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On the importance of electrostatics in stabilization of stacked guanine–adenine complexes appearing in B-DNA crystals
Journal of Molecular Structure: THEOCHEM 895 (2009) 161–167
Contents lists available at ScienceDirect
Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
On the importance of electrostatics in stabilization of stacked guanine–adenine complexes appearing in B-DNA crystals _ * _ Zaneta Czyznikowska Institute of Organic and Pharmaceutical Chemistry, The National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635 Athens, Greece ´ ska 13–15, 85–067 Bydgoszcz, Poland Faculty of Farmacy, Collegium Medicum, Nicolaus Copernicus University, Jagiellon
a r t i c l e
i n f o
Article history: Received 20 July 2008 Received in revised form 19 October 2008 Accepted 22 October 2008 Available online 8 November 2008 Keywords: Intermolecular interaction energy Electrostatic component Stacking Nucleic acid bases
a b s t r a c t In this paper, the importance of the first-order electrostatic energy in stabilization of stacked guanine– adenine complexes is discussed for conformations of the complexes appearing in B-DNA crystals. The interaction energy components were calculated at the SCF level of theory using variational–perturbational scheme and compared with the total MP2 intermolecular interaction energy. It is demonstrated that electrostatic energy plays an important role in the stabilization of analyzed structures. Moreover, the results of calculations show that the electrostatic component is much more dependent on the conformations of guanine–adenine complexes than the total MP2 interaction energy. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The stabilization and conformation of biochemically important macromolecules are dependent on non-covalent interactions. These forces determine to a large extent the structure of DNA, RNA, multiprotein and protein–ligand complexes. Furthermore, they play crucial role in the molecular-recognition and drug intercalation processes. The stabilization of biologically significant complexes is a consequence of interplay of different contributions to intermolecular interaction energy. In the case of nucleic acids, two types of non-covalent interactions are significant, i.e. electrostatics and London dispersion forces [1,2]. Many computational studies on interactions of isolated nucleic acid bases (NABs) were performed with the aim of determination of accurate intermolecular interaction energies and evaluation of the impact of environment on stabilization of investigated complexes [3–7]. Nevertheless, the knowledge of the nature of interactions in hydrogen-bonded and stacked systems is crucial for understanding of such interesting phenomena as replication, transcription and dynamic properties of nucleic acids. Recently, several investigations on the nature of intermolecular interactions in nucleic acid base complexes have been presented [8–15]. The results of calculations performed for numerous H-bonded nucleic acid base complexes prove that electrostatic term is mostly dominant but induction and dispersion contributions are also non-negligible * Address: Institute of Organic and Pharmaceutical Chemistry, The National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635 Athens, Greece. E-mail address: [email protected] 0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.10.040
[16]. It was also found that the variations in the values of interaction energy components, upon in-plane rotations of bases near the minima, do not exceed 3 kcal/mol. It is now well recognized that the dispersion interaction is of paramount importance for the stabilization of stacked base-pairs [8,9]. However, it was also reported that the first-order electrostatic energy and the induction component are also important [17]. Although several investigations have recently been performed on the nature of interactions in nucleic acid base complexes there is still need for the systematic study of the interaction energy components for larger population of structures in order to draw more general conclusions. The analysis of stacked nucleic acid base complexes, based on the empirical potentials, demonstrated that the mutual orientation of bases was mainly due to the electrostatic component and stabilization due to the dispersion energy term [11,18]. The majority of non-empirical calculations of the intermolecular interaction energy components for stacked complexes were performed using single selected conformations appearing in B-DNA crystals or average geometries for a given base-pair [8,10,12,17]. The use of base-step (rise, slide, shift, tilt, roll and twist) and basepair (shear, stretch, stagger, opening, buckle and propeller) parameters, describing mutual orientation of bases, constitutes the basis for more systematic analysis of the dependence of the interaction energy on the structure of NAB complexes. The conformational properties and stability of base-pairs, based on the above parameters, were analyzed in details employing the empirical potentials [19]. It was noticed that the electrostatic and van der Waals interactions and the structural parameters describing mutual
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orientation of nucleic acid bases in DNA fragments were strongly interdependent. Namely, it was observed that the contribution of van der Waals forces to the total stabilization energy was significantly rise-, tilt- and roll-dependent. On the other hand, the electrostatic energy is mainly determined by the values of shift and slide parameters. The twist parameter, however, does not affect the total values of stacking energy. The central subject of the present investigation is the analysis of the importance of the electrostatic interaction in stabilization of stacked guanine–adenine complexes appearing in B-DNA crystals. The set comprising forty-eight structures of G/A pair is large enough to study both the energetic diversity and the role of electrostatics, and other components as well, in stabilization of the complexes. Another point of interest in this study, hardly touched on in the literature, is the analysis of the dependence of the interaction energy components on the base-step parameters.
