Mechanism of the Secondary Structure Dependence of the Infrared

Dec 16, 2011 - The mechanism of the secondary structure dependence of the infrared (IR) intensity of the amide II mode of peptide chains is examined ...
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Mechanism of the Secondary Structure Dependence of the Infrared Intensity of the Amide II Mode of Peptide Chains Hajime Torii* Department of Chemistry, School of Education, Shizuoka University, 836 Ohya, Shizuoka 422-8529, Japan S Supporting Information *

ABSTRACT: The mechanism of the secondary structure dependence of the infrared (IR) intensity of the amide II mode of peptide chains is examined theoretically. It is shown that a large interpeptide flux of electrons (charge flux) is induced by the amide II mode of peptide chain in the C5 (β-strand) conformation through the H···O interaction, giving rise to large IR intensity enhancement. Taking into account also that this IR intensity enhancement does not occur in the case of the C7 conformation (with intrastrand hydrogen bonding), it is concluded that strong secondary structure dependence of the amide II IR intensity is related to the amplitude of the charge flux and the intrachain relative configuration of peptide groups. These results provide deeper insight into the structural information contained in vibrational spectroscopic features and will be useful, for example, for analyzing the structural variations induced by some changes in the thermodynamic state. SECTION: Biophysical Chemistry

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protein, it was shown that the amide II/amide I IR intensity ratio increases as the α-helix content decreases.33 A recent experimental and theoretical study also indicated that the IR intensity of the amide II mode depends on the secondary structure.34 However, the mechanism giving rise to this secondary structure dependence is not yet known. By clarifying the mechanism, it will become possible to correctly extract the structural information contained in this spectroscopic feature. Knowledge on the mechanism of intensity variation is useful not only in ordinary linear (one-dimensional) IR spectroscopy but also (and even more) in two-dimensional IR spectroscopy,15,27,35−42 because the intensity is proportional to the fourth of the dipole derivative in the latter but to the square of it in the former. In the present study, for the purpose of clarifying this mechanism, a theoretical analysis is carried out on the modulation in the electron density induced by the amide II mode, taking alanine dipeptide-d10 (CD3CONH−CDCD3− CONHCD 3 ) as a model system. Four representative conformations [C5 (β-strand, Φ = Ψ = 180.0°), C7 (Φ = −83.7° and Ψ = 75.0°), ppII (polyproline II, Φ = −75.0° and Ψ = 145.0°), and α-helix (Φ = −57.0° and Ψ = −47.0°)] shown in Figure 1 and some conformations close to C5 are considered. The peptide groups were numbered as peptide group 1 and 2 from the N terminus. The modulation in the electron density are calculated as the electron density derivative30,43,44 δ(∂ρ(el)(r)/∂QAII) [≡ (∂ρ(el)(r)/∂QAII)dipeptide − (∂ρ(el)(r)/ ∂QAII)isolated], where QAII represents the amide II vibrational coordinate, with the density functional theoretical (DFT)

he peptide group is a repeat unit of peptide chains such as polypeptides and proteins, and has some characteristic vibrational modes called amide I, II, III, and so on. There have been a large amount of experimental and theoretical studies on those modes, especially with regard to their frequency positions in relation to the secondary structures of peptide chains. For example, it is well-known that the peak frequency position of the amide I infrared (IR) band depends sensitively on the secondary structure (α-helix, β-sheet, etc.),1−7 because of the vibrational coupling between peptide groups controlled by the through-space8−16 and through-bond11−14,17,18 interaction mechanisms and the electrostatic environmental effects including the effect of hydrogen bonding.19−27 It is also known that the frequency position of the amide III mode is well correlated to the Ψ dihedral angle of the peptide chain.28,29 By contrast, little is known about the intensities of those modes, although intensity is another important factor that constitutes the band profile of each vibrational mode. Concerning the IR intensity of the amide I mode, it has been clarified that it is enhanced by about 1.7 times upon hydrogen-bond formation with three water molecules (two on the CO group and one on the N−H group).30 An intensity enhancement is also seen upon halogen-bond formation with a halogen-containing molecule.30 Then, are there any interesting features also for the IR intensities of the other amide modes? Concerning this point, an interesting feature seems to be present for the IR intensity of the amide II mode, which is located in the 1600−1500 cm−1 region (just below the amide I mode) and consists mainly of the N−H bending. Previous experimental studies on polypeptides in solution showed that the IR intensity of the amide II mode is ∼3 × 102 km mol−1 for β-sheet and “random coil”, while it is 1.3−1.6 × 102 km mol−1 for α-helix.31,32 In another study on heat denaturation of a © 2011 American Chemical Society

