Analysis of Kinetics of Electron Transfer in the Reaction Centers of Photosynthetic Bacteria Using the Rips—Jortner Model

Abstract

Electron transfer in protein structures is usually analyzed within the framework of the theory of extrasphere electron transport using nonadiabatic approximation. According to this theory, the electron transfer constant k et during rapid reorganization of the matrix ( Ӷ { λ h ν /4 π } ) may be presented as follows:(1)∆ G is the free energy of the reaction, λ is the energy of the nuclear reorganization, v is the frequency of nuclear reorganization, R is the transfer distance, m is the electron mass, and H is the height of the tunneling barrier [1,2]. According to this approximation, the kinetics of the electron transfer must be exponential and its temperature dependence is determined by the activation energy E a = .The authors of [3] studied the electron transfer in the structure of the reaction centers of the photosynthesizing bacteria Rhodopseudomonas viridis from the reduced heme of cytochrome c 380 to the P + cation-radical of a bacteriochlorophyll dimer. The cytochrome contains four hemes with reduction potentials of 380, 20, 310, and -60 mV. It was established that the kinetics of the electron transfer is not exponential, and the character of kinetic curves varies with temperature and the degree of reduction of adjacent hemes in the cytochrome. The authors of [4] explained the changes in kinetic curves by a combined action of two factors-the molecular dynamics of the protein globule and a change in the electron energy level in heme c 380 due toelectrostatic interaction of this electron with additional electrons during reduction of hemes c 310 and c 20 . It was assumed for the second (heme c 310 is also reduced) or third stage of reduction (hemes c 310 and c 20 are reduced) that ∆ G i = ∆ G 1 + δ i and H i = H 1 -δ i , where ∆ G 1 and H 1 are the free energy of the reaction and the height of the tunneling barrier, respectively, for the first stage of reduction and δ i is the energy of electrostatic interaction ( i = 2, 3). However, despite an important role of protein molecular dynamics in the reaction of electron transfer, the authors of [4] analyzed the constants observed within the framework of a nonadiabatic approximation, according to which the rate of relaxation processes in the matrix does not influence the kinetics of transfer. Using such approach and assuming that ∆ G 3 = λ , the authors of [4] found that ∆ G 1 = 0.14 eV, ∆ G 2 = 0.18 eV, ∆ G 3 = 0.29 eV, and λ = 0.29 eV. In this case, according to Eq. (1), E a is 0 for the third degree of reduction and the rate of electron transfer does not depend on temperature. However, this result contradicts the data presented in Fig. 10 from [3], according to which the initial rate of electron transfer depends on temperature for all degrees of the cytochrome reduction.In this study, we analyzed the aforementioned reactions with the use of the adiabatic Rips-Jortner approximation [5], which takes into account the dynamics using parameters τ 0 and β . These parameters are used in the Cole-Davidson model to describe the dielectric response of a medium ( 0 ≤ β ≤ 1 ...

Application of dynamic disorder approach to the temperature dependent non-exponential electron transfer kinetics inRhodopseudomonas viridis

“…The protein medium was treated as frozen (τ = ∞) on the timescale of the reaction. On the other hand, the expansion of the dynamically controlled ET regime, where both the timescales of protein relaxation and electron transfer are comparable, is confined in the range of 295-251 K. Earlier, Kotelnikov et al proposed a model of dynamic heterogeneity based on the Cole-Davidson distribution of relaxation times [36][37][38].…”