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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”.

No MeSH data available.


Visualization of the edge-to-edge distance (black straight line) and the center-to-center distance (black broken line) drawn on the calculated map of the mean-square tunneling currents corrected by the quantum-interference <J̃ab2> (taken from Ref. 33). Protein conformation together with that of donor and acceptor are drawn by the ball and stick model. The orange and green balls indicate the atoms constituting the conjugated part and non-conjugated part of donor and acceptor, respectively. The red pipes represent the electron tunneling pathways whose widths are proportional to the magnitude of <J̃ab2>. We observed two main tunneling routes: Trp route passing through Trp residue and Met route passing through a part of Met.
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f2-4_19: Visualization of the edge-to-edge distance (black straight line) and the center-to-center distance (black broken line) drawn on the calculated map of the mean-square tunneling currents corrected by the quantum-interference <J̃ab2> (taken from Ref. 33). Protein conformation together with that of donor and acceptor are drawn by the ball and stick model. The orange and green balls indicate the atoms constituting the conjugated part and non-conjugated part of donor and acceptor, respectively. The red pipes represent the electron tunneling pathways whose widths are proportional to the magnitude of <J̃ab2>. We observed two main tunneling routes: Trp route passing through Trp residue and Met route passing through a part of Met.

Mentions: We first define two kinds of the distance between donor and acceptor. The first is the shortest edge-to-edge distance of π-conjugated region, REE, which measures between oxygen atom bonded to C131 of BPhe and C6 of QA. This kind of edge-to-edge distance was used by the Dutton group4. The second is the center-to-center distance RCC which measures the distance between the center of the polycyclic ring of BPhe and the center of the aromatic ring of QA. This kind of distance was used by Luo et al.23. In Figure 2 we represents these two kinds of distance by the straight line (REE) and the dotted line (RCC). In the same Figure, the average tunneling routes (Trp route and Met route) which were recently obtained are drawn by the red pipes (the pipe width is proportional to the magnitude of the mean-square of the tunneling current corrected by the quantum interference effect)33. The distance REE is closely along the Trp route and roughly along the Met route.


Correlation between square of electron tunneling matrix element and donor-acceptor distance in fluctuating protein media
Visualization of the edge-to-edge distance (black straight line) and the center-to-center distance (black broken line) drawn on the calculated map of the mean-square tunneling currents corrected by the quantum-interference <J̃ab2> (taken from Ref. 33). Protein conformation together with that of donor and acceptor are drawn by the ball and stick model. The orange and green balls indicate the atoms constituting the conjugated part and non-conjugated part of donor and acceptor, respectively. The red pipes represent the electron tunneling pathways whose widths are proportional to the magnitude of <J̃ab2>. We observed two main tunneling routes: Trp route passing through Trp residue and Met route passing through a part of Met.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC5036608&req=5

f2-4_19: Visualization of the edge-to-edge distance (black straight line) and the center-to-center distance (black broken line) drawn on the calculated map of the mean-square tunneling currents corrected by the quantum-interference <J̃ab2> (taken from Ref. 33). Protein conformation together with that of donor and acceptor are drawn by the ball and stick model. The orange and green balls indicate the atoms constituting the conjugated part and non-conjugated part of donor and acceptor, respectively. The red pipes represent the electron tunneling pathways whose widths are proportional to the magnitude of <J̃ab2>. We observed two main tunneling routes: Trp route passing through Trp residue and Met route passing through a part of Met.
Mentions: We first define two kinds of the distance between donor and acceptor. The first is the shortest edge-to-edge distance of π-conjugated region, REE, which measures between oxygen atom bonded to C131 of BPhe and C6 of QA. This kind of edge-to-edge distance was used by the Dutton group4. The second is the center-to-center distance RCC which measures the distance between the center of the polycyclic ring of BPhe and the center of the aromatic ring of QA. This kind of distance was used by Luo et al.23. In Figure 2 we represents these two kinds of distance by the straight line (REE) and the dotted line (RCC). In the same Figure, the average tunneling routes (Trp route and Met route) which were recently obtained are drawn by the red pipes (the pipe width is proportional to the magnitude of the mean-square of the tunneling current corrected by the quantum interference effect)33. The distance REE is closely along the Trp route and roughly along the Met route.

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.