Received: November 21, 2011 Accepted: December 16, 2011 Published: December 16, 2011 112

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Figure 3. The IR intensities calculated for the amide II modes of peptide groups 1 and 2 of alanine dipeptide-d10 in some conformations close to C5. Figure 1. Structures of alanine dipeptide-d10 in the four representative conformations considered in this study; (a) C5 (β-strand), (b) C7, (c) ppII, and (d) α-helix. Peptide group 1 is located on the right, and peptide 2 is on the left.

2 remains approximately the same (with the enhancement factor in the range of 0.97−1.17). These calculated results are reasonably consistent with the observed spectral features stated in the introduction part that the IR intensity of the amide II mode is stronger for β-sheet than for α-helix,31,32 and the amide II/amide I IR intensity ratio increases as the α-helix content decreases.33 It should be remarked that the sum of the IR intensities calculated here for the two peptide groups in each conformation is nearly equal (with the maximum deviation of 17.7 km mol−1) to the total IR intensity calculated directly from the amide II normal modes, indicating that the APV method is sufficiently well applicable in the present cases. Inspecting the structures of the four representative conformations shown in Figure 1, it is noticed that the IR intensity enhancement calculated for peptide 1 of C5 may be related to the H···O interaction between the N−H group of peptide 1 and the CO group of peptide 2. However, it is clear that the existence of this hydrogen-bond like interaction alone is not sufficient for explaining the IR intensity enhancement, because the IR intensity calculated for peptide 2 of C7, whose N−H group forms a true hydrogen bond with the CO group of peptide 1, is not at all enhanced, and is even reduced, as shown in Figure 2. The electron density derivative of the amide II mode δ(∂ρ(el)(r)/∂QAII) calculated for peptide 1 of C5 is shown in Figure 4a. It is clearly seen that, although only the atoms in peptide 1 are vibrating, the electron density modulation is not confined to peptide 1 but is delocalized also to the spatial region of peptide 2. Part of this delocalized electron density modulation originates from polarization within peptide 2 (because of its polarizability). However, the running integral (blue dotted line in the 1D plot in Figure 4a) is negative throughout the central region of the molecule, indicating that a charge flux is induced between peptide groups 1 and 2. Evaluating at the center of H···O between the N−H group of peptide 1 and the CO group of peptide 2, the amplitude of this interpeptide charge flux amounts to 2.9 × 10−2 e Å−1 amu−1/2 (3.5 × 10−4 e a0−1 me−1/2). It is as large as about onesixth of the intermolecular charge flux induced by the OH stretching mode of hydrogen-bonded water (∼0.18 e Å−1 amu−1/2),43 which is well-known as a vibrational mode showing large IR intensity enhancement upon hydrogen bond formation. The vibration-induced modulation of the H···O distance (related to the N−H···O or O−H···O geometry and the vibrational pattern) is considered to be an important factor that generates this charge flux. (This also explains the absence of IR intensity enhancement for the amide II mode of longchain α-helix.) In the present case, the electron density

method at the B3LYP/6-31+G(2df,p) level. The average partial vector (APV) method23 was employed to extract the vibrational patterns of individual peptide groups. All the DFT calculations were done using the Gaussian 03 program,45 while the theoretical treatments before and after the DFT calculations were carried out with our original programs. The details of the computational procedure are described in the Supporting Information. The (linear) IR intensities calculated for the amide II modes of peptide groups 1 and 2 of alanine dipeptide-d10 in four representative conformations (C5, C7, ppII, and α-helix) are shown in Figure 2. It is clearly seen that, compared with the IR

Figure 2. The IR intensities calculated for the amide II modes of peptide groups 1 and 2 of alanine dipeptide-d10 in four representative conformations.

intensity of an isolated peptide group [248.4 km mol−1, calculated for N-methylacetamide-d6 (CD3CONHCD3)], the IR intensity is particularly enhanced for peptide 1 of C5 (458.2 km mol−1, 1.84 times). For the other cases shown in Figure 2, the IR intensity enhancement, if any, is not so large (at most only 1.14 times). The IR intensities calculated for some conformations close to C5 (−210° ≤ Φ ≤ −120°, 120° ≤ Ψ ≤ 210°) are shown in Figure 3. It is recognized that the IR intensity enhancement calculated for peptide 1 depends rather sharply on the secondary structure. For example, if Φ is changed from −180° to −120° or Ψ is changed from 180° to 120°, with the other dihedral angle being unchanged (at ±180°), the IR intensity enhancement factor is reduced from 1.84 to 1.33. By contrast, the IR intensity calculated for peptide 113

