FapydG in the Shadow of OXOdG—A Theoretical Study of Clustered DNA Lesions

Genetic information, irrespective of cell type (normal or cancerous), is exposed to a range of harmful factors, which can lead to more than 80 different types of DNA damage. Of these, oxoG and FapyG have been identified as the most abundant in normoxic and hypoxic conditions, respectively. This article considers d[AFapyGAOXOGA]*[TCTCT] (oligo-FapyG) with clustered DNA lesions (CDLs) containing both the above types of damage at the M06-2x/6-31++G** level of theory in the condensed phase. Furthermore, the electronic properties of oligo-FapyG were analysed in both equilibrated and non-equilibrated solvation–solute interaction modes. The vertical/adiabatic ionization potential (VIP, AIP) and electron affinity (VEA, AEA) of the investigated ds-oligo were found as follows in [eV]: 5.87/5.39 and −1.41/−2.09, respectively. The optimization of the four ds-DNA spatial geometries revealed that the transFapydG was energetically privileged. Additionally, CDLs were found to have little influence on the ds-oligo structure. Furthermore, for the FapyGC base-pair isolated from the discussed ds-oligo, the ionization potential and electron affinity values were higher than those assigned to OXOGC. Finally, a comparison of the influence of FapyGC and OXOGC on charge transfer revealed that, in contrast to the OXOGC base-pair, which, as expected, acted as a radical cation/anion sink in the oligo-FapyG structure, FapyGC did not significantly affect charge transfer (electron–hole and excess–electron). The results presented below indicate that 7,8-dihydro-8-oxo-2′-deoxyguanosine plays a significant role in charge transfer through ds-DNA containing CDL and indirectly has an influence on the DNA lesion recognition and repair process. In contrast, the electronic properties obtained for 2,6-diamino-4-hydroxy-5-foramido-2′deoxypyrimidine were found to be too weak to compete with OXOG to influence charge transfer through the discussed ds-DNA containing CDL. Because increases in multi-damage site formation are observed during radio- or chemotherapy, understanding their role in the above processes can be crucial for the efficiency and safety of medical cancer treatment.


