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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 the mutual correlation function r(τ) for TDA2 and REE or RCC.
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f6-4_19: Plot of the mutual correlation function r(τ) for TDA2 and REE or RCC.

Mentions: We calculated r(τ) using the 106 sets of data for TDA2 and RDA in the time range T=1 ns. In Figure 6, we plotted the calculated r(τ) as a function of τ by the red curve in case of RDA= REE and the green curve in case of RDA= RCC. We find that r(τ) of the red curve has a rather sharp peak while r(τ) of the green curve has broad peak. We also find that these r(τ)’s are almost symmetrical with respect to τ=0. The value of r(0) in the case RDA= REE or RDA= RCC is −0.23 or −0.15, respectively. The value of /r(0)/ represents how much synchronously the variation of TDA2 takes place with that of RDA. The maximum value of /r(0)/ is 1. The sign of r(0) is plus or minus depending on the variation of TDA2 is in phase or out of phase with that of RDA. The above value of r(0) for RDA denotes that the variations of TDA2 and RDA are out of phase with a certain amount of synchronism to one another. The smaller value of /r(0)/ for RCC denotes that the degree of synchronism is smaller than that for REE. We define the time where the value of r(τ) becomes 1/e time of r(0) as the mutual correlation time τc. We read 90 fs for the red curve and 240 fs for the green curve in Figure 6. We consider that the dynamical correlation between the fluctuations of TDA2 and RDA continues on time scale of τc. Therefore, we can say that the dynamical correlation between TDA2 and RCC is maintained for larger time than that between TDA2 and REE. In Figure 7, we plotted the traces of the data points of log10TDA2 and REE during the time τc starting from six typical times in the 1 ns simulation. We see that the traces of the data points abruptly change. We tried to fit the data points to the following linear function(5)lnTDA2=αE−βEREEThe straight lines in Figure 7 show those fitted lines. We observe that the slope βE changes abruptly form traces to traces. This fact indicates that almost no dynamical correlation exists between ln TDA2 and REE in the very short time range of tens fs. The similar result was obtained for ln TDA2 and RCC.


Correlation between square of electron tunneling matrix element and donor-acceptor distance in fluctuating protein media
Plot of the mutual correlation function r(τ) for TDA2 and REE or RCC.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5036608&req=5

f6-4_19: Plot of the mutual correlation function r(τ) for TDA2 and REE or RCC.
Mentions: We calculated r(τ) using the 106 sets of data for TDA2 and RDA in the time range T=1 ns. In Figure 6, we plotted the calculated r(τ) as a function of τ by the red curve in case of RDA= REE and the green curve in case of RDA= RCC. We find that r(τ) of the red curve has a rather sharp peak while r(τ) of the green curve has broad peak. We also find that these r(τ)’s are almost symmetrical with respect to τ=0. The value of r(0) in the case RDA= REE or RDA= RCC is −0.23 or −0.15, respectively. The value of /r(0)/ represents how much synchronously the variation of TDA2 takes place with that of RDA. The maximum value of /r(0)/ is 1. The sign of r(0) is plus or minus depending on the variation of TDA2 is in phase or out of phase with that of RDA. The above value of r(0) for RDA denotes that the variations of TDA2 and RDA are out of phase with a certain amount of synchronism to one another. The smaller value of /r(0)/ for RCC denotes that the degree of synchronism is smaller than that for REE. We define the time where the value of r(τ) becomes 1/e time of r(0) as the mutual correlation time τc. We read 90 fs for the red curve and 240 fs for the green curve in Figure 6. We consider that the dynamical correlation between the fluctuations of TDA2 and RDA continues on time scale of τc. Therefore, we can say that the dynamical correlation between TDA2 and RCC is maintained for larger time than that between TDA2 and REE. In Figure 7, we plotted the traces of the data points of log10TDA2 and REE during the time τc starting from six typical times in the 1 ns simulation. We see that the traces of the data points abruptly change. We tried to fit the data points to the following linear function(5)lnTDA2=αE−βEREEThe straight lines in Figure 7 show those fitted lines. We observe that the slope βE changes abruptly form traces to traces. This fact indicates that almost no dynamical correlation exists between ln TDA2 and REE in the very short time range of tens fs. The similar result was obtained for ln TDA2 and RCC.

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 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.