Bidirectional Electron-Transfer in Polypeptides with Various Secondary Structures

The protein-mediated bidirectional electron transfer (ET) is the foundation of protein molecular wire, and plays an important role in the rapid detection of oxo-guanine-adenine DNA mismatches by MutY glycosylase. However, the influences of structural transitions on bidirectional ET are still not clear. In this work, the modified through-bond coupling (MTBC) model was further refined to correlate the structural transition and ET rate more quantitatively. With this model, various polyglycine structures (310-helix, α-helix, β-sheets, linear, polyproline helical I and II) were studied to explore the influences of structural transitions on bidirectional ET. It was found that the HOMO-LUMO gaps (ΔE) in CN (from the carboxyl to amino terminus) direction are much lower than that in opposite direction, except for polypro I. However, with the equal tunneling energy, the differences between bidirectional ET rates are slight for all structures. In structural transitions, we found that the ET rates are not only affected by the Ramachandran angles, but also correlated to the alignment of C = O vectors, the alignment of peptide planes and the rearrangement of other structure factors. The detailed information can be used to rationalize the inhomogeneous ET across different protein structures and design more efficient protein molecular wires.

The assaults of endogenous and exogenous oxidative agents often lead to the oxidation of genomic DNA, which may cause aging, cancers, and neurological syndromes such as Alzheimer's disease and amyotrophic lateral sclerosis [1][2][3][4][5][6] . A frequently observed oxidative damage is 7,8-dihydro-8-oxo-2′-deoxyguanosine (OG). It forms a stable base pair with 2′-deoxyadenosine (A), and would result in a G:C to T:A transversion mutation in replication 7 . Fortunately, the efficient repair systems for OG:A mismatch appear to be developed in organisms 8,9 . As the first and crucial step, MutY glycosylase specifically recognizes the mismatch and removes misincorporated adenine from DNA 10,11 .
As a human analog of the base excision repair (BER) enzymes, the adenine glycosylase activity and catalytic strategies of MutY have been investigated extensively [12][13][14][15][16] . Based on experimental studies, Barton et al. [15][16][17][18] proposed an important model to elucidate the rapid detection and reorganization of MutY. If there is no DNA damage between two neighboring binding sites, the binding of one enzyme will drive electron-transfer (ET) to DNA duplex by the oxidation of inner [Fe 4 -S 4 ] 2+ cluster, and then DNA-mediated charge transfer (CT) will lead to reduction and redistribution of former bound MutY. In the presence of a mismatch, the DNA CT and the protein oxidation do not occur. The more strongly binding between the DNA duplex and the MutY in reduced state increases the likelihood of the enzyme approaching and repairing the lesion. In this model, the protein-mediated ET occurs in direction CN (from the carboxyl to amino terminus) or NC when MutY binds to or dissociates from DNA duplex. It indicates that the bidirectional ET in protein would play an important role in the recognizing and repairing process.
In addition, the protein molecular wire architectures were found in Geobacter and Shewanella bacteria recently 19,20 , and have gathered widespread interest [21][22][23] . It is also based on the ability of efficient bidirectional ET in protein. However, the influences of structural transitions on bidirectional ET are not clear, and the proteins are usually treated as homogeneous tunneling barriers.
In our previous works, a polypeptide model with S −1 CH2CH2NH-head group was selected to study the bidirectional electron delocalizations and the influences of structural transitions on π*C = O energies, and a modified through-bond coupling (MTBC) model was proposed to correlate the structural detail and ET rate [24][25][26] . In this work, the MTBC model was further refined to reflect the influences of structural transitions on ET rate more quantitatively. With this model, we attempt to explore the ET differences through different areas of the same protein as well as ET difference along different directions. However, it is difficult to do high precision calculations for the large proteins. As is known to us, the biological functions of proteins mainly correlate with the special three-dimensional (3D) structures, and the 3D structures can be deconstructed into a limited number of secondary structural elements; i.e., helices, strands, and turns 27,28 . Accordingly, the study on polypeptide fragments with various secondary structures is a reasonable approximation to understand and mimic protein-related biological processes [29][30][31] . In addition, the bifunctional model proposed by Schlag et al. [32][33][34] indicated that the ET in polypeptides should be controlled by the internal rotations of Ramachandran angles. This influence was further confirmed by a recent electrochemical study 35 . The investigation on different secondary structures should be helpful to explore the influences of structural transitions on ET.