Introduction
Genetic information in the sequence of nucleobases of DNA is continuously exposed to harmful extra-and intra-cellular factors, both chemical and physical. These factors can lead to the formation of various types of DNA damage. To date, more than 80 different kinds of DNA lesions have been identified, including base-free sites, DNA-DNA or protein-DNA cross-links, tandem or clustered types, and sugar or base modifications [1]. From the perspective of future generations, it is highly desirable to preserve genetic information in its unchanged state. To this end, during evolution, prokaryotic and eukaryotic cells have developed DNA damage response (DDR) systems. The most common are base and nucleotide excision repair (BER, NER), mismatch repair, homologous recombination, and non-homologous end joining, all of which remove lesions in a substrate-dependent manner [2]. Disruption of these processes can lead to mutations which cause cancer and accelerate the aging process. Of all the nucleosides, 2 -deoxyguaosine is especially sensitive to Int. J. Mol. Sci. 2023, 24, 5361 2 of 14 harmful effects because of its particularly low oxidation potential (E O dG/dG• = 1.29 V) [3,4]. The lesion derived from guanosine has been identified as the most common. Its distribution depends on the endocellular environment (hypoxic or normoxic), the presence of a 2-deoxyribose substituent, and the ways in which hydroxyl radicals (•OH) are generated.
It should be noted that the cancer cells in close proximity to blood vases were welloxygenated and that, as the distance increases, the condition of the microenvironment becomes hypoxic. The above oxygen gradient causes plasticity in the tumour cells and therefore increases their aggressive and metastatic phenotype. Additionally, an increase in the hypoxia-incubator factor can create an acidic environment, which results in tumour drug resistance, apoptosis/autophagy, various DNA damage, etc. For details, please refer to Shu and Simon's recent and valuable work [5,6]. Moreover, dG can be also oxidized by other reactive oxygen and nitrogen species, free electrons, radiation, CO 3 •− , etc. [7][8][9][10]. The 7,8-dihydro-8-oxo-2 -deoxyguanosine ( OXO dG) has been identified as one of the most frequent dG lesions and is keenly studied because of its relative ease of measurement, chemical synthesis, and the different methods of its introduction into the oligonucleotide structure. The second most common dG lesion is 2,6-diamino-4-hydroxy-5-foramido-2 deoxypyrimidine ( Fapy dG) [11]. In contrast to OXO dG, which is the predominant lesion formed in the presence of oxygen, Fapy dG is known to be the main lesion formed in hypoxic conditions [12]. However, in both cases, the shared intermediate 2-amino-8-hydroxy-1,7,9-thihydropurine-6-one (8-OHdG rad ), which is formed in the presence of •OH, has been noted. Depending on the condition of the medium, 8-OHdG rad can be converted into OXO dG by one-electron oxidation or Fapy dG by one-electron reduction, as shown in Figure 1. The above is justified by the high reaction constant of 8-OHdG rad with oxygen, i.e., k = 2 × 10 9 m −1 s −1 , while the constant of the imidazole ring-opening process has been found to be four magnitudes lower (k = 2 × 10 5 m −1 s −1 ) [13]. mutations which cause cancer and accelerate the aging process. Of all the nucleosides, 2′deoxyguaosine is especially sensitive to harmful effects because of its particularly low oxidation potential (E O dG/dG•= 1.29 V) [3,4]. The lesion derived from guanosine has been identified as the most common. Its distribution depends on the endocellular environment (hypoxic or normoxic), the presence of a 2-deoxyribose substituent, and the ways in which hydroxyl radicals (•OH) are generated.
It should be noted that the cancer cells in close proximity to blood vases were welloxygenated and that, as the distance increases, the condition of the microenvironment becomes hypoxic. The above oxygen gradient causes plasticity in the tumour cells and therefore increases their aggressive and metastatic phenotype. Additionally, an increase in the hypoxia-incubator factor can create an acidic environment, which results in tumour drug resistance, apoptosis/autophagy, various DNA damage, etc. For details, please refer to Shu and Simon's recent and valuable work [5,6]. Moreover, dG can be also oxidized by other reactive oxygen and nitrogen species, free electrons, radiation, CO3 •̶ , etc. [7][8][9][10]. The 7,8-dihydro-8-oxo-2′-deoxyguanosine ( OXO dG) has been identified as one of the most frequent dG lesions and is keenly studied because of its relative ease of measurement, chemical synthesis, and the different methods of its introduction into the oligonucleotide structure. The second most common dG lesion is 2,6-diamino-4-hydroxy-5-foramido-2′deoxypyrimidine ( Fapy dG) [11]. In contrast to OXO dG, which is the predominant lesion formed in the presence of oxygen, Fapy dG is known to be the main lesion formed in hypoxic conditions [12]. However, in both cases, the shared intermediate 2-amino-8-hydroxy-1,7,9thihydropurine-6-one (8-OHdG rad ), which is formed in the presence of •OH, has been noted. Depending on the condition of the medium, 8-OHdG rad can be converted into OXO dG by one-electron oxidation or Fapy dG by one-electron reduction, as shown in Figure  1. The above is justified by the high reaction constant of 8-OHdG rad with oxygen, i.e., k = 2 × 10 9 m −1 s −1 , while the constant of the imidazole ring-opening process has been found to be four magnitudes lower (k = 2 × 10 5 m −1 s −1 ) [13].  [14]. In the same studies, OXO dG was found to be between 0.07 and 0.15, depending on the cell lines. Arczewska et al. noted the frequency of Fapy G in Caenorhabditis elegans (the medical and toxicological model organism) genome as 7.79 ± 0.47/10 6 DNA bases, while, in the case of OXO G, using the phenol extraction protocol for isolating genetic material, the frequency was 20.66 per 10 6 [15]. Recently, Dizdaroglu et al. noted the OXO G and Fapy G levels as 14.62 ± 1.45 and 8.08 ± 0.9 per 10 6 DNA bases, respectively, using the high-salt DNA extraction method [11]. As discussed above, DNA damage frequency depends on several factors, such as the detection method, cell line, and isolation protocol; however, there is no doubt that the levels of Fapy G and OXO G have always been at a similar level. Because of the  [14]. In the same studies, OXO dG was found to be between 0.07 and 0.15, depending on the cell lines. Arczewska et al. noted the frequency of Fapy G in Caenorhabditis elegans (the medical and toxicological model organism) genome as 7.79 ± 0.47/10 6 DNA bases, while, in the case of OXO G, using the phenol extraction protocol for isolating genetic material, the frequency was 20.66 per 10 6 [15]. Recently, Dizdaroglu et al. noted the OXO G and Fapy G levels as 14.62 ± 1.45 and 8.08 ± 0.9 per 10 6 DNA bases, respectively, using the high-salt DNA extraction method [11]. As discussed above, DNA damage frequency depends on several factors, such as the detection method, cell line, and isolation protocol; however, there is no doubt that the levels of Fapy G and OXO G have always been at a similar level. Because of the difficulty of chemically synthesizing Fapy dG into DNA, the biochemical and biological roles of this lesion are limited. However, research has indicated that the methylated form of Fapy G ( ME-Fapy G) almost completely inhibits DNA strand elongation, which suggests that it is more likely to be a lethal lesion than a mutagenic one [16]. The transversion potential G→C or G→T was noted as very low, as the polymerase inserts cytosine opposite ME-Fapy G [17]. However, when Fapy G was synthesized and introduced into the specified/required place of an oligonucleotide, its mutagenic potential was confirmed [18,19]. As in the case of OXO G, Fapy G can form a base pair (BP) with adenine; furthermore, base misincorporation was observed to occur at the same level as for oxidized guanine [20]. Therefore, the presence of 2,6-diamino-4-hydroxy-5-foramido-2 deoxypyrimidine in the genome can lead to a mutation if it is not correctly repaired. Research has shown that Fapy G is effectively removed from double-stranded (ds) DNA via formamidopyrimidine-DNA glycosylase (Fpg), which initiates the cascade of BER proteins [21]. This bifunctional glycosylase cut off Fapy G more effectively when it formed a canonical base-pair with cytosine instead of adenine. Other enzymes involved in base excision repair machinery can also cleave the modification under discussion. OGG1 is active towards both Fapy dG and OXO dG (but not Fapy dA). In contrast to the above, Nei-like protein 1 (NEIL1) glycosylase removes Fapy G but is inactive towards OXO G [22]. Consequently, the loss of the above proteins' activity could be the source of GC→TA transversion. To avoid such a mutation, during evolution, organisms have developed adenosine DNA glycosylase (MutY), which removes adenine from its pair with dG, OXO dG, or Fapy dG [23]. Even though it is not abundant, MytY [24] can scan the Escherichia coli genome in less than 10 min, which would almost be impossible to achieve with the application of the classical conformation of the DNA-protein switching mechanism [25]. As an alternative to the above mechanism, DNA damage site detection through electron transfer between two proteins containing [4Fe-4S] clusters was proposed by Barton et al. [26]. Lin et al. Postulated that OXO GA can accept the ejected electron and trigger MutY into action [25]. Even though this process has been investigated in the context of an OXO GA base pair, the influence of Fapy G on charge transfer through the double helix and its direct comparison with 7,8-dihydro-8-oxo-2 -deoxyguanosine remains unclear. With the above in mind, this article presents, for the first time, a theoretical investigation into the influence of Fapy dG and OXO dG as part of a clustered DNA lesion (CDL) on the excess-electron and electron-hole migration process through double-stranded DNA. In addition, because all the biological processes take place in an aqueous environment, both non-equilibrated and equilibrated solvent models were taken into theoretical consideration.

