Binding Energies and Hydrogen Bonds Effects on DNA-cisplatin Interactions: A DFT-xTB Study

xTB and DFT-CAM-B3LYP were used to study hydrogen bonds in DNA base pairs and DNA-cisplatin complexes. Structure, binding energies and electron density are analyzed. xTB has proven to be an accurate method of obtaining structures and binding energies in DNA structures. Our xTB values for DNA base binding energy the pairs were in the same order and in some cases better than the CAM-B3LYP values compared to the experimental values. Double-stranded DNA-cisplatin structures have been calculated and the hydrogen bonds of water molecules are a decisive factor contribution to the preference for the cisplatin-Guanine interaction. Higher values of the water hydrogen binding energies were obtained in cisplatin-guanine structures. Furthermore, the electrostatic potential was used to investigate and improve the analyzes of the DNA-cisplatin structures.


Introduction
All the genetic information necessary for living organisms is encoded in the structure of DNA [1].Understanding this complex structure involves describing the structure in a medium where the solvent and temperature effects are relevant [2] [3].From a structural point of view, the bases of a double helix are almost parallel to each other, united by hydrogen bonds and intra-and inter-base interactions [4].
The interaction with ions (Na + , K + or Mg 2+ ) is another aspect that makes the complex and challenging study.Neutralizing the negative charge is one of the keys points for DNA stabilization [5] [6].With regard to chemotherapeutic processes, the interaction of the double helix with metallic compounds is the main point for understanding various processes resulting from this interaction.Cisplatin is one of the best metal-based chemotherapy drugs and is widely used to treat cancers, such as testis, ovary, lung, colon of the uterus, bladder, head and neck [7] [8].However, it is not possible to achieve greater clinical efficiency with cisplatin due to the many adverse reactions generated by its use.The main reported reactions are adverse effects such as gastrointestinal toxicity, nephrotoxicity, hepatotoxicity, ototoxicity, neurotoxicity and drug resistance.Adverse effects occur because most chemotherapy drugs act in a non-specific way, which can also destroy healthy cells.
The mechanism of cisplatin action in the cellular environment is extensively discussed in several references [9], [10], [11], [8].Initially it involves a reaction with water to replace the chlorine atoms present in the cisplatin molecule with OH groups.This is a process called aquatation or activation.The reason these complexes act as antitumor agents is the result of the formation of cytotoxic lesions in platinum DNA adducts, but there is still debate over how these drugs work [12], [7], [13].The accepted thesis that the anti-tumor activity of cisplatin originates from the interaction with N atoms of the purine base (Guanine or Adenine).Formation of cross-links (intra and inter) results in contortions in the geometry of the double helix [14].There are still continuous debates on which of the cisplatin-DNA adducts are most significant toward cell death, linkages between subsequent pairs of the same helix result in more effective cytotoxicity [14] [7].Additionally, theoretical results have shown a preference cisplatin bonding for the Guanine base over Adenine through the analysis of stabilization energies between the different complexes.Considerable theoretical efforts have been focused on cisplatin-DNA interaction to provide detailed insight at molecular level.Spectral analyses [15] [16], structure-activity studies [17], aquation processes [18][19] [20], structural properties of cisplatin-DNA complexes [21] [22], effect on DNA base pairing [23] and chemical reactions responsible are some of the most studied properties.The effect of strong hydrogen bonds was mentioned in the article of Baik et al [24] as one of the determining factors in the interaction preference for guanine.Robertazzi and Platts [25] and studied hydrogen bonds between bases to analyze cisplatin's preference for bases.Hybrid QM/MM with the ONIOM approach of cisplatin with DNA dimer and octamer structures [26], demonstrates that the structure obtained with explicit solvent are closer to the NMR structures.It is observed that there is still a lack of clear understanding of how hydrogen bonds can affect the formation of cisplatin bonds with DNA bases.
The aim of this study was use the recently recently developed a extended tight binding (xTB) approaches for study the hydrogen bonds in the cisplatin interaction with DNA.DFT methods were used as a benchmark for hydrogen bonding distances and energies.A systematic study of hydrogen bonds in base pairs and the interaction of cisplatin with DNA fragments was done.The combination of semi-empirical and DFT methods has proven useful for modeling a system with more than 120 atoms.Results for structures, bond distances and bond energies will be analyzed from the perspective of understanding the effects of intrabase interaction and the hydrogen bonds of the explicit water molecules of the hydrated cisplatin.

