Metal-Assisted Proton Transfer in Guanine-Cytosine Pair: An Approach from Quantum Chemistry

From the view of chemistry, DNA is one of the most remarkable examples for self-assembled materials existing in nature. It is said that the phosphoric acid has hydrophilic properties. This is why DNA is stable in aqueous phase. Moreover, there are two kinds of interaction which stabilizes the whole structures of DNA base pairs. These interactions are the driving force of self-assemble which leads to beautiful double helix structure. Structures of double-stranded DNA are stable in aqueous solution, because there are two kinds of interaction between Watson–Crick nucleobases. The first is the hydrogen bonding between nucleobases, where an A-T and a G-C base pairs have two and three hydrogen bonds per pair, respectively. The second is a base stacking interaction caused by π-π interaction between the base pairs. This type of interaction mainly originates from the van der Waals forces.

169 kJ/mol), we use the quantum chemical approach to obtain the potential energy of the proton.The quantum chemical methods (e.g.Hartree-Fock (HF), post-HF theories and density functioanl theory (DFT)) are derived from the Schrödinger equation or Kohn-Sham equation.Since the introduction of the program package such as GAUSSIAN, the quantum chemical approaches have recently been a powerful tool to investigate the molecular properties which include the PES.Many theoretical studies have investigated the PT reactions in AT and GC pairs.Florian et al. investigated the energetics of the PT reactions in GC and AT pairs [4,5].They reported that the GC pair was more stable than its DPT product G*C* by 10 kcal/mol, and the barrier height was estimated to be 14-20 kcal/mol.The DPT reaction would occur rather than the SPT reaction because the SPT reaction causes the charge separation, forming no stable product in the ground state.As an approach to the PES of proton between base pair, Villani has investigated the PES of the protons between AT and GC pair [6] and we also performed the dynamics simulation in semi-classical method [7].However, these PT reactions can occur easily in the presence of chemical modification of nucleobases such as metal complex binding or ionization of GC pair [8].We take a cisplatin ([Pt(NH 3 ) 2 Cl 2 ]) bound GC pair as an example of metal complex bound DNA base pair [9,10].Since cisplatin was discovered by Rosenberg et al. in 1969 [11], Pt complexes have received much attention for their effects as antitumor drugs.Cisplatin distorts the structure of DNA by making a bridged structure with N 7 of guanine (G) or adenine (A).It causes a cell disorder that leads to apoptosis of the living cell.Because cisplatin contains only 11 atoms, it has been a good target for study by quantum chemistry and has been investigated from both the experimental and theoretical viewpoints.Experimentally, it is known that the bridged structure consists of 65% 1,2-d (GpG) (denoted as cis-G-Pt-G), 25% 1,2-d (ApG) (cis-G-Pt-A), and the rest is other bridged structures [12].Nevertheless, the existence of 1,2-d (ApA) (cis-A-Pt-A) is difficult to confirm.The distorted DNAs are observed in X-ray analysis at 1.65-2.50Å resolutions and in NMR experiments.These structures can be freely taken from the protein databank (PDB).We draw the whole structure of DNA and cisplatin bound DNA in Figure 3. From theoretical aspects, cisplatin has many interesting topics such as a ligand substitution, a hydration reaction, differences with transplatin and DNA binding.Ligands of cisplatin become NH 3 and/or H 2 O by hydration reactions, depending on the pH of the solution.Note that the ligands of cisplatin in the human body are recognized as NH 3 .In view of the DNA binding, there have been many studies of the reaction between cisplatin and DNA bases.In particular, Burda's group [13,14] assumed [cis-Pt(NH 3 ) 2 (N 7 -G(or A)),(N 7 -G(or A))] 2+ as the bridging structures and estimated binding energies of Pt-G and Pt-A.They found that the binding of base pair to the Pt atomtend to occur in the order of cis-G-Pt-G, cis-G-Pt-A, and cis-A-Pt-A.The angle of N 7 -Pt-N 7 was about 90° for all cases.They confirmed that these bridges were stabilized by a hydrogen bond between G (or A) and a ligand of the Pt atom, such as H 2 O and/or NH 3 .Furthermore, reactions between cisplatin and two DNA purine bases (such as 1,2-d (GpG), 1,2-d (GpA)) were studied.Their calculated results of reaction barriers and the reaction constants of substitution reactions reproduced the experimental data well.There are two possible influences of Pt-DNA formation: (1) global structural changes, such as the distortion of the DNA duplex structure, or (2) local structural changes, such as a DNA mutation because of proton-transfer reactions.The former case is very hard to tackle with full quantum chemistry computation, because such a system is too huge study with currently available computational resource.For the latter case, the DNA mutation can be estimated using small molecular systems such as several DNA base pairs.In this chapter, we will discuss the possibilities of simultaneous single proton transfers in one or two base pair(s).In Section 2, we will introduce a quantum chemical calculation methods, which we used on the basis of the quantum mechanics.As an application to the DNA-systems, we discuss the possibility of proton-transfer reactions in GC pair in Section 3 & 4. In Section 5, we give the concluding remarks.