2. Results and discussion In this study forty-eight stacked complexes formed by guanine and adenine are analyzed and discussed. The geometries of the monomers were optimized at the MP2/6-31G++(d,p) level of theory using the Gaussian03 package [20] and used for generation of geometry of complexes with the aid of 3DNA program [21]. The conformation of duplexes was controlled by two sets of six mutually dependent parameters used for description of nucleic acids structure. The geometry of two hydrogen-bonded guanine– cytosine and adenine–thymine pairs is determined by shear, stretch, stagger, buckle, propeller and opening. The next six parameters, namely shift, slide, rise, tilt, roll and twist, are responsible for mutual orientation of stacked guanine and adenine [22]. The graphical representation of these parameters is presented in Fig. 1. The values of these parameters were taken from the Nucleic Acid Database [23].
Fig. 1. The structural step parameters describing mutual orientation of bases in complex.
Fig. 2. The intermolecular interaction energy, calculated at the MP2/aug-cc-pVDZ level of theory, together with the electrostatic component for the guanine–adenine dimer in conformations appearing in B-DNA.
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The intermolecular interaction energy (DEMP2) for all investigated guanine–adenine pairs was calculated at the MP2/aug-ccpVDZ level of theory using the MOLPRO package [24] and corrected for the basis set superposition error (BSSE) [25]:
Table 1 The intermolecular interaction energy components for investigated complexes. All values are given in kcal/mol. Complex
DEMP2
ð10Þ el
HL ex
DEHF del
DEHL
ð2Þ MP
BD0001 BD0002a BD0002b BD0004 BD0005 BD0018 BD0019 BD0024a BD0024b BD0029 BD0032 BD0037 BD0041 BD0052a BD0052b BD0052c BD0054 BD0069 BD0070 BD0080 BD0082 BD0084 BD0087 BD0090a BD0090b BDF068 BDJ008 BDJ025a BDJ025b BDJ031 BDJ036 BDJ037 BDJ060a BDJ060b BDJ081a BDJ081b BDL002 BDL005 BDL012 BDL020 BDL028 BDL029 BDL042 BDL084 DD0081 UDI030 UDJ060 UDM010
8.96 10.25 10.05 10.39 10.39 10.64 10.99 0.95 0.93 10.16 10.07 9.28 10.23 10.82 9.42 10.86 10.12 10.29 9.15 10.03 6.98 4.11 0.36 9.73 9.73 10.35 9.04 10.57 9.77 11.01 9.87 10.29 10.58 9.68 9.70 10.14 10.23 10.35 8.29 10.28 10.89 10.03 8.87 10.34 10.10 9.35 10.67 9.50
4.10 3.70 4.94 9.38 3.95 5.16 6.19 0.18 0.10 4.25 3.59 5.17 4.03 4.69 2.60 5.97 3.99 6.90 5.16 3.42 5.39 14.21 0.10 4.11 4.07 4.72 3.75 3.80 5.92 4.54 3.54 4.39 5.26 2.63 5.28 6.26 5.83 4.03 9.59 3.79 5.32 5.89 3.27 4.52 3.69 4.40 4.52 4.39
5.25 7.50 9.17 16.87 7.41 9.55 11.82 0.01 0.01 7.98 6.73 7.40 6.87 9.28 6.03 12.31 6.82 11.93 7.78 7.04 14.46 29.87 0.00 6.80 6.19 7.68 5.66 7.89 11.14 10.41 8.61 9.89 10.12 5.15 11.21 17.15 13.75 8.20 22.93 8.04 11.30 13.52 4.82 7.89 8.11 6.31 9.95 6.60
0.65 1.04 1.05 1.67 1.03 1.19 1.50 0.16 0.17 0.99 0.95 0.87 0.93 1.26 0.94 1.42 0.90 1.28 0.84 1.08 1.69 3.25 0.04 0.86 0.81 1.00 0.73 1.16 1.09 1.49 1.13 1.34 1.38 0.88 1.32 2.43 1.58 1.12 2.63 1.08 1.40 1.61 0.65 0.98 1.08 0.79 1.33 0.75
1.15 3.80 4.23 7.49 3.46 4.40 5.62 0.17 0.09 3.73 3.13 2.23 2.84 4.59 3.43 6.34 2.83 5.03 2.63 3.61 9.08 15.66 0.10 2.69 2.13 2.96 1.91 4.08 5.22 5.87 5.07 5.50 4.86 2.52 5.94 10.89 7.91 4.17 13.34 4.25 5.99 7.63 1.55 3.37 4.42 1.91 5.44 2.22
9.46 13.01 13.23 16.21 12.82 13.85 15.12 0.62 0.67 12.91 12.25 10.64 12.14 14.14 11.91 15.78 12.05 14.05 10.94 12.56 14.36 16.52 0.42 11.56 11.04 12.31 10.22 13.50 13.90 15.40 13.81 14.45 14.06 11.32 14.31 18.60 16.56 13.40 19.01 13.45 15.48 16.05 9.76 12.73 13.45 10.47 14.78 10.96
Fig. 3. The structure of BD0084 complex.