Results
In this study, the short ds-oligonucleotide containing Fapy G and OXO G was taken into consideration, i.e., d[A 1 F G 2 A 3 O G 4 A 5 ]*[T 1 C 2 T 3 C 4 T 5 ] (Figure 2), referred to throughout as oligo-Fapy G. As mentioned in the introduction, both lesions are formed via an 8-OH-dG radical intermediate initiated by •OH activity [27]. Furthermore, because the imidazole ring is open, Fapy G is, in fact, the pyrimidine that bonds to the 2-deoxyribose ring via the N9 atom ( Figure 3). This indicates that the Fapy dG structure has a high level of conformational flexibility. Even though N9 lost its tertiary and aromatic character, Fapy dG was adopted in a ds-DNA anti-conformation instead of syn [18]. Additionally, as shown in Figure 3, four rotameric forms can be selected depending on rotation around the N7-C8 and C5-N7 linkages. For the energy calculation study, the base-pair's geometries, formed by Fapy dG and dC, were isolated from the four optimized ds-pentamers containing the different rotameric forms of Fapy G ( Figure 3). All the ds-DNA spatial structures were fully optimized using Our Own N-layered Integrated Molecular Orbital and Molecular Mechanics (ONIOMs) method in the aqueous phase (please see the Materials and Method section). The comparison of calculated isolated base pair energies (M06-2x/6-31++G** in condensed phase) reveals the following order of stability: trans-2 (−1855.373892), cis-1 (−1855.373868), cis-2 (−1855.371179), trans-1 (−1855.367282), with all energies given in Hartree.

Electronic Properties and Geometry of oligo-Fapy G
The stability of a double helix mainly depends on the following energies: the hydrogen bond (HB) energy between base pairs, staking interaction (ST) energy, and solvation shell-solute interaction energy [28]. In the latter case, which was tangentially covered in PCM, EHB and EST could be related to the HB length and the distance between the two neighbouring BPs (rise parameter), which were calculated in this study according optimized spatial geometry at the M06-2x/D95** level of theory in the aqueous phase using the PCM solvation model.

Electronic Properties and Geometry of oligo-Fapy G
The stability of a double helix mainly depends on the following energies: the hydrogen bond (HB) energy between base pairs, staking interaction (ST) energy, and solvation shell-solute interaction energy [28]. In the latter case, which was tangentially covered in PCM, EHB and EST could be related to the HB length and the distance between the two neighbouring BPs (rise parameter), which were calculated in this study according