A brief introduction to the quantum chemical calculations
In this section, we briefly explain the quantum chemical approaches used in this chapter.There are two main methods in the filed of quantum chemistry.The former is ab initio calculation, which is mainly used in Section 3. The latter is density functional theory (DFT), which is used in Section 4. Because of the limitation in this chapter, for the reader who wants to know the detail of the theory, we refer some textbooks for the quantum chemical approaches [15,16].

Ab initio theory
The field of quantum chemistry starts from solving the Schrödinger equation for the electrons in the molecule.Because nuclei are much heavier than electrons, we can approximate that the electrons moves in the field of fixed nuclei.Then the Schrödinger equation for the electrons becomes equation (1).
where A (and B in (2)), (and ) represent the position of nuclei and electrons, respectively.Note here that we chose the "atomic unit" in which we set m=ћ=e=1 for simplicity.This approximation, called Born-Oppenheimer approximation, is central to quantum chemistry.The total energy E total includes the repulsion between fixed nuclei, i.e., As a wave function Ψ for the electrons, quantum chemists adopt the Slater determinant shown in (3).
(,,, ) The variable x i denotes both the coordinate r and its spin state ( or ).(2N)! -1/2 is a normalization factor.This determinant satisfies the requirement called antisymmetry principle, where a sign of the wave function is changed by interchanging positions of a pair of electrons.In the quantum chemical calculation, each molecular orbital can be described as the linear combination of atomic orbitals (LCAO) n (r) such as Our goal is to minimize the E elec =<Ψ|H elec |Ψ> subject to the constraint that the trial wave function must be orthonormalized by using a variational method.This scheme is called as "Hartree-Fock(HF) theory".HF theory is categolized into the mean field theory.
where the fourth term arise from the antisymmetry principle and is referred as exhange contribution.Within the LCAO approach, above nonlinear coupled equations result in a following secular equation, where where H kl and V klmn are one-and two-electron matrix elements, respectively, and mn is the density matrix.Since the two-electron term depends on the input density matrix, the HF equation is solved self-consistently.HF theory covers 99.5% of the total energy of the whole molecule.However, the remaining 0.5% (equals to the order of 1-10 kcal/mol for small molecules) is quite important in the field of chemistry.To reach this accuracy, we have to consider the "electron correlation" which is the interaction between electrons.There are so many approaches (post-HF theories) to obtain the electron correlation energy.The most frequently used theory for application is the second order of Møller-Plesset (MP2) theory which is the perturbation theory for the dynamical electron correlation.This method is efficient when the HF theory gives the good results.Moreover, the computational cost is the lowest among the post-HF theories.In Section 3, we adopted this theory to obtain the PES of the proton between guanine and cytosine.

Density functional theory
The DFT is derived from the Hohenberg-Kohn theorem, which consists of two theorems: (1) The ground state electron density ρ 0 (r) of a many electron system in the presence of an external potential uniquely determines the external potential.(2) The functional E[ρ] for the ground state energy is minimized by the ground state electron density ρ 0 , i.e.E[ρ 0 ]≤E[ρ] for every trial electron density ρ.When we determine i (r) as a molecular orbital, as we derived the HF equation in previous paragraph, the total electron density can be determined as This summation for variable i runs to the number of occupied molecular orbitals N occ .Kohn-Sham equation can be written as follows: where V H is the Hartree potential which expresses the Coulomb interaction between two electrons.The term v XC [ρ] is "exchange-correlation" potential which replaces the effect from the exchange of electrons used in the HF & post-HF theories.Since the equation ( 9) is similar to the equation ( 5), DFT can be used by the same procedure, i.e.LCAO approxach, as the HF theory.Although DFT includes the electron correlation effects through the empirical correlation potential, the computational cost is much lower than post HF methods.However, no one knows the exact formulation for the correlation potential so far.To obtain the exchange-correlation energy, many types of model exchange-correlation functional have been proposed.Among them, Becke proposed the exchange-correlation functional which includes the HF exchange energy.This method is often called "hybrid functional".In Section 4, we used "mPW1PW91", one of the hybrid functionals.The detailed expressions are given in ref 17.

