Destructive interference in the electron Tunneling through protein media

We investigated the origin of the very rapid and large fluctuation of the electron tunneling matrix element TDA due to the thermal fluctuation of protein conformation which was recently observed by the simulation study (Daizadeh, L; Medvedev, E. S.; Stuchebrukhov, A. A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 3703). We made analysis of this phenomena by using the interatomic tunneling current map of Ru-modified azurins. We defined a new index, degree of destructive interference Q, by making an average of the intermediate level for the interatomic tunneling currents. We found an empirical relation that \T-DA] is proportional to Q(-1) holds true in the course of thermal fluctuation of protein conformation. Comparing maps of the interatomic tunneling currents with different values of Q, we found that the very rapid (in much less than 1 ps) and large amount (maximally 2 orders of magnitude) of fluctuations in T-DA are caused by the reconnection and the change in the direction of interatomic tunneling currents with considerable amplitudes. By taking the statistical average for the dynamics effect of log \T-DA\, we found that the range of the averaged dynamic modification of electron transfer rate amounts to more than 2 orders of magnitude in the Ru-modified azurins. In the systems with a large range of dynamic modification, this nuclear dynamics effect contributes to enhance the thermally averaged electron transfer rate considerably.