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DFT study of H-bonds in the peptide secondary structures: The backbone–side-chain and polar side-chains interactions
Journal of Molecular Structure 972 (2010) 11–15
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
DFT study of H-bonds in the peptide secondary structures: The backbone–side-chain and polar side-chains interactions M.V. Vener *, A.N. Egorova, D.P. Fomin, V.G. Tsirelson Department of Quantum Chemistry, Mendeleev University of Chemical Technology, Miusskaya Square 9, 125047 Moscow, Russia
a r t i c l e
i n f o
Article history: Received 30 November 2009 Received in revised form 19 January 2010 Accepted 22 January 2010 Available online 1 February 2010 Keywords: H-bonds Peptide secondary structures Topological analysis Frequency shifts
a b s t r a c t The backbone–side-chain interactions in the peptide secondary structures are studied by the density functional theory methods with/without periodic boundary conditions. The alanine-based two-stranded b-sheet structure infinite models and the cluster models of the C5 structures modified by the glutamic acid residue are considered. Several low-energy structures have been localized in the BLYP/plane-wave and the BLYP/6-311++G** approximations. Combined use of the quantum-topological analysis of the electron density and frequency shifts enables us to detect and describe quantitatively the non-covalent interactions and H-bonds. We found that the strongest backbone–side-chain interaction (37 kJ/mol) is due to the intra-chain H-bond formed by the C@O backbone group and by the COOH side-chain group. The OH. . .O distance equals to 1.727 Å and the frequency shift of the OH stretching vibration is 370 cm1. The polar side-chains interaction is studied in the infinite model of the alanine-based two-stranded b-sheet structure modified by the glutamic acid/lysine residues. Moderate inter-chain H-bond (40 kJ/ mol) is formed by glutamic acid COOH group and lysine NH2 group. The OH. . .N distance equals to 1.707 Å and the frequency shift of the OH stretching vibration is 770 cm1. Ó 2010 Published by Elsevier B.V.
1. Introduction The crystalline structure of peptides is usually studied by the low-resolution (1.4–1.9 Å) diffraction methods, e.g. see [1], which do not allow the positions of the hydrogen atoms to be determined. On the other hand, spectroscopic investigations of oligoand polypeptides in the gas phase and in the solutions are blurred by the spectral line overlap and solvent effects [2–4]. The mentioned factors complicate a quantitative characterization of noncovalent interactions and hydrogen bonds (H-bonds) defining the intrinsic local conformational preferences of the peptide secondary structures. To overcome these difficulties, the quantumchemical computations are widely used. There exists several theoretical ways to describe the 3D architecture, inter- and intrachain interactions in the peptide secondary structures [5]: (a) the application of accurate methods to study small model molecules (the cluster models) as the components of the real systems [6–8]; (b) the use of hybrid quantum mechanics/molecular mechanics approaches as ONIOM etc. [9,10]; (c) the application of density functional theory (DFT) methods with periodic boundary conditions [11–16]. The last way enables one to get rid of the ‘‘terminal effects” which are typical for the cluster models and to * Corresponding author. Tel.: +7 499 978 9584; fax: +7 495 609 2964. E-mail address: [email protected] (M.V. Vener). 0022-2860/$ - see front matter Ó 2010 Published by Elsevier B.V. doi:10.1016/j.molstruc.2010.01.057
consider all types of the secondary structures at the same computational level. Very recently, we developed the approach [16] which is based on the combined use of the DFT methods with/ without periodic boundary conditions. The essential features of our approach are the following. (i) All types of the secondary structures (up to 11 residues), including the protein a-helixes, are studied at the DFT level. (ii) The effects of complexity (introduction of large residues and consideration of the solvent effects) can be studied step by step. The simultaneous consideration of the frequency shifts and electron-density properties enabled us to describe quantitatively the non-covalent interactions and Hbonds in oligo- and polyalanines [16]. In the present paper, we extend this approach to study the backbone–side-chain and polar side-chains interactions in the infinite models of the alaninebased two-stranded b-sheets modified by the glutamic acid (Glu) and glutamic acid/lysine (Lys) residues, respectively. For the sake of comparison, the cluster models are also considered in the case of the backbone–side-chain interactions. The aim of this paper is threefold: (1) to describe quantitatively backbone–side-chain and polar side-chain interactions in the alanine-based secondary structures modified by Glu/Lys residues; (2) to compare the results obtained for the cluster models and the infinite periodical models; (3) to create a reliable polypeptide salt-bridge model on the basis of the two-stranded b-sheets structure modified by the Glu/Lys residues.
