The transition flux formula for the coupling matrix element of long-distance electron transfer reactions is discussed. Here we present a new derivation which is based on the Golden Rule approach. The electronic Franck-Condon factor that appears in the multielectronic formulation of the coupling element is discussed using the concept of tunneling time. An application of the tunneling flux theory to electron transfer reactions in a model system based on the low-potential heme and high-potential heme (heme bL)/(heme bH) redox pair of ubiquinol:cytochrome c oxidoreductase complex is described; the results are compared to those obtained by measuring energy splitting of the donor/acceptor multielectronic states and the direct calculation method.

Recent interest in polarizable embedding methods for electronic excited states has so far been focused on optical absorption and emission spectra calculations. To explore the suitability of these methods for excited-state reactions, we constructed a simple molecular system with an electronic crossing coupled to a polarizable species: the triatomic LiFBe. We found that current polarizable QM/MM methods inadequately describe the potential energy surfaces in this system, particularly close to the electronic crossing, so we developed a new polarizable embedding method called dynamically weighted polarizable QM/MM. The new method reproduces the potential energy surfaces of LiFBe from full-system multireference configuration interaction singles and doubles calculations with near-quantitative accuracy.

Complex I (CI) is the first enzyme of the mitochondrial respiratory chain and couples the electron transfer with proton pumping. Mutations in genes encoding CI subunits can frequently cause inborn metabolic errors. We applied proteome and metabolome profiling of patient-derived cells harboring pathogenic mutations in two distinct CI genes to elucidate underlying pathomechanisms on the molecular level. Our results indicated that the electron transfer within CI was interrupted in both patients by different mechanisms. We showed that the biallelic mutations in NDUFS1 led to a decreased stability of the entire N-module of CI and disrupted the electron transfer between two iron–sulfur clusters. Strikingly interesting and in contrast to the proteome, metabolome profiling illustrated that the pattern of dysregulated metabolites was almost identical in both patients, such as the inhibitory feedback on the TCA cycle and altered glutathione levels, indicative for reactive oxygen species (ROS) stress. Our findings deciphered pathological mechanisms of CI deficiency to better understand inborn metabolic errors.

The most detailed and comprehensive to date study of electron transfer reactions in the respiratory complex III of aerobic cells, also known as bc1 complex, is reported. In the framework of the tunneling current theory, electron tunneling rates and atomistic tunneling pathways between different redox centers were investigated for all electron transfer reactions comprising different stages of the proton-motive Q-cycle. The calculations reveal that complex III is a smart nanomachine, which under certain conditions undergoes conformational changes gating electron transfer, or channeling electrons to specific pathways. One-electron tunneling approximation was adopted in the tunneling calculations, which were performed using hybrid Broken-Symmetry (BS) unrestricted DFT/ZINDO levels of theory. The tunneling orbitals were determined using an exact biorthogonalization scheme that uniquely separates pairs of tunneling orbitals with small overlaps out of the remaining Franck-Condon orbitals with significant overlap. Electron transfer rates in different redox pairs show exponential distance dependence, in agreement with the reported experimental data; some reactions involve coupled proton transfer. Proper treatment of a concerted two-electron bifurcated tunneling reaction at the Q(o) site is given.

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Respiratory complex I catalyzes two-electron/two-proton reduction of a ubiquinone (Q) substrate bound at its Q-binding pocket; upon reduction, ubiquinole carries electrons further down the electron transport chain. The mechanism of this two-electron transfer reaction is poorly understood. Here we consider a hypothetical scheme in which two electrons transfer together with two protons in a concerted fashion. On one side, a coupled electron/proton transfer occurs from the reduced N2 FeS cluster and protonated His38 residue, respectively, while on the other side a hydrogen atom transfer occurs from the neutral Tyr87 residue, generating a tyrosyl radical. A method to evaluate the coupling matrix element that corresponds to a concerted tunneling of two electrons was developed. Overall, our calculations indicate that the concerted reaction is feasible, in which case a transient tyrosyl radical is formed during the catalytic cycle of the enzyme.

Disulfide cross-linking is one of the fundamental covalent bonds that exist prevalently in many biological molecules that is involved in versatile functional activities such as antibody stability, viral assembly, and protein folding. Additionally, it is a crucial factor in various industrial applications. Therefore, a fundamental understanding of its reaction mechanism would help gain insight into its different functional activities. Computational simulation of the disulfide cross-linking reaction with hydrogen peroxide (H2O2) was performed at the integrated quantum mechanical/molecular mechanical (QM/MM) level of theory in a water box under periodic boundary conditions. A benchmarking study for the barrier height of the disulfide formation step was performed on a model system between methanethiol and methane sulfenic acid to determine, for the QM system, the best-fit density functional theory (DFT) functional/basis set combination that produces comparable results to a higher-level theory of the coupled-cluster method. Computational results show that the disulfide cross-linking reaction with H2O2 reagent can proceed through a one-step or a two-step pathway for the high pK a cysteines or two different pathways for the low pK a cysteines to ultimately produce the sulfenic acid/sulfenate intermediate complex. Subsequently, those intermediates react with another neutral/anionic cysteine residue to form the cysteine product. In addition, the solvent-assisted proton-exchange/proton-transfer effects were examined on the energetic barriers for the different transition states, and the molecular contributions of the chemically involved water molecules were studied in detail.

In different X-ray crystal structures of bc1 complex, some of the key residues of electron tunneling pathways are observed in different conformations; here we examine their relative importance in modulating electron transfer and propose their possible gating function in the Q-cycle. The study includes inter-monomeric electron transfer; here we provide atomistic details of the reaction, and discuss the possible roles of inter-monomeric electronic communication in bc(1) complex. Binding of natural ligands or inhibitors leads to local conformational changes which propagate through protein and control the conformation of key residues involved in the electron tunneling pathways. Aromatic-aromatic interactions are highly utilized in the communication network since the key residues are aromatic in nature. The calculations show that there is a substantial change of the electron transfer rates between different redox pairs depending on the different conformations acquired by the key residues of the complex.