ONIOM method
The computational cost of ab inito or DFT is over O(N 3 ) where N denotes the number of atoms.Therefore, it is necessary to reduce the computational cost for larger sized molecules which is discussed in this chapter.
ONIOM, which is the abbreviation of "our own n-layered integrated molecular orbital and molecular mechanics" proposed by Morokuma et al. [18], is one of the candidates for the approximate ways of this problem.ONIOM is a kind of the hybrid methods for quantum mechanics/molecular mechanics (QM/MM) calculation, which is de facto standard of biophysical simulations.This method divides the whole molecule into two (or more) parts in order to enable us to compute different level of theories, i.e., large small small ONIOM low high low When we choose the QM (ab initio or DFT) as the higher level calculation and molecular mechanics (MM) as the lower level, we can perform the QM/MM like calculations with this method.In the ONIOM calculation, we replace the boundary atom with a hydrogen atoms.
Figure 4 shows the simple scheme for ONIOM calculations.The potential function of MM E MM are generally written as follows: These terms are the stretch (bonds), bend (bond angles), torsional (dihedral angles) and nonbonded interactions (van der Waals interaction and Coulomb interaction).The constants r eq , θ eq , are obtained by geometry optimization with quantum chemical calculation.We also The variable q i is called as "MM charge" which depends on the computational models.We used this scheme in Section 4.
Fig. 4.An image of ONIOM scheme.In general, the region in orange is computed by the lower level theory such as molecular mechanics (MM).The region in blue is for higher level theory such as ab initio or DFT.

Computational details
Firstly, we focused on the proton-transfer reaction between a GC pair.We simplified the model to the system which consists of one GC pair and cisplatin, i.e. [Pt(NH 3 ) 3 GC] 2+ .Geometry optimizations were first performed by the MP2 method.As the platinum is a heavy element, we have to consider the relativistic effect.In order to reduce the computational cost, we adopted an effective core potential (ECP) which implicitly includes the relativistic effect.As a typical ECP, we used the LanL2DZ basis function (We here denote this set of calculation as "MP2/LanL2DZ").Later hydrogen bonding energy was calculated at those optimized structures with correction of a basis set superposition by the counterpoise method.All calculations were performed by GAUSSIAN03 [19].The hydrogen bond lengths, energies, induced charges and all possible proton transfer reactions among the bases were calculated.

Local changes of properties in platinum complex bound GC pair
In this subsection, we compared neutral GC pair with the platinum complex bound GC pair.Especially, we focused on the hydrogen bonding energy, hydrogen bonding length and IR spectra.First, we summarized the results of the optimization in Table 1.

Hydrogen bond length and energy:
The major difference between normal GC pair and platinum complex bound GC pair is the length between O 6 (G) and N 4 (C).This is caused by Pt 2+ cation which attracts the O 6 (G).As a result, the hydrogen bond length O 6 (G)-N 4 (C) becomes larger.On the other hand, the hydrogen bond length N 1 (G)-N 3 (C) is not affected by the platinum complex binding.The hydrogen bond energy of the base pairs is given by the energy difference between [Pt(NH 3 ) 3 G] 2+ + C and [Pt(NH 3 ) 3 GC] 2+ .The results show that the hydrogen bond energy increases by 4 kcal/mol by Pt complex formation.Changes in IR spectra: Next, the vibrational analyses were performed by MP2/LanL2DZ at the optimized structure obtained by the same method.The GC pair has three peaks of N-H stretching modes related to the hydrogen bonds.We defined three N-H stretching modes O 6 …H-N 4 , N 1 -H…N 3 and N 2 -H…O 2 as stretch1, stretch 2 and stretch 3, respectively.Figure 5 shows the results of peak shifts before and after the Pt binding.In the case of N-H stretch between O 6 (G)-N 4 (C), about 250 cm -1 blue shift was observed and the intensity became lower.This means the hydrogen bonding becomes distant and weaker.In the case of N-H stretch between N 2 (G)-O 2 (C), on the other hand, about 300 cm -1 red shift was observed and the intensity became higher showing that the hydrogen bonding becomes stronger.These shifts can be explained by the hydrogen bonding length.In the case of N-H stretch between N 1 (G)-N 3 (C), about 400 cm -1 red shift was observed.From these results, it was found that the additional hydrogen bond between the H atom of the ligand and O 6 of G affects the stability of the complex.Fig. 5. IR spectra of GC pair and platinum complex bound GC pair.The peak numbers correspond to the N-H stretching modes.