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
2. The secondary-structure models and computational methods In this study, we use two sets of the secondary-structure models. The first one includes the C5 conformers [2,17] of CH3CONH– Glu–CONHCH3 molecule. The BLYP/6-311++G** calculations have been carried out using the PC version [18] of the GAMESS(US) program package [19]. The minimum-energy states of the structures under investigation have been confirmed by calculating the harmonic frequencies. The quantum-topological electron-density properties have been evaluated according to Bader [20] with the AIMPAC computer program suite [21,22]. We have considered such the features of the H. . .A (A@O, N, C, H) bond critical point in the electron density as the values of electron density, qb, and the potential energy density, Vb. The first value may be measured experimentally by means of the X-ray diffraction, while Vb is used to estimate the energy Eint of the particular non-covalent interaction [23–25] using empirical relationship (in the atomic units):
Eint ¼ ð1=2ÞV b :
ð1Þ
Details of the electron-density quantum-topological analysis of the oligopeptide cluster models have been published elsewhere [16,26]. The second set includes the periodical models mimicking backbone–side-chain (model A) and polar side-chains (model B) interactions in the polypeptides, see Fig. 1. The following unit cell parameters were used: a = 14.0 Å, b = 18.5 Å, c = 16.0 Å, a = b = c = 90.0° (model A) and a = 14.0 Å, b = 15.0 Å, c = 18.5 Å, a = a = b = 90.0° (model B). The considered infinite structures are periodical in the a direction and have an equivalent backbone. The a parameter is the same for them and was borrowed from Refs. [14,16], in which the infinite models of the polyalanine b-sheet
Fig. 1. The periodical models mimicking backbone–side-chain (model A, upper panel) and side-chain–side-chain interactions (model B, lower panel) in the polypeptides. Ala, Glu and Lys stand for the alanine, glutamic acid and lysine residues, respectively.
structures were considered. The values of the b and c parameters of model A and c parameter of model B were increased in comparison with those of the infinite polyalanine model to ensure no interactions between pairs of strands modified by polar residues. The DFT calculations with periodic boundary conditions were carried out using the CPMD program package [27]; the BLYP functional [28] and Troullier–Martins [29] pseudo-potentials for core electrons have been used. The kinetic energy cut-off for the plane wave basis set was 100 Ry and k-space sampling was limited to the C point. The minimum-energy states of the structures have been confirmed by calculating the harmonic frequencies. To get rid of small imaginary frequencies (20 cm1) a single criterion on the maximum energy gradient component controls the optimization process was set to 5 106 hartree/bohr. Tolerance on the energy controlling the self-consistent field convergence for geometry optimization was taking as 5 107 hartree. The atomic displacement values in numerical second derivative calculations were set to 0.03 born. Obtained geometrical parameters have been used in computation of periodical electronic wave-functions by the CRYSTAL98 program [30] at the B3LYP/6-31G level of approximation. The quantum-topological analysis of the crystalline electron density was performed by the TOPOND computer program [31]. Details of the electron-density topological analysis of the periodical models were presented elsewhere [32].
3. Results and discussion 3.1. The backbone–side-chain interactions Several low-energy C5 conformers of CH3CONH–Glu–CONHCH3 have been localized on the potential energy surface. The structures of the most stable conformers, which differ from each other by the side-chain orientation, are given in Fig. 2. Due to the backbone– side-chain interaction, the eight-member and nine-member pseudo-cycles are formed; these structures are denoted as C5_C8 and C5_C9, correspondingly. Relative energy values of the low-energy conformers and selected characteristics of C5 H-bonds are given in Table 1. In the cluster-model approximation, the interaction between the adjacent NAH and C@O groups causes the formation of the five-member pseudo-cycles (C5 H-bonds). The intramolecular C5 H-bond is relatively week and is characterized by the small value of the electron density at the bond critical point (0.02 a.u.), which is typical for the non-linear intramolecular H-bonds, e.g. see [33]. According to Table 1, the C5 H-bond disappears if the H. . .O distance becomes longer than 2.2 Å. The species with similar types of the side-chain–backbone interactions are localized for the periodic model of the alanine-based antiparallel two-stranded
Fig. 2. The low-energy C5 conformers of CH3CONH–Glu–CONHCH3. The intra-chain H-bonds forming by the backbone NH/Ca@O groups with the COOH fragment of the glutamic acid residue (Table 2) are given by the broken line.
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
Table 1 Relative stability, D, and selected parameters of the intra-chain H-bonds, formed by the interaction of the adjacent backbone NAH and C@O groups of the low-energy C5 conformers of CH3CONH–Glu–CONHCH3 (in regular letters) and model A of the infinite antiparallel b-stranded structures (in italics). qb stands for the electron density at the critical point of the H-bonds and Eint is interaction energy of the considered H-bond. Structure
D, kJ/mol
R(H. . .O), Å
Dihedral angle \NHOC ð Þ
qb, a.u.
Eint, kJ/mol
C5_C8
0 0 3.9 –4.0 4.3 –1.0
2.129 2.313 2.160 2.385 2.230 2.406
1.4 1.4 0.5 1.4 –5.4 –2.0
0.022 – 0.020 – – –
20 – 20 – – –
C5_C9 C5_C8 (type 2)a a b
This structure differs from C5_C8 by orientation of the glutamic acid residue. Interaction energy Eint is estimated from the computed Vb value, see Eq. (1).
Table 2 Selected characteristics of the intra-chain H-bonds formed by the backbone NH/Ca@Oa groups with the COOH fragment of the glutamic acid residueb computed for the cluster (in regular letters) and infinite models (in italics). Dm stands for the frequency shift of the stretching vibration of the corresponding group.c Structure
H-bonded fragment
R(H. . .O), Å
qb, a.u.