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DEMP2 ¼ EG=A EG EA :
ð1Þ
where EG/A represents the interaction energy of guanine–adenine complex and EG, EA stand for the energies of monomers of guanine and adenine in the dimer-centered basis set. The intermolecular interaction energy for stacked bases in conformations appearing in B-DNA crystals is presented in Fig. 2. We follow the notation used in the Nucleic Acid Database for labelling the structures [23]. The average value of intermolecular interaction energy is equal 9.3 kcal/mol. The benchmark CCSD(T) interaction energy for stacked guanine–adenine complex was found to be CCSDðTÞ 11.4 kcal/mol ðDECBS Þ [6]. The majority of investigated G/A complexes are characterized by strong attraction with the values of DEMP2 falling into the range between 9.5 and 11.0 kcal/mol. This is consistent with the observation made by Šponer et al., who reported that most of the crystallographic structures of base-pairs were almost isoenergetic [26]. Among the considered set of structures, three weakly bound complexes were found (BD0024a, BD0024b, BD0087). It can be caused by very small overlap of monomer rings in complexes. The other reason is that the values of rise parameter in these structures exceed 5 Å. The decomposition of intermolecular interaction energy of guanine–adenine complexes was performed using the variational–perturbational scheme [27–29], as implemented in modified version of GAMESS US package [30–32]. Within this approach, the total intermolecular interaction energy calculated at the MP2 level of theory is decomposed into the Hartree–Fock contribution and the correlation correction:
DEMP2 ¼ DESCF þ ð2Þ MP :
ð2Þ SCF
The self-consistent field (DE ) interaction energy is further decomposed into the first-order electrostatic ðel ð10Þ Þ, Heitler–London exchange ðexHL Þ and delocalization components ðDEHF del Þ: HF HL DESCF ¼ el ð10Þ þ ex þ DEdel :
ð3Þ
The delocalization contribution contains the charge transfer, induction, and other higher-order Hartree–Fock terms. To make a valid comparison with the DEMP2 data, we also use the aug-ccpVDZ basis set at the SCF level of theory. The correlation correction ð2Þ ðMP Þ to DEMP2, which includes the electron correlation effects, was calculated as the difference between total intermolecular interaction energy and Hartree–Fock interaction energy. The total intermolecular interaction energy and the DESCF comð2Þ ponents together with the MP are presented in Table 1. The data show, as expected, that stabilization of analyzed complexes originates mainly from correlation effects. Indeed, it was confirmed by earlier investigations that stacked systems were stabilized due to the dispersion interactions [8–12]. As it was mentioned in the previous section, electrostatic energy can also significantly influence the stabilization of nucleic acid base complexes. Šponer and collaborators showed that electrostatic contribution, estimated using the Coulombic expression with atom centered point charges,
Fig. 4. The structure of BD0087 complex.
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Fig. 5. The influence of variability of shift (a) and slide (b) parameters on the electrostatic component.
were very sensitive to conformation of NAB complexes [26]. In the case of almost all guanine–adenine structures, electrostatic term accounts for the substantial part of stabilizing contributions. As it is seen the electrostatic interactions are much more structuredependent than the total MP2 interaction energy is. The average value of the first-order electrostatic term is equal to 4.7 kcal/ mol. The largest absolute value of electrostatic energy (14.2 kcal/mol) is observed for the complex denoted as BD0084. The value of the exchange component for this complex is equal
to 29 kcal/mol. In this case, the G/A pair is also stabilized by delocalization component that is equal to 3.25 kcal/mol. Among the considered set, one structure is found to be destabilized by the first-order electrostatic interaction (BD0087). The geometries of both structures, i.e. BD0084 and BD0087, are presented in Figs. 3 and 4, respectively. The values of delocalization energy term fall into rather shallow range, i.e. between 0.0 and 3.2 kcal/mol with the average value equal to 1.2 kcal/mol. The relative insignificance of the
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Fig. 6. The influence of variability of rise (a) and twist (b) parameters on the electrostatic component.
