Coupling Between Hydrogen Atoms Transfer and Stacking Interaction

Article pubs.acs.org/JPCB

Coupling Between Hydrogen Atoms Transfer and Stacking Interaction in Adenine-Thymine/Guanine-Cytosine Complexes: A Theoretical Study Giovanni Villani* Istituto di Chimica dei Composti OrganoMetallici, ICCOMUOS Pisa Area della Ricerca del CNR, Via G. Moruzzi, 1, I-56124 Pisa, Italy S Supporting Information *

ABSTRACT: Four different complexes of two base pairs, an adenine−thymine and a guanine−cytosine one, have been studied in order to understand the modifications induced by the staking interaction between the two base pairs on the hydrogen atoms transfers between the bases in either base pair. The inclusion of these two kinds of interactions allows us to clarify if some properties, as the mechanism of hydrogen transfer, is exclusively a local effect of a base pair or can be modified by a more long-range interaction between the base pairs. The results on these four complexes are compared with those of the monomeric systems, the A−T and G−C base pair, and with those of the A−T and G−C dimers. The specificity of each complex and of each hydrogen bond has been analyzed.

1. INTRODUCTION Two are the principal nonbonding interactions present in the DNA: the hydrogen bond and the stacking interaction. The first is a polar interaction that bonds two bases and it generates the base pair and is named interstrand because is an interaction between the two chains; the second is a apolar π−π interaction and it is named intrastrand because is an interaction inside a chain. Both types of interactions are largely considered in literature, but rarely have they been considered together, with the modification induced by one on the other.1−8 In particular, in literature, there can be found a study on the dimers of the A−T3 base pair and others on the G−C4−8 system, but the structures of the complexes between two different base pairs have never been studied, and only the stacked energy of all ten dimers have been computed.1,2 These last complexes are important in itself and also in order to complete the ten different cases of two base pairs along the DNA. From the first ab initio papers of Florián et al.,9,10 several theoretical studies of hydrogen transfer on both adenine− thymine11−14 and guanine−cytosine base pairs15−22 have been reported in literature. Generally, there is a greater interest in the of G−C base pair due to a higher stability of the imino-enol tautomers of this base pair. In fact, in the case of A−T base pair the two energy minima (Watson−Crick and imino-enol structure) are separated by a low-lying transition state, whereas in the case of G−C base pair, the two minima are well separated from a transition state and a double proton transfer23 is a thermodynamic possible process in the gas phase. In any case, both the imino-enol tautomer of A−T and those of the G−C base pairs can be present in a not negligible amounts.14,15 © 2014 American Chemical Society

Experimental results on DNA structure, elasticity and deformation can be used for studying the stacking interaction starting from the base-pair level. This approach describes the relative location and orientation of neighboring base pairs in terms of intuitive parameters such as twist, rise, slide, roll, and so forth,24−27 and is useful to provide a mechanical interpretation of the biological function of a particular sequence of base pairs in DNA.28 It is well known that many biological processes and technological applications of nucleic acids rely on the sequence heterogeneity. First of all, A−T and G−C base pairs have different relative binding strength due to the presence of two rather than three interbase hydrogen bonds. Moreover, the stacking interaction between neighboring base pairs depends on sequence. As a consequence, it has been observed that mechanical and structural properties (such as flexibility, helical twist, and even helix type) are also influenced by the sequence.28−31 To highlight the effects of sequence on the thermodynamics of DNA, it is sufficient to point out that the melting temperature of two oligomers with the same length, but different sequences can vary by more than 50 °C and two sequences of the same length and the same number of A−T and G−C base pairs can still have melting temperatures that differ by more than 10 °C.32 The coupling of stacking and hydrogen bond interactions has been evidenced in experimental data. On crystalline DNA, some DNA structural parameters have been found to be sequence Received: March 20, 2014 Revised: April 22, 2014 Published: April 29, 2014 5439