Eint, kJ/mol
Dm(AH), cm1
C5_C8
NH. . .O@C
2.047 2.335 1.737 1.743 2.084 2.268
0.020 0.011 0.041 0.039 0.020 0.014
17 11 46 37 16 13
103 65 395 373 107 71
a
C5_C9
C @O. . .HO
C5_C8 (type 2)
NH. . .O@C
Ca stands for the backbone carbon atom, and C is the carbon atom of the COOH group. The H-bonds are shown in Fig. 1. c The computed harmonic frequencies of the ‘‘free” group vibrations in the cluster model are: m(NH) = 3507 cm1 and m(OH) = 3593 cm1; in the infinite models they are: m(NH) = 3463 cm1 and m(OH) = 3582 cm1. a
b
b-sheet structure modified by the Glu residue (Model A, Fig. 1). In accord with Ref. [16], the C5 H-bonds are absent in the periodical structures. This is due to the fact that the H. . .O distance in the considered five-member pseudo-cycles is systematically longer in the periodical structures than in cluster models (Table 1). Relative stability of the periodical structures differs slightly from that of the cluster models with the similar types of the side-chain orientation. According to Table 1, the C5_C8 structure corresponds to the global minimum on the potential energy surface in the cluster approximation, while it represents the second minimum in the infinite-model approximation. However, the computed values of relative energies of the three low-energy conformers are close to each other and their difference is of an order of kBT at room temperature. The C5_C8 (type 2) structure is by 10 kJ/mol more stable than the next stable structures, which are therefore not considered in this study. Selected characteristics of the intra-chain H-bonds, forming by the backbone NH/Ca@O groups with the COOH fragment of the Glu residue are given in Table 2. Formation of the intra-chain Hbonds causes a red shift of the stretching vibrations of the NH/ OH groups. Relatively large value of the frequency shift Dm(OH) = Dm(OH)free–Dm(OH) obtained for the O–H. . .O bond in the C5_C9 structure imply that it can be treated as the moderate H-bond [34]. The energy of this interaction is found to be much larger than that of the C5 H-bonds, c.f. Tables 1 and 2. In accord with [16], increase of the H-bond strength is accompanied with increase of the corresponding qb values. Quantum-topological analysis of the electron density enables us to detect and to describe quantitatively non-classical interactions of the CH. . .O type in the considered structures [35]. These non-covalent interactions play an important role in biochemistry in particular, in stabilization of a-helix structure by polar side-chain interactions [35]. Selected characteristics of these interactions are given in Table 3. The energies of these interactions are around 10 kJ/mol and they can be treated as van-der-Waals ones. The H. . .O distances in the CH. . .O fragments are found to be very sensi-
Table 3 Selected characteristics of the most strong intra-chain non-covalent interactions detected for the low-energy C5 conformers of CH3CONH–Glu–CONHCH3 (in regular letters) and model A of the infinite antiparallel b-stranded structures (in italics). qb stands for the electron density at the critical point of the H-bonds and Eint is interaction energy of the considered H-bond. Structure
Interactiona
R(H. . .O), Å
qb, a.u.
Eint, kJ/mol
C5_C8
Ca@O. . . HCc
2.408 2.443 2.802 2.514 2.623 2.743 2.678 2.693 2.811 2.866 2.704 2.442
0.012 0.011 – 0.11 0.009 0.007 0.008 0.007 0.008 – – 0.012
9 10 – 11 7 6 6 6 5 – – 10
a
C H. . .O@C C5_C9
Ca@O. . .HCc CaH. . .OAC
C5_C8 (type 2)a
N. . .HCb CaH. . .O@C
a Ca stands for the backbone carbon atom, Cb and Cc are the side-chain carbon atoms, and C is the carbon atom of the COOH group.
tive to the computational level and the model used in calculations, see Table 3. As a result, the number and type of weak backbone– side-chain interactions detected in the cluster and infinite models are different for the structures with the similar orientation of the Glu residue. For H. . .O distances larger than 2.7 Å we did not find the bond critical point for the CH. . .O interactions. This is in accord with results of the previous computational studies of in the peptide secondary structures [36–38].
3.2. The polar side-chain interactions Model B, see Fig. 1, was used to study the Glu. . .Lys interactions. The global-minimum structure is characterized by the inter-chain OAH. . .N bond (Fig. 3) with the relatively short H. . . N distance (1.707 Å). The frequency shift of the OH stretching vibration, in
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
Fig. 3. The inter-chain H-bond forming by glutamic acid COH group and lysine NH2 group in model B structure.
Table 4 Computed values of the H. . .X distance, X@O, N, the electron density at the H-bond critical point, qb, the interaction energy, Eint, and frequency shifts, Dm(AH), of the strongest Hbonds in the alanine-based infinite models of antiparallel b-sheet modified by polar residues. Interaction
H-bond
R(H. . .X), Å
qb, a.u.