Therefore, a series of model polypeptides with different secondary structures and changing lengths were constructed to investigate the protein-mediated bidirectional ET. In order to minimize the influence of donor and accepter on fragment structures and ET properties along different directions, the α-C radicals that are commonly found in peptides and proteins were adopted as donor and accepter [36][37][38] , as been used in the previous studies [39][40][41] . By analyzing the electronic structures and ET rates, the effects of structural transitions on bidirectional ET are discussed as well.

Methods
The refined MTBC model. In proteins, the electronic interactions between donors and acceptors are usually rather weak, and the ET processes involve the electron couplings through peptide chains 42,43 . As discussed in our previous work 25 , the ET rates through different fragments of the same system should be correlated to their coupling strengths (∏ε) along tunneling pathway, and the decay factors (ε) obtained from MTBC model would be underestimated if minor contributions are neglected. In this work, all the couplings between bonding and antibonding orbitals as well as the couplings through per-bond, per second neighbor bond and per C = O Pi pathways (Fig. 1A) are treated as different contributions, and then are combined together as follows 39,44 .
In equation (1), the ε Bond,Dih or Pi represents the per-step decay factor along per-bond, per second neighbor bond or per C=O Pi pathway. F ij is the Fock matrix element between bonding (b) and antibonding (a) orbitals from Natural Bond Orbitals (NBO) 44,45 analysis. E, E a or E b represents the energy of tunneling electron, antibonding or bonding orbital respectively. As to equation (2), ε Total,Glyi is the total coupling strength through the i glycine unit. ε Bond , ε Dih or ε Pi represent the per-step decay factor along per-bond, per second neighbor bond or per C=O Pi pathway (Fig. 1A), and the coupling steps are marked with subscript 1, 2 or 3. The total coupling strength along a polypeptide chain can be given as The ω, ϕ and ψ represent the dihedrals that define the specific secondary structures, and the corresponding values were given in Table 1. Taking •CH 2 -NH(Gly) 2 CO-CH 2 • as an example, the geometries of different secondary structures were shown in Fig. 1C. All of the polypeptide structures were optimized using wB97X-D functional and 6-311+G(d) basis set 49,50 . In order to maintain the specific secondary structures, the ω, ϕ and ψ dihedrals were constrained during geometry optimizations 47,48 . Furthermore, the HCH bond angles of the neutral triplet biradical were fixed at 120°3 9-41 . The NBO analyses were carried out at wB97X-D /6-311++G(d,p) level of theory, and the polarizable continuum model (PCM) 51 with dielectric constant 4.0 was adopted to simulate the protein environment. The data for electronic structure analyses and the parameters for the refined MTBC model were extracted from NBO results directly. All the ab initio calculations were carried out using Gaussian09 software packages 52 .

Results and Discussion
Bidirectional ET rates in different secondary structures. As mentioned above, a main purpose of this work is to study the ET differences through different areas of the same protein. Since it is difficult to do high precision calculations for the large proteins, the typical secondary structures were treated as different fragments to study the ET differences approximately. The tunneling energy (E) is about −5 ~ −6 eV for typical biological donors and accepters, and can be tuned by changing the donor and acceptor structures [53][54][55] . In this work, the uniform tunneling energy −6 eV was adopted to evaluate the bidirectional coupling strengths of various polypeptide structures. In order to eliminate the influence of terminal groups, the relative decay factor through a glycine unit (ε ave,Gly ) can be obtained as 40,41 ε ε where n and n+2 represent the number of glycine units in the polypeptide models. Then, the distance-dependent parameter (β) is calculated as 56 ave Gly ave Gly , ,  where Δr ave,Gly is the average distance between carbonyl C atoms of neighboring units, defined as the effective ET distance. As shown in Table 2, the calculated β values are about 1.32 and 1.06 Å −1 for α-helix and β-strand structures, in good agreement with the experimental data (1.3 and 1.1 Å −1 ) 56 . Furthermore, the calculated β parameters of other secondary structures (about 0.80, 1.06, 1.21 and 1.32 Å −1 for linear, polypro II, polypro I and 3 10 -helix) are also distributed within the range of experimental values (about from 0.80 to 1.4 Å −1 ) 57 . The results suggest that the MTBC model refined in this work is suitable to investigate the influences of structural transitions on protein-mediated ET.