Electronic Properties and Geometry of Oligo-Fapy G
The stability of a double helix mainly depends on the following energies: the hydrogen bond (HB) energy between base pairs, staking interaction (ST) energy, and solvation shell-solute interaction energy [28]. In the latter case, which was tangentially covered in PCM, E HB and E ST could be related to the HB length and the distance between the two neighbouring BPs (rise parameter), which were calculated in this study according to the standard reference frame for the description of nucleic acids [29]. As shown in Table 1, the presence of Fapy G and OXO G did not change the HB length and rise parameter significantly in comparison to the corresponding native ds-oligo. In the case of the proposed ds-pentamer, both lesions are flanked by canonical base pairs from their 3 -and 5 -end sites. Additionally, Fapy dG and OXO dG did not interact together directly. Given this, the "global" vertical and adiabatic ionization potential and electronic affinity in non-equilibrated and equilibrated solvent interaction modes were calculated, as presented in Table 2. The results show that the complete ds-DNA and base-pair skeletons had the greatest differences in the case of vertical electron affinity calculated in the non-equilibrated mode (∆ = 0.25 eV), while, for the others, the difference was negligible. However, the appearance of Fapy G and OXO G in the ds-DNA structure causes a vertical and adiabatic ionization potential decrease of around 0.20eV. In contrast, almost no influence on the electron affinity properties was observed ( Table 2). Table 2. Electronic properties, in [eV], of oligo-Fapy G: Vertical (VIP), adiabatic ionization potential (AIP) and vertical (VEA), adiabatic (AEA) electron affinity calculated at the M062x/6-31++G** level of theory in the aqueous phase. (a,c) complete double helix and (b,d) base-pair skeleton, NE-nonequilibrated solvent-solute interaction, EQ-equilibrated solvent-solute interaction, * data calculated for corresponding native ds-oligo [30]. Root-Mean-Square Deviation (RMSD) of atomic positions in [Å 2 ], calculated for neutral, anionic and cationic forms of oligo-Fapy G. The row data have been given in Table S1  The global structural changes, forced by electron attachment or electron loss, were assigned as differences between atomic positions between neutral versus anionic or cationic forms of oligo-Fapy G and expressed as RMSD in [Å 2 ] ( Table 2). As expected, the charge changes were compensated for by the flexible phosphate-sugar backbone, while the internal part containing base pairs showed almost no deviation. Furthermore, the appearance of an extra electron in the system results in an RMSD value that is about twice as high as the value for the case of a lost electron.

The Charge and Spin Distribution Oligo-Fapy G Structure
It is worthwhile to investigate the influence of CDL containing two lesions formed via the same intermediate, i.e., Fapy G and OXO G, on charge and spin distribution. For this proposal, the Hirschfeld methodology was applied [31]. In addition, the initial stage of the charged molecule formation, after electron adoption or ejection, was examined in light of the non-equilibrated solvent-solute interaction. The radical cation or anion migrates through stacked base pairs, and, for this reason, only the internal skeleton of ds-DNA was considered in this study. As shown in Figure 4, the radical cation (electron hole) formed (charge: 84% and spin: 90%) settles mainly on the OXO G 4 :::C 2 base pair, with some dispersion over A 3 T 3 and A 5 T 1 . The differences in charge and spin distribution between the non-equilibrated and equilibrated state of the vertical cation was less than 5% per the BPs mentioned. This finding is consistent with previous experimental and theoretical results [32,33]. It is important to note that no extra charge and spin was found within the Fapy G 2 ::C 4 moiety. The situation becomes different when an extra electron is introduced into the oligo-Fapy G structure. The initiation point of the discussed system has been described using the non-equilibrated solvent-solute interaction. The negative charge and spin are dispersed over A 5 T 1 , O G 4 C 2 , A 3 T 3 base pairs as follows (% of charge/spin): 9/7, 70/81, and 15/11, respectively. Surprisingly, after solvent-solute equilibration, the layout discussed above changed, and the density [%] of charge/spin of the extra electron increases at A 5 T 1 (28/26), with subsequent decreases at an O G 4 C 2 (59/66) moiety, as shown in Figure 4. However, after structure relaxation towards the adiabatic radical anion forms, the negative charge was observed almost exclusively at the OXO G 4 C 2 moiety (spin 94% and charge 80%). charge changes were compensated for by the flexible phosphate-sugar backbone, while the internal part containing base pairs showed almost no deviation. Furthermore, the appearance of an extra electron in the system results in an RMSD value that is about twice as high as the value for the case of a lost electron.