Potential energy surface of proton
The other hydrogen bonds become closer because of the electrostatic interaction induced by the Pt binding.Especially, N 1 (G) and N 3 (C) become closer and the potential energy curve of the hydrogen atom between them has a double minimum.Next we proceed to investigate a feature of local changes at the hydrogen bonds by observing the PES as a function of positions of H atoms in order to understand the peak shifts.The GC pair has three hydrogen bonds: O 6 …H-N 4 , N 1 -H…N 3 and N 2 -H…O 2 , respectively.We focused on the two protons: O 6 …H-N 4 and N 1 -H…N 3 , which were concerned with the SPT or DPT reactions as shown in the introduction.We obtained an energy of optimized geometryV(x,y) as a function of bond length O 6 -H (x) and N 1 -H (y).We fitted the PES as the following equation.

V(x,y)=
, 6 where C ij is the expansion coefficient.We used the PES of normal GC pair computed by Villani [6].We draw the PESs as shown in Figure 6 and listed the expansion coefficients in Table 2.
There are explicit differences in PESs after the Pt binding.In the normal GC pair, two local minima were found, which correspond to the DPT reaction.On the other hand, O 6 -H are fixed near the global minimum, N 1 -H has two minima in the platinum complex bound GC pair.The former is near N 1 -H=1.10 and the latter is near N 1 -H=1.70,respectively, which corresponds to SPT reaction.It was confirmed that its energy difference and energy barrier are very small.

Proton-transfer reaction in Pt+GC pair
We show the existence of the structure that undergoes SPT reaction between N 1 (G) and N 3 (C), which is hereafter denoted as a G -C + pair.The barrier of the DPT reaction, which occurs www.intechopen.com  in normal GC pair, is 15.2 kcal/mol, which gives the similar result to Florian's work [5].On the other hand, there is no DPT structure of the cisplatin bound GC pair. Figure 7 sketches the optimized structures of the GC and G -C + pairs, and the transition state (TS).It is confirmed that all of the structures keep their planarity, even after the Pt complex binding and proton transfer.Nevertheless, the distances between the atoms involved in hydrogen bond vary significantly as shown in Table 3.The hydrogen bond of O 6 N 4 increases by 0.15 Å due to the influence of the "additional" hydrogen bond between O 6 and the ligand of cisplatin.The other hydrogen bonds shrink because of the electrostatic interaction induced by the Pt binding, as discussed below.In particular, the hydrogen bond between N 2 (G) and O 2 (C) decreases by 0.19 Å.There is a weak dependence of the ligands in these distances of hydorgen bonds for the GC pair.On the other hand, a stronger dependence is found for the distance between bases of G -C + pair.O 6 N 4 , N 1 N 3 , and N 2 O 2 distances in G -C + pair are shortened by 0.05, 0.08, and 0.02 Å compared with the normal GC pair, respectively.These facts indicate that all of the hydrogen bonds become stronger in comparison with the normal GC pair.In what follows, we examine where these differences arise.Charge distributions: The natural bond orbital (NBO) charges of atoms associated with hydrogen bonds and Pt-G coordination, listed in Table 4, shows that in the GC pair the charge on O 6 of G increases by interaction with the ligand of Pt.The hydrogen bond strength between a ligand and O 6 of G influence the charge of O 6 , which leads to the difference in the whole hydrogen bonds.The NBO charge on Pt decreases.Therefore, a charge transfer takes place mainly from the guanine and partially from the cytosine to the Pt atom.Such a charge transfer leads to a decrease in the charge on N 1 in guanine and an increase in the charges on all H atoms between the bases.The foregoing discussion gives clues for the reasons why the hydrogen bonds are strengthened: (i) the charge transfer mainly from O 6 of G to the Pt and H atoms, and (ii) additional formation of a hydrogen bond between L 1 and O 6 of G, as pointed out above.Strong dependences of the ligand on the charge of Pt, N 7 , and O 6 are found.In the platinum bound GC pair, only a small influence is observed in the Mulliken charges on the atoms in C, whereas the changes are more significant in the G -C + pair.The charges on all the heavy elements except for O 6 increase compaired to the GC pair.Moreover, strong influences of the ligand on the charge are found for Pt, N 7 , O 6 , as well as N 1 .For further understanding of the interactions among the Pt atom, ligands, and the bases, the sum of the NBO charge on the bases and the ligands are listed in   2+ .In the normal GC pair, both G and C are almost neutral.In contrast, both G and C in the platinum bound GC pair are positive due to the charge transfer from the bases mainly to the Pt atom.As for the G -C + pair, however, G and C become negative and positive, respectively.Note here that C includes the hydrogen atom that initially belongs to the G in the GC pair as a result of SPT from G to C. Since the charge on the Pt atom increases, charge transfer from G to the ligands of cisplatin accompanies the SPT reaction.