dx.doi.org/10.1021/jp502792r | J. Phys. Chem. B 2014, 118, 5439−5452

The Journal of Physical Chemistry B

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dependent,29,33−35 and thermodynamic studies36 and measurements of the two-bond deuterium isotope shift37 also have suggested this coupling. A simple theoretical model that includes both the hydrogen transfer and the stacking interaction in the study of DNA is the coarse-graining model, where some simulations for a given sequence of around one hundred of base pairs can be done for nanoseconds time at a fixed temperature. For example, in ref 38, a nucleotide is replaced by a particle and a potential function is adopted for interactions between the particles: Morse-type function for the hydrogen bonds in base pairs and a weak harmonic oscillator for the π-stack effect between the base-pairs. It is proved that to simulate long time and length scale processes involving DNA, the use of a coarse-grained description can be adequate.39 The effects of the stacking interaction on the A−T and G−C base pairs have been studied quantum mechanically in dimers of the A−T and G−C base pairs.1−7 Recently, Acosta-Silva et al.22 carried out a complete DFT optimization of different structures of G−C and Gil et al.40 of A−U and A−T dimers. The firsts start from the discrepancy between the theoretical and experimental results about the relative length of the different hydrogen bonds in the G−C base pair and suggest that the stacking can be one of the factor to explain this disparity between theory and experiment. In fact, they found in their calculations that the stacking leads to an increase of the OG---H hydrogen bond in the OG---H-NC H-bridge with a simultaneous decrease in the NGH---OC one. The seconds found in the A−T dimers that the NA--H hydrogen bond in the NA---H-NT H-bridge is weakened by the stacking interaction, whereas the effect of stacking interaction on the NA-H---OT H-bridge depends on the system considered, with an increase of the H---OT hydrogen bond length in some cases and a decrease in others. Our previous results on A−T7 and G− C8 dimers support the idea that the variations of the properties due to the coupling of hydrogen transfer and stacking interaction depends upon the dimer considered and are different for one or the other hydrogen bond. Also, the different mechanisms of double hydrogen transfer (step-to-step and concerted) can be modified by the stacking interaction between the base pairs. Hence, some generalizations found in literature must be analyzed in detail. The goal of this paper is to achieve a deeper description of the mutual relationship between the stacking and the hydrogen bonding interactions in the complexes of the adenine−thymine/ guanine−cytosine, considering all the four distinguishable cases (see later). In literature, in fact, are present only the cases of dimers of A−T and G−C, as we said, but it is not present a study of the systems considered here. Its importance for a complete description of base pair/base pair interaction in DNA is obvious. In fact, when all possible cases of neighboring base pairs will been considered, it will be possible a quantum mechanical study of a specific polypeptide that goes beyond the oversimplified coarsegrain model and allows to understand, with the same kind and with the correct precision, both the strictly local effects (into the base pair) as well as those due to the long-range (between the base pairs) interactions.

(a) We have assumed the antiparallel strands of DNA, where the asymmetric 5′ end is related to the bases 1 and 4 and the 3′ end to the bases 3 and 2 (see Figure of ref 8), with the names of these four complexes (AC/GT, CT/AG, TC/GA, and TG/CA) following the convention (base 1 base 3/base 4 base 2) of ref 41. (b) We have not included in the study the two sugar− phosphate backbones between the bases 1 and 3 and the bases 2 and 4 because these have minor influence on both the stacking geometry and on the hydrogen atoms transfer.42−45 (c) The calculations have been performed with Gaussian package (2009 A.146) on density functional theory (DFT) in cc-pVDZ basis set, with the M06-2X47 functional of Thrular. (d) We have simplified the notation of the H-bridge in the adenine−thymine base pair with, in all cases, the first heavy atom on the adenine base and similarly in the guanine− cytosine one, with the first atom on the guanine base. (e) We have performed a partial optimization of the internal coordinates of these systems. In particular, we have fixed the N−H distance in one of the two H-bridge of the A−T base pair (or of the three ones in G−C) and we have optimized all others internal coordinates. This allows us to follow the minimum energy path of the multidimensional (in internal coordinates) PES, with a constraint in one specific coordinate. In particular, we have analyzed the effect of the movement of a hydrogen atom in a base pair on the atoms in the other base pair. (f) We have also analyzed the simultaneous movement of two hydrogen atoms in two H-bonds of different base pairs and compared these cases with the independent movements of these atoms. In these cases, two constraints are assumed in the optimization of the structures. The choice of which pair of hydrogen movements must be considered is not so easy as in the A−T and G−C dimers, where two similar Hbridges in the two base pairs have been assumed. To do this choice in this study, we have analyzed the variations of the natural charges of the atoms involved in the five Hbridges, when a specific hydrogen atom moves.

3. RESULTS AND DISCUSSION For obtaining the optimized structures of the four complexes in study (AC/GT, CT/AG, TC/GA, and TG/CA), as in our previous paper on A−T and G−C dimers, we start from the four different starting points of ref 41 for each complex: the geometries derived from fiber diffraction data, idealized geometries with partial inclusion of geometrical parameters known from X-ray studies and selecting appropriate geometries obtained from molecular dynamics (MD) simulations (from random and average studies). In the cases of AC/GT and TC/ GA complexes, only one stable structure is found, independently from the starting point. In the CT/AG and TG/CA cases, two stable structures have been found. In particular, in the first complex two practically isoenergetic structures, but with dipole momentum of 7.17 and 6.61 D, and we have chosen to use the first structure for studying the coupling between the stacking interaction and the hydrogen atom transfer because three starting points give this structure and only one (MD from average study) gives the last structure. In the case of TG/CA complex, instead, the choice of the structure is determined from the stability because these two structures have a difference of

2. COMPUTATIONAL METHODS In this paper, we have studied the four complexes of adenine− thymine and guanine−cytosine base pairs. After having studied the three adenine−thymine dimers7 and the three guanine− cytosine ones,8 these are the last cases of the ten canonical stacked two base pairs.41 As in our previous papers,7,8 5440



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Figure 1. Lateral vision of the optimized structures of AC/GT, CT/AG, TC/GA, and TG/CA systems.

Figure 2. Vision from the above of the optimized structures of Figure 1. The up base pair is evidenced with dark bonds and shadows of the atoms and the down with the bright.

energy of around 6.8 kcal/mol. In this case, the most stable structure has been utilized for studying the coupling between the stacking and the hydrogen bond. In Figure 1 and 2 are shown the structure of each complex used, in two visions (lateral (Figure 1) and from above (Figure 2)).

