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

Correlation between fluctuations of the square of electron tunneling matrix element T(DA)(2) and the donor-acceptor distance R(DA) 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(DA); edge-to-edge distance R(EE) and center-to-center distance R(CC). The value of T(DA)(2) distributed over more than 5 orders of magnitude and the fluctuation of the value of R(DA) distributed over more than 1.8 Å for the 10(6) instantaneous conformations of 1 ns simulation. We made analysis of the time-averaged correlation step by step as follows. We divide the 10(6) simulation data into 1000/t parts of small data set to obtain the averaged data points of <T(DA)(2)>(t) and <R(EE)>(t) or <R(CC)>(t). Plotting the 1000/t sets of log(10) <T(DA)(2)>(t) as a function of <R(EE)>(t) or <R(CC)>(t), we made a principal coordinate analysis for these distributions. The slopes <β(E)>(t) and <β(C)>(t) 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 <T(DA)(2)>(t) vs <R(EE)>(t) 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 <T(DA)(2)>(t) vs <R(CC)>(t). These results indicate that only the correlation between <T(DA)(2)>(t) and <R(EE)>(t) 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”.