Eint, kJ/mol
Dm(AH), cm1
Backbone–backbone Backbone–side-chain Side-chain–side-chain
NH. . .O OH. . .O OH. . .N
2.081 1.727 1.707
0.018 0.039 0.046
17 37 40
85 373 770
comparison with the frequency of the ‘‘free” OH group, is larger than 700 cm1. Such frequency shift value is typical for moderate H-bonds [34]. Computed values of the OAH distance of 1.021 Å and the electron density at the H-bond critical point of 0.05 a.u. indicate the ‘‘intermediate” type of non-covalent interactions, which is placed between the ideal shared (covalent) and closedshell interactions [32]. Table 4 shows that the polar side-chain interactions cause the formation of moderate inter-chain H-bond (40 kJ/mol). It is much stronger than inter-chain H-bonds, caused by backbone–backbone interactions. The proton sits near the oxygen atom in the inter-chain H-bond (Fig. 3) however the OAH bond is relatively long. Account for the solvent effects will contract the O. . .N distance and shift the proton position from O to N [39]. As a result, one can expect the formation of a Glu. . .Lys+ salt-bridge [40–42].
4. Conclusions Simultaneous consideration of the frequency shifts of the H-bonded groups and the quantum-topological analysis of the electron density enables us to detect and describe quantitatively different types of the H-bonds and non-covalent interactions in oligo- and polypeptides modified by the glutamic acid residue. In contrast to the backbone–backbone interactions, which are relatively weak (17 kJ/mol), the moderate H-bond of the OH. . .O type appears as a result of the backbone–side-chain interactions. Its energy equals to 37 kJ/mol, while the frequency shift of the OH stretch is around 370 cm1. Relative stability of the periodical structures differs slightly from that of the cluster models with the similar type of the sidechain orientation. Due to the geometrical changes, the number and type of weak backbone–side-chain interactions detected in the cluster and infinite models are different. It means that the results obtained in the cluster approximation should be applied for the description of real periodical systems with caution.
The polar side-chains interaction occurs between glutamic acid COOH group and lysine NH2 group of the infinite model of the alanine-bases two-stranded b-sheet structure. The OH. . .N distance equals to 1.707 Å and the frequency shift of the OH stretching vibration is 770 cm1. Thus, the computed values indicate the formation of moderate inter-chain H-bond (to 40 kJ/mol). Acknowledgements This study was supported by Russian Foundation for Basic Research (Grants 08-03-00361 and 08-03-00515). References [1] M. Marcuart, J. Walter, J. Deisenhofer, W. Bode, R. Huber, Acta Cryst. B 39 (1983) 480. [2] E. Vass, M. Hollósi, F. Besson, R. Buchet, Chem. Rev. 103 (2003) 1917 (and references therein). [3] W. Chin, F. Piuzzi, I. Dimicoli, M. Mons, Phys. Chem. Chem. Phys. 8 (2006) 1033. [4] I. Compagnon, J. Oomens, G. Meijer, G. von Helden, J. Am. Chem. Soc. 128 (2006) 3592. [5] S. Jia, Z. Mo, Y. Dai, X. Zhang, H. Yang, Y. Qi, Int. J. Mol. Sci. 10 (2009) 3358. [6] R.A. Friesner, B.D. Duniezt, Acc. Chem. Res. 34 (2001) 351. [7] S. Scheiner, J. Phys. Chem. B 110 (2006) 18670. [8] C.A. Rice, I. Dauster, M. Suhm, J. Chem. Phys. 126 (2007) 134313. [9] R. Wieczorek, J.J. Dannenberg, J. Phys. Chem. B 112 (2008) 1320. [10] R. Viswanathan, J.J. Dannenberg, J. Phys. Chem. B 112 (2008) 5199. [11] J. Ireta, J. Neugebauer, M. Scheffler, A. Rojo, M. Galván, J. Phys. Chem. B 107 (2003) 1432. [12] J. Rossmeisl, I. Kristensen, M. Gregensen, K.W. Jakobsen, J.K. Nørskov, J. Am. Chem. Soc. 125 (2003) 16383. [13] S. Franzen, J. Phys. Chem. A 107 (2003) 9898. [14] J. Rossmeisl, J.K. Nørskov, K.W. Jacobsen, J. Am. Chem. Soc. 126 (2004) 13140. [15] L. Ismer, J. Ireta, S. Boeck, J. Neugebauer, Phys. Rev. E 71 (2005) 031911. [16] M.V. Vener, A.N. Egorova, D.P. Fomin, V.G. Tsirelson, J. Phys. Org. Chem. 22 (2009) 177. [17] A.K. Thakur, R. Kishore, Biopolymers 81 (2006) 440. [18] A.A. Granovsky, PC GAMESS version 7.0, http://classic.chem.msu.su/gran/ gamess/index.html. [19] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 (1993) 1347. [20] R.F.W. Bader, Atoms in Molecules. A Quantum Theory, Oxford University Press, New York, 1990.
