The Modified Through-Bond Coupling Model And Its Application In Electron Transfer Of Protein

The electron transfer (ET) is a fundamental issue in current biology. It has significant implications in photosynthesis, respiration, metabolism, redox enzyme catalysis, signal transduction and etc. The ET investigations of these processes will promote the development of biology, medicine and other correlative knowledge.In biomolecules, the distances between donors and acceptors are usually large. The long-range electron transfer (ET) is mediated by the bridge which connects the weakly coupled donor and acceptor. In ET theory, these reactions are ascribed to nonadiabatic ET. According to the quantum model and Marcus'semi-classical model, the ET rate will be approximately proportional to the square of total coupling matrix element between the donor and acceptor. Thus, the computation of the coupling matrix element is crucial to the investigation of ET rate. At present, there are 4 methods to calculate the electron coupling matrix element; i.e., two states variation method, the method using Koopmans'theory, partition technological method and Gneralized Mulliken-Hush (GMH) method. However, all of these 4 methods can not reflect the relationship between structural detail and electron transfer rate. Recently, more and more studies have revealed that the ET in biomolecule is greatly influenced by the conformational details.In this work, we proposed a theoretical model to investigate the relationship between structural details and electron transfer rates at ab initio level, and then applied it to the ET of protein. The decisive factors of ET rates in structural transitions were explored, which will help to design functional proteins.I. The modified through-bond coupling (MTBC) modelOn the basis of Beratan, Miller and Jordan's studies, we proposed a modified through-bond coupling (MTBC) model to correlate the structural factors and ET rates, in which the coupling elements are derived directly from ab initio calculations.According to the quantum model, the rate of nonadiabatic ET is given as where TDA and FC are the electron-tunneling matrix element and Franck-Condon factor, respectively. By defining an ET pathway as a collection of interacting bonds that make contributions to the donor-acceptor interaction, Beratan et al. developed a classical per-bond pathway model using a basis of atoms. For a single physical pathway, the electron-tunneling matrix element (tDA) is written as whereεi represents the decay factor per step along the ET pathway. The prefactor P is dependent on the interactions between the electron donor (acceptor) with the first (last) atom of the bridge. By neglecting the interactions between different pathways, the total coupling element is the algebraic sum over all the pathwaysThus, the coupling element is the product of per-step decay factors (εi). Since the values ofεi are sensitive to the chemical environments, the classical pathway model correlated the molecular structures and the ET rates. However, the use of atom basis overestimates theεi values, and neglects the influences of dihedrals. In fact, theεi values were orbtained by semi-empirical parameters instead of ab initio calculation in Beratan's studies, and as a natural result their values will be seriously influenced by the selection of semi-empirical parameters. Furthermore, only the contribution of bond length was considered in the semi-empirical method. In the latter developed through-bond coupling (TBC) model, the Fock matrix elements derived from the natural bond orbitals were used to calculate theεi values, which resolves the problems of atom basis. However, the TBC model only considered the anti-bonding contributions in ET.By integrating the merits of the previous models, a modified through-bond coupling (MTBC) model was proposed to investigate the influences of structural factors on ET rates. In the MTBC model, the Fock matrix elements derived from the natural bond orbitals were used to calculate the values ofεi, and the decay factor per step is the summation of bonding and anti-bonding interactions. Since theεi, values are derived directly from ab initio calculations, the results are sensitive to chemical environments and can correctly reflect structural changes. In addition, with the NBO technique, the Ab initio wave functions are mainly characterized by terms of localized bonding orbitals, antibonding orbital s and lone pairs, which correspond closely to the pictures of molecular structures. Therefore, the dominant pathways may reflect the ET processes in biomolecules. It is reasonable to assume that the ET rate is mainly influenced by the dominant pathway. For the same biomolecule with different structures, the analyses of decay factors along dominant pathways are expected to reveal the relationships between structural transitions and ET rates.In general, the effective ET pathways in proteins are composed of covalent bonds and hydrogen bonds. In the MTBC model, theεi between two covalent bonds is given asFor the ET through hydrogen bonds, the lone pairs may be closely involved in the electron couplings. When the coupling occurs from covalent bond to the lone pair, the decay factor can be written asFor the coupling from lone pair to covalent bond, the decay factor isFour hydrocarbon di-radicals with the experimental data available were selected to test the MTBC model simply. It was found that the MTBC model shows obvious improvement and thus better agreement with the experimental results when compared with the previous models. It urges us to study the electron transfers (ET) in biological systems with the MTBC model. Ⅱ. The investigations of