The most stable structure is that of the TG/CA complex and the other three structures have a difference of energy of 6.9 (AC/ GT), 8.1 (CT/AG), and 8.3 kcal/mol (TC/GA), more large than the differences of energy between the different structures in the A−T and C-G dimers. In Figure 1 and 2, it is evident that 5441



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Table 1aDistances and Angles of the Atoms of the Three H-Bridges of the G−C and of the Two H-Bridges of the A−T Base Pairsa OG---H-NC GC AT AC/GT AC/GT CT/AG CT/AG TC/GA TC/GA TG/CA TG/CA a

u d u d u d u d

NG-H---NC/NA----H-NT

NG-H---O C/NA-H---O T

O−N

O---H

OĤ N

N−N

H---N

NĤ N

N−O

H---O

NĤ N

2.767

1.727

178.6

2.823 2.759

1.786 1.718

179.3 176.3

2.772

1.735

176.2

2.809

1.776

179.4

2.908 2.785 2.871 2.921 2.924 2.814 2.752 2.886 2.802 2.914

1.873 1.728 1.825 1.889 1.894 1.758 1.687 1.849 1.807 1.878

175.8 178.9 175.5 172.5 172.4 174.7 175.2 173.3 158.1 173.6

2.915 2.944 2.834 2.870 2.940 2.933 3.050 2.936 3.009 2.915

1.891 1.926 1.823 1.852 1.920 1.923 2.057 1.912 2.013 1.897

177.7 172.9 167.8 171.6 174.4 169.0 162.9 175.2 163.2 171.4

Distances (Å) and angles (degrees).

TG/CA but decreases in the TC/GA one; and the H---OC in NGH---OC increases in CT/AG, TC/GA, and TG/CA but decreases in the AC/GT system. Moreover, in the hydrogen bonds of the A−T base pair of the complexes, the H---N(O) distances increases in all complexes, except the H---NA distance of NA---HNT bridge in the TC/GA system. Comparing the variations of the Wiberg indexes (Table 1b) and those of the hydrogen bond distances, we can see that in general it is true that an increase of the distance means a decrease of the strength of this bond, but the more complex variations in the NG-H---NC and NA----H-NT H-bridges signal that one must advise caution in this type of generalization. A second general consideration, related to the strength of the different hydrogen bonds of these complexes, can be done by the Wiberg indexes of Table 1b. Similar to the monomeric case, the strongest hydrogen bond is NA---H of the NA---H-NT H-bridge, as shown for example from the TC/GA case where the Wiberg index of this hydrogen bond is more than four times larger of that of H---OT in the NAH---OT H-bridge. In this Table 1b, we have also shown the Wiberg indexes of both the covalent and the hydrogen bond of these H-bridges. From the comparison between the stacked cases and the monomer one, we can point out that an increase of the strength of the hydrogen bond generally means a decrease of the corresponding covalent bond of the same H-bridge and vice versa. We note that this is a general rule that resume a more complex situation, as demonstrated for example from the CT/ AG complex where both the NT-H and the H---NA Wiberg indexes of the NA---H-NT H-bridge decrease, compared to the AT monomer. In Figure 3, we have shown the potential energy curves of the four complexes in study (AC/GT, CT/AG, TC/GA, and TG/ CA) as a function of the difference of the N−H distance from the equilibrium value in one of the H-bridges. Here, and in all following figures, the curve (black) is used to refer to the NA-H--OT H-bridge, (red) to NA---H-NT, (green) to OG---H-NC, (blue) to NG-H---NC, and (teal) to NG-H---OC. In Figure 4, there are the energy differences between the curves of Figure 3 and those of the A−T (Figure 3a of ref 7) and the G−C (Figure 4 of ref 8) monomers. In all this figure, we have assumed as distinguished coordinate only the N−H covalent bond of each H-bridge, but we should remember that this does not mean to assume a monodimensional cut in the internal coordinates of the multidimensional PES. In fact, due to the optimization (with only the N−H distance constrained) of all other coordinates, every bonds and angles are modified at each point of this potential energy curve. In fact, if we do not consider these changes and we perform only a monodimensional cut in the N−

there is a different overlap between the two base pairs due to their relative positions, from the larger in the AC/GT complex to the smaller in the TG/CA one, because the first the two base pairs are almost superposed and the last the two base pairs are almost orthogonal. Also, the different planarity of these complexes are evident in Figure 1. Table 1 shows the distances and the angles (part a) and the Wiberg indexes (part b) of the atoms of the three H-bridges of Table 1bWiberg Indexes of the Atoms of the Three H-Bridges of the G−C and of the Two H-Bridges of the A−T Base Pairs OG---H-NC GC AT AC/GT AC/GT CT/AG CT/AG TC/GA TC/GA TG/CA TG/CA

