Hirotaka Nishioka

Average Electron Tunneling Route of the Electron Transfer in Protein Media

We present a new theoretical method to determine and visualize the average tunneling route of the electron transfer (ET) in protein media. In this, we properly took into account the fluctuation of the tunneling currents and the quantum-interference effect. The route was correlated with the electronic factor in the case of ET by the elastic tunneling mechanism. We expanded by the interatomic tunneling currents s. Incorporating the quantum-interference effect into the mean-square interatomic tunneling currents, denoted as , we could express as a sum of variant Plancks over 2pi(2). Drawing the distribution of on the protein structure, we obtain the map which visually represents which parts of bonds and spaces most significantly contribute to . We applied this method to the ET from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobacter sphaeroides. We obtained s by a combined method of molecular dynamics simulations and quantum chemical calculations. In calculating , we found that much destructive interference works among the interatomic tunneling currents even after taking the average. We drew the map by a pipe model where atoms a and b are connected by a pipe with width proportional to the magnitude of . We found that two groups of s, which are mutually coupled with high correlation in each group, have broad pipes and form the average tunneling routes, called Trp route and Met route. Each of the two average tunneling routes is composed of a few major pathways in the Pathways model which are fused at considerable part to each other. We also analyzed the average tunneling route for the ET by the inelastic tunneling mechanism.

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

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 t and t or t. Plotting the 1000/t sets of log10 t as a function of t or t, we made a principal coordinate analysis for these distributions. The slopes t and 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 t vs 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 t vs t. These results indicate that only the correlation between t and 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”.

Temperature dependence of the inelastic electron tunneling

The property of the anomalous inverted region in the energy gap law which was found in the recent non-Condon theory of the electron transfer (ET) in protein media is investigated in more detail in relation to the inelastic electron tunneling. The physical aspect of the inelastic electron tunneling is theoretically discussed and schematically explained. Since it was previously shown that the inelastic electron tunneling mechanism worked significantly due to an exponential-like decay of the autocorrelation function of the electron tunneling matrix element with a small correlation time at 300 K, we investigated whether the similar exponential-like decay of the autocorrelation function is obtained or not and how the correlation time is changed at low temperatures. For this purpose, numerical calculations for the electron tunneling matrix element in the ET at 77 K from bacteriopheophytin (Bph) anion to the primary quinone in the reaction center of photosynthetic bacteria Rhodobacter sphaeroides are made. The results are that almost exponential-like decay of the autocorrelation function was obtained even at 77 K and the half decay time was of the similar magnitude to that at 300 K. Physical meaning of this temperature dependence is discussed.