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Figure 4. Two-dimensional (yz) contour plot of ∫ dx δ(∂ρ(el)(r)/ ∂QAII), one-dimensional plot of ∫ ∫ dx dy δ(∂ρ(el)(r)/∂QAII) (black solid line), and its running integral (blue dotted line) calculated at the B3LYP/6-31+G(2df,p) level for the amide II mode (QAII) of (a) peptide 1 of alanine dipeptide-d10 in the C5 conformation and (b) peptide 2 of alanine dipeptide-d10 in the C7 conformation. The black filled circles show the atoms constituting the molecule, which are arranged as shown in Figure 1. The y axis (vertical in this figure) is taken along the bisection of N−Cα−C for the C5 conformation, and of the C−N bonds in the two peptide groups for the C7 conformation. The contours in the two-dimensional plot are drawn with the interval of 1.2 × 10−5 a0−3 me−1/2 in the range from −30 × 10−5 a0−3 me−1/2 to 30 × 10−5 a0−3 me−1/2, with the color code shown on the left-hand side of plot a.

Figure 5. Two-dimensional (yz) contour plot of ∫ dx δ(∂ρ(el)(r)/ ∂QAII), one-dimensional plot of ∫ dx dy δ(∂ρ(el)(r)/∂QAII) (black solid line), and its running integral (blue dotted line) calculated at the B3LYP/6-31+G(2df,p) level for artificially formed complexes (a) and (b) CD3CONHD···DCONHCD3 CD3CONHCD2CD3···DCONHCD3, where QAII represents the amide II mode of peptide 1 (drawn on the right), and the z axis (horizontal in this figure) is taken along the line connecting H of peptide 1 and C of peptide 2. The black filled circles show the atoms constituting the complexes. The contours in the two-dimensional plot are drawn with the interval of 1.2 × 10−5 a0−3 me−1/2 in the range from −30 × 10−5 a0−3 me−1/2 to 30 × 10−5 a0−3 me−1/2, with the color code shown on the left-hand side of plot a.

modulation shown in Figure 4a induces a dipole derivative of 0.90 D Å−1 amu−1/2, out of which the contribution of the interpeptide charge flux is considered to be ∼0.50 D Å−1 amu−1/2, based on the distance of ∼3.6 Å between the C−N bond centers of the two peptide groups as an estimate of the interpeptide distance. Without this dipole derivative of 0.90 D Å−1 amu−1/2, the IR intensity would become 247.5 km mol−1 (corresponding to the dipole derivative of 2.42 D Å−1 amu−1/2). This indicates that the electron density modulation shown in Figure 4a explains the large IR intensity enhancement (to 458.2 km mol−1). To see that the interpeptide charge flux is induced mainly through the H···O interaction and not through the covalent connection between peptide groups 1 and 2, the electron density modulations δ(∂ρ(el)(r)/∂QAII) are calculated for two molecular complexes (CD 3CONHD···DCONHCD3 and CD3CONHCD2CD3···DCONHCD3) that are formed artificially for this purpose with the same H···O structural feature as that of alanine dipeptide-d10 C5. (See Supporting Information for details.) The results are shown in Figure 5. It is seen that, in

these cases also, the electron density modulation is delocalized, and the running integral is negative throughout the central region of the system. The amplitude of the interpeptide charge flux is 3.2 × 10−2 e Å−1 amu−1/2 (3.9 × 10−4 e a0−1 me−1/2) evaluated at the H···O center, or 2.3 × 10−2 e Å−1 amu−1/2 (2.9 × 10−4 e a0−1 me−1/2) evaluated at the nodal line of the twodimensional plot (slightly to the right of the H···O center) for CD3CONHD···DCONHCD3 shown in Figure 5a, and 3.0 × 10−2 e Å−1 amu−1/2 (3.8 × 10−4 e a0−1 me−1/2) or 2.0 × 10−2 e Å−1 amu−1/2 (2.4 × 10−4 e a0−1 me−1/2), respectively, for CD3CONHCD2CD3···DCONHCD3 shown in Figure 5b. Estimating in a way similar to the case of alanine dipeptided10, these interpeptide charge fluxes induce dipole derivatives of 0.4−0.6 D Å−1 amu−1/2. Because of the charge flux, the IR intensity is significantly enhanced (from 202.7 to 405.1 km mol−1 for CD3CONHD···DCONHCD3, and from 237.3 to 410.7 km mol−1 for CD3CONHCD2CD3···DCONHCD3). 114