u d u d u d u d

NG-H---NC/NA--H-NT

NG-H---O C/NAH---O T

H−N

O---H

N−H

H---N

N−H

H---O

0.672

0.085

0.686 0.669

0.071 0.086

0.678

0.076

0.697

0.068

0.675 0.616 0.638 0.665 0.673 0.612 0.591 0.654 0.648 0.658

0.066 0.109 0.085 0.068 0.066 0.108 0.125 0.076 0.082 0.072

0.732 0.733 0.711 0.724 0.747 0.735 0.747 0.737 0.741 0.732

0.048 0.043 0.053 0.051 0.043 0.042 0.028 0.044 0.038 0.046

the G−C and of the two H-bridges of the A−T base pairs (the subscript u and d in this table mean “up” and “down” base pair, respectively). From the analysis of the Table 1, some considerations can be done. First of all, we would like to discuss the effect of the inclusion of the stacking interaction between the base pairs on the length (and the strength) of the hydrogen bonds. We remember that in general an increase of the H---X distance in a Y-H---X H-bridge corresponds to a decrease of the strength of this hydrogen bond. If this is true also in these complexes, it can be verified by the Wiberg indexes. From the comparison between the monomeric base pairs and these complexes, it is evident that the adding of stacking interaction has not the same effect in all systems and in all hydrogen bonds. In fact, from the analysis of Table 1a, one can see that the variation of the length of the hydrogen bonds are quantitatively, and also qualitatively, different in a complex or in another one. In particular, in the G− C base pair of the complexes (compared with the monomer), the OG---H distance in the OG---H-NC H-bridge increases in the AC/ GT, TC/GA, and TG/CA systems but decreases in the CT/AG one; the H---N in NG-H---NC increases in AC/GT, CT/AG, and 5442



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Figure 3. Potential energy curves of the hydrogen bonds as a function of the difference of the N−H distance from the equilibrium value. Distances are in angstrom and energy in kilocalories per mole. For the explanation, see the text.

H internal coordinate, a large hysteresis, with a large energy barrier, is found. As a consequence, the PES shown Figure 3 can be considered a good approximation of the PES of the true reaction coordinate of the hydrogen transfer in each bridge, if this last process has its driving force in the N−H stretching. Two general considerations must be made. First of all, in this paper (already in the title) we have spoken of “hydrogen atom transfer”, instead of “proton transfer”, as in literature. In our previous papers,7,8,14,15,48−54 in fact, we have demonstrated by the analysis of atomic charges during the passage of this atom from the donor to the acceptor that the hydrogen charge changes little, and there is never one has a proton passage and an electron that remains in the original fragment. Second, during these hydrogen movements, only one coordinate is fixed and the others optimized. Nothing guaranteed us that our model with two free base pairs, without the lateral backbones, remains valid in all cases studied, and a large out-ofplane displacement could not be found. In reality, we have found that the stable structures of Figures 1 and 2 do not change much, and our model remains valid in all cases. In all cases of Figure 3, the zero point of energy is the more stable TG/CA complex. Instead, in all cases of Figure 4, we have assumed the minimum of each H-bridge as the zero point energy, in order to compare easily the variation of energy due to stacking interaction for the hydrogen movement in each H-bridge.

In Figure 3, one can see that the movement of the hydrogen atom in all H-bridges gives similar PES, except the movement of the hydrogen atom from guanine to cytosine (in the NG-H---OC H-bridge) that, as both in the G−C monomer and in the dimers, has a larger difference of energy. This movement, with a difference of energy of 35−45 kcal/mol, requires too much energy in the transfer of hydrogen from one base to another. In Figure 3, it is also evident that some hydrogen transfer has a barrier and a second stable position along the curve and other, after the barrier, has a large flat curve of virtually identical energy. Of course, there are differences between a complex and another one in the position, height, and width of the barrier of this process and in the stability of the tautomer (or zwitterion) generated by this transfer. Note that the transfer of the hydrogen atom in the NA---H-NT H-bridge of the CT/AG complex and in OG---H-NC of the TC/GA complex generates a PES practically without barrier and a very large subsequent isoenergetic part of PES. In Figure 4, we have shown the differences of energy (for all Hbridges and complexes) between the hydrogen movement in a specific H-bridge and complex and in the monomeric structure of AT or GC, in order to highlight the variations induced by the stacking interaction. Some considerations can be made. First of all, in these as in the other results of this paper, the quantitative and the qualitative behavior of the results are different for each 5443



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Figure 4. Difference of the potential energy curves between each hydrogen bond in the complex and in the correspondent monomeric base pair as a function of the difference of the N−H distance from the equilibrium value. Distances are in angstrom and energy in kilocalories per mole. For the explanation, see the text.

Table 2aVariation Induced in The NA---H-NT and NA-H---OT H-Bridge during the Movement of the Hydrogen Atom in the Other H-Bridge of the AT Base Paira NA-H---OT/NA---H-NT

NA---H---NT/NA-H---OT

Δd

AT

AC/GT

CT/AG

TC/GA

TG/GA

AT

AC/GT

CT/AG

TC/GA

TG/GA

−0.10 0.15 0.30 0.45 0.6 0.75 0.9

−0.003 0.021 0.548 0.627 0.671 0.708 0.738

−0.002 0.015 0.075 0.615 0.691 0.704 0.749

−0.002 0.010 0.046 0.710 0.777 0.799 0.728

−0.001 0.010 0.573 0.651 0.658 0.694 0.786

−0.002 0.009 0.547 0. 597 0.634 0.673 0.550

−0.002 0.007 0.024 0.047 0.081 0.485 0.528

−0.002 0.008 0.028 0.053 0.080 0.215 0.501

−0.001 0.006 0.017 0.029 0.042 0.056 0.068

−0.001 0.005 0.011 0.021 0.034 0.039 0.076

0.000 0.005 0.013 0.026 0.064 0.089 0.058

a

Variation of the NT-H or NA-H distance in the NA---H-NT or NA-H---OT bridge when the hydrogen atom moves in NA-H---OT or NA---H-NT Hbridge (Δd = (NA(T)-H)eq − (N A(T)-H)). All distances are in angstrom.

