On the Dimers Stability of Allicin and Its Derivatives Interacting with AT, GC, and DNA Bridge: DFT Study

Allicin and its derivatives are physiologically active molecules with many potential health benefits. It is not clear if they have a direct effect on DNA or protein. In order to elucidate the allicin and its derivatives’ effect on DNA base pairs, we investigated various complexes of base pair and its bridge with an allicin and its derivatives.The investigated allicin derivatives were (E)-Ajoene, (Z)-Ajoene, Amz121, and Bmz73 radicals.The DFT calculation results revealed that the investigated molecules would favor binding to bridge of the base pairs instead of directly affecting the base pairs. The Bmz73 radical could break DNA by change bonding in it because the Bmz73 radical significantly affected the P-O bond of the bridge of base pair.


Introduction
Infections that develop into chronic conditions are a fastgrowing problem; especially it is important in the developed world [1,2]. In relation to emerging multiresistant bacteria, development of antimicrobials and new treatment strategies of infections should be expected to become a high-priority research area [2]. Indeed, garlic has been used for centuries because of its therapeutic and health-promoting properties [3,4]. Allicin is almost exclusively responsible for the antimicrobial activity of freshly crushed garlic [4]. Allicin is a physiologically active molecule with many potential health benefits [4] but there are many unanswered questions about its functions [1,[5][6][7][8][9][10][11][12][13]. Allicin is active against a broader spectrum of microorganisms than most of the commonly used antibiotics. For example, allicin is active against both Gram positive (e.g., Bacillus and Streptococcus) and Gram negative bacteria (e.g., Salmonella typhimurium and Agrobacterium tumefaciens), whereas penicillin is practically not effective against the latter [14,15]. Allicin is also active against human pathogens that are resistant against certain antibiotics [1,16]. Beyond its well documented strong antibacterial properties allicin also shows toxic effects towards fungal cells and is able to inhibit spore germination and hyphal growth in vivo and in vitro [1,17]. Allicin showed promising activity against many plant-pathogenic fungal species, including pests, which are of economic importance also [4].
When allicin is inside the cell, the antibiotic efficiency depends upon reaching and reacting with its targets and on the importance of those targets to the cell [4]. Sulfonic acids have been studied in many chemical reactions [18][19][20]. However, the transformation rate of allicin depends on the applied techniques of transformation, temperature, and solvents nature [21]. There are additional potent antithrombotic agent from garlic which are (E,Z)-Ajoene [22][23][24] which have neuroprotective effects also [23]. The Ajoene structures are formed from a chemical reaction involving two allicin molecules. On the other hand the allicin molecule is unstable structure which forms radicals over chemical reactions depending on the environment. Depending on homolytic cleavage or heterolytic cleavage of the S-S bonds in the allicin there are allicin derivative radicals after dissociation of the S-S bond [25]. The most stable radicals are labeled as Amz121 and Bmz73 [25] (Figure 2). Allicin radicals are good candidates for possible DNA damage also [25].
Does allicin have an effect on DNA, RNA, and/or protein synthesis ( Figure 1) [4]? In 1988, Feldberg et al. investigated the effect of allicin on the synthesis of DNA, RNA, and proteins in Salmonella typhimurium [26]. Unfortunately, it remains unclear if the effect observed really showed a direct decrease in DNA, RNA, and protein synthesis ( Figure 1) [4]. The possible allicin attacks on proteins are over disulfide exchange reaction what can lead to misfolding or break-off of the protein. Another possible attack is directly to DNA which can be two types directly affecting DNA or by structures after disulfide exchange reaction what can lead to break-off or blocking DNA from its usage. According to Durlak et al. [9] CPMD simulations and DFT and MP2 methodology analysis there are about 20 conformers of allicin which have quite similar energies. In solvent any of allicin conformer can easy become from one to the other type conformer and the trans-allicin structure does not exist [9]. According to other DFT calculations together with experiment the alkali metal ions can strengthen the S1S1 bond in the allicin, while protonation or the loss of an electron weakens the S1S1 bond [27]. In the gas phase the dehydration reaction mechanism takes place easier for the allicin radical cation than for the protonated allicin [25]. According to other DFT analyses [28] it is more difficult in the intramolecular to transfer H atom during decomposition of allicin in ethanol.
The allicin derivatives which may be important for biological activity are allicin, Ajoene structures, or allicin radicals while possible effects are on protein or on DNA. This work was dedicated for computational analysis for the possible DNA damage models ( Figure 2). In the present study, in order to elucidate the allicin and its derivatives effect on DNA base pairs, the stable structures and their electronic properties for the complexes of G-C, A-T base pairs, and base pairs bridge with an allicin, (E)-Ajoene, (Z)-Ajoene, and allicin radicals ( Figure 3) by using the DFT calculations in vacuum were investigated. The results revealed that the allicin, Ajoene, and its allicin radical prefer to interact with the bridge of the base pairs. The calculation results showed that allicin and its derivative molecules would favor binding to bridge of the base pairs instead of directly affecting the C-G or A-T base pairs.
According to [36] the optimization calculations should be performed by increasing basis set. The calculations were done in such way. Zero-point energy (ZPVE) corrections were not applied for the modeling of the complexes. BSSE-corrected energies were not taken for the analysis of final 45 groundstate complexes because the results should not change significantly as it is shown in [33]. All stationary points were   modeled in the gas phase (vacuum). Additionally, the allicin molecules were characterized by frequency analysis where frequency calculations having all real frequencies identify minimum structures. There were analyses of chemical bonds of calculated complexes in the paper. The bond analysis was performed by analyzing Wiberg bond index. Primary focus was on the Wiberg bond index values between complex structures by looking for largest values. Also the distances between S atom of the interacting structure and nearest atom of the investigated structures were measured. Mulliken and NBO charges and HUMO-LUMO gap calculations for all the structures and complexes were performed.
Binding energies in the paper were calculated according to the following formula: where Δ is final binding energy, 12 is energy of optimized interacting and investigated structures complex, 1 is optimized interacting structure energy, and 2 is optimized investigated structure energy.

