Many experiments have been done to determine how far and how freely holes can move along the stack of base pairs in DNA. The results of these experiments are usually described in terms of a parameter β under the assumption that it describes an exponential decay with distance. The reported values range from β< 0.2/A to β > 1.4/A. For the larger values of β, the transport can be accounted for as single step superexchange-mediated hole trans- fer. To account for the smaller values. hopping models have been proposed, the simplest being nearest-neighbor hopping. This model assumes that. between hops, the hole is localized on a single base with no overlap to neighbors. Noting that an electron or hole added to a DNA stack, as to other essentially one-dimensional entities, should distort its structure to form a polaron. Schuster and coworkers [Henderson, P. T., Jones, D., Hampikian, G., Kan, Y. & Schuster. G. B. (1999) Proc. Natl. Acad. Sci. USA 96, 8353--8358 and Ly, D., Sanii, L. & Schuster, G. B. (1999),. Am. Chem. Soc. 121, 9400--9410l proposed that transport occurs by polaron hopping between sites having approximately equal energies as a result of overlap. A recent experimental determination by Wan et al. [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014--6019] of the time required for an injected hole on DNA to travel a known distance leads to a large value of the diffusion constant. From this constant, a mobility of 0.2 cm~2/V.s was deduced, orders of magnitude larger than typical hopping mobilities. We suggest that this ultra fast transport is due to polaron drift, which has been shown to lead to similar mobilities in chains of conjugated polymers. Using a simple model for the polaron, similar to that used for conjugated polymers such as polyacetylene, we show that, for reasonable values of the parameters, an injected electron or hole can form a polaron on a DNA stack.
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