delocalization term was also reported by Hill et al. [17]. The investigation of Hill et al., performed for single configurations of complexes of ten different duplexes from the crystals structures, shows also that the first-order electrostatic component exhibit the same trend as the total intermolecular energy. The results presented herein for guanine–adenine system lead to contradictory conclusion than that of Hill et al. [17]. It is also not observed here that the exchange and correlation terms are opposite in sign and of comparable magnitude. We rather see that the correlation
correction is of much larger absolute value than the exchange component. Figs. 5–7 present the dependence of the electrostatic component on the structural base-step parameters. In order to put the analysis of Figs. 5–7 on quantitative basis, the Pearson productmoment correlation coefficients between the base-step parameters and all the calculated intermolecular interaction components were determined (see Table 2). The largest variance in common, equal to 73%, is observed between the total MP2 intermolecular interaction
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Fig. 7. The influence of variability of roll (a) and tilt (b) parameters on the electrostatic component.
energy and the value of rise parameter. With the exception of corð2Þ relation between rise parameter and the MP term, the variance in common between other parameters and energy components is less than 30%. The similar dependences for total intermolecular interacel and value of shift tion energy and value of rise parameter and ð10Þ parameter are observed. The unambiguous interpretation of the data presented both in Figs. 5–7 and Table 2 is not straightforward since every structure is described by the unique set of parameters.
3. Conclusions In the present contribution we discussed the intermolecular interaction energy and its components for guanine–adenine system in conformations appearing in B-DNA. The analysis of the results of calculations presented here, for the set comprising fortyeight G/A structures, shows relatively insignificant diversity of the interaction energy. Contrary, the electrostatic component re-
_ Czyz_ nikowska / Journal of Molecular Structure: THEOCHEM 895 (2009) 161–167 Z. Table 2 The Pearson product-moment correlation coefficient between the geomertical basestep parameters and the intermolecular interaction energy as well as its components. Parameter
DEMP2
ð10Þ el
ð2Þ MP
HL ex
DEHF del
Rise Twist Shift Roll Tilt Slide
0.86 0.52 0.21 0.23 0.09 0.00
0.58 0.01 0.52 0.31 0.25 0.24
0.83 0.28 0.21 0.02 0.05 0.05
0.50 0.04 0.30 0.25 0.11 0.15
0.53 0.04 0.19 0.21 0.04 0.06
veal much larger sensitivity to the variations of structural parameters. As expected, the correlation correction to the interaction energy is the most dominant factor determining the stability of investigated complexes. The first-order electrostatic contribution, although in most cases canceled out by exchange component, is also found to be substantial. Additionally, we noticed significant correlation between the rise parameter and both the total MP2 ð2Þ interaction energy as well as correlation correction, MP . Acknowledgement This work was partly supported by computational grant from PCSS (Poznan Supercomputing and Networking Center). The allocation of computing time is greatly appreciated. References [1] P. Hobza, R. Zachradník, K. Müller-Dethlefs, Collect. Czech. Chem. Commun. 71 (2006) 443–531. [2] K. Müller-Dethlefs, P. Hobza, Chem. Rev. 100 (2000) 143–167. [3] I. Da˛bkowska, P. Jurecˇka, P. Hobza, J. Chem. Phys. 122 (2005) 204322. [4] I. Da˛bkowska, H.V. Gonzales, P. Jurecˇka, P. Hobza, J. Phys. Chem. A 109 (2005) 1131–1136. [5] J. Šponer, P. Jurecˇka, I. Marchan, F.J. Luque, M. Orozco, P. Hobza, Chem. Eur. J. 12 (2006) 2854–2865. ˇ erny´, P. Hobza, Phys. Chem. Chem. Phys. 8 (2006) [6] P. Jurecˇka, J. Šponer, J. C 1985–1993. [7] T.L. McConnell, S.D. Wetmore, J. Phys. Chem. B 111 (2007) 2999–3009. [8] A. Hesselmann, G. Jansen, M. Schütz, J. Am. Chem. Soc. 128 (2006) 11730– 11731. [9] R. Sedlák, P. Jurecˇka, P. Hobza, J. Chem. Phys. 127 (2007) 075104.