Summary of section 3
We have numerically elucidated the changes in the hydrogen bonds of the base pairs due to Pt complex formation by means of MP2 theory.For the platinum bound GC pair, the hydrogen bonding energy exceeds by 310 kcal/mol than GC pair without platinum complex.The hydrogen bond between O 6 N 4 is lengthened, whereas the other hydrogen bonds are shortened.These observations are explained by a rearrangement of the charge distribution.In this section, we revealed that the binding of platinum complex causes a single proton-transfer (SPT) reaction between N 1 (G) and N 3 (C) in the GC pair.Note here that the SPT reaction does not occur in the GC pair itself, while double proton-transfer (DPT) does.Its reaction barrier decreases from 15-20 kcal/mol of the DPT reaction without the Pt complex to 1.5-3 kcal/mol of the SPT reaction with the Pt complex.The structure that underwent the SPT reaction is as stable as the original structure.

Global and local change of GC pairs by coordination of platinum complex
In stacked two GC pairs, althogh DPT reactions can occur independently.However, these reactions hardly take place because of high energy barriers as seen in one GC pair [20].For further research, it is natural to study what happens when two or more base pairs are stacked.For the simplicity, we hereafter denote a "G -C + pair" (the product of SPT reaction in GC pair) as a "G*C pair".

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Metal-Assisted Proton Transfer in Guanine-Cytosine Pair: An Approach from Quantum Chemistry 179

Computational details
Modeling: We first define two types of model systems: the "two base pair" (2bps) model and the "four base pair" (4bps) model.The former consists of two base pairs and cisplatin without the backbone molecules, such as sugar and phosphate groups, while the latter consists of four base pairs and the backbone molecules so that it includes the effects of both the backbone molecules and base stacking.The 2bps model is small enough to compute with the full quantum chemistry calculation.Density functional theory (DFT) was adopted and the modified Parr-Wang functional (mPW1PW91) was chosen as an exchange-correlation functional, because the functional is modified to better describe the hydrogen bonding.For the calculations described in this chapter, the Stuttgart/Dresden ECPs were used for the Pt atom and the 6-31G (d, p) basis for the other atoms.ONIOM method: To investigate the effects of DNA stacking, the backbone and counter cations, we proceeded to the 4bps model by ONIOM method introduced in Section 2.3.We here treated two of the four base pairs as the higher layer and the rest as the lower layer.We utilized the method used in the 2bps model for the higher level calculation and the universal force fields (UFF) for the lower level calculation in ONIOM cacluation.We took the initial structure 1,2-d (CpX 1 pX 2 pT) from PDB (PDBID:1A84), where X 1 and X 2 are purine moieties bound to the Pt complex so that there are three patterns of X 1 and X 2 .The ligands of the cisplatin were assumed as NH 3 , as in the human body.We also assumed that the Pt atom binds to N 7 of G and A. To keep the whole system neutral, we added sodium atom at every PO 4 -molecule as the counter cation.Table 6.Energy differences of substitution reaction (in kcal/mol) Why cisplatin prefers guanine to adenine: Figure 9 shows the reason why cisplatin prefers guanine to adenine.It is known that cisplatin attacks to major groove of DNA base.Guanine has N 7 and O 6 which attract positive charge.On the other hand, adenine has amino group in N 6 .One of H atoms in amino group prevent positive charge from attacking to major groove.

2bps model
If cisplatin binds to adenine, this amino group has to be rotated which needs much energy.Thus, cisplatin prefers guanine to adenine.Table 6 shows this tendency exactly.Therefore, we will focus on the models of cis-(CG) p -Pt-(GC) d and cis-(CG)-Pt-(AT) in further discussion.
Fig. 9.The major groove of GC and AT pair where cisplatin attacks.In the case of AT pair, amino group of N 6 (A) prevents cisplatin from attacking to N 7 .