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[33] I. Majerz, T. Dziembowska, J. Phys. Org. Chem. 21 (2008) 876. [34] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48. [35] Z. Chi, C.A. Olsen, A.J. Bell, N.R. Kallenbach, Biopolymers (Peptide Sci.) 60 (2001) 366. [36] C.F. Matta, N. Castillo, R.J. Boyd, J. Phys. Chem. B 110 (2006) 563. [37] R. Parthasarathi, S.S. Raman, V. Subramanian, T. Ramasami, J. Phys. Chem. A 111 (2007) 7141. [38] S.M. LaPointe, S. Farrag, H.J. Bohórquez, R.J. Boyd, J. Phys. Chem. B 113 (2009) 10957. [39] S. Kong, I.G. Shenderovich, M.V. Vener, DFT study of the proton transfer effect on vibrations of strong (short) intermolecular OAH. . .N/O. . .HAN+ hydrogen bonds in aprotic solvents, J. Phys. Chem. A, accepted for publication. [40] J.M. Scholtz, H. Qian, V.R. Robbins, R.L. Baldwin, Biochemistry 32 (1993) 9668. [41] A.G. Therien, F.E.M. Grant, C.M. Deber, Nat. Struct. Biol. 8 (2001) 597. [42] R. Geney, M. Layten, R. Gomperts, V. Hornak, C. Simmerling, J. Chem. Theory Comput. 2 (2006) 115.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
DFT study of H-bonds in the peptide secondary structures: The backbone–side-chain and polar side-chains interactions M.V. Vener *, A.N. Egorova, D.P. Fomin, V.G. Tsirelson Department of Quantum Chemistry, Mendeleev University of Chemical Technology, Miusskaya Square 9, 125047 Moscow, Russia
a r t i c l e
i n f o
Article history: Received 30 November 2009 Received in revised form 19 January 2010 Accepted 22 January 2010 Available online 1 February 2010 Keywords: H-bonds Peptide secondary structures Topological analysis Frequency shifts
a b s t r a c t The backbone–side-chain interactions in the peptide secondary structures are studied by the density functional theory methods with/without periodic boundary conditions. The alanine-based two-stranded b-sheet structure infinite models and the cluster models of the C5 structures modified by the glutamic acid residue are considered. Several low-energy structures have been localized in the BLYP/plane-wave and the BLYP/6-311++G** approximations. Combined use of the quantum-topological analysis of the electron density and frequency shifts enables us to detect and describe quantitatively the non-covalent interactions and H-bonds. We found that the strongest backbone–side-chain interaction (37 kJ/mol) is due to the intra-chain H-bond formed by the C@O backbone group and by the COOH side-chain group. The OH. . .O distance equals to 1.727 Å and the frequency shift of the OH stretching vibration is 370 cm1. The polar side-chains interaction is studied in the infinite model of the alanine-based two-stranded b-sheet structure modified by the glutamic acid/lysine residues. Moderate inter-chain H-bond (40 kJ/ mol) is formed by glutamic acid COOH group and lysine NH2 group. The OH. . .N distance equals to 1.707 Å and the frequency shift of the OH stretching vibration is 770 cm1. Ó 2010 Published by Elsevier B.V.
1. Introduction The crystalline structure of peptides is usually studied by the low-resolution (1.4–1.9 Å) diffraction methods, e.g. see [1], which do not allow the positions of the hydrogen atoms to be determined. On the other hand, spectroscopic investigations of oligoand polypeptides in the gas phase and in the solutions are blurred by the spectral line overlap and solvent effects [2–4]. The mentioned factors complicate a quantitative characterization of noncovalent interactions and hydrogen bonds (H-bonds) defining the intrinsic local conformational preferences of the peptide secondary structures. To overcome these difficulties, the quantumchemical computations are widely used. There exists several theoretical ways to describe the 3D architecture, inter- and intrachain interactions in the peptide secondary structures [5]: (a) the application of accurate methods to study small model molecules (the cluster models) as the components of the real systems [6–8]; (b) the use of hybrid quantum mechanics/molecular mechanics approaches as ONIOM etc. [9,10]; (c) the application of density functional theory (DFT) methods with periodic boundary conditions [11–16]. The last way enables one to get rid of the ‘‘terminal effects” which are typical for the cluster models and to * Corresponding author. Tel.: +7 499 978 9584; fax: +7 495 609 2964. E-mail address: [email protected] (M.V. Vener). 0022-2860/$ - see front matter Ó 2010 Published by Elsevier B.V. doi:10.1016/j.molstruc.2010.01.057
consider all types of the secondary structures at the same computational level. Very recently, we developed the approach [16] which is based on the combined use of the DFT methods with/ without periodic boundary conditions. The essential features of our approach are the following. (i) All types of the secondary structures (up to 11 residues), including the protein a-helixes, are studied at the DFT level. (ii) The effects of complexity (introduction of large residues and consideration of the solvent effects) can be studied step by step. The simultaneous consideration of the frequency shifts and electron-density properties enabled us to describe quantitatively the non-covalent interactions and Hbonds in oligo- and polyalanines [16]. In the present paper, we extend this approach to study the backbone–side-chain and polar side-chains interactions in the infinite models of the alaninebased two-stranded b-sheets modified by the glutamic acid (Glu) and glutamic acid/lysine (Lys) residues, respectively. For the sake of comparison, the cluster models are also considered in the case of the backbone–side-chain interactions. The aim of this paper is threefold: (1) to describe quantitatively backbone–side-chain and polar side-chain interactions in the alanine-based secondary structures modified by Glu/Lys residues; (2) to compare the results obtained for the cluster models and the infinite periodical models; (3) to create a reliable polypeptide salt-bridge model on the basis of the two-stranded b-sheets structure modified by the Glu/Lys residues.