ET in proteinIn this paper, we have investigated the ET process in an enzyme named MutY which specifically recognizes 7,8-dihydro-8-oxo-2'-deoxyguanosine:2'-deoxyadenosi-ne (OG:A) mismatches in DNA. With the exception of RNA viruses, all the organisms store their permanent information in DNA, and their gene codes are generally represented with the sequence of nucleotides. Accordingly, the intact and stable sequence of DNA is a prerequisite to reserve the life characteristics of filial generations. However, under the complicated cellular environment, many physical or chemical factors such as alkylating and oxidative agents, exposure to radiation, spontaneous hydrolysis, and errors during DNA replication can cause damages to the DNA structures or alterations of the DNA sequences. The changes may increase genetic diversities, but more often leads to unwanted mutations and even diseases. Accordingly, the efficient DNA repair systems have to be developed in organisms. Base excision repair (BER) is one of the most common repair pathways. The BER enzymes are closely involved in the removal of damaged bases, the first and crucial step of the BER processes. Among the BER class of enzymes, MutY is the unique one in that it catalyzes N-glycosidic bond hydrolysis to excise a normal base (A) paired with a damaged base (OG). As a human analog of the BER enzymes, the adenine glycosylase activity and catalytic strategies of MutY have been studied extensively. The experimental results indicated that the [Fe4S4]2+ cluster in MutY plays a crucial role for the adenine glycosylase activity and the binding affinity with substrates, although it does not participate in the protein folding or cause large structural alterations. Based on experimental studies, Barton et al. proposed a model to elucidate the rapid detection and reorganization of MutY during the DNA damage processes. When the binding between MutY and DNA occurs, the oxidation of [Fe4-S4]2+ drives CT to DNA duplex. Then the DNA-mediated CT among oxidized proteins lead to reduction of MutY, which facilitate the dissociation of MutY from DNA and redistribution of MutY along DNA duplex. Since the DNA-mediated charge-transfer can not proceed through the DNA damage, MutY recognizes the mismatch quickly and efficiently. In this model, the [Fe4S4]2+/3+ donates electrons when MutY binds to DNA, and accepts electrons when the protein dissociates from the DNA duplex. That is, the ET process will occur via two opposite directions in the same polypeptide chain. We believe that the investigation of the ET process along the polypeptide chain, which connects the [Fe4-S4] cluster and DNA duplex, is helpful for understanding the repair mechanism, and then provides theoretical aid for the designing of enzyme drug. The main studies in this paper are summaried as follows:1. The electronic structure of the polypeptide chain from MutY is investigated at ab initio level. At present, it is impossible to do first-principle calculation for so large biomolecule. Because of the crucial role of the [Fe4-S4]2+/3+ cluster described above, a short polypeptide chain is truncated from the terminus connecting with [Fe4-S4]2+/3+ cluster to construct the computational model. The Natural Bond Orbitals (NBO) technique is employed to analyze the electron delocalizations, the distribution of NBO charges and the energies of frontier orbitals along model polypeptides. The results indicated that:(1) The electron delocalization in polypeptides can occur in two opposite directions, direction A is from the carboxyl end to amino end, and direction B is from the amino end to carboxyl end. The delocalization in the direction from carboxyl end to amino end (direction A) is the dominant one. The intramolecular O…H-N type hydrogen bonds play an important role in the electron-transfer process. Although the delocalization direction in O…H-N bond is from amino end to carboxyl end (direction B), it is more helpful to promote the delocalization of electron in opposite direction. The occupation numbers of NBOs and the distribution of NBO charges confirm this conclusion.(2) The energies of lowest unoccupied NBO in each glucine (Gly) unit decrease from carboxyl end to amino end. And, the energies of lowest occupied NBO are much lower when the intramolecular O…H-N hydrogen bond is formed. As a reasonable approximation, the negative charge will transfer through the lowest unoccupied molecular orbital (LUMO) of the peptide subgroups. Furthermore, the ET occurs in direction A (B) when MutY binds to (dissociates from) DNA duplex. According to the present result, the binding between protein and DNA would take place easily, and the dissociation process should be activated by another repair protein bound at a certain distance. It confirms the rationality of the repair mechanism proposed by Barton et al. 2. With the MTBC model, the coupling elements along the polypeptide chain from MutY were investigated. By analyzing the coupling elements along the dominant pathway, we investigate the relationship between several structural factors and ET rates. The results indicared that:(1) The coupling elements are greatly influenced by the structural details. It was found that the decay factor per glycine unit increases with the decrease of the neighboring carbonyl O-O distance. The trans-isomers have the strongest through-bond couplings, and the deviations will lead to weak couplings and smaller decay factors.(2) As to the ET in direction A, the decay factor per-unit increases from the carboxyl end to the amino end. For the ET in direction B, the decay factor per-unit decreases from the amino end to the carboxyl end. Thus, the ET in direction A should take place easier than direction B. It is consistent well with the results of electronic structure.