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Metal-Assisted Proton Transfer in Guanine-Cytosine Pair: An Approach from Quantum Chemistry 181 Proton-transfer reactions in 2bps model: Next, we discuss the possibility of multiple protontransfer reactions in these systems.Here we depict a restricted two-dimensional potential energy surface (PES) of two different hydrogen atoms between N 1 (G p/d ) and N 3 (C p/d ) in figure 10, where the geometry except for the two hydrogen atoms is fixed.The rigid PES used here is very rough approximation, because it does not consider the effect of structure relaxation.Nevertheless, it is at least useful to intuitively understand the proton transfer reactions between bases.In this subsection, we depicted this PES in order to confirm whether proton-transferred structures exist or not two stacked base pairs.The origin of the PESs are at the center of both hydrogen bonds, and the PESs were plotted every 0.05 Å.From this figure, it shown that there are three possible minima, at the points marked as X in the figures.No two simultaneous SPT reactions are found because the potential energy of cis-(CG*) p -Pt-(G*C) d is very high as shown in ▲.We here confirmed that one SPT reaction can occur even in two GC pairs.Figure 11    This implies that a multiple SPT reactions can occur in cis-(CG)-Pt-(AT).Nevertheless, the energy difference between local minima is so large that the proton-transfer reaction may not occur at room temperature.The tendency does not change even after the SPT reaction took place in the GC pair.Table 8 summarizes the possibilities for multiple proton-transfer reactions in all the systems.Note that the SPT reaction occurs in platinum-bound GC pair, and the DPT reaction occurs in AT pair.The DPT reaction can also be found even after the SPT reaction between N 1 (G) and N 3 (C) has occurred.The SPT reaction in the AT pair cannot occur, because the Pt complex binding increases the distance between N 1 (A) and N 3 (T).In every case of the DPT reactions, the product of DPT reaction becomes more unstable than the original structure.

4bps models
Our calculations elucidated that SPT structures of the cis-(CG)-Pt-(GC) type can exist even in 4bps models.Two different optimized structures are shown in Figure 13, which shows one planar GC and one distorted GC pair as well as the 2bps model of cis-(CG)-Pt-(GC).We also found that the backbone and stacking bases do not change their postion much from their original geometry during the SPT reaction.
We extracted the higher layer, i.e., the 2bps and Pt complex, from the 4bps model to shown in Table 9.From this table, the energy differences between the original structure and the proton-transferred structures are estimated as 3-3.5 kcal/mol.From these results, the reaction energy of the SPT reaction is estimated to be lower than the case of 2bps model.The distance Pt-G is defined as the distance between Pt and N7 of guanine.b: The angle Gp-Pt-Gd is defined as N7 (Gp)-Pt-N7 (Gd).c: The unit of distance is angstrom, the unit of angle is degree.For further research, it is also necessary to discuss the possibilities of proton-transfer in larger system.In such systems, it is necessary to consider not only the optimized structure but also structural fluctuations.The mean structure between the original and the SPT structures may be observed at room temperature.The dynamic effects will be investigated in our future work.

Summary of section 4
The binding affinity of cisplatin to base pairs were in the following order in our calculation, cis-(CG)-Pt-(GC), cis-(CG)-Pt-(AT), and cis-(TA)-Pt-(AT), when complementary base pairs were taken into account.From their energetics, the structure of cis(TA)-Pt-(AT) is expected to be notfound at room temperature.The SPT reaction can occur in systems that consist of two base pairs and cisplatin.The reaction barrier is as low as 6-7 kcal/mol, which is similar to the case of one GC pair with cisplatin, and the SPT structure is as stable as the original structure.From these results, it is possible that the coordination of cisplatin to DNA causes a mispairing of the GC pair that leads to a mutation of the DNA.The SPT reaction causes this in one of the GC pairs.On the other hand, two simultaneous SPT structures like cis-(CG*)-Pt-(G*C) are forbidden.This is explained by the analysis of charge distributions.After one SPT reaction occurs, the proton donor G becomes negative and the proton acceptor C positive.At the same time, the other C also becomes positive through electrostatic effect from virtically stacked base pair that under went SPT reaction.Therefore, the subsequent SPT reaction from the other G is forbidden by Coulomb repulsion.The SPT reaction between G and C can occur with cis-(CG)-Pt-(AT).This result is similar to the case of one GC pair.By using the ONIOM method, the SPT reaction is also shown to occur in the system consisting of cisplatin and four base pairs containing the backbone molecules (4bps model).