hydrogen bond and each complex. There is a case where the movement in a H-bridge is very slightly modified by the stacking interaction, for example, that in the NA---H-NT H-bridge in the AC/GT complex, where this difference is in the range from −0.70 to 1.10 kcal/mol (red curve) and case where this modification is large, for example, in the OG---H-NC H-bridge in the TG/CA complex, where this difference is in the range form 0.47 to 14.24 kcal/mol (curve). It is also evident that the inclusion of the stacking interaction can lower or higher the energy of the hydrogen transfer and can modify mainly the barrier or all values of the PES along this movement. In any case,

the greater stabilizations are for the H-bridges of the AT base pair in the CT/AG and TC/GA cases and the greater destabilizations for the OG---H-NC H-bridge in all complexes. For comparing the mechanism (concerted or sep-to-step) of hydrogen atoms transfer of the monomer and of the complexes in Table 2, we have shown the variation from the equilibrium value of the N−H distance of another H-bridge of the same base pair when a hydrogen atom moves in a specific H-bridge. In particular, in this Table, we have three parts: in (a), there are the variation induced in the NA---H-NT and NA-H---OT H-bridge during the movement of the hydrogen atom in the other H5444



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Table 2bVariations in the OG---H-NC H-Bridge While the Hydrogen Atom Moves in The NG-H---OC and NG-H---NC Onesa NG-H---OC/OG---H-NC

NG-H---NC/OG---H-NC

Δd

GC

AC/GT

CT/AG

TC/GA

TG/GA

GC

AC/GT

CT/AG

TC/GA

TG/GA

−0.10 0.15 0.30 0.45 0.6 0.75 0.9

−0.002 0.006 0.023 0.054 0.374 0.552 0.539

−0.003 0.015 0.032 0.062 0.051 0.053 0.050

−0.001 0.003 0.011 0.042 0.034 0.405 0.448

0.000 0.001 0.019 0.023 0.042 0.078 0.122

−0.001 0.003 0.008 0.018 0.027 0.039 0.048

−0.004 0.019 0.115 0.506 0.561 0.617 0.685

−0.003 0.011 0.037 0.481 0.519 0.622 0.695

−0.003 0.017 0.041 0.499 0.544 0.606 0.696

−0.001 0.009 0.022 0.074 0.208 0.563 0.647

−0.001 0.010 0.049 0.347 0.493 0.548 0.569

Variation of the NC-H distance in the OG---H-NC bridge, when the hydrogen atom moves in NG-H---OC or NG-H---NC H-bridge (Δd = (NG-H)eq − (NG-H)). All distances are in angstrom. a

Table 2cVariations in the NG-H---OC and NG-H---NC H-Bridges When the Hydrogen Moves in the OG-H---NC Onesa OG---H-NC/NG-H---OC

OG---H-NC/NG-H---NC

Δd

GC

AC/GT

CT/AG

TC/GA

TG/GA

GC

AC/GT

CT/AG

TC/GA

TG/GA

−0.10 0.15 0.30 0.45 0.6 0.75 0.9

−0.001 0.003 0.009 0.115 0.020 −0.006 −0.006

−0.001 0.004 0.007 0.015 0.016 0.020 0.020

−0.001 0.002 0.005 0.005 0.012 0.016 0.022

0.000 0.002 0.004 −0.006 −0.005 −0.005 −0.006

−0.001 0.002 0.006 0.010 0.014 0.018 0.020

−0.003 0.016 0.042 0.066 0.830 0.802 0.864

−0.003 0.015 0.032 0.062 0.051 0.053 0.050

−0.003 0.014 0.019 0.017 0.052 0.060 0.064

−0.001 0.010 0.021 0.671 0.714 0.767 0.872

−0.002 0.011 0.038 0.070 0.089 0.119 0.141

a

Variation of the NG-H distance in the NG-H---OC or NG-H---NC H-bridge when the hydrogen atom moves in the OG---H-NC H-bridge (Δd = (NCH)eq − (NC-H)). All distances are in angstrom.

