Polarons and Transport in DNA

Abstract

It has been widely considered that the wavefunction of an extra electron or hole on the base stack of a DNA molecule is confined to a single site, i.e., base or base pair. There is, however, a theorem that an extra carrier on a one-dimensional chain minimizes its energy by forming a large polaron, its wavefunction extended over a number of sites. Thus it is expected, and calculations show, that the wavefunction of an extra electron or hole on DNA is delocalized, even for an arbitrary base sequence. The hole wavefunction is centered on a guanine (G) because the HOMO of G is higher by many kT than that of the other bases. To understand the significance of this and how it affects transport, we begin by reviewing the experimental data on electron and hole diffusion in solution and drift in an electric field in air or vacuum. The finding of Giese's group, that a hole moves by tunneling between Gs when there is a random sequence of bases with Gs within four sites of each other, can be reinterpreted as tunneling of the hole polaron from a position where it is centered on one G to a position where it is centered on another G. Further experiments show that if a G is followed by a series of four or more adenine-thymine pairs (A:Ts), a hole has some probability of hopping from G onto the bridge of As with thermal energy and then moving rapidly along the As almost unattenuated. Consistent with the idea of the hole being localized to one site, it was suggested that the motion along the As is nearest-neighbor hopping. We suggest that the motion along the As is polaron drift. Some evidence for this is the experiment of Kendrick and Giese which shows that a hole introduced on an A migrates through an (A:T) n sequence in a manner independent of n. We present a number of additional arguments, some based on excitons and exciplexes in DNA, that an extra hole or electron propagates as a large polaron. The properties and the motion of a large polaron in DNA are calculated with a simple tight-binding model. Additional evidence that an extra hole is not localized to one site comes from the excellent agreement with experiment of our calculations based on the polaron model of the relative trap depths of G, GG, and GGG traps. The large polaron model can also account for the switch from tunneling to on-bridge propagation as the number of A:Ts between the Gs goes beyond three. Including in the calculations the solvent and counterions makes little change in the extent of the polaron but greatly increases its binding energy and has a strong drag effect on its mobility. For DNA in air or vacuum propagation may also be by large polarons, but more must be known, e.g., about disorder in a low-humidity environment and how the negative charge on the backbone is compensated, before a definite conclusion can be reached.