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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 log10 <TDA2>t as a function of <RCC>t for three kinds of t (2, 20, and 200 ps). The primary axis for the distribution of each time average is drawn. The totally averaged point is represented by the yellow star.
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f9-4_19: Plot of log10 <TDA2>t as a function of <RCC>t for three kinds of t (2, 20, and 200 ps). The primary axis for the distribution of each time average is drawn. The totally averaged point is represented by the yellow star.

Mentions: We also calculated the correlation diagram of log10 <TDA2>t and <RCC>t and plotted in Figure 9. We fit the data points to the following linear function:(7)ln<TDA2>t=<αC>t−<βC>t<RCC>tThen, we made the principal coordinate analysis for the scattered data points for each time. In Table 2 we listed the calculated values of the slope <βC>t and the ellipticity <ε>t for 8 kinds of t. We see that <βC>t is large at small value of t and it is decreased as t is increased (<βC>t = 8.944 for t=1 ps; <βC>t = 2.456 for t=333 ps). We also see that <ε>t remains almost at the level of 0.5 to 0.6 until t=333 ps. This fact indicates that the correlation between log10 <TDA2>t and <RCC>t remains weak for all the value of t until 333 ps. We have drawn the primary axes for t=2, 20, and 200 ps by the green, blue, and red lines in the Figure 9. We clearly see that the slope <βC>t decreases very much with time.


Correlation between square of electron tunneling matrix element and donor-acceptor distance in fluctuating protein media
Plot of log10 <TDA2>t as a function of <RCC>t for three kinds of t (2, 20, and 200 ps). The primary axis for the distribution of each time average is drawn. The totally averaged point is represented by the yellow star.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5036608&req=5

f9-4_19: Plot of log10 <TDA2>t as a function of <RCC>t for three kinds of t (2, 20, and 200 ps). The primary axis for the distribution of each time average is drawn. The totally averaged point is represented by the yellow star.
Mentions: We also calculated the correlation diagram of log10 <TDA2>t and <RCC>t and plotted in Figure 9. We fit the data points to the following linear function:(7)ln<TDA2>t=<αC>t−<βC>t<RCC>tThen, we made the principal coordinate analysis for the scattered data points for each time. In Table 2 we listed the calculated values of the slope <βC>t and the ellipticity <ε>t for 8 kinds of t. We see that <βC>t is large at small value of t and it is decreased as t is increased (<βC>t = 8.944 for t=1 ps; <βC>t = 2.456 for t=333 ps). We also see that <ε>t remains almost at the level of 0.5 to 0.6 until t=333 ps. This fact indicates that the correlation between log10 <TDA2>t and <RCC>t remains weak for all the value of t until 333 ps. We have drawn the primary axes for t=2, 20, and 200 ps by the green, blue, and red lines in the Figure 9. We clearly see that the slope <βC>t decreases very much with time.

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.


Related in: MedlinePlus