Conclusion
We investigated the change of proton-transfer reactions in DNA base pairs caused by the coordination of cisplatin by density functional theory (DFT) and ONIOM method.When the cisplatin binds to GC pair, the structure undergoes intermolecular proton transfer from G to C (denoted as G*C pair) resulting in an increase of the bonding energy by 3-10 kcal/mol.This renders the structure to be metastable due to (a) successive processes of charge transfer from G to cisplatin thereby stabilizing the GC and G*C pairs and (b) an additional hydrogen bond between G and the ligand of Pt atom.From the energetics of two base pairs with the cisplatin, it is theoretically confirmed that the Pt complex is likely to bind in the following In contrast to cisplatin, multiple single proton-transfer reactions may occur in the system consisted of two base pairs with transplatin.The optimized structure agrees with the experimental data for Pt-G coordination except for the hydrogen bond length.

Fig. 3 .
Fig. 3. Observed structure of normal DNA (B-type) and distorted structure by cisplatin.

Fig. 6 .
Fig. 6.The potential energy surface of two protons in (a) normal GC pair (b) platinum complex bound GC pair.The unit of the number is kcal/mol.

Fig. 7 .
Fig. 7.The reaction diagram for proton-transfer reaction in GC pair.(a) normal GC pair (b) platinum complex bound GC pair.In (a), double proton-transfer reaction occurred, and in (b), single proton-transfer reaction occurred.

Figure 8
shows the all optimized geometries of the three types of model molecules: cis-(CG)-Pt-(GC), cis-(CG)-Pt-(AT) and cis-(TA)-Pt-(AT).The structure of cis-(CG)-Pt-(GC) was distorted in comparison with those in the DNA because of repulsion between the two O 6 atoms.Although one of the GC pairs keeps a planar structure, the other GC pair was greatly distorted.We distinguish them by referring to the former planar pair as the "(GC) p pair" and the latter distored pair as the "(GC) d pair".This distortion may lead to the stabiity of whole system in cis-(CG)-Pt-(GC).Hereafter, we will describe the structure of the 2bps model in the form cis-(GC) p -Pt-(GC) d .Unlike the structures of cis-(GC) p -Pt-(GC) d , all base pairs in the cis-(CG)-Pt-(AT) and cis-(TA)-Pt-(AT) almost keep their planarity.We evaluated the binding energy of cisplatin and the base pair.To estimate the hydrogen bonding energy, we assumed a two-step reaction: (1) [Pt (NH 3 ) 4 ] 2+ + B p -B´p -> [Pt (NH 3 ) 3 B p B´p] 2+ + NH 3 (reaction energy: ΔE 1 ) (2) [Pt (NH 3 ) 3 B p B´p] 2+ + B d B´d -> [cis-Pt (NH 3 ) 2 B p B´p B d B´d] 2+ + NH 3 (reaction energy: ΔE 2 ), where B x is A or G, B´x represents the complementary base of B x (x = p, d).Results are shown in Table 6.Comparing the ΔE 1 values, the binding energy of Pt-(GC) is much higher than that of Pt-(AT), by 30 kcal/mol.ΔE 1 is larger than ΔE 2 because of the Coulomb repulsion between the original [Pt (NH 3 ) 3 B p B´p] 2+ and the additional base pair.Moreover the bases are likely to bind to the Pt complex in the order cis-(CG)-Pt-(GC), cis-(CG)-Pt-(AT) and cis-(TA)-Pt-(AT).In particular, the binding energy of the cis-(TA)-Pt-(AT) is remarkably low compared with those of cis-(CG)-Pt-(GC) and cis-(CG)-Pt-(AT).These results support both experimental evidence and the tendencies of the models studied by Burda and Leszyczynski [13], as mentioned in the introduction.
shows the results of geometry optimization of cis-(CG) p -Pt-(GC) d , cis-(CG*) p -Pt-(GC) d and cis-(CG) p -Pt-(G*C) d , where G* again means the guanine donating a proton.This result is similar to the SPT reaction in one GC pair calculation described in previous subsections, where the reaction barrier is about 5-6 kcal/mol.The difference of the energy barrier between cis-(CG*) p -Pt-(GC) d and cis-(CG) p -Pt-(G*C) d i s b e c a u s e o f t h e difference in their planarity.A structure of two simultaneous SPT, cis-(CG*) p -Pt-(G*C) d , cannot be found, as expected from the potential surface depicted in figure 10.Next, the sum of charges obtained by the natural bonding orbital (NBO) is analyzed.Table 7 lists the results of the sum of the NBO charges.Every part of cis-(CG )p -Pt-(GC) d has a positive charge, but both C p and C d are almost neutral.When the SPT reaction occurs, the

