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Quantum Theory of DNA—
An Approach to Electron Transfer in DNA H. Sugawara, 2005Work being done with H. Ikemura
1. Introduction motivation ⇔ Ikemura ConjectureIkemura Conjecture“Electron transfer in DNA is playing an important role in the information exchanges among the various sections of DNA.”
Example
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Standard technique in particle theory and in condensed matter theory but maybe not in quantum chemistry.Consider electrons interacting with the centers of potential (ions) located at Ri:
2. Field Theory Technique
electromagnetic interactions (gauge principle)
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◎ electron-phonon interactions
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3. Hartree approximations
Include in V(x) → Veff
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Further approximations
only nearest neighbors
Then we have
Special case of H→ Su-Schrieffer-Heegger Hamiltonian , constant , longitudinal →
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can also be defined in a similar wayThen we replace
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Here was utilized
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RNA transcription
DNA replication
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◎ Consider classical and longitudinal oscillation
◎ general case with classical oscillation
localized (tightly bound) wave function
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WKB solution
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◎ The localization depends on the sign of and of
◎ Back to the descrete description
applications
(1) Luminescence quenching(2) Electric current(3) Absorption of light
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Luminescence quenching
quenching occurs by a hole propagation inside DNA
Note 1. Prokariote ・・・ closed string 2. Eukariote ・・・ open string end: telomere with certain protein
mixed system
Ru-ligand
absorptionluminescence
Rh provides electrons quenching⇒
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Probability of quenching
DNA electrons transfer to (from) metals
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Density at Lh
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Electric current in DNA
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Coupling to backbone electrons
This may be important in explaining the current?
add
22There must be an overlap
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(1) Ef is within the band
(2) Ef is outside of the band
semiconductor-like
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Optical absorption (Sarukura’s proposal)
em interaction
excited band
ground band
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absorption rate
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Conclusion
(1) Comparison with experiments(2) Bound states with proteins(3) Quantized phonon(4) Improvement of approximations
remaining problems
(1) Three dimensional string action for DNA is derived(2) Approximate -electron wave functions are derived(3) Applications to luminescence quenching, electric current
through DNA and optical absorption are formulated