In addition, the average per-unit decay factors (ε ave,Gly ) are reported in Table 3. The minor differences between bidirectional coupling strengths ascertains the shuttle function of protein molecular wire, and guarantees the rapid dissociation and redistribution of MutY in efficient DNA damage detection.

The influences of structural transitions on protein-mediated ET.
To explore the influences of structural transitions, the average per-bond decay factors were calculated for the three types of pathways (ε perBond,Bond , ε perBond,Dih , ε perBond,Pi ). As reported in Table 4, the contributions of per-bond pathway (ε perBond,Bond ) are similar (0.32 ± 0.02) in all structures, and the differences in coupling strength across different structures should be mainly resulted from the per second neighbor bond and per C=O Pi contributions.
As to the per second neighbor bond pathway, the coupling strength is correlated to the rotations of dihedral angles. Take n-hexane as an ideal example ( Fig. 2A), the effect of rotation around C 3 -C 4 bond on C 2 -C 3 /C 4 -C 5 coupling was investigated by constrained optimizations and the refined MTBC model. As shown in Fig. 2B, the ε perBond,Dih values of E at −6 eV decrease when ψ C2C3C4C5 rotates from 0° to 85° (at an interval of 5°), and then increase a little faster when ψ C2C3C4C5 rotates from 85° to 180°. Accordingly, the ε perBond,Dih values of various polypeptide structures would increase in the order of α-helix < polypro I < 3 10 -helix,polypro II < β-strand < linear (Table 4). In addition, it was found that the energies of antibonding and bonding orbitals change less than ±2‰ in rotation, and the difference in coupling strength should be mainly attributed to the change of |F ij |.
As to per C=O Pi pathway, we found that the coupling strength is not only correlated to the alignment of C=O vectors, but also affected by the alignment of peptide planes and the rearrangement of polypeptide structures. Taking two optimized formaldehyde molecules as an ideal model , 6 parameters (d, θ, τ1, τ2, ζ1 and ζ2, Fig. 3A) were used to describe the alignment of C=O vectors and peptide planes approximatively, where d represents the distance between the midpoints (M1 and M2) of neighboring C=O bonds, θ is the angle between C1=O1 and M1-M2, τ1 indicates the C2=O2 rotation around M2 inner C1-O1-M2 plane, τ2 represents the C2=O2   Taking ε perBond,Pi along CN direction as an example, the changing curves were shown in Fig. 3B to Fig. 3F, and the corresponding sites of different secondary structures were marked. It was found that the ε perBond,Pi values decrease with the increasing distance d (Fig. 3B). As to θ, the highest sites appear around 0°, 45°, 135° and 180°, while the lowest sites appear around 15° and 165° (Fig. 3B).  (Fig. 3C). As to τ2 (Fig. 3D), the ε perBond,Pi values decrease with the deviation of C2=O2 from C1-O1-M2 plane for β-strand (τ1 = 164°), linear (τ1 = −165°), polypro I (τ1 = −52°) and polypro II (τ1 = −150°). For 310-helix (τ1 = −40°), α-helix (τ1 = −13°), the decay factors decrease first and then increase with the deviation of C2=O2 from C1-O1-M2 plane. As to ζ1 and ζ2, since the initial structures vary considerably, the curve shapes are different. Taking α-helix (τ1 = −13°, τ2 = 8°) and β-strand (τ1 = 164°, τ2 = 4°) model as an example, in which the two H-C-O planes are almost parallel packing, the decay factors would decrease with  Table 4. Decomposition of the per-bond decay factors (ε perBond ). the deviation from parallel packing (Fig. 3E,F). In addition, we noticed that there are some sharp discontinuities on the τ1 scanning curves. Taking 310-helix (blue line in Fig. 3C) and β-strand (pink line in Fig. 3C) Table 5. It was found that the energies of antibonding and bonding orbitals change slightly (less than ±7%), and the significant difference in coupling strength (about ±13% ~ ±54%) should be mainly attributed to the change of |F ij |. Furthermore, it was found that the ε perBond,Pi values of formaldehyde models truncated from polypeptide chains are different from the values of whole chain models (Table 6). Thus, the rearrangement of other structure factors maybe also affect the ε perBond,Pi values, and the ratio (polypeptide model/ truncated formaldehyde model) is 0.79, 0.96, 0.79, 1.14, 1.09 or 0.99 for 310-helix, α-helix, β-strand, linear, polypro I or polypro II structure respectively. Integrating all factors, the ε perBond,Pi values decrease in the order of polypro II> α-helix> polypro I, linear, 3 10 -helix, β-strand.