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
2. The secondary-structure models and computational methods In this study, we use two sets of the secondary-structure models. The first one includes the C5 conformers [2,17] of CH3CONH– Glu–CONHCH3 molecule. The BLYP/6-311++G** calculations have been carried out using the PC version [18] of the GAMESS(US) program package [19]. The minimum-energy states of the structures under investigation have been confirmed by calculating the harmonic frequencies. The quantum-topological electron-density properties have been evaluated according to Bader [20] with the AIMPAC computer program suite [21,22]. We have considered such the features of the H. . .A (A@O, N, C, H) bond critical point in the electron density as the values of electron density, qb, and the potential energy density, Vb. The first value may be measured experimentally by means of the X-ray diffraction, while Vb is used to estimate the energy Eint of the particular non-covalent interaction [23–25] using empirical relationship (in the atomic units):
Eint ¼ ð1=2ÞV b :
ð1Þ
Details of the electron-density quantum-topological analysis of the oligopeptide cluster models have been published elsewhere [16,26]. The second set includes the periodical models mimicking backbone–side-chain (model A) and polar side-chains (model B) interactions in the polypeptides, see Fig. 1. The following unit cell parameters were used: a = 14.0 Å, b = 18.5 Å, c = 16.0 Å, a = b = c = 90.0° (model A) and a = 14.0 Å, b = 15.0 Å, c = 18.5 Å, a = a = b = 90.0° (model B). The considered infinite structures are periodical in the a direction and have an equivalent backbone. The a parameter is the same for them and was borrowed from Refs. [14,16], in which the infinite models of the polyalanine b-sheet
Fig. 1. The periodical models mimicking backbone–side-chain (model A, upper panel) and side-chain–side-chain interactions (model B, lower panel) in the polypeptides. Ala, Glu and Lys stand for the alanine, glutamic acid and lysine residues, respectively.
structures were considered. The values of the b and c parameters of model A and c parameter of model B were increased in comparison with those of the infinite polyalanine model to ensure no interactions between pairs of strands modified by polar residues. The DFT calculations with periodic boundary conditions were carried out using the CPMD program package [27]; the BLYP functional [28] and Troullier–Martins [29] pseudo-potentials for core electrons have been used. The kinetic energy cut-off for the plane wave basis set was 100 Ry and k-space sampling was limited to the C point. The minimum-energy states of the structures have been confirmed by calculating the harmonic frequencies. To get rid of small imaginary frequencies (20 cm1) a single criterion on the maximum energy gradient component controls the optimization process was set to 5 106 hartree/bohr. Tolerance on the energy controlling the self-consistent field convergence for geometry optimization was taking as 5 107 hartree. The atomic displacement values in numerical second derivative calculations were set to 0.03 born. Obtained geometrical parameters have been used in computation of periodical electronic wave-functions by the CRYSTAL98 program [30] at the B3LYP/6-31G level of approximation. The quantum-topological analysis of the crystalline electron density was performed by the TOPOND computer program [31]. Details of the electron-density topological analysis of the periodical models were presented elsewhere [32].
3. Results and discussion 3.1. The backbone–side-chain interactions Several low-energy C5 conformers of CH3CONH–Glu–CONHCH3 have been localized on the potential energy surface. The structures of the most stable conformers, which differ from each other by the side-chain orientation, are given in Fig. 2. Due to the backbone– side-chain interaction, the eight-member and nine-member pseudo-cycles are formed; these structures are denoted as C5_C8 and C5_C9, correspondingly. Relative energy values of the low-energy conformers and selected characteristics of C5 H-bonds are given in Table 1. In the cluster-model approximation, the interaction between the adjacent NAH and C@O groups causes the formation of the five-member pseudo-cycles (C5 H-bonds). The intramolecular C5 H-bond is relatively week and is characterized by the small value of the electron density at the bond critical point (0.02 a.u.), which is typical for the non-linear intramolecular H-bonds, e.g. see [33]. According to Table 1, the C5 H-bond disappears if the H. . .O distance becomes longer than 2.2 Å. The species with similar types of the side-chain–backbone interactions are localized for the periodic model of the alanine-based antiparallel two-stranded
Fig. 2. The low-energy C5 conformers of CH3CONH–Glu–CONHCH3. The intra-chain H-bonds forming by the backbone NH/Ca@O groups with the COOH fragment of the glutamic acid residue (Table 2) are given by the broken line.
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
Table 1 Relative stability, D, and selected parameters of the intra-chain H-bonds, formed by the interaction of the adjacent backbone NAH and C@O groups of the low-energy C5 conformers of CH3CONH–Glu–CONHCH3 (in regular letters) and model A of the infinite antiparallel b-stranded structures (in italics). qb stands for the electron density at the critical point of the H-bonds and Eint is interaction energy of the considered H-bond. Structure
D, kJ/mol
R(H. . .O), Å
Dihedral angle \NHOC ð Þ
qb, a.u.
Eint, kJ/mol
C5_C8
0 0 3.9 –4.0 4.3 –1.0
2.129 2.313 2.160 2.385 2.230 2.406
1.4 1.4 0.5 1.4 –5.4 –2.0
0.022 – 0.020 – – –
20 – 20 – – –
C5_C9 C5_C8 (type 2)a a b
This structure differs from C5_C8 by orientation of the glutamic acid residue. Interaction energy Eint is estimated from the computed Vb value, see Eq. (1).