bridge (NA-H---OT and NA---H-NT, respectively) of the AT base pair; in (b), the variations in the OG---H-NC H-bridge while the hydrogen atom moves in the NG-H---OC and NG-H---NC ones; in (c), those in the NG-H---OC and NG-H---NC H-bridges when the hydrogen moves in the OG-H---NC one. For all parts of Table 2, we have shown the monomeric base pair and the four AC/GT, CT/AG, TC/GA, and TG/CA complexes. From the analysis of Table 2, it is evident that (1) The movement of the hydrogen atom in the NA-H---OT H-bridge generates a concerted movement of the hydrogen atom in the NA---H-NT H-bridge in all systems in study. This means that the inclusion of the stacking interaction and the differences between the different complexes does not modify the mechanism, in this case. (2) The movement of the hydrogen atom in the NA---H-NT H-bridge is followed from the reverse movement from the adenine to thymine (a step-to-step mechanism) in the AT base pair. The inclusion of the stacking interaction modifies this mechanism. In particular, this movement is not followed from the reverse movement in the CT/AG, TC/GA, and TG/CA complexes, but it is similar to that of the monomer in the AC/GT complex. (3) The movement of the hydrogen atom from the guanine to cytosine (in both H-bridges) generates the reverse concerted movement from the cytosine to guanine in the OG---H-NC H-bridge in the monomeric GC base pair. This mechanism remains unchanged only for the movement in the NG-H---NC H-bridge (in all complexes) but is completely modified for the NG-H---OC one. (4) The movement of the hydrogen atom from the cytosine to guanine is followed from the movement of the hydrogen atom in the reversal direction only in the NG-H---NC Hbridge in the monomeric GC base pair, but the hydrogen atom does not move in the NG-H---OC H-bridge. In this

case, the inclusion of the stacking interaction in the complexes does not change the situation in the NG-H---OC bridge but modify that in the NG-H---NC H-bridge for all complexes, except for the TC/GA one. In order to understand the coupling between the movement in a H-bridge of a base pair with that in a H-bridge of the other base pair, we study the modifications of the natural charges of the 15 atoms involved in the five hydrogen bonds between the base pairs. These atoms can be separated in three groups, those of the donors of hydrogen, of the hydrogen atoms, and of the acceptors of hydrogen. We show the variations of the natural atomic charges of the donor (Figure SI1, Supporting Information), hydrogen (Figure 5), and acceptor atom (Supporting Information Figure SI2) of the NA-H---OT H-bridge in the AC/GT, CT/AG, TC/GA, and TG/CA complexes. Similarly, in Figure 6 and Supporting Information Figures SI3 and SI4, we have those of NA---H-NT; in Figure 7 and Supporting Information Figures SI5 and SI6, of OG---H-NC; and in Figure 8 and Supporting Information Figure SI7 and SI8, those of NGH---NC. The cases related to the NG-H---OC H-bridge have not been reported because the variation of energy due to the movement of the hydrogen atom in this H-bridge is too large (see Figure 3). We remember that in each figure, as in all other cases, the curve is used to refer to (black) NA-H---OT H-bridge, (red) to NA---HNT, (green) to OG---H-NC, (blue) to NG-H---NC, and (teal) to NG-H---OC. From the analysis of these figures, we can note that (1) During the passage of the hydrogen atom from the adenine to the thymine (Figure 5 and Supporting Information Figures SI1 and SI2), there is a similar behavior for all complexes (see black curves). The atomic charge of the donor (nitrogen atom of adenine) initially becomes more negative, with a minimum when the hydrogen atom is in the midst of the two heavy atoms of 5445



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Figure 5. Natural atomic charges of the hydrogen atoms of the five (three in GC and two in AT) H-bridges during the movement (Δdistance in angstroms) of the hydrogen atom in the NA-H---OT H-bridge. For the explanation, see the text.

base pair with the OG---H-NC and NG-H---NC ones of the G−C. (2) In Figure 6 and Supporting Information Figures SI3 and SI4, we have analyzed the same charge modifications due to the movement of the hydrogen atom from the thymine to the adenine in the NA---H-NT H-bridge (the red curves). Now, the atomic charge of the donor (Supporting Information Figure SI3) becomes initially more negative but come back practically at the initial value when the passage is terminated in the AC/GT complex, whereas in the others, it remains constant after the passage. The atomic charge of the hydrogen atom (Figure 6) becomes more positive and, after, constant in all complexes, and that of the acceptor (Supporting Information Figures SI5 and SI4) changes little (less negative during the passage). The atomic charges of the atoms of the other H-bridge of the A−T base pair change more, even though its hydrogen atom moves from the adenine to thymine in a step-to-step process (it moves when the other hydrogen is arrived on the acceptor). Related to the H-bridges of the G−C base pair, now the most coupled bridge is the OG---H-NC one. (3) In Figure 7 and Supporting Information Figures SI6 and SI5 we have shown the modifications of the charges due to the movement of hydrogen atom in the OG---H-NC Hbridge from the cytosine to the guanine (the green curves). Now, the behavior of these changes are similar to those of NA-H---OT for the donor and for the hydrogen atom, and

the bridge, then there is a decrease of this negative charge with, after the complete passage of this atom, a stabilization in an intermediate value. Even though this behavior is similar in the different complexes, the quantitative variations are specific of each complex, as is evident by the comparison of the different systems of Supporting Information Figure SI1. The charge of the hydrogen atom of this H-bridge (Figure 5) becomes more and more positive and that of the acceptor atom (in this case the oxygen of the thymine) (Supporting Information Figure SI2) more negative, with a rapid change in the midst of this hydrogen passage. During this passage, the atomic charges (see red curves) of the atoms of the other H-bridge of the A−T base pair change less and in some complexes remain unchanged, even though its hydrogen atom moves from its donor to its acceptor atom, with a concerted movement of these two hydrogens (Table 2a), one from adenine to thymine and the other from thymine to adenine and the formation of the imino-enol tautomer. The atomic charges (the green, blue, and teal curves) of the atoms of the H-bridges of the G−T base pair change little in any case, but these little changes are the proof of a coupling between the movement of the hydrogen atoms in the two base pairs, coupling due to the stacking influence on the hydrogen transfer. We are using these changes for determining the most coupled H-bridges of the two base pairs. In this case, the NA-H---OT H-bridge of the A−T 5446



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Figure 6. As in Figure 5, but for the movement of the hydrogen atom in the NA---H-NT H-bridge.