The Charge and Spin Distribution Oligo-Fapy G Structure
It is worthwhile to investigate the influence of CDL containing two lesions formed via the same intermediate, i.e., Fapy G and OXO G, on charge and spin distribution. For this proposal, the Hirschfeld methodology was applied [31]. In addition, the initial stage of the charged molecule formation, after electron adoption or ejection, was examined in light of the non-equilibrated solvent-solute interaction. The radical cation or anion migrates through stacked base pairs, and, for this reason, only the internal skeleton of ds-DNA was considered in this study. As shown in Figure 4, the radical cation (electron hole) formed (charge: 84% and spin: 90%) settles mainly on the OXO G4:::C2 base pair, with some dispersion over A3T3 and A5T1. The differences in charge and spin distribution between the non-equilibrated and equilibrated state of the vertical cation was less than 5% per the BPs mentioned. This finding is consistent with previous experimental and theoretical results [32,33]. It is important to note that no extra charge and spin was found within the Fapy G2::C4 moiety. The situation becomes different when an extra electron is introduced into the oligo-Fapy G structure. The initiation point of the discussed system has been described using the non-equilibrated solvent-solute interaction. The negative charge and spin are dispersed over A5T1, O G4C2, A3T3 base pairs as follows (% of charge/spin): 9/7, 70/81, and 15/11, respectively. Surprisingly, after solvent-solute equilibration, the layout discussed above changed, and the density [%] of charge/spin of the extra electron increases at A5T1 (28/26), with subsequent decreases at an O G4C2(59/66) moiety, as shown in Figure 4. However, after structure relaxation towards the adiabatic radical anion forms, the negative charge was observed almost exclusively at the OXO G4C2 moiety (spin 94% and charge 80%).   Table S2. F = Fapy, O = OXO.

Electronic Properties of a Single Base-Pair Extracted from Oligo-Fapy G
For this study, the spatial geometry of oligo-Fapy G was optimized in its neutral, anion, and cation forms. Such a strategy allowed the calculation of each base-pair's electronic properties, as shown in Table 3. Table 3. Electronic properties of isolated base pairs from oligo-Fapy G: vertical (VIP), adiabatic ionization potential (AIP), and vertical (VEA) and adiabatic (AEA) electron affinity calculated at the M062x/6-31++G** level of theory in the condensed phase. The row data has been given in supplementary materials Table S3. An analysis of the results elucidated that the OXO G 4 C 2 base-pair adopted the lowest vertical and adiabatic ionization potentials, i.e., 5.9 and 5.56 eV, respectively. For the other base pairs, the difference between VIP and AIP was negligible, which indicates that the electron-hole can travel without nucleus movement. Moreover, the vertical ionization potential value (6.17 eV) of Fapy G 2 C 4 was found comparable to that assigned for the GC base pairs extracted from corresponding unmodified ds-oligo [30]. This was partially confirmed by an analysis of the vertical and adiabatic electron affinity of the base pairs belonging to oligo-Fapy G. The OXO GC moiety demonstrated its predisposition to excess electron adoption, with the highest absolute values of VEA (1.53 eV) and AEA (1.97 eV) being noted. As expected, the Fapy GC base pairs adopted a slightly lower vertical value, i.e., 1.46 eV.

The Rate Constant of Charge Transfer through Oligo-Fapy G
Charge transfer through ds-DNA can occur in its oxidized or reductive state, as described by Marcus theory, i.e., the charge transfer depends on the k HT (rate constant), ∆G (driving force), λ (reorganization), E a (activation), and V da (electron coupling) energies [34]. All these parameters for this study were calculated at the M06-2x/6-31++G** level of theory in the aqueous phase. For details, please see reference [35]. Furthermore, the influence of two different DNA lesions, Fapy G and OXO G (forming CDL), on hole and electron migration through the double helix were taken into consideration in light of the Marcus theory. As shown in Table 4, the highest E a was observed in the cases of electron-hole transfer between Fapy G 2 C 2 and next to A 1 T 1 and A 3 T 3 . On the other hand, when Fapy G becomes the bridge between the two BPs, i.e., A 1 T 1 and A 3 T 3, E a adopted a negative value, which results in k HT being undetectable. The above indicates that the transfer between A 1 T 5 , A 3 T 3 , and A 5 T 1 pairs should be unaffected and extremely fast. Additionally, the k HT value obtained for the electron-hole transfer towards OXO G was in a range of 10 8 to 10 14 [s −1 ]. Moreover, the influence of Fapy G on the excess electron transfer was less visible in each point of deliberation, with adopted values in a range of between 10 12 and 10 13 [s −1 ]. An exception is when Fapy G becomes the bridge, i.e., A 1 T 1 ←A 3 T 3 , for which the activation and reorganization become negative. This indicates that Fapy G accelerated the electron transfer, as opposed to OXO G, for which 4.7 × 10 −13 [s −1 ] k HT was found. Table 4. Charge transfer parameters. The ∆G-driving force, λ-reorganization energy, E a -activation energy, V 12 -electron coupling, and k HT -charge rate constant of permissible transfer between base pairs of oligo-Fapy G, calculated at the m062x/6-31++G** level of theory in the aqueous phase and given in eV. Arrows indicate the direction of charge migration. The row data have been given in Table S4.

