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. Related in: MedlinePlus |
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Mentions: Next we investigate the correlation between TDA2 and RDA by taking time average step by step. We divide the 1 ns simulation data (106 data points) into 1000/t parts of time length t to obtain the averages <TDA2>t and <REE>t or <RCC>t. When t is very large, the number of the averaged data points of <TDA2>t, <REE>t and <RCC>t is very small. In such case, we shift the starting time for dividing the 1 ns simulation data in plural ways until we can obtain more than 20 averaged data points. For example, when t=200 ps, we adopt the starting times for dividing the simulation data at 40i ps (i=0, ..., 3) to give 21 averaged data points as a total. In Figure 8, we showed the calculated diagram between log10 <TDA2>t and <REE>t for three kinds of t; 2, 20, and 200 ps represented by the symbols of green plus, blue closed square and red closed circles, respectively. We also marked the totally averaged (for 1 ns) values of log10 <TDA2>t and <REE>t by the yellow star. We see that the distribution of the averaged data points appears to converge to a straight line as t becomes large. Then, we try to fit the averaged data points to the following function:(6)ln<TDA2>t=<αE>t−<βE>t<REE>tFor this purpose, we made the principal coordinate analysis for the scattered data points. Here, we treat the coordinate log10 <TDA2>t and the coordinate <REE>t equivalently in the analysis. The primary axis corresponds to the linear function of equation (6). Then, we calculated the standard deviation <σ1>t along the primary axis, the standard deviation <σ2>t along the secondary axis, and the ratio <σ2>t/<σ1>t (≡ <ε>t) which is the ellipticity when the distribution of the averaged data points for each t is approximated as ellipsoid as a whole. In Table 1 we listed the calculated values of the slope <βE>t and the ellipticity <ε>t for 8 kinds of t. We see that <βE>t is very large at small value of t and it is decreased smoothly as t is increased (<βE>t = 8.452 for t = 1 ps; <βE>t = 1.817 for t=333 ps). We have drawn these primary axes for t=2, 20, and 200 ps by the green, blue, and red lines, respectively, in Figure 8. We clearly observe that the slope of the primary axis decreases very much with time. In Table 1, we see that <ε>t remains at a constant level of about 0.5 until about 10 ps and then it rapidly decreases down to 0.155 as t is increased from 10 ps to 333 ps. When the ellipticity is small, we can say that the correlation between log10 <TDA2>t and <REE>t is very strong. Then, we conclude that the correlation between log10 <TDA2>t and <REE>t becomes stronger and converges to a straight line more and more as t is increased. |
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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.