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Contents lists available at ScienceDirect
Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
On the importance of electrostatics in stabilization of stacked guanine–adenine complexes appearing in B-DNA crystals _ * _ Zaneta Czyznikowska Institute of Organic and Pharmaceutical Chemistry, The National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635 Athens, Greece ´ ska 13–15, 85–067 Bydgoszcz, Poland Faculty of Farmacy, Collegium Medicum, Nicolaus Copernicus University, Jagiellon
a r t i c l e
i n f o
Article history: Received 20 July 2008 Received in revised form 19 October 2008 Accepted 22 October 2008 Available online 8 November 2008 Keywords: Intermolecular interaction energy Electrostatic component Stacking Nucleic acid bases
a b s t r a c t In this paper, the importance of the first-order electrostatic energy in stabilization of stacked guanine– adenine complexes is discussed for conformations of the complexes appearing in B-DNA crystals. The interaction energy components were calculated at the SCF level of theory using variational–perturbational scheme and compared with the total MP2 intermolecular interaction energy. It is demonstrated that electrostatic energy plays an important role in the stabilization of analyzed structures. Moreover, the results of calculations show that the electrostatic component is much more dependent on the conformations of guanine–adenine complexes than the total MP2 interaction energy. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The stabilization and conformation of biochemically important macromolecules are dependent on non-covalent interactions. These forces determine to a large extent the structure of DNA, RNA, multiprotein and protein–ligand complexes. Furthermore, they play crucial role in the molecular-recognition and drug intercalation processes. The stabilization of biologically significant complexes is a consequence of interplay of different contributions to intermolecular interaction energy. In the case of nucleic acids, two types of non-covalent interactions are significant, i.e. electrostatics and London dispersion forces [1,2]. Many computational studies on interactions of isolated nucleic acid bases (NABs) were performed with the aim of determination of accurate intermolecular interaction energies and evaluation of the impact of environment on stabilization of investigated complexes [3–7]. Nevertheless, the knowledge of the nature of interactions in hydrogen-bonded and stacked systems is crucial for understanding of such interesting phenomena as replication, transcription and dynamic properties of nucleic acids. Recently, several investigations on the nature of intermolecular interactions in nucleic acid base complexes have been presented [8–15]. The results of calculations performed for numerous H-bonded nucleic acid base complexes prove that electrostatic term is mostly dominant but induction and dispersion contributions are also non-negligible * Address: Institute of Organic and Pharmaceutical Chemistry, The National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635 Athens, Greece. E-mail address: [email protected] 0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.10.040
[16]. It was also found that the variations in the values of interaction energy components, upon in-plane rotations of bases near the minima, do not exceed 3 kcal/mol. It is now well recognized that the dispersion interaction is of paramount importance for the stabilization of stacked base-pairs [8,9]. However, it was also reported that the first-order electrostatic energy and the induction component are also important [17]. Although several investigations have recently been performed on the nature of interactions in nucleic acid base complexes there is still need for the systematic study of the interaction energy components for larger population of structures in order to draw more general conclusions. The analysis of stacked nucleic acid base complexes, based on the empirical potentials, demonstrated that the mutual orientation of bases was mainly due to the electrostatic component and stabilization due to the dispersion energy term [11,18]. The majority of non-empirical calculations of the intermolecular interaction energy components for stacked complexes were performed using single selected conformations appearing in B-DNA crystals or average geometries for a given base-pair [8,10,12,17]. The use of base-step (rise, slide, shift, tilt, roll and twist) and basepair (shear, stretch, stagger, opening, buckle and propeller) parameters, describing mutual orientation of bases, constitutes the basis for more systematic analysis of the dependence of the interaction energy on the structure of NAB complexes. The conformational properties and stability of base-pairs, based on the above parameters, were analyzed in details employing the empirical potentials [19]. It was noticed that the electrostatic and van der Waals interactions and the structural parameters describing mutual
162
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orientation of nucleic acid bases in DNA fragments were strongly interdependent. Namely, it was observed that the contribution of van der Waals forces to the total stabilization energy was significantly rise-, tilt- and roll-dependent. On the other hand, the electrostatic energy is mainly determined by the values of shift and slide parameters. The twist parameter, however, does not affect the total values of stacking energy. The central subject of the present investigation is the analysis of the importance of the electrostatic interaction in stabilization of stacked guanine–adenine complexes appearing in B-DNA crystals. The set comprising forty-eight structures of G/A pair is large enough to study both the energetic diversity and the role of electrostatics, and other components as well, in stabilization of the complexes. Another point of interest in this study, hardly touched on in the literature, is the analysis of the dependence of the interaction energy components on the base-step parameters.