System
λ ∆G E a V 12 k HT (s −1 ) The above results coincide well with the assigned charge energy barrier as presented in Figure 5. The charge migration barrier can be discussed in vertical and adiabatic modes on account of the nature of the process, as described in a previous study [35]. In brief, the oligo-Fapy G was initially divided into three ds-trimmers: A 1 Fapy G 2 A 3 , Fapy G 2 A 3 OXO G 4 , and A 3 OXO G 4 A 5 (the system notation was reduced to a purine strand only). The barriers of radical cation/anion transfer can be calculated as an iterative single-step super-exchange or hole/electron hopping process, as depicted in Figure 5. The details have been given in the Supplementary Materials and Table S5. As expected, the radical cation migration from the Fapy GC→AT (~0.5 eV) or from the OXO GC→AT (~1.4 eV) pairs were unprivileged (∆G Barrier of reaction was noted as positive; see Table S2). The above indicates that OXO GC constituted a more effective electron-hole trap than Fapy GC. This was confirmed by the negative ∆G Barrier value of the reverse process, i.e., AT→ Fapy GC (−0.49 eV) or AT→ OXO GC (−1.1 eV).
The situation is similar to the previously discussed excess-electron transfer. As presented in Figure 5 and Table S2, the difference between the adiabatic and vertical modes around Fapy GC was negligible. Moreover, the ∆G value ranged from 0.09 eV to −0.09 eV. As previously, the OXO GC pair can be recognized as a sink of the excess electron, which was confirmed by the significantly negative ∆G values of A 3 T 3 → OXO G 4 C 2 , A 5 T 1 → OXO G 4 C 2 and Fapy G 2 C 4 → OXO G 4 C 2 as follows (vertical/adiabatic mode) in   Table S5.

Discussion
The double helix contained two main structural subunits: (A) a phosphate-sugar backbone, which is highly flexible and can compensate for geometry changes forced by external factors, and (B) a rigid internal skeleton formed by the complementary aromatic nucleo-base connected by hydrogen bonds together with a stacking interaction stabilizing the ds-oligonucleotide structure [36]. Research recognizes that the latter rigid structure allows ds-DNA to act as a nanowire capable of transferring the electron-hole (radical cation) or excess electron over a long distance, possibly more than a thousand nucleosides, according to Barton et al. [37]. This is in good agreement with research showing that glycosylases such as MutY or Endo III can communicate via ds-DNA scanning in the effective detection of lesions [38]. It should be mentioned here that other proteins involved in the replication and repair of genetic material probably use a similar mechanism, many of which contain the [4Fe-4S] cluster [39].
Of all the DNA lesions, clustered DNA lesions (CDLs), defined as two or more lesions per one or two double-helix turns, pose a particularly serious challenge for DNA repair systems [40]. During CDL removal from the genome, cell "rescue" systems try to avoid a double-strand break (DSB) formation, which is potentially lethal [41]. In the vast majority of DNA damage in the genome, Fapy G was yielded by a one-electron reduction process, while OXO G was yielded by one-electron oxidation. As mentioned in the introduction, these two lesions are formed preferably in conditions of hypoxia and normoxia, respectively. This suggests that they could demonstrate a different influence on charge transfer through the double helix. In the studies presented here, all the energies of d[A Fapy GA OXO GA]*[TCTCT] (oligo-Fapy G) with clustered DNA lesions containing both above damage types at the M06-2x/6-31++G** level of theory in the condensed phase were considered; the ds-oligo geometries in question were optimized at the M06-2x/D95**level of theory in the condensed phase. The analysis of four optimized oligo-Fapy G spatial geometries contained in the Fapy dG structure in the two cis and two trans-rotameric forms showed the trans-2 to be energetically privileged (Figure 3). Therefore, the ds-oligo containing a trans-2 rotamer of Fapy G was selected for further theoretical discussion, as  Table S5.

