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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