Correlation between square of electron tunneling matrix element and donor-acceptor distance in fluctuating protein...

Correlation between fluctuations of the square of electron tunneling matrix element T² and the donor-acceptor distance R in the electron transfer (ET) reaction from bacteriopheophytin anion to the primary quinone of the reaction center in the photosynthetic bacteria Rhodobacter sphaeroides is investigated by a combined study of molecular dynamics simulations of the protein conformation fluctuation and quantum chemical calculations. We adopted two kinds of R ; edge-to-edge distance R and center-to-center distance R . The value of T² distributed over more than 5 orders of magnitude and the fluctuation of the value of R distributed over more than 1.8 Å for the 10⁶ instantaneous conformations of 1 ns simulation. We made analysis of the time-averaged correlation step by step as follows. We divide the 10⁶ simulation data into 1000/t parts of small data set to obtain the averaged data points of <T²> and <R > or <R > . Plotting the 1000/t sets of log₁₀ <T²> as a function of <R > or <R > , we made a principal coordinate analysis for these distributions. The slopes <β > and <β > of the primary axis are very large at small value of t and they are decreased considerably as t becomes large. The ellipticity for the distribution of <T²> vs <R > which can be a measure for the degree of correlation became very small when t is large, while it does not hold for the distribution of <T²> vs <R > . These results indicate that only the correlation between <T²> and <R > for large t satisfies the well-known linear relation ("Dutton law"), although the slope is larger than the original value 1.4 Å^-1. Based on the present result, we examined the analysis of the dynamic disorder by means of the single-molecule spectroscopy by Xie and co-workers with use of the "Dutton law".