Diffusion Approach to Long Distance Charge Migration in DNA:  Time-Dependent and Steady-State Analytical Solutions for the Product Yields

Abstract

In this study we report analytical solutions for both time-dependent and steady-state problems of unbiased charge transfer through a regular DNA sequence via a hopping mechanism. The phenomenon is treated as a diffusion of charge in a one-dimensional array of equally spaced and energetically equivalent temporary trapping sites. The solutions take into account the rates of charge hopping (k), side reactions (k r ), and charge transfer to a terminal charge acceptor (k t ). A detailed analysis of the time-dependent problem is performed for the diffusion-controlled regime, i.e., under the assumption that k t ≫ k, which is also equivalent to the fast relaxation limit of charge trapping. The analysis shows that the kinetics of charge hopping through DNA is always multiexponential, but under certain circumstances it can be asymptotically approximated by a single-exponential term. In that case, the efficiency of charge transfer can be characterized by a single rate constant k CT = 1.23kN −2 + k r , where N is the DNA length expressed in terms of the number of equidistant trapping sites and k r is the rate of competing chemical processes. The absolute yield of charge transfer under steady-state conditions in general is obtained as Y ∞ = ω [α sinh(αN) + ω cosh(αN)] −1 , where α = (2k r /k) 1/2 and ω = 2k t /k. For the diffusion-controlled regime and small N, in particular, it turns into the known "algebraic" dependence Y ∞ = [1 + (k r /k)N 2 ] −1 . At large N the solution is asymptotically exponential with the parameter α mimicking the tunneling parameter β in agreement with earlier predictions. Similar equations and distance dependencies have also been obtained for the damage ratios at the intermediate and terminal trapping sites in DNA. The nonlinear least-squares fit of one of these equations to experimental yields of guanine oxidation available from the literature returns kinetic parameters that are in reasonable agreement with those obtained by Bixon et al. [Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11713-11716] by numerical simulations, suggesting that these two approaches are physically equivalent.

Mechanisms of Strand Break Formation in DNA due to the Direct Effect of Ionizing Radiation: The Dependency of Free Base Release on the Length of Alternating CG Oligodeoxynucleotides

“…This distance depends on the relative rates of trapping and transfer, described by the parameter α. Whereas values of α are unknown in solid state DNA, a value of 0.34 was calculated24 from data on holes photochemically generated in DNA in dilute aqueous solution 31. The best fit value, α = 0.012 in Table 2, is an order of magnitude smaller; this is reasonable given the expectation that the trapping rate should be significantly slower in the solid state.…”

“…An analytical solution to the steady-state problem of 1D diffusion of a hole through the DNA base stack has been presented previously 24. A similar approach was applied to hole scavenging by a dRib(Cn′–H) • radical residing in the i th position of an oligomer of length N .…”

Study of charge transport mechanisms in125I-induced DNA damage at various temperatures

“…Charges travelling along DNA molecules (either radical cations or anions) (Berlin et al, 2001, Bixon and Jortner, 2001, Jortner et al, 1998, Roginskaya et al, 2004, Boon and Barton, 2002, Giese and Biland, 2002, Giese, 2002, Giese and Wessely, 2001) can cause damage to DNA nucleotides (Burrows and Muller, 1998, Armitage, 1998, Cai and Sevilla, 2003). The two main mechanisms of charge transport along DNA molecules are tunneling (or superexchange) and hopping (Berlin et al, 2001, Jortner et al, 1998, Giese, 2000, Boon and Barton, 2002, Conwell, 2004).…”

“…The two main mechanisms of charge transport along DNA molecules are tunneling (or superexchange) and hopping (Berlin et al, 2001, Jortner et al, 1998, Giese, 2000, Boon and Barton, 2002, Conwell, 2004). Tunneling is the direct transport of charge from a donor to an acceptor within DNA, while hopping is the transport of a charge through discrete steps along the DNA nucleotides (Berlin et al, 2001, Jortner et al, 1998, Boon and Barton, 2002, Giese and Biland, 2002, Roginskaya et al, 2004). Of these two mechanisms the charge hopping is more temperature dependent because it requires thermal energy to overcome the shallow barriers that trap charge at low temperatures (Berlin et al, 2001, Bixon and Jortner, 2001, Conwell, 2004, Cai et al, 2000).…”

A multi-scale method for the calculation of charge transfer rates through the Π-stack of DNA: application to DNA dynamics

“…Secondly, the conformation dependent charge hopping rates between successive bases are calculated using the Marcus equation. Thirdly, these individual hopping rates are combined to give an overall charge transfer rate through the dodecamer 21 using an algorithm which evolves the position of the charge stochastically as a function of time.…”