2. Results and discussion In this study forty-eight stacked complexes formed by guanine and adenine are analyzed and discussed. The geometries of the monomers were optimized at the MP2/6-31G++(d,p) level of theory using the Gaussian03 package [20] and used for generation of geometry of complexes with the aid of 3DNA program [21]. The conformation of duplexes was controlled by two sets of six mutually dependent parameters used for description of nucleic acids structure. The geometry of two hydrogen-bonded guanine– cytosine and adenine–thymine pairs is determined by shear, stretch, stagger, buckle, propeller and opening. The next six parameters, namely shift, slide, rise, tilt, roll and twist, are responsible for mutual orientation of stacked guanine and adenine [22]. The graphical representation of these parameters is presented in Fig. 1. The values of these parameters were taken from the Nucleic Acid Database [23].
Fig. 1. The structural step parameters describing mutual orientation of bases in complex.
Fig. 2. The intermolecular interaction energy, calculated at the MP2/aug-cc-pVDZ level of theory, together with the electrostatic component for the guanine–adenine dimer in conformations appearing in B-DNA.
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The intermolecular interaction energy (DEMP2) for all investigated guanine–adenine pairs was calculated at the MP2/aug-ccpVDZ level of theory using the MOLPRO package [24] and corrected for the basis set superposition error (BSSE) [25]:
Table 1 The intermolecular interaction energy components for investigated complexes. All values are given in kcal/mol. Complex
DEMP2
ð10Þ el
HL ex
DEHF del
DEHL
ð2Þ MP
BD0001 BD0002a BD0002b BD0004 BD0005 BD0018 BD0019 BD0024a BD0024b BD0029 BD0032 BD0037 BD0041 BD0052a BD0052b BD0052c BD0054 BD0069 BD0070 BD0080 BD0082 BD0084 BD0087 BD0090a BD0090b BDF068 BDJ008 BDJ025a BDJ025b BDJ031 BDJ036 BDJ037 BDJ060a BDJ060b BDJ081a BDJ081b BDL002 BDL005 BDL012 BDL020 BDL028 BDL029 BDL042 BDL084 DD0081 UDI030 UDJ060 UDM010
8.96 10.25 10.05 10.39 10.39 10.64 10.99 0.95 0.93 10.16 10.07 9.28 10.23 10.82 9.42 10.86 10.12 10.29 9.15 10.03 6.98 4.11 0.36 9.73 9.73 10.35 9.04 10.57 9.77 11.01 9.87 10.29 10.58 9.68 9.70 10.14 10.23 10.35 8.29 10.28 10.89 10.03 8.87 10.34 10.10 9.35 10.67 9.50
4.10 3.70 4.94 9.38 3.95 5.16 6.19 0.18 0.10 4.25 3.59 5.17 4.03 4.69 2.60 5.97 3.99 6.90 5.16 3.42 5.39 14.21 0.10 4.11 4.07 4.72 3.75 3.80 5.92 4.54 3.54 4.39 5.26 2.63 5.28 6.26 5.83 4.03 9.59 3.79 5.32 5.89 3.27 4.52 3.69 4.40 4.52 4.39
5.25 7.50 9.17 16.87 7.41 9.55 11.82 0.01 0.01 7.98 6.73 7.40 6.87 9.28 6.03 12.31 6.82 11.93 7.78 7.04 14.46 29.87 0.00 6.80 6.19 7.68 5.66 7.89 11.14 10.41 8.61 9.89 10.12 5.15 11.21 17.15 13.75 8.20 22.93 8.04 11.30 13.52 4.82 7.89 8.11 6.31 9.95 6.60
0.65 1.04 1.05 1.67 1.03 1.19 1.50 0.16 0.17 0.99 0.95 0.87 0.93 1.26 0.94 1.42 0.90 1.28 0.84 1.08 1.69 3.25 0.04 0.86 0.81 1.00 0.73 1.16 1.09 1.49 1.13 1.34 1.38 0.88 1.32 2.43 1.58 1.12 2.63 1.08 1.40 1.61 0.65 0.98 1.08 0.79 1.33 0.75
1.15 3.80 4.23 7.49 3.46 4.40 5.62 0.17 0.09 3.73 3.13 2.23 2.84 4.59 3.43 6.34 2.83 5.03 2.63 3.61 9.08 15.66 0.10 2.69 2.13 2.96 1.91 4.08 5.22 5.87 5.07 5.50 4.86 2.52 5.94 10.89 7.91 4.17 13.34 4.25 5.99 7.63 1.55 3.37 4.42 1.91 5.44 2.22
9.46 13.01 13.23 16.21 12.82 13.85 15.12 0.62 0.67 12.91 12.25 10.64 12.14 14.14 11.91 15.78 12.05 14.05 10.94 12.56 14.36 16.52 0.42 11.56 11.04 12.31 10.22 13.50 13.90 15.40 13.81 14.45 14.06 11.32 14.31 18.60 16.56 13.40 19.01 13.45 15.48 16.05 9.76 12.73 13.45 10.47 14.78 10.96
Fig. 3. The structure of BD0084 complex.