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Therefore, it is confirmed that the interpeptide charge flux is induced mainly through the H···O interaction. Then, why is the IR intensity calculated for peptide 2 of C7 not enhanced, in spite of the existence of the N−H···OC hydrogen bond? The electron density derivative δ(∂ρ(el)(r)/ ∂QAII) calculated for this case is shown in Figure 4b. It is seen that, although to a smaller extent than the case of peptide 1 of C5, the electron density modulation is delocalized, and the running integral is negative throughout the central region of the molecule. Evaluated at the H···O center, the amplitude of the interpeptide charge flux is 1.3 × 10−2 e Å−1 amu−1/2 (1.7 × 10−4 e a0−1 me−1/2), which is as large as about a half of that calculated for peptide 1 of C5. The smaller amplitude obtained for C7 is considered to be related to the difference in the N−H···O angle θ, 110.5° (sin θ = 0.94) for C5 and 143.0° (sin θ = 0.60) for C7, considering the extent of vibration-induced modulation of the H···O distance. However, this amplitude alone is not sufficient for explaining the difference in the extent of IR intensity enhancement. In fact, what is significantly different between the two cases is the direction of the dipole derivative induced by the electron density modulation relative to that of the dipole derivative that the amide II mode originally has. In the case of peptide 1 of C5, the electron density modulation shown in Figure 4a induces a dipole derivative of 0.90 D Å−1 amu−1/2 as discussed above, and this is nearly parallel to the original one (of 2.42 D Å−1 amu−1/2), making an angle of only 6.4°. In the case of peptide 2 of C7, however, the electron density modulation shown in Figure 4b induces a dipole derivative of 0.55 D Å−1 amu−1/2, but this is nearly perpendicular to the original one (of 2.24 D Å−1 amu−1/2), making an angle of 105.2°. Since the IR intensity is proportional to the square of the magnitude of the dipole derivative, the original and induced components have a large cross term when they are nearly parallel, but do not when they are nearly perpendicular to each other. This cross term gives rise to the IR intensity of 183.0 km mol−1 in the case of peptide 1 of C5, but −27.4 km mol−1 (negative because the angle is larger than 90°) in the case of peptide 2 of C7, explaining a large part of the difference in the IR intensity between the two cases. This result means that the extent of IR intensity enhancement of the amide II mode is related not only to the amplitude of the interpeptide charge flux but also to the relative configuration of the two peptide groups. In both cases, the dipole derivative that the amide II mode originally has is nearly parallel to the direction that the H atom moves in the vibration, i.e., the direction perpendicular to the N−H bond within the plane of the (vibrating) peptide group (making an angle of 12.0° and 13.5° for the cases of peptide 1 of C5 and peptide 2 of C7, respectively), while the dipole derivative induced by the electron density modulation is nearly perpendicular to the C O bond of the N−H···OC interaction within the plane of the (interacting) peptide group (making an angle of 1.9° and 7.5° for the cases of C5 and C7, respectively). The difference in the structural characteristics in this respect gives rise to the sensitivity of the IR intensity of the amide II mode to the secondary structure of peptide chains. In summary, it has been shown that a large interpeptide charge flux is induced by the amide II mode of peptide chain in the C5 (β-strand) conformation through the H···O interaction, and this gives rise to large IR intensity enhancement. This IR intensity enhancement is specific to C5 and does not occur for C7 (with intrastrand hydrogen bonding), because of the

geometrical relation between the dipole derivative induced by the interpeptide interaction and the dipole derivative that the amide II mode originally has, which is intimately related to the relative configuration of the N−H and CO bonds in the N− H···OC interaction. We expect that the results of the present study have widened our knowledge on the structural information contained in vibrational spectroscopic features and will be useful, for example, for analyzing the structural variations induced by some changes in the thermodynamic state.

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ASSOCIATED CONTENT

S Supporting Information *

The details of the computational procedures are described. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Telephone and Fax: +81-54-238-4624. E-mail: torii@ed. shizuoka.ac.jp.

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ACKNOWLEDGMENTS This study was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology.

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