Complexes of the Interacting Structures with the DNA
Parts. For the modeling in this paper the primary idea was that the S-S must be active part for the possible interactions. Thus it was enough to have one stable conformer which had open form of the S-S bond. The interacting structures were allicin, (E)-Ajoene, (Z)-Ajoene, and allicin radicals labeled as Amz121 and Bmz73 similar to [24] (Figure 3). Frequency calculations showed the trans-allicin structure had five imaginary frequencies. The cis-allicin structures had not imaginary frequencies what meant they were in the minimum. Before modeling complexes all structures where optimized separately. The primary DNA structure was taken from PDB bank [37]. The DNA was divided into three major parts: G-C base pair, A-T base pair, and bridge of base pairs as it is shown in Figure 2. After optimization of DNA structural parts (G-C base pair, A-T base pair, and bridge of base pairs) the final structures were compared with crystallographic data [37]. The structures were quite similar and the difference was up to 5% for the bond lengths, angles, and dihedral angles. In order to find the most preferable interacting site of possible allicin derivatives around the DNA, artificial initial model structures were made by patterns as shown in Figure 2. The S atom or S atoms from S-S bond were put as close to the DNA parts as possible. There were three major starting model positions for optimizations where the interacting structure was from different side of the investigated structure. In Figure 2 allicin cases with G-C base pair (Figure 2(a)), A-T base pair (Figure 2(b)), and bridge of base pairs (Figure 2(c)) are shown after the final optimizations. In Figure 2 the X sign represents the initial position before the optimization. Positions 1, 2, and 3 ( Figure 2) were the patterns of artificial made initial model structures for the investigated complexes. The model structural parts were taken from separately optimized structures. Similar complexes were modeled and calculated with all interacting structures. The ground-state differences Δ between same type complexes with different positions are shown in Table 1. There was no particular one position for interacting structure where the all complexes would be in the lowest ground state (Table 1).

Results and Discussion
3.1. Allicin Interaction with the DNA Structural Parts. Firstly, allicin molecule was put at three positions around G-C, A-T, and the bridge of the base pairs as shown in Figure 2.
The results are presented in Table 1. The nearest position between allicin S and G-C part is 3.57Å. The nearest distance to the A-T pair is 4.01Å. The nearest O of the base pairs bridge from the allicin is 3.74Å. In all cases the Wiberg bond index between dimer parts was almost zero: the largest value was 0.015 for S and H atoms in the case with G-C base pair (Table 1) There was suggestion that the something would change if we put several allicin molecules. So two and three allicin complexes were used but there were no significant differences in results. There were several cases when one of the three types of allicin moved between A-T and G-C groups but this is unrealistic: in investigated model the A-T (or G-C) groups could freely move in the calculation space what is not true for the real DNA sequence. The binding energies between allicin and G-C base pairs varied form 14.87 kJ/mol to 31.75 kJ/mol. Similar results were between allicin and A-T base pairs where the binding energies varied from 21.48 kJ/mol to 28.32 kJ/mol. The binding energies were almost twice stronger for the base pair bridge then for G-C or A-T base pairs, which varied from 42.8 kJ/mol to 68.61 kJ/mol. Thus the results suggested that allicin molecules would favor binding to bridge of the base pairs and the calculated binding energies could be up to 70 kJ/mol. The calculation results showed that allicin molecule did not change significantly bonding between atoms of the DNA structural parts.

Ajoene Interaction with the DNA Structural Parts.
With the same procedures as with allicin molecule, the calculations were performed for Ajoene molecules and those molecules are labeled as (E)-Ajoene and (Z)-Ajoene ( Figure 3). The modeling was performed according to Figure 2 schema and results are presented in Table 1 where nearest positions between the S atom of Ajoene and O and N atoms of G-C, A-T, and the base pairs bridge are shown. In all cases the Wiberg bond index between dimer parts were almost zero: the largest value was 0.028 between H and O atoms in the case of (E)-Ajoene and bridge of the base pair complex ( Table 1). The S atoms of (E)-Ajoene had zero and −0.06 Mulliken charges and 0.14 and 0.08 NBO charges. The charge values for the S atoms of (E)-Ajoene were similar in complexes and they varied in 0.05 range. The S atoms of (Z)-Ajoene had

Allicin Radicals Interaction with the DNA Structural
Parts. Additional similar calculations were performed using allicin radicals: Amz121 and Bmz73 ( Table 1)

Conclusions
The DFT calculations with B3LYP/cc-pVTZ were performed between interacting structures and DNA parts (G-C and A-T base pairs and the base pairs bridge) where interacting structures were allicin, Ajoene structures, and allicin radicals. The allicin analyses suggested the allicin structure was in minimum when it has cis-configuration. In all case of the allicin, Ajoene molecules with the DNA parts had almost zero Wiberg bond indexes. Allicin radicals had Wiberg bond indexes from 0.5 to 0.9 with the DNA structural parts. In Bmz73 radical case it significantly affected the P-O bonding of the bridge of base pair. This means that the Bmz73 radical could break DNA by change bonding in it. All calculation results showed that allicin and its derivative molecules would favor binding to the bridge of the base pairs instead of directly affecting C-G or A-T base pairs.

Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this article.