 20000 40000 60000 time

  24. Strong dynamic disorder - “jumping“ spreading unbound part of initial state a=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type III “Impulses” at acceptor - strong dynamic disorder (time dependent coupling) induces non exponential decay of norm norm time

  25. Strong dynamic disorder - “jumping“ a=6.426, pot. type IV, GAAAAAAGabs, dyn. dis. type III last A-base is almost not populated(still the same mechanism) norm, population time

  26. Outline 1. Methods 2. Short DNA bridges 3. Dynamic disorder 4. Long-range transport in DNA 5. Outlook

  27. Long range transport • Motivation: • 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 bases System: GTTGTTGTTGTTGabs Method: direct solving of TDSE in Kronig-Penney model

  28. Long range transport between G bases a=8, pot. type I, GTTGTTGTTGTTGabs, dyn. dis. type I logarithm of probability density GTTGTTGTTGTTK 0E+6 2E+6 4E+6 6E+6 time

  29. t = 0 a.u. t = 5E5 a.u. t = 1.5E6 a.u. 0.1 t = 2.5E6 a.u. 0.01 0.001 0.0001 -20 0 20 40 60 80 100 120 Long range transport between G bases a=8, pot. type I, GTTGTTGTTGTTGabs, dyn. dis. type I 1 logarithm of probability density G T T G T T G T T G T T K

  30. influence of dyn. dis. Long range transport between G bases norm, population time

  31. Long range transport between G bases • Conclusions: • 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

  32. 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)

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