(3) For the amino acid residues in peptides and proteins which are not close in sequence, the electron couplings through direct bonds may undergo numerous bonds whereas through hydrogen bonds will save many steps. Although the decay factors through hydrogen bonds are calculated to be approximates one-third of that through the covalent bonds, the ET through hydrogen bond save 12 coupling steps, causing the coupling element 1012 larger than that through covalent bonds. It is in good agreement with the analyses of electronic structures.3. In order to study the influence of structural transitions on electronic structures, four types of secondary structures (310-helix,α-helix, antiparallelβ-sheet and linear) are constructed on the basis of the previous computational model. The electron delocalizations, the distribution of NBO charges and the energies of frontier orbitals of each secondary structure are analized by the Natural Bond Orbitals (NBO) technique. Furthermore, the complicated three-dimensional (3D) structures of proteins can be deconstructed into a limited number of secondary structures. The investigations on polypeptides with different secondary structures are expected to be helpful for understanding the protein-mediated ET processes. It was found that:(1) For all polypeptide structures, the delocalization interactions mainly occur in direction A (from cthe carboxyl end to the amino end). As to the 310-helix andα-helix structures, although the delocalizations though hydrogen bonds are in direction B (from the amino end to the carboxyl end), the formations of them promote the delocalization interactions in direction A obviously. However, the strengths of delocalizations in 310-helix and a-helix polypeptides are still lower than that in liner structures.(2) For all polypeptide structures here, the LUMO energies decrease from carboxyl end to amino end obviously. As to the polypeptide-mediated ET in direction A, the superexchange mechanism would be adopted. In direction B, the thermally activated hopping mechanism should be adopted. Correlated to the repair mechanism of MutY, it confirms that the dissociation of a bound enzyme is facilitated when another repair protein binds to neighboring site.(3) The distributions of NBO charges indicate that the ET in linear and antiparallelβ-sheet polypeptides should be more effective than that in 310-helix and a-helix structures without hydrogen bond. The analyses of LUMO energies in glycine subgroups reveal the similar result. When the number of glycine units increases up to three, with the formations of hydrogen bonds, the ET in 310-helix and a-helix will be superior to that in linear and antiparallelβ-sheet.4. The electron transfers (ET) of polypeptides with six different secondary structures (310-helix, a-helix, P-sheets, linear, polyproline helical I and II) were investigated with the MTBC model to ascertain the the influencing factors to the ET rates in structural transitions. It was found that:(1) As to the ET through covalent pathways, the coupling elements increase in the order of polypro I< polyproⅡ≈α-helix<310-helix<β-strand< linear. The structural transitions of polypeptides cause the changes of the ET rates, which can be accurately characterized by the MTBC model. Previously, the similar sequence was given for a-helix,310-helix,β-strand and linear structures by analyzing the electronic structures.(2) The above order and differences of ET rates in various secondary structures can be elucidated by the dihedrals and molecular dipoles. Firstly, the backbone cis-isomers in 310-helix, a-helix, polypro I and polypro II rather than inβ-strand and linear increase the coupling steps and generally decrease the ET rates. Secondly, the decay factors through covalent bonds are influenced by the dihedrals, and the deviations from trans-isomers weaken the through-bond interactions. Accordingly, the short-range ET rates increase in the order ofα-helix< 310-helix<β-strand< linear. Thirdly, the lower ET rates of polypro I and polypro II thanα-helix and 310-helix are correlated with the lower molecular dipoles. In addition, it is found that the influences of molecular dipoles are finely reflected by the alignments of carbonyl groups.(3) As to theα-helix polypeptide, the long-range ET is mainly mediated by the hydrogen bond network, and thus leads to much higher ET rates than linear andβ-strand structures, consistent well with the analyses of electronic structures. The decay factors through hydrogen bonds (εH) are found to be affected by the electrostatic fields generated from the molecular dipoles. TheεH values along the hydrogen bond network increase from the carboxyl terminus to the amino terminus until the 6th hydrogen bond (εH6), and then begin to drop down, which is probably due to the longer ET distances and the constant electrostatic fields since the 14th unit.In summary, ET in polypeptide chain can occur at two opposite directions, and the electron transfer in the direction from carboxyl end to amino end should be easier than opposite one; the influences of structural transitions on ET rates can be characterized by the rotations of dihedrals, the alignments of carbonyl groups and the formations of intra-molecular hydrogen bonds. In detail, the deviations from trans-isomers weaken the through-bond interactions; the electrostatic fields generated from the alignments of carbonyl groups will greatly influence the ET rates; the formations of intra-molecular hydrogen bonds remarkably decrease the effective ET distances and coupling-step numbers, and thus promote the ET processes obviously.