Discussion
The double helix contained two main structural subunits: (A) a phosphate-sugar backbone, which is highly flexible and can compensate for geometry changes forced by external factors, and (B) a rigid internal skeleton formed by the complementary aromatic nucleo-base connected by hydrogen bonds together with a stacking interaction stabilizing the ds-oligonucleotide structure [36]. Research recognizes that the latter rigid structure allows ds-DNA to act as a nanowire capable of transferring the electron-hole (radical cation) or excess electron over a long distance, possibly more than a thousand nucleosides, according to Barton et al. [37]. This is in good agreement with research showing that glycosylases such as MutY or Endo III can communicate via ds-DNA scanning in the effective detection of lesions [38]. It should be mentioned here that other proteins involved in the replication and repair of genetic material probably use a similar mechanism, many of which contain the [4Fe-4S] cluster [39].
Of all the DNA lesions, clustered DNA lesions (CDLs), defined as two or more lesions per one or two double-helix turns, pose a particularly serious challenge for DNA repair systems [40]. During CDL removal from the genome, cell "rescue" systems try to avoid a double-strand break (DSB) formation, which is potentially lethal [41]. In the vast majority of DNA damage in the genome, Fapy G was yielded by a one-electron reduction process, while OXO G was yielded by one-electron oxidation. As mentioned in the introduction, these two lesions are formed preferably in conditions of hypoxia and normoxia, respectively. This suggests that they could demonstrate a different influence on charge transfer through the double helix. In the studies presented here, all the energies of d[A Fapy GA OXO GA]*[TCTCT] (oligo-Fapy G) with clustered DNA lesions containing both above damage types at the M06-2x/6-31++G** level of theory in the condensed phase were considered; the ds-oligo geometries in question were optimized at the M06-2x/D95**level of theory in the condensed phase. The analysis of four optimized oligo-Fapy G spatial geometries contained in the Fapy dG structure in the two cis and two trans-rotameric forms showed the trans-2 to be energetically privileged (Figure 3). Therefore, the ds-oligo containing a trans-2 rotamer of Fapy G was selected for further theoretical discussion, as depicted in Figure 2. It should be noted that, using alternative calculation methods, some research groups assigned the domination of the cis form over trans for the isolated Fapy dG [18,24,42,43]. The comparative structural analysis presented in this article showed that the influence of a multi-damage site including Fapy G and OXO G as subunits on the discussed ds-oligo structure was noted as negligible according to the standard DNA reference frame for the analysis of structural parameters (Table 1). Moreover, the presented results are in good agreement with previous results obtained for ds-oligo containing two OXO G as a clustered damage moiety [30], which indicates that the lesion only has a negligible effect on the 3D structure of ds-DNA.
The adoption or loss of an electron by ds-DNA leads to radical cation or radical anion formation, which can migrate through a double helix for more than 200Å [44]. Most studies have discussed the electronic properties of double-stranded trimers, which are a good model for discussing single lesions, but unfortunately fail in the case of CDLs [45,46]. For these reasons, investigating the influence of the CDLs on charge transfer through a double helix, as discussed in this study, seems eminently justified.
As mentioned above, the loss or adoption of an electron can initiate electron-hole or extra electron migration through ds-DNA [47]. This process is performed using charge displacement through a π-stacked base-pair ladder. The data presented in Table 2 indicates that, during vertical anion radical formation, the involvement of the sugar-phosphate backbone appears to be minimal. This observation tallies with data obtained for the corresponding native ds-oligo [30]. Additionally, the resent research of Sevilla et al. shows that, for this process, solute-solvent interaction is crucial at the beginning point [28].
These charge and spin distribution results ( Figure 4) indicate that charge transfers, through a double helix containing the discussed CDL to the destination point ( OXO G 2 C 4 ), should be almost unaffected by the presence of Fapy G 2 C 4 . OXO G is simply preferred over Fapy G as the point where the electron-hole settles in the genome. Similar to the above, the Fapy G::C moiety present in the oligo-Fapy G was not affected by an extra electron, which suggests that, in the electron transfer process through the double helix, 2,6-diamino-4hydroxy-5-foramido-2 deoxypyrimidine plays a negligible role. Moreover, 94% and 80% spin and charge, respectively, were found on OXO G 4 C 2 .
The charge transfer process through ds-DNA can be discussed as single-step tunnelling, a random-walk multistep, and polaron-like hopping [48]. Each type of hole or electron migration strictly depends on the mutual positions, spatial geometries, and individual electronic properties of the base pairs. It should be pointed out here that these factors are different when they are calculated for isolated BP and BPs extracted from a ds-oligo structure, as shown in previous research [35]. An incoherent charge migration through the double helix can be observed on the hundreds of base pairs and depends on the nature of the bridge between the donor and acceptor [48]. On the other hand, at a distance of only a few BPs, tunneling paths can be noted. Even though the above mechanisms are different, the geometry and electronic properties of purine/pyrimidine moieties are crucial. OXO dG, when present in the ds-oligo structure, has been identified as a radical cation sink and terminates its movement [49]. According to the results presented above, it can be assumed that charge transfer through Fapy G 2 C 4 as a bridge should be unaffected (Table 4), similar to what was noted for a canonical BP [32,50]. In addition, the OXO GC moiety of clustered DNA damage can be predicted as the end point of the extra electron transfer. Furthermore, the electron transfer through the discussed ds-pentamer should not be affected other than by OXO GC base pairs on account of the similarity between VEA and AEA values in their cases (Table 3). Conversely, the presence of Fapy G in the investigated system effectively slows down the hole transfer via a single-step tunneling process. The above yields k HT values close to zero even though the ∆G was negative (Table 4). Additionally, as shown in Figure 5 and Table S2, no differences between the vertical and adiabatic modes were noted for the charge transfer in the proximity of the Fapy GC base-pair. Moreover, the hole-hopping barrier between A 1 T 5 ←→A 3 T 3 and A 5 T 1 ←→A 3 T 3 was measured as almost zero eV for both vertical and adiabatic modes ( Figure 5). As above, the radical cation migration from Fapy GC towards OXO GC over the AT bridge was noted as privileged.

