Calculation of Quantum Parameters for Nonadiabatic Redox Reactions. Application to Photoreduction of Flavin in DNA Photolyase

A simple practical way to account for the effect of quantum modes on electron transfer (ET) is to use the Jortner expression for ET rate. The expression includes two quantum parameters which describe the properties of high-frequency modes in the system. In our recent paper ( J. Chem. Phys. 2000, 112, 9015), we developed a method to calculate these parameters for redox cofactors from ab initio data on their potential energy surfaces. In this paper, we extend our method to include the solvent, which is treated as a continuous dielectric medium. As an example, two reactions describing photoreduction of the flavin cofactor in DNA photolyase (an enzyme that repairs thymine dimers in DNA) are investigated. We calculated the quantum parameters for each cofactor (flavin radical, tryptophan, tryptophan cation radical, and tyrosine), as well as for water, which was used as a model medium, and then obtained the dependence of ET rates k ET on the driving force Δ G 0 in a wide range of Δ G 0 . As expected, the quantum modes tend to flatten the log k ET vs Δ G 0 dependence in the inverted region, and the calculation provides a quantitative estimate of this effect. A similar effect has been predicted to originate from inelastic tunneling (Medvedev, E. S.; Stuchebrukhov, A. A. J. Chem. Phys. 1997, 107, 3821). This effect makes k ET relatively insensitive to Δ G 0 variations, compared with the classical Marcus theory, and might be of importance for biological ET systems to ensure their stable performance.