163
DEMP2 ¼ EG=A EG EA :
ð1Þ
where EG/A represents the interaction energy of guanine–adenine complex and EG, EA stand for the energies of monomers of guanine and adenine in the dimer-centered basis set. The intermolecular interaction energy for stacked bases in conformations appearing in B-DNA crystals is presented in Fig. 2. We follow the notation used in the Nucleic Acid Database for labelling the structures [23]. The average value of intermolecular interaction energy is equal 9.3 kcal/mol. The benchmark CCSD(T) interaction energy for stacked guanine–adenine complex was found to be CCSDðTÞ 11.4 kcal/mol ðDECBS Þ [6]. The majority of investigated G/A complexes are characterized by strong attraction with the values of DEMP2 falling into the range between 9.5 and 11.0 kcal/mol. This is consistent with the observation made by Šponer et al., who reported that most of the crystallographic structures of base-pairs were almost isoenergetic [26]. Among the considered set of structures, three weakly bound complexes were found (BD0024a, BD0024b, BD0087). It can be caused by very small overlap of monomer rings in complexes. The other reason is that the values of rise parameter in these structures exceed 5 Å. The decomposition of intermolecular interaction energy of guanine–adenine complexes was performed using the variational–perturbational scheme [27–29], as implemented in modified version of GAMESS US package [30–32]. Within this approach, the total intermolecular interaction energy calculated at the MP2 level of theory is decomposed into the Hartree–Fock contribution and the correlation correction:
DEMP2 ¼ DESCF þ ð2Þ MP :
ð2Þ SCF
The self-consistent field (DE ) interaction energy is further decomposed into the first-order electrostatic ðel ð10Þ Þ, Heitler–London exchange ðexHL Þ and delocalization components ðDEHF del Þ: HF HL DESCF ¼ el ð10Þ þ ex þ DEdel :
ð3Þ
The delocalization contribution contains the charge transfer, induction, and other higher-order Hartree–Fock terms. To make a valid comparison with the DEMP2 data, we also use the aug-ccpVDZ basis set at the SCF level of theory. The correlation correction ð2Þ ðMP Þ to DEMP2, which includes the electron correlation effects, was calculated as the difference between total intermolecular interaction energy and Hartree–Fock interaction energy. The total intermolecular interaction energy and the DESCF comð2Þ ponents together with the MP are presented in Table 1. The data show, as expected, that stabilization of analyzed complexes originates mainly from correlation effects. Indeed, it was confirmed by earlier investigations that stacked systems were stabilized due to the dispersion interactions [8–12]. As it was mentioned in the previous section, electrostatic energy can also significantly influence the stabilization of nucleic acid base complexes. Šponer and collaborators showed that electrostatic contribution, estimated using the Coulombic expression with atom centered point charges,
Fig. 4. The structure of BD0087 complex.
164
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Fig. 5. The influence of variability of shift (a) and slide (b) parameters on the electrostatic component.
were very sensitive to conformation of NAB complexes [26]. In the case of almost all guanine–adenine structures, electrostatic term accounts for the substantial part of stabilizing contributions. As it is seen the electrostatic interactions are much more structuredependent than the total MP2 interaction energy is. The average value of the first-order electrostatic term is equal to 4.7 kcal/ mol. The largest absolute value of electrostatic energy (14.2 kcal/mol) is observed for the complex denoted as BD0084. The value of the exchange component for this complex is equal
to 29 kcal/mol. In this case, the G/A pair is also stabilized by delocalization component that is equal to 3.25 kcal/mol. Among the considered set, one structure is found to be destabilized by the first-order electrostatic interaction (BD0087). The geometries of both structures, i.e. BD0084 and BD0087, are presented in Figs. 3 and 4, respectively. The values of delocalization energy term fall into rather shallow range, i.e. between 0.0 and 3.2 kcal/mol with the average value equal to 1.2 kcal/mol. The relative insignificance of the
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165
Fig. 6. The influence of variability of rise (a) and twist (b) parameters on the electrostatic component.