Theoretical Methods
The gas-phase Adenine-Thimine (AT) and Guanine-Cytosine (CG) base pairs equilibrium geometries were obtained with the semiempirical GFN2-xTB [27], [28] and the hybrid exchange-correlation functional CAM-B3LYP [29].All the geometries were optimized using analytical gradient techniques and frequencies were calculated by numerical differentiation of analytical energy gradients.In the DFT calculations, the D3 contain pairwise along three-body terms in the form of Axilrod-Teller-Muto three-body corrections [30] were used in combinations with aug-cc-pVDZ basis set.
The binding energies were calculated at GFN2-xTB level and the DFT/CAM-B3LYP/aug-cc-pVDZ by the difference of the total energy and the monomer energies.At the DFT level the BSSE [31] error was accounted for using the standard counterpoise approach by Boys and Bernardi [32].Additionally the zero point energy ∆E zep and the vibrational energy difference as one goes from 0 to 298.15 K ∆E vib .Bond enthalpies ∆H were calculated with the sum of differences in electronic energy, zero point and vibrational energy.
The hydrogen bond effect of the water molecule on the cisplatin bonding were included using the micro-solvation model.In our case two models with double strand DNA and two base pairs was used, one model with CG bases and another with AT bases.In this model, ciplatin is linked by covalent bonds with the two base pairs of the double helix through the Pt and the N atoms of the bases.Additionally, water molecules are included as part of the cisplatin hydration process, the two cisplatin bonded water molecules were included.The resulting structures in the model led to 134 and 137 atoms for CG-DNA-cisplatin+2H 2 O and AT-DNA-cisplatin+2H 2 O respectively.The minimum energy structure of these models was calculated at the xTB level and the implicit solvent model ALPB was also included.Four different geometries were obtained, all with positive frequencies.Binding energies and of the hydrogenbonded and cisplatine-DNA complexes were calculated at the optimized geometries at BP86 and CAM-B3LYP with the def2-SVP basis set, except for the Pt atom were the well-known Los Alamos LANL2TZ effective core potentials were used [36].All the calculations were performed using the ORCA code [37][38] and the tight binding geometries were calculated using the xTB software [28] [27].The initial geometries were obtained using the Gabedit a graphical user interface to computational chemistry packages [39].All the electrostatic potential surfaces were calculated using Python script provided by Marius Retegan [40].