In addition, it is necessary to point out that the refined MTBC model is based on the hypothesis that the polypeptide structures do not change in ET process. For ET systems with obvious structure fluctuation, the model should be used with enough sampling structures, and the accuracy remains to be tested. As reported above, the data from MTBC model are sensitive to many structural parameters, the results here from average structures may be changed in these systems.
Bidirectional HOMO-LUMO gaps in various polypeptide structures. In this work, the neutral methylene radicals were used as donors and accepters. It allows us to analyze the bidirectional gaps (ΔE) between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) of the same polypeptide chain, and the differences should be only attributed to the structural transitions. In Fig. 4, the bidirectional HOMO-LUMO gaps of different secondary structures were plotted with the number of glycine units  Table 5. The Fock matrix elements and the orbital energies (eV) for the discontinuity points in τ1 scan of 3 10helix and β-strand model (Fig. 3C).   (n). For the 3 10 58 , 62.5% of the total residues form 15 α-helices. As a result of much lower ΔE in CN direction, the binding between protein and DNA would take place easier, and the dissociation process should be activated by another redox enzyme. It confirms the rationality of the repair mechanism proposed by Barton et al.

Conclusions
In the present work, the MTBC model was further refined to reflect the influences of structural transitions on ET rate more quantitatively. With this model, various polyglycine structures, which are terminated by neutral methylene radicals, were selected to investigate the protein-mediated bidirectional ET. According to the electronic structure analyses, the secondary structures can be divided into two types; i.e., A with positive dipoles in CN direction (α-helix, 3 10 -helix and polypro II) and B with negative dipoles in the same direction (β-strand, linear and polypro I). For type A, the HOMO-LUMO gaps (ΔE) in CN direction decrease with the increasing glycine units, and the decreasing ranges decrease in the same order of positive dipoles (α-helix> 3 10 -helix> polypro II). As to type B, similar trend occurs but in the opposite direction NC. As to the bidirectional ET, the HOMO-LUMO gaps in CN direction are obviously lower than that in opposite direction, except for polypro I. Thus, the ET would take place easier in CN direction. However, as to the ET with the same tunneling energy, the differences between bidirectional coupling strengths are slight for all structures. It provides the theoretical support for the shuttle function of protein molecular wire and the rapid dissociation and redistribution model of MutY in efficient DNA damage detection. Furthermore, with the refined MTBC model, the influences of structural transitions on ET rate were also investigated. It was found that the coupling strengths are not only affected by the Ramachandran angles, but also correlated to the alignment of C=O vectors, the alignment of peptide planes and the rearrangement of other structure factors. The results here would provide a theoretical evidence for the coupled dynamics of proteins, and can be used to rationalize the differences of ET across different protein structures and design more efficient protein molecular wires.