Structural fluctuations, such as phonons and proton motion in hydrogen bonding play an important role in charge conduction of biopolymers. Different from the phonons which are oscillatory motions in a single-minimum potential, the proton can tunnel form one side of a hydrogen bond to another in a double-minimum potential just as a particle moving in a two-level system.; This proton transfer reaction is especially important in double-stranded DNA since the cause of tautomeric base pair by proton transfer could induce genetic mutation in DNA, as pointed out by Watson and Crick. In the stacking base pairs of DNA, since the π electrons can be transferred across the base pairs, the proton transfer and the electron conduction in DNA can be affected by each other. Although until now the nature of DNA electronic ground state is still a controversy, due to the low dimensionality of DNA, we can investigate the motions of the protons and charges in DNA by considering various one-dimensional electron systems with the effects of structural fluctuations.; Three models are proposed for the possibly different charge conductions in DNA. For the model of conductors, the coupling between electrons and protons can stablize the excited state of proton transfer in the hydrogen bond and make it more likely. The DNA sequences with strong electron-proton coupling or a good electrical conduction may result in genetic mutations. In the Mott insulator, the soliton created from the Umklapp process can delocalize the proton in a hydrogen bond and be stabilized by the effects of two-level system and acoustical phonons. For the model of the band insulator, we found that the charge trapped by either the hydrogen bonds or phonons can form a polaron. The polaron diffusion in the continuous media can correspond to the multiple-step hopping mechanism in the discrete model and derive the reaction rate of the long-range charge transfer in DNA. The result in the optical case is in agreement with the experimental results.
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