Table 2 Selected characteristics of the intra-chain H-bonds formed by the backbone NH/Ca@Oa groups with the COOH fragment of the glutamic acid residueb computed for the cluster (in regular letters) and infinite models (in italics). Dm stands for the frequency shift of the stretching vibration of the corresponding group.c Structure
H-bonded fragment
R(H. . .O), Å
qb, a.u.
Eint, kJ/mol
Dm(AH), cm1
C5_C8
NH. . .O@C
2.047 2.335 1.737 1.743 2.084 2.268
0.020 0.011 0.041 0.039 0.020 0.014
17 11 46 37 16 13
103 65 395 373 107 71
a
C5_C9
C @O. . .HO
C5_C8 (type 2)
NH. . .O@C
Ca stands for the backbone carbon atom, and C is the carbon atom of the COOH group. The H-bonds are shown in Fig. 1. c The computed harmonic frequencies of the ‘‘free” group vibrations in the cluster model are: m(NH) = 3507 cm1 and m(OH) = 3593 cm1; in the infinite models they are: m(NH) = 3463 cm1 and m(OH) = 3582 cm1. a
b
b-sheet structure modified by the Glu residue (Model A, Fig. 1). In accord with Ref. [16], the C5 H-bonds are absent in the periodical structures. This is due to the fact that the H. . .O distance in the considered five-member pseudo-cycles is systematically longer in the periodical structures than in cluster models (Table 1). Relative stability of the periodical structures differs slightly from that of the cluster models with the similar types of the side-chain orientation. According to Table 1, the C5_C8 structure corresponds to the global minimum on the potential energy surface in the cluster approximation, while it represents the second minimum in the infinite-model approximation. However, the computed values of relative energies of the three low-energy conformers are close to each other and their difference is of an order of kBT at room temperature. The C5_C8 (type 2) structure is by 10 kJ/mol more stable than the next stable structures, which are therefore not considered in this study. Selected characteristics of the intra-chain H-bonds, forming by the backbone NH/Ca@O groups with the COOH fragment of the Glu residue are given in Table 2. Formation of the intra-chain Hbonds causes a red shift of the stretching vibrations of the NH/ OH groups. Relatively large value of the frequency shift Dm(OH) = Dm(OH)free–Dm(OH) obtained for the O–H. . .O bond in the C5_C9 structure imply that it can be treated as the moderate H-bond [34]. The energy of this interaction is found to be much larger than that of the C5 H-bonds, c.f. Tables 1 and 2. In accord with [16], increase of the H-bond strength is accompanied with increase of the corresponding qb values. Quantum-topological analysis of the electron density enables us to detect and to describe quantitatively non-classical interactions of the CH. . .O type in the considered structures [35]. These non-covalent interactions play an important role in biochemistry in particular, in stabilization of a-helix structure by polar side-chain interactions [35]. Selected characteristics of these interactions are given in Table 3. The energies of these interactions are around 10 kJ/mol and they can be treated as van-der-Waals ones. The H. . .O distances in the CH. . .O fragments are found to be very sensi-
Table 3 Selected characteristics of the most strong intra-chain non-covalent interactions detected for the low-energy C5 conformers of CH3CONH–Glu–CONHCH3 (in regular letters) and model A of the infinite antiparallel b-stranded structures (in italics). qb stands for the electron density at the critical point of the H-bonds and Eint is interaction energy of the considered H-bond. Structure
Interactiona
R(H. . .O), Å
qb, a.u.
Eint, kJ/mol
C5_C8
Ca@O. . . HCc
2.408 2.443 2.802 2.514 2.623 2.743 2.678 2.693 2.811 2.866 2.704 2.442
0.012 0.011 – 0.11 0.009 0.007 0.008 0.007 0.008 – – 0.012
9 10 – 11 7 6 6 6 5 – – 10
a
C H. . .O@C C5_C9
Ca@O. . .HCc CaH. . .OAC
C5_C8 (type 2)a
N. . .HCb CaH. . .O@C
a Ca stands for the backbone carbon atom, Cb and Cc are the side-chain carbon atoms, and C is the carbon atom of the COOH group.
tive to the computational level and the model used in calculations, see Table 3. As a result, the number and type of weak backbone– side-chain interactions detected in the cluster and infinite models are different for the structures with the similar orientation of the Glu residue. For H. . .O distances larger than 2.7 Å we did not find the bond critical point for the CH. . .O interactions. This is in accord with results of the previous computational studies of in the peptide secondary structures [36–38].
3.2. The polar side-chain interactions Model B, see Fig. 1, was used to study the Glu. . .Lys interactions. The global-minimum structure is characterized by the inter-chain OAH. . .N bond (Fig. 3) with the relatively short H. . . N distance (1.707 Å). The frequency shift of the OH stretching vibration, in
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M.V. Vener et al. / Journal of Molecular Structure 972 (2010) 11–15
Fig. 3. The inter-chain H-bond forming by glutamic acid COH group and lysine NH2 group in model B structure.