Materials and Methods
The starting geometries of bi-stranded oligo-Fapy G were built using BIOVIA Discovery Studio Visualizer v20.1.0.19295 software [51] and noted accordingly: d[A 1 Fapy G 2 A 3 OXO G 4 A 5 ]*d[T 5 C 4 T 3 C 2 T 1 ]. The Cartesian coordinates (i.e.: pdb files) of discussed ds-oligo structure have been given in the supplementary materials.
The negative charges of the phosphate groups were neutralized via the addition of protons, and the other atoms were saturated using additional hydrogen atoms. The structure optimizations of oligo-Fapy G were performed using the Our Own N-layered Integrated Molecular Orbital and Molecular Mechanics (ONIOMs) strategy [52]. The structures of ds-oligos were divided into high-HL (nucleobases, M06-2X/D95**) and low-LL (sugarphosphate backbone, M06-2X/sto-3G) levels of calculation [53]. All calculations were performed in the aqueous phase. The M06-2X function with an augmented and polarized valence double-ζ basis set 6-31++G** was used for energy calculations. For all the optimized geometries, charge, and spin analyses were achieved using the Hirshfeld methodology at the M06-2X/6-31++G** level of theory [31]. The electronic properties of molecules were calculated as described previously [35,54]. The transition dipole moment of excited states and the single point calculation at the M06-2X/6-31++G** level of theory were performed using time-dependent DFT (TD-DFT) methodology [55]. Electron coupling was calculated according to the Generalized Mulliken-Hush model [56]. The solvation-solute interaction was investigated in both non-equilibrium (NE) and equilibrated (EQ) modes [57]. All the calculations of the electronic properties, i.e., VIP NE (vertical ionization potential in NE state), VIP EQ (vertical ionization potential in EQ state), AIP (adiabatic ionization potential); VEA NE (vertical electron affinity in NE state), VEA EQ (vertical electron affinity in EQ state), AEA (adiabatic electron affinity), were conducted in [eV], as described previously [34]. All the above calculations were performed with the Gaussian G16 (version C.01) software package [58].

Conclusions
Genetic information, irrespective of cell type-normal or cancerous-is exposed to various harmful factors which can lead to more than 80 different types of DNA damage. Of these, oxo G and Fapy G have been identified as the most abundant in normoxic and hypoxic conditions, respectively.
This study considered all the energies of d[A Fapy GA OXO GA]*[TCTCT] (oligo-Fapy G) with clustered DNA lesions containing both above damage types at the M06-2x/6-31++G** level of theory in the condensed phase; the ds-oligo geometries in question were optimized at the M06-2x/D95** level of theory in the condensed phase. The electronic properties of oligo-Fapy G were analysed in equilibrated and non-equilibrated solvation-solute interaction modes.
• The vertical/adiabatic ionization potential (VIP EQ , AIP) and electron affinity (VEA, AEA) of the investigated ds-oligo were noted in [eV] as 5.87/5.39 and −1.41/−2.09, respectively; • The analysis of four optimized oligo-Fapy G spatial geometries contained in the Fapy dG structure in the two cis and two trans-rotameric forms showed the trans-2 to be energetically privileged. Subsequently, the influence of a multi-damage site including Fapy G and OXO G as subunits on the discussed ds-oligo structure was noted as negligible according to the standard DNA reference frame for the analysis of structural parameters. Furthermore, neither the adoption of an excess electron or the loss of an electron by the oligo-Fapy G forced a significant macromolecule structural distortion; • Additionally, for the Fapy GC base-pair isolated from the discussed ds-oligo, the ionization potential and electron affinity values were observed to be higher than those assigned for OXO GC; • These results imply that Fapy GC does not have a significant effect on electron-hole or excess-electron charge transfer. In parallel to this, the OXO GC base-pair becomes the radical cation/anion sink in the oligo-Fapy G structure, as expected.
The results presented above indicate that 7,8-dihydro-8-oxo-2 -deoxyguanosine plays a significant role in charge transfer through ds-DNA containing CDLs and indirectly has an impact on DNA lesion recognition and repair processes. Conversely, the electronic properties obtained for 2,6-diamino-4-hydroxy-5-foramido-2 deoxypyrimidine were found to be too weak to compete with OXO G in influencing a charge transfer through the discussed ds-DNA containing CDLs.
The results presented in the article shed further light on clustered DNA damage, which might be useful for the safety of future generations. Man's continual desire to colonize worlds beyond Earth requires a study of astronaut safety protocols and research into nutrition, among other things. In addition, as our longevity increases, so too do incidents of cancer. The slowdown and weakness of DNA damage repair machinery is also an age-dependent process. Therefore, it is vital to consider and further investigate "patientfriendly" radiotherapy treatments that use ionization radiation for killing cancer cells. New forays into radiotherapy are necessary to make the dose delivery more effective while reducing the detrimental and highly undesirable effects on healthy tissue surrounding a tumour. The discovery of a different kind of DNA damage raises the question of its influence, not only on the CDL repair, formation, and DNA replication processes, but also on charge transfer, and therefore on DNA damage recognition. Therefore, the results presented in this article show the possible role of Fapy dG in the "DNA recognition and repair machinery" from the perspective of multiple local damaged sites composed of different lesions, i.e., OXO dG.