Watson-Crick Base Pairs.
The structures represented through the bond distances are described in the tables 1 and 2. Our initial analysis is dedicated on the difference between the theoretical values at the DFT/CAM-B3LYP and xTB models.Both gas and solvent phases were calculated and experimental values were also included.For the experimental values in the bond distances, crystal structures of sodium adenylyl-3',5'-uridine (ApU) hexahydrate and crystal structure of sodium guanylyl-3',5'-cytid (GpC) nonahydrate reported by Seeman, Rosenberg and co-authors [41,42].In the last line of the tables we present the average value of the differences between the calculated values and the experimental values.It was observed that both xTB and CAM-B3LYP methods have a close behavior in describing bond distances.All the values of distances and differences were presented in a supplementary file.Analyzing in terms of the differences between the calculated and experimental values, we obtained the largest differences in the covalent bonds for the C9-N11 and C5-C12 bonds for the Guanine molecule in the CG Watson-Crick pair.At the C5-C12 bond distance, the xTB model leads higher values of order of 0.04 Å.For the CAM-B3LYP, the C5-C12 bond was also greater than the experimental value, but the difference is slightly smaller, approximately 0.03 Å.The C9-N11 was obtained with differences of 0.038 Å and 0.043 Å for the DFT method in solution and in the gas phase respectively.For the AT pair, the greatest differences were observed for the Adenine C6-C15 and N11-C12 bonds, with differences between the calculated and experimental values ranging from 0.03 Å to 0.04 Å.In the gas phase the C20-C25 covalent bond, we obtained 0.04 and 0.042 for the xTB and DFT methods respectively.In solution these values reduced to 0.033 Å and 0.032 Å for xTB and DFT.
The hydrogen bonds is the central topic of this work, the triplet hydrogen bond of the CG complex are highlighted at the end of the table 1.The greatest difference are obtained for the N23-O7 bond, differences of order 0.2 Å and 0.12 Å for the xTB method in gas phase and in solution respectively.For the CAM-B3LYP method, these values were 0.17 Å and 0.057 Å in gas and in solution respectively.These numbers are in agreement with our previous reported results [43] [44] obtained at HF, BP86 and B3LYP levels of theory.Compared to the experimental values, our best values obtained in the implicit solution model, indicating a contribution from the environment, backbone and ions [45].For the AT hydrogen bonds, lower values for the differences between bond distances with values of 0.082 Å and 0.092 Å in the xTB method in solution.In the DFT method, these values were lower, 0.047 Å and 0.038 Å.A general way to see how each methodology performs when describing the title the distances are through the absolute mean difference, represented in the last line of the tables 1 and 2. The model that includes solvation leads to lower values of the average differences.In both methods, the average values in solution for the CG complex reduce the average value reduces approximately 22%.For the AT complex, the average values in solution suffer a smaller reduction, 5 and 15% for CAM-B3LYP and xTB, respectively.These values are an indication of the interactions of the ions Table 3 Binding energy in (kcal/mol) for Guanine-Cytosine and Adenine-Thymine base pairs.∆Ezpe is the zero point vibrational energy and ∆E vib is the change in the vibrational energy difference as one goes from 0 to 298. 15  1 ∆Hexp from mass spectrometry data of Yanson et al. [46] for GC with 9-methylguanine and 1methylcytosine.
and backbone disregarded in our model.As expected, the comparison between the DFT and semi-empirical models shows that all mean values are smaller.For the CG complex, the value was 28 % lower both in the gas phase and in solution, a similar value was observed for the AT complex in solution.In the case of the gas phase, this speed is around 34 % lower, going from 0.035 to 0.023.Table 3 provides the calculated values of the gas phase binding energies for CG and AT complexes considering the absence of the solution in the experimental data.To compare the calculated values with the gas-phase experimental enthalpy ∆H [46] we calculate the ZPE ∆E ZP E and the vibrational ∆E vib difference energies for both CG and AT complexes in order to get (∆E +∆E ZP E +∆E vib−298 ).One extensive analysis of interaction energies in bases with different methods can be found in references [45][47] [43] [44].The theoretical values for the CG pair are mostly overestimated when compared with the experimental ∆H values.Our calculated value for the CG pair was 27.68 kcal/mol is slightly above the value of 21.0 kcal/mol.In the xTB method we obtained a value of 25.8 kcal/mol.In the AT pair we obtained values comparatively closer to the experimental value of 12 kcal/mol, 12.98 and 13.66 kcal/mol respectively for the xTB and CAM-B3LYP methods.Despite the small difference between the methods, the xTB values were a little closer to the experimental ones.
In order to contemplate the effects of the solvent, solvation causes the weakening of hydrogen bonds and a consequent reduction in binding energy.In our previous work using a sequential Monte Carlo/DFT methodology to generate the configurations in solution and calculate the binding energy by DFT methods [44], the CG binding energy is weakened to about 70% of the value obtained for an isolated complex.More recent estimates using a detailed analysis of the energy components via DFT showed a reduction of approximately 50% for the AT pair and a little more than 55 % for the CG pair [48].In the values calculated by us using the xTB method using total energy, we obtained a reduction from 29.2 to 17.2 kcal/mol (40 %) in the case of CG and 16.1 to 11.1 kcal/mol (32%) for the AT complex.By analyzing these values and our previous values we can conclude that the xTB method leads to satisfactory results, considering that our previous values included explicit water molecules.

Hydrogen bonds on DNA-cisplatin interactions
Table 4 Bonding distance ( Å) of Pt atom and DNA bases molecules.The G-Pt-G and A-Pt-A was the distances of the CG-DNA-cisplatin+2H2O and the CG-DNA-cisplatin+2H2O models, respectively.In this section we explore the effects of hydrogen bonds on the binding of cisplatin to DNA and the stability of the bonds.A model with CG bases and another with AT was used in our simulations.In our model we consider the presence of two water molecules resulting from the dehydration of cisplatin during binding with the DNA.Minimum energy geometries with two CG base pairs linked to cisplatin and two water molecules, named CG-DNA-cisplatin+2H 2 O, were obtained at the xTB method.The same methodology was used for obtain AT geometries and we called AT-DNA-cisplatin+2H 2 O. Two minimum structures were found for each model, named Struct-A and Struct-B.In figure 2 we show the structure of CG and AT-cisplatin+2H 2 O and supplementary material all the four optimized structures.