Table 4 Computed values of the H. . .X distance, X@O, N, the electron density at the H-bond critical point, qb, the interaction energy, Eint, and frequency shifts, Dm(AH), of the strongest Hbonds in the alanine-based infinite models of antiparallel b-sheet modified by polar residues. Interaction
H-bond
R(H. . .X), Å
qb, a.u.
Eint, kJ/mol
Dm(AH), cm1
Backbone–backbone Backbone–side-chain Side-chain–side-chain
NH. . .O OH. . .O OH. . .N
2.081 1.727 1.707
0.018 0.039 0.046
17 37 40
85 373 770
comparison with the frequency of the ‘‘free” OH group, is larger than 700 cm1. Such frequency shift value is typical for moderate H-bonds [34]. Computed values of the OAH distance of 1.021 Å and the electron density at the H-bond critical point of 0.05 a.u. indicate the ‘‘intermediate” type of non-covalent interactions, which is placed between the ideal shared (covalent) and closedshell interactions [32]. Table 4 shows that the polar side-chain interactions cause the formation of moderate inter-chain H-bond (40 kJ/mol). It is much stronger than inter-chain H-bonds, caused by backbone–backbone interactions. The proton sits near the oxygen atom in the inter-chain H-bond (Fig. 3) however the OAH bond is relatively long. Account for the solvent effects will contract the O. . .N distance and shift the proton position from O to N [39]. As a result, one can expect the formation of a Glu. . .Lys+ salt-bridge [40–42].
4. Conclusions Simultaneous consideration of the frequency shifts of the H-bonded groups and the quantum-topological analysis of the electron density enables us to detect and describe quantitatively different types of the H-bonds and non-covalent interactions in oligo- and polypeptides modified by the glutamic acid residue. In contrast to the backbone–backbone interactions, which are relatively weak (17 kJ/mol), the moderate H-bond of the OH. . .O type appears as a result of the backbone–side-chain interactions. Its energy equals to 37 kJ/mol, while the frequency shift of the OH stretch is around 370 cm1. Relative stability of the periodical structures differs slightly from that of the cluster models with the similar type of the sidechain orientation. Due to the geometrical changes, the number and type of weak backbone–side-chain interactions detected in the cluster and infinite models are different. It means that the results obtained in the cluster approximation should be applied for the description of real periodical systems with caution.
The polar side-chains interaction occurs between glutamic acid COOH group and lysine NH2 group of the infinite model of the alanine-bases two-stranded b-sheet structure. The OH. . .N distance equals to 1.707 Å and the frequency shift of the OH stretching vibration is 770 cm1. Thus, the computed values indicate the formation of moderate inter-chain H-bond (to 40 kJ/mol). Acknowledgements This study was supported by Russian Foundation for Basic Research (Grants 08-03-00361 and 08-03-00515). References [1] M. Marcuart, J. Walter, J. Deisenhofer, W. Bode, R. Huber, Acta Cryst. B 39 (1983) 480. [2] E. Vass, M. Hollósi, F. Besson, R. Buchet, Chem. Rev. 103 (2003) 1917 (and references therein). [3] W. Chin, F. Piuzzi, I. Dimicoli, M. Mons, Phys. Chem. Chem. Phys. 8 (2006) 1033. [4] I. Compagnon, J. Oomens, G. Meijer, G. von Helden, J. Am. Chem. Soc. 128 (2006) 3592. [5] S. Jia, Z. Mo, Y. Dai, X. Zhang, H. Yang, Y. Qi, Int. J. Mol. Sci. 10 (2009) 3358. [6] R.A. Friesner, B.D. Duniezt, Acc. Chem. Res. 34 (2001) 351. [7] S. Scheiner, J. Phys. Chem. B 110 (2006) 18670. [8] C.A. Rice, I. Dauster, M. Suhm, J. Chem. Phys. 126 (2007) 134313. [9] R. Wieczorek, J.J. Dannenberg, J. Phys. Chem. B 112 (2008) 1320. [10] R. Viswanathan, J.J. Dannenberg, J. Phys. Chem. B 112 (2008) 5199. [11] J. Ireta, J. Neugebauer, M. Scheffler, A. Rojo, M. Galván, J. Phys. Chem. B 107 (2003) 1432. [12] J. Rossmeisl, I. Kristensen, M. Gregensen, K.W. Jakobsen, J.K. Nørskov, J. Am. Chem. Soc. 125 (2003) 16383. [13] S. Franzen, J. Phys. Chem. A 107 (2003) 9898. [14] J. Rossmeisl, J.K. Nørskov, K.W. Jacobsen, J. Am. Chem. Soc. 126 (2004) 13140. [15] L. Ismer, J. Ireta, S. Boeck, J. Neugebauer, Phys. Rev. E 71 (2005) 031911. [16] M.V. Vener, A.N. Egorova, D.P. Fomin, V.G. Tsirelson, J. Phys. Org. Chem. 22 (2009) 177. [17] A.K. Thakur, R. Kishore, Biopolymers 81 (2006) 440. [18] A.A. Granovsky, PC GAMESS version 7.0, http://classic.chem.msu.su/gran/ gamess/index.html. [19] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 (1993) 1347. [20] R.F.W. Bader, Atoms in Molecules. A Quantum Theory, Oxford University Press, New York, 1990.
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