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

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ABSTRACT

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 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 <TDA2>t and <REE>t or <RCC>t. Plotting the 1000/t sets of log10 <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>tvs <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>tvs <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”.

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Plot of <ε>tvs <βE>t or <βC>t for the various values of t. The red pluses represent the data points for the time in the range 1–10 ps, the red open circles represent the data points for the time in the range 10–100 ps and the red closed circles represent the data points for the time in the range 100–333 ps for the edge-to-edge distance. The red solid line is extrapolation to the larger time. The red square denoted by S represents the data point of <ε>S and <βE>S in the stationary state. The green symbols are the data points for the center-to-center distance. The notation is the same as that of the red symbols.
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f10-4_19: Plot of <ε>tvs <βE>t or <βC>t for the various values of t. The red pluses represent the data points for the time in the range 1–10 ps, the red open circles represent the data points for the time in the range 10–100 ps and the red closed circles represent the data points for the time in the range 100–333 ps for the edge-to-edge distance. The red solid line is extrapolation to the larger time. The red square denoted by S represents the data point of <ε>S and <βE>S in the stationary state. The green symbols are the data points for the center-to-center distance. The notation is the same as that of the red symbols.

Mentions: In order to see the time variation of <ε>t and <βE>t or <βC>t in more detail, we plotted in Figure 10 the diagram for the ellipticity <ε>t and the slope <βE>t or <βC>t using the data of 90 kinds of t for 1–10 ps, the data points of 18 kinds of t for 10–100 ps and the data points of 8 kinds of t for 100–333 ps. We find that the red line which passes the red circles sharply declines when t is larger than 10 ps and approaches the stationary state value represented by the red square. The evaluation of this point is discussed in the next section. In the case of <βC>t, <ε>t does not decrease until 333 ps.


Correlation between square of electron tunneling matrix element and donor-acceptor distance in fluctuating protein media
Plot of <ε>tvs <βE>t or <βC>t for the various values of t. The red pluses represent the data points for the time in the range 1–10 ps, the red open circles represent the data points for the time in the range 10–100 ps and the red closed circles represent the data points for the time in the range 100–333 ps for the edge-to-edge distance. The red solid line is extrapolation to the larger time. The red square denoted by S represents the data point of <ε>S and <βE>S in the stationary state. The green symbols are the data points for the center-to-center distance. The notation is the same as that of the red symbols.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5036608&req=5

f10-4_19: Plot of <ε>tvs <βE>t or <βC>t for the various values of t. The red pluses represent the data points for the time in the range 1–10 ps, the red open circles represent the data points for the time in the range 10–100 ps and the red closed circles represent the data points for the time in the range 100–333 ps for the edge-to-edge distance. The red solid line is extrapolation to the larger time. The red square denoted by S represents the data point of <ε>S and <βE>S in the stationary state. The green symbols are the data points for the center-to-center distance. The notation is the same as that of the red symbols.
Mentions: In order to see the time variation of <ε>t and <βE>t or <βC>t in more detail, we plotted in Figure 10 the diagram for the ellipticity <ε>t and the slope <βE>t or <βC>t using the data of 90 kinds of t for 1–10 ps, the data points of 18 kinds of t for 10–100 ps and the data points of 8 kinds of t for 100–333 ps. We find that the red line which passes the red circles sharply declines when t is larger than 10 ps and approaches the stationary state value represented by the red square. The evaluation of this point is discussed in the next section. In the case of <βC>t, <ε>t does not decrease until 333 ps.

View Article: PubMed Central - PubMed

ABSTRACT

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 &Aring; 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 &lt;TDA2&gt;t and &lt;REE&gt;t or &lt;RCC&gt;t. Plotting the 1000/t sets of log10 &lt;TDA2&gt;t as a function of &lt;REE&gt;t or &lt;RCC&gt;t, we made a principal coordinate analysis for these distributions. The slopes &lt;&beta;E&gt;t and &lt;&beta;C&gt;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 &lt;TDA2&gt;tvs &lt;REE&gt;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 &lt;TDA2&gt;tvs &lt;RCC&gt;t. These results indicate that only the correlation between &lt;TDA2&gt;t and &lt;REE&gt;t for large t satisfies the well-known linear relation (&ldquo;Dutton law&rdquo;), although the slope is larger than the original value 1.4 &Aring;&minus;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 &ldquo;Dutton law&rdquo;.

No MeSH data available.