Correlation between fluctuations of the square of electron tunneling matrix element
TDA2 and the donor-acceptor distance
RDA 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
RDA; edge-to-edge distance
REE and center-to-center distance
RCC. The value of
TDA2 distributed over more than 5 orders of magnitude and the fluctuation of the value of
RDA 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 <
TDA2>
t and <
REE>
t or <
RCC>
t. Plotting the 1000/
t sets of log
10 <
TDA2>
t as a function of <
REE>
t or <
RCC>
t, we made a principal coordinate analysis for these distributions. The slopes <
βE>
t and <
βC>
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 <
TDA2>
t vs <
REE>
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 <
TDA2>
t vs <
RCC>
t. These results indicate that only the correlation between <
TDA2>
t and <
REE>
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”.
View full abstract