Fig. 10 .
Fig. 10.(a) Definitions of variables in a 2bps model of cis-(CG) p -Pt-(GC) d .Only the hydrogen atoms surrounded by the dotted line in each GC pair were moved.(b) The potential energy surface of hydrogen atoms.The numbers on each axis represent the distance between N 1 (G) and the hydrogen atom (in Å).The origin is set at the point where both hydrogen atoms are at the middle of the hydrogen bonding.

Fig. 12 .
Fig. 12. Definitions of variables in the 2bps model of the cis-(CG)-Pt-(AT).The numbers in the contour plots represent the energy in kcal/mol.

Fig. 13 .
Fig. 13.The optimized structures of the 4bps models of (a) cis-(CG) p -Pt-(GC) d , (b) cis-(CG*) p -Pt-(GC) d , and (c) cis-(CG) p -Pt-(G*C) d .Atoms depicted with balls are set to higher layer and with wires are set to lower layer in ONIOM calculations.
Without the effects of the backbone and the stacking base pairs, the structure of cis-(CG) p -Pt-(GC) d is so distorted that we cannot expect it to describe the actual structure in the DNA.The optimized structure of the 4bps cis-(CG)-Pt-(GC) model agrees with results from NMR experiments in view of the Pt-G coordination, but not of the hydrogen bond length.Because the structures of cis-(CG*) p -Pt-(GC) d and cis-(CG) p -Pt-(G*C) d are as stable as the original one, their mean structures may be observed in experiments.
order: cis-(CG)-Pt-(GC), cis-(CG)-Pt-(AT), cis-(TA)-Pt-(AT).The Pt atom is expected to bind to the N 7 site of G and A. This result supports the experimental evidence, where the structure cis-A-Pt-A is seldom observed at room temperature.The single proton-transfer reaction occurs in one of the two GC pairs.No simultaneous single proton-transfer reaction can occur in both base pairs.Two different single proton-transferred structures (cis-(CG*) d -Pt-(GC) p and cis-(CG) d -Pt-(G*C) p , where * means a proton donor of G) are as stable as the original structures (CG) d -Pt-(GC) p .The same tendency was observed with cis-(CG*)-Pt-(AT).

Table 1 .
Summary of the change caused by the coordination of platinum complex.

Table 2 .
Expansion coefficients of C ij in platinum complex bound GC pair.

Table 3 .
Hydrogen bonding length in Pt+GC pairs (in Å)

Table 5 .
As a reference, the total charges in the unbound case is estimated
a: The "2bps model" was used.b: The optimized NH3 and [Pt(NH3)4] 2+ is used for energy calculation.c: The numbers in parentheses represent the energy including zero-point energy.

Table 9 .
The differences of energy in "4bps model" molecules (in kcal/mol)We next compared the optimized structure with experimental data from the protein data bank (PDBID: 1A84, 1AU5 and 1KSB) as summarized in Table10.The hydrogen bond lengths of 1A84 and the optimized structure show poor agreement with each other, where the distance between (O 6 ) d and (N 4 ) d is about 3.3 Å in the former, which is too large to form hydrogen bonds.Except for this result, the optimized 4bps model of cis-(CG) p -Pt-(GC) d agrees well with the experimental data in the coordination Pt-G and the error is within 0.05 Å.On the other hand, the error of the hydrogen bond length is significant, e.g., the hydrogen bond length of (O 2 ) p -(N 2 ) p is 2.75 Å for the 4bps model of cis-(CG) p -Pt-(GC) d and 2.96 Å for 1AU5.This is because the energies of cis-(CG*) p -Pt-(GC) d and cis-(CG) p -Pt-(G*C) d are as stable as those of cis-(CG) p -Pt-(GC) d so that the mean of these structures may be observed in the experiment because of the low energy barrier of the SPT reaction.Indeed, the error is improved when the structures of cis-(CG*) p -Pt-(GC) d and cis-(CG) p -Pt-(G*C) d are taken into account.In this case, it is possible that the dynamic fluctuations may dominate the structure of the system. a:

Table 10 .
Selected lengths of optimized geometries and the experimental data from the protein databank