In order to test the coupling between the movements of a hydrogen atom in a bridge of the up base pair with one in the down base pair, we have computed the potential energy curves due to the simultaneous movement of these two hydrogen atoms. In particular, in Figure 9, we compare the potential energy curves of the two simultaneous movements in different base pair (the red curves) with the sum of the potential energy curves of the two independent movements (the black curves). In the first case, we assume two constraints (the positions of the two hydrogen atoms in the H-bridge of the up and down base pair), whereas in the last, we assume only one constraint to time (the position of the hydrogen atom in the up or in the down base pair) and then we add these energy values. Differently from the case of the AT and GC dimers of refs 7 and 8, now we cannot assume the coupling of the same H-bridge in the up and down base pair. Due to the results of the figures of the natural charges, we analyzed the following coupling: (a) NA-H---OT with OG---H-NC and NG-H---NC for the AC/ GT complex. (b) NA-H---OT with NG-H---NC and NA---H-NT with OG---HNC for the CT/AG complex. (c) NA---H-NT with OG---H-NC for the TC/GA complex. (d) NA-H---OT with OG---H-NC and NG-H---NC for the TG/ CA complex.

with a small change of the charge of the acceptor except in the TC/GA complex (similar to those of Supporting Information Figure SI2). Now, the changes of the natural charges of the other atoms involved in the H-bridges of the some base pair (the blue and teal curves) are larger and substantial for the acceptor atom. This means that the three H-bridges of the G−C base pair are more coupled each other than those of the A−T one. Compared to these couplings, those with the H-bridges of the different base pair are less relevant, of course, that with the NA-H---OT H-bridge more important, over all in the TC/GA and TG/ CA complexes and in the acceptor atom (Supporting Information Figure SI6). (4) Finally, in Figure 8 and Supporting Information Figures SI7 and SI8, there are the changes of the atomic charges due to the hydrogen movement in the NG-H---NC Hbridge, from the guanine to the cytosine (the blue curves). Now the charge variations of the donor atom (Supporting Information Figure SI7) is similar to that of the NA-H---OT H-bridge but not that of the hydrogen atom (more complex behavior) and of the acceptor atom (less negative charge during the passage). Also in this case, the most coupled H-bridge of the other base pair is the NA-H---OT one, over all in the TC/GA and TG/CA complexes and in the acceptor atom (Supporting Information Figure SI8). 5447



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Figure 7. As in Figure 5, but for the movement of the hydrogen atom in the OG---H-NC H-bridge.

H-bridge, the H---NC in NG-H---NC, and the H---OC in NG-H--OC generally increases in the complexes, but the first decreases in the CT/AG system, the second in TC/GA, and the last in the AC/GT one. Moreover, in the hydrogen bonds of the A−T base pair of these complexes, the H---X distance increases in all complexes, except the H---NA distance of the NT-H---NA Hbridge in the TC/GA system. We can say that the stacking interaction generally weakens the hydrogen bonds between the base pairs, with the exception explicated. Second, the variation of the PES during the movement of a hydrogen atom in a H-bridge. As in the monomer and in the dimers, the movement of the hydrogen atom from the guanine to the cytosine in the NG-H---OC H-bridge is the only one with difference of energy larger than the others. In the cases shown, there are differences between the complexes due to the presence or lack of presence of a barrier in this process of transfer and in the position, height, and width of this barrier. There is a case where the movement in a H-bridge is very slightly modified by the stacking interaction (for example, in the NA---H-NT H-bridge in the AC/GT complex) and a case where this modification is large (for example in the OG---H-NC H-bridge in the TG/CA complex). In any case, the greater stabilizations can be found for the H-bridges of the AT base pair in the CT/AG and TC/GA complexes and the greater destabilizations for the OG---H-NC Hbridge.

In Figure 9, we have shown the results for the most relevant cases (the other cases, not reported, are less significant) of the four complexes. In particular, the PES due to the movement of two hydrogen atoms in NA-H---OT and OG---H-NC for the AC/ GT and for the TG/CA complex and in NA---H-NT and OG---HNC for the CT/AG and TC/GA one. It is easy to see that the coupling between the hydrogen movement in a base pair with the movement in the other one can support the hydrogen atoms transfers (AC/GT, CT/AG, and TG/CA systems) or can disadvantage (TC/GA) these transfers. In any cases, there is a sufficient large coupling of these two movements that generates a consistent modification of the PES of the two hydrogen atoms transfers.