G-Pt
In a first analysis, we observed the formation of covalent bonds between cisplatin and the bases Guanine and Adenine through the Pt atom.In table 4 we show the distances between the Pt atom and the N atoms of the bases.The reported experimental [49] results show distances between the Pt and N atoms of the bases at 2.050 and 2.055 Å for the G-Pt-G.Our values were in the same order, 2.044 and 2.047 Å, for the first bond of structure A and B. For the second bond, higher values 2.095 and 2.102 Å were found in our model.For the A-Pt-A bonds, these parameters are very close for the first bond and slightly smaller for the second bond, resulting in the distances of 2.081 and 2.074 Å.Another key parameter is the angle between the Guanine planes determined to be 81.2 ± 4.3 degrees.Our values for the angles of the two CG-DNA geometries were slightly higher at 88 and 88.8 degrees.As can be seen in figure 2 hydrogen bonds were formed by the water molecules and the oxygen atoms of Guanine molecule with distances of 1.88 and 1.90 Å.For the AT-cisplatin structure one hydrogen bond interacts to Adenine with 1.71 Å and the other water molecule interact with the NH 3 group of cisplatin with and distance of 1.91 Å.All the structures can be found in the supplementary material.The binding energies for the minimum energy structures were calculated and the values outlined in table 5.For the xTB values we obtain higher values for structure B, with a binding energy of 30.0 kcal/mol.A better description of binding energies was obtained by the DFT functionals BP86 and CAM-B3LYP.For the DFT results, stronger hydrogen bonds between water molecules and CG-DNA-cisplatin structures were obtained.For structure A in the CAM-B3LYP functional this energy is about 2kcal/mol higher for CG-DNA-cisplatin, compared to AT structure.For other structures this difference is even greater.In the competition of cisplatin interaction with purine bases, Guanine or Adenine, hydrogen bonds are an important component, in particular hydrogen bonded waters close to the cisplatin interaction region.Through these results we can see a preference in the formation of hydrogen bonds between water molecules and Guanine oxygen atoms.The cisplatin-DNA reaction goes through a transition state formed by strong hydrogen bonds of water molecules.Our previous results [44] on hydration of CG bases also indicate strong hydrogen bonds in the oxo group C -O of the Guanine base.The hydrogen bonds of amine on Pt and the oxo group at reported by Lippard and his coworkers [24] was not observed in our model.From an electrostatic perspective, this interaction can be analyzed in terms of the electrostatic potential of DNA, mainly of the bases that interact with cisplatin.In particular in the case of the cisplatin-DNA interaction, we use a two-pair structure in the neutral state.The calculation of the electrostatic potential in the ground state showed us the regions of highest and lowest potential.Comparing both surfaces for CG-DNA and AT-DNA in figure 3, we can see the base region of Guanine is a region with negative electrostatic potential favorable to the formation of hydrogen bonds.In our point of view, the electrostatic potential and the formation of hydrogen bonds have an important contribution to the preference that cisplatin has for the Guanine bases of DNA.Therefore, this systematic study of geometry, energy and electronic structure was conducted to explain the preference of cisplatin interacting with the Guanine base.We focus our efforts on the effect of hydrogen bonds and their contribution on cisplatin-Guanine interaction.We know, however, that other effects such as covalent interaction and thermal effects are also important and will be investigated in the future.

Conclusion
In this work we obtained the structural and electronic properties of hydrogen bonds in base pairs and the interaction of cisplatin with DNA.The hydrogen bonds were described with reasonable accuracy by the xTB method.Although the precision of the binding distance values was described with lower precision than DFT methods, in our case using the CAM-B3LYP functional, the binding energies obtained were well described both in the isolated phase and in solution.Our values for binding energies are similar to those obtained with DFT/CAM-B3LYP and in the case of solvation the reduction in the value of binding energy is 30 to 40% in agreement with the best in agreement with the best estimates reported in the literature.In the cisplatin-DNA interaction, hydrogen bonds are important in determining the preference of the cisplatin-Guanine interaction.Structures with 2-3 kcal/mol higher binding energies were obtained.In our analysis using electrostatic potential and hydrogen bonds, we obtained a clear interpretation of the preference in the interaction between cisplatin and bases Guanine and Adenine.Therefore, xTB proved to be an effective methodology for studying hydrogen bonds and even interactions involving heavy atoms, such as Pt.

Fig. 1
Fig. 1 Cytosine-Guanine (in top) and Thymine-Adenine (in botton) base pairs and atom labels used in the tables 1 and 2.

Fig. 2
Fig. 2 CG-DNA-cisplatin+2H2O (top) and AT-DNA-cisplatin+2H2O (bottom).Highlighted in the figure are the hydrogen bonds formed by water molecules with the base and cisplatin.

Fig. 3
Fig. 3 Surface of electrostatic potential of the GC-DNA structure (in top) and AT-DNA structure (in botton).Colors ware used to show the regions of the values in the electrostatic potential.

Table 1
Bond Distances ( Å) for Guanine-Cytosine in gas phase and water solvent.

Table 2
Bond Distances ( Å) in Adenine-Thymine in gas phase and water solvent.
Yang et al.'s NMR structure of a cisplatin-DNA octamer.

Table 5
Hydrogen bonding energies (Kcal/mol) of the two different structures in CG and AT model of DNA-cisplatin structure calculated at xTB minimum structures.