delocalization term was also reported by Hill et al. [17]. The investigation of Hill et al., performed for single configurations of complexes of ten different duplexes from the crystals structures, shows also that the first-order electrostatic component exhibit the same trend as the total intermolecular energy. The results presented herein for guanine–adenine system lead to contradictory conclusion than that of Hill et al. [17]. It is also not observed here that the exchange and correlation terms are opposite in sign and of comparable magnitude. We rather see that the correlation
correction is of much larger absolute value than the exchange component. Figs. 5–7 present the dependence of the electrostatic component on the structural base-step parameters. In order to put the analysis of Figs. 5–7 on quantitative basis, the Pearson productmoment correlation coefficients between the base-step parameters and all the calculated intermolecular interaction components were determined (see Table 2). The largest variance in common, equal to 73%, is observed between the total MP2 intermolecular interaction
166
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Fig. 7. The influence of variability of roll (a) and tilt (b) parameters on the electrostatic component.
energy and the value of rise parameter. With the exception of corð2Þ relation between rise parameter and the MP term, the variance in common between other parameters and energy components is less than 30%. The similar dependences for total intermolecular interacel and value of shift tion energy and value of rise parameter and ð10Þ parameter are observed. The unambiguous interpretation of the data presented both in Figs. 5–7 and Table 2 is not straightforward since every structure is described by the unique set of parameters.
3. Conclusions In the present contribution we discussed the intermolecular interaction energy and its components for guanine–adenine system in conformations appearing in B-DNA. The analysis of the results of calculations presented here, for the set comprising fortyeight G/A structures, shows relatively insignificant diversity of the interaction energy. Contrary, the electrostatic component re-
_ Czyz_ nikowska / Journal of Molecular Structure: THEOCHEM 895 (2009) 161–167 Z. Table 2 The Pearson product-moment correlation coefficient between the geomertical basestep parameters and the intermolecular interaction energy as well as its components. Parameter
DEMP2
ð10Þ el
ð2Þ MP
HL ex
DEHF del
Rise Twist Shift Roll Tilt Slide
0.86 0.52 0.21 0.23 0.09 0.00
0.58 0.01 0.52 0.31 0.25 0.24
0.83 0.28 0.21 0.02 0.05 0.05
0.50 0.04 0.30 0.25 0.11 0.15
0.53 0.04 0.19 0.21 0.04 0.06
veal much larger sensitivity to the variations of structural parameters. As expected, the correlation correction to the interaction energy is the most dominant factor determining the stability of investigated complexes. The first-order electrostatic contribution, although in most cases canceled out by exchange component, is also found to be substantial. Additionally, we noticed significant correlation between the rise parameter and both the total MP2 ð2Þ interaction energy as well as correlation correction, MP . Acknowledgement This work was partly supported by computational grant from PCSS (Poznan Supercomputing and Networking Center). The allocation of computing time is greatly appreciated. References [1] P. Hobza, R. Zachradník, K. Müller-Dethlefs, Collect. Czech. Chem. Commun. 71 (2006) 443–531. [2] K. Müller-Dethlefs, P. Hobza, Chem. Rev. 100 (2000) 143–167. [3] I. Da˛bkowska, P. Jurecˇka, P. Hobza, J. Chem. Phys. 122 (2005) 204322. [4] I. Da˛bkowska, H.V. Gonzales, P. Jurecˇka, P. Hobza, J. Phys. Chem. A 109 (2005) 1131–1136. [5] J. Šponer, P. Jurecˇka, I. Marchan, F.J. Luque, M. Orozco, P. Hobza, Chem. Eur. J. 12 (2006) 2854–2865. ˇ erny´, P. Hobza, Phys. Chem. Chem. Phys. 8 (2006) [6] P. Jurecˇka, J. Šponer, J. C 1985–1993. [7] T.L. McConnell, S.D. Wetmore, J. Phys. Chem. B 111 (2007) 2999–3009. [8] A. Hesselmann, G. Jansen, M. Schütz, J. Am. Chem. Soc. 128 (2006) 11730– 11731. [9] R. Sedlák, P. Jurecˇka, P. Hobza, J. Chem. Phys. 127 (2007) 075104.
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