4. CONCLUSION There are some general considerations that can be obtained comparing the monomeric base pairs and the A−T and G−C dimers and the complexes in the study and, hence, related to the modifications induced by the inclusion of the stacking interaction or different type of stacking interaction. First of all, the variation of the strength of the hydrogen bonds between the bases. From these comparisons, it is evident that the addition of a stacking interaction does not have the same effect in all systems and in all hydrogen bonds. In particular, in the G−C base pair of these complexes, the O---H distance in the OG---H-N 5448



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Figure 8. As in Figure 5, but for the movement of the hydrogen atom in the NG-H---NC H-bridge.

when the movement of the hydrogen atom is in these H-bridges of the GC base pair, and for the NA---H-NT H-bridge with the movement in the OG---H-NC one. Fifth, the coupling between the movement in a base pair with the movement in the other one can modify considerably the PES of the hydrogen atoms transfers and can be of support to these transfers or can be a disadvantage. A final set of considerations can be made on the dynamics of these systems. Several that can be important are the movements of these systems (and of the fragments of DNA), the tilt, the twist and so on, but these large movements (related to the large masses) can be considered separated from the faster and engaging only the mass of a hydrogen atom movement of tunnelling in the H-bridge. For this reason, the dynamics of these other movements has not been included in this calculation. From the potential energy curves of Figures 3 and 4 one can see that, if an additional stable position along the bridges exists, this is flat. This is considered in literature the proof of an unstable and insignificant tautomer (above all for the A−T cases), but we believe that this picture is too static. In a time-dependent picture, there is a flux of population between these different situations (different positions of the hydrogen atoms), and we have already demonstrated with time-dependent calculations (hence, with the inclusion of the tunnel effect) that a flat and wide minimum in these systems does not mean a negligible probability of the populations of these structures.14,15,48−50 Moreover, one must

Third, the variation of the mechanism (concerted or step-bystep) of the hydrogen transfer in a base pair. The inclusion of the stacking interaction and the differences between the different complexes does not modify the mechanism of the movement of the hydrogen atom in the NA-H---OT H-bridge, whereas the movement of the hydrogen atom in the NA---H-NT H-bridge is similar to that of the monomer only in the AC/GT complex, whereas in the others, this movement is not followed from the reverse movement from the adenine to the thymine. The movement of the hydrogen atom from the guanine to the cytosine generates the reverse movement from the cytosine to the guanine in a concerted way in the monomeric GC base pair and remains unchanged only for the movement in the NG-H--NC H-bridge (in all complexes) but is completely modified for the NG-H---OC H-bridge. The movement of the hydrogen atom from the cytosine to the guanine is followed from the movement of the hydrogen atom in the NG-H---NC H-bridge in the monomeric GC base pair. In this case, the inclusion of the stacking interaction in the complexes does not change the movement in the NG-H---OC H-bridge but modifies that in the NG-H---NC one. Fourth, using the change of atomic charges, we determine the most coupled movement of two hydrogen atoms in the bridge of two different base pairs. In these cases, for the movement in the NA-H---OT H-bridge, the most coupled hydrogen movement is that in the OG---H-NC and in the NG-H---NC ones, and vice versa 5449



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Figure 9. Potential energy curves of the movement of two hydrogen atoms in two H-bridges (see text) of different base pairs: two-dimensional (the black curves) simultaneous movement of the hydrogen atoms and their independent movements (the red curves). Distance is in angstroms and energy is in kilocalories per mole.

not forget that the systems studied here are only a model of a real piece of DNA, mainly for the absence of the characteristics environmental interactions present in the real case (ions, water molecules, etc.) and these physical and chemical interactions could modified the hydrogen transfer, as shown in literature.55,56 In particular, the presence of water molecules can be very important, but the inclusion of this solvent can be done only with the explicit inclusion of these molecules (due to their hydrogen bonds with the base pairs) and this requires a specific study, as demonstrated by us.53,54 In any case, the model applied here can be considered a sufficient realistic model for studying the essential relation between the hydrogen bonds and the stacking interaction.

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H-bridges, respectively. This material is available free of charge via Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Fiethen, A.; Jansen, G.; Hesselmann, A.; Schutz, M. Stacking Energies for Average B-DNA Structures from the Combined Density Functional Theory and Symmetry-Adapted Perturbation Theory Approach. J. Am. Chem. Soc. 2008, 130, 1802−1803. (2) Cooper, V. R.; Thonhauser, T.; Puzder, A.; Schröder, E.; Lundqvist, B. I.; Langreth, D. C. Stacking Interactions and the Twist of DNA. J. Am. Chem. Soc. 2008, 130, 1304−1308. (3) Shishkin, O. V.; Elstner, M.; Fraunheim, T.; Suhai, S. Structure of Stacked Dimers of N-Methylated Watson−Crick Adenine−Thymine Base Pairs. Int. J. Mol. Sci. 2003, 4, 537−547.

ASSOCIATED CONTENT

S Supporting Information *

Eight figures. In particular, the natural atomic charges of the donor atoms (Figure SI1, SI3, SI5, and SI7) and of the acceptor atoms (Figure SI2, SI4, SI6, and SI8) of the five (three in GC and two in AT) H-bridges during the movement of the hydrogen atom in the NA-H---OT, NA---H-NT, OG---H-NC, and NG-H---NC 5450



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Coupling Between Hydrogen Atoms Transfer and Stacking Interaction

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