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Secondary Structure Dependence and Hydration Effect of the Infrared Intensity of the Amide II Mode of Peptide Chains Hajime Torii*,†,‡ and Megumi Kawanaka† †

Department of Chemistry, Faculty of Education, Shizuoka University, 836 Ohya, Shizuoka 422-8529, Japan Department of Optoelectronics and Nanostructure Science, Graduate School of Science and Technology, Shizuoka University, 836 Ohya, Shizuoka 422-8529, Japan

‡

S Supporting Information *

ABSTRACT: Every vibrational mode to be used as a marker of the structural, dynamical, and/or interaction properties demands our good understanding of the relations between those properties and the spectral features. The present study is devoted to elucidating the effects of secondary structure variations and hydration on the infrared (IR) intensity of the amide II mode of peptide chains. It is shown that the IR intensity is significantly enhanced for the C5 (fully extended planar β-strand) conformation because of the interpeptide charge flux through the H···O interaction of the C5 ring, and there is a small cooperative effect giving rise to a larger enhancement for a consecutive C5 conformation. In contrast, the IR intensity is reduced for the α-helix conformation because of the partially canceling polarization effect of the hydrogen-bond accepting O atom in the NH···OC hydrogen bond and the absence of the interpeptide charge flux. With regard to the hydration effect, it is found that the IR intensity enhancement/reduction depends critically on the angular position of the hydrating water molecule, and is related to the presence/absence of the intermolecular charge flux and the polarization effect. It is suggested that, both for the secondary structure dependence and for the hydration effect, the geometrical relation between the vibrating N−H bond and the H···O interaction (of the C5 ring and/or the hydrogen bond) is an essential factor determining the enhancement/reduction of the IR intensity of the amide II mode. conformation (the fully extended planar β-strand conformation) was examined theoretically. By calculating and analyzing the modulations in the electron density induced by the amide II mode of each peptide group in alanine dipeptide-d 10 [CD3CONH−CDCD3−CONHCD3] in the form of the electron density derivative ∂ρ(el)(r)/∂QamII, which is related to the electronic contribution of the dipole derivative ∂μ(el)/∂QamII as40−45

1. INTRODUCTION The amide II mode is one of the characteristic vibrational modes of the peptide group, which is a repeat unit of peptide chains such as polypeptides and proteins, and is mainly composed of the bending of the N−H bond.1−4 Because the N−H bond is a hydrogen-bond donating group, the properties [frequency positions, infrared (IR) intensities, etc.] of the amide II mode are expected to be rather sensitive to the hydration of the peptide group and the secondary structure. In fact, for example, it has been observed that, on heat denaturation of a protein, the amide II/amide I IR intensity ratio increases as the α-helix content decreases.5 However, compared with the amide I6−21 and III modes,22−26 for which the relations among the spectral, structural, dynamical, and/or interaction properties are rather well-known, the amide II mode has been less extensively studied so far, so that further studies on its properties will be needed to improve its utility in structural and dynamical analyses of peptide chains to the level realized for the amide I and III modes. Especially, our better understanding on the intensity variations with the hydration and secondary structure is desirable in view of its application to nonlinear vibrational spectroscopy,27−39 because the spectral features in those cases are related to a higher power of the dipole derivatives than in the ordinary linear vibrational spectroscopy. In our previous study,40 the mechanism of the IR intensity enhancement of the amide II mode occurring for the C5 © XXXX American Chemical Society

∂μ(el) /∂Q amII = −e

∫ d r r(∂ρ(el)(r)/∂Q amII)

(1)

where QamII represents the amide II vibrational coordinate, it was clarified that the enhancement of the IR intensity (proportional to the square of the dipole derivative) arises from the flux of electron density through the H···O interaction between peptide groups (called interpeptide charge f lux). This type of charge flux is induced also for the C7 conformation, but the occurrence of IR intensity enhancement is limited only to the conformations close to C5 because of the geometrical relation between H···O and N−H. Therefore, this mechanism is considered to be an important factor giving rise to the Special Issue: Bruce C. Garrett Festschrift Received: August 24, 2015 Revised: October 29, 2015

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DOI: 10.1021/acs.jpcb.5b08258 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Figure 1. IR intensities of the amide II modes of peptide groups 2 and 3 (shown in parts a and b, respectively) calculated for alanine tetrapeptide-d18 [CD3CO−(NHCDCD3CO−)3NHCD3] in 125 conformations. In part a, the conformations of residues 1 and 2 (between which peptide group 2 is located) are labeled at the lower and upper parts on the abscissa, and the conformation of residue 3 is indicated by color (red, C5; yellow, pltd; green, C7; blue, ppII; black, α). In part b, the conformations of residues 2 and 3 (between which peptide group 3 is located) are labeled at the lower and upper parts on the abscissa, and the conformation of residue 1 is indicated by color (red, C5; yellow, pltd; green, C7, blue, ppII, black, α). The APV method is used to obtain the vibrational motions of the individual peptide groups from the four amide II eigenmodes calculated for each conformation. The IR intensity calculated for an isolated N-methylacetamide-d6 molecule [CD3CONHCD3] is indicated by a dotted line.

the hydration water is an essential factor for both the frequency position and the IR intensity.21 Therefore, in the present study, this type of analysis is conducted for the amide II mode. The combined effect of hydration and secondary structure on the IR intensity of the amide II mode is also discussed.

secondary structure dependence of the IR intensity of the amide II mode observed in previous studies.5,31,33,46−51 The present study is focused on the following three main questions in relation to this subject. (1) Is there any chainlength dependence in the IR intensity enhancement of the amide II mode of the C5 conformation? (2) How do the interpeptide hydrogen bonds affect the IR intensity of the amide II mode of the α-helix conformation? (3) How do the peptide−water hydrogen bonds affect the IR intensity of the amide II mode of a hydrated peptide chain? Among these, the second one is related to the absolute IR intensity of 1.3−1.6 × 102 km mol−1 observed for an α-helical peptide chain,47 which is significantly weaker than that calculated40 for an isolated peptide group (248.4 km mol−1). To solve this question, an analysis should be conducted for a peptide chain that is sufficiently long to form at least one turn of the α-helix. An analysis for such a long chain will also be useful for examining the presence/absence of the cooperative effect (giving rise to the chain-length dependence) in the IR intensity enhancement obtained for the C5 conformation. Peptide chains of length up to alanine hexapeptide-d26 are selected for these purposes. With regard to the hydration effect (the third point), it has recently been clarified for the amide I mode that the angular position of

2. COMPUTATIONAL PROCEDURE Calculations were done for the following five series of systems: (i) alanine tetrapeptide-d18 [CD3CO− (NHCDCD3CO−)3NHCD3] in 125 (= 53) conformations, with one of the five typical conformations [C5, pleated β (abbreviated as pltd), C7, polyproline II (abbreviated as ppII), and α-helix] for the three alanine residues, (ii) alanine tripeptide-d14 to hexapeptide-d26 [CD3CO− (NHCDCD3CO−)nNHCD3, n = 2−5] in the consecutive C5 conformation (for all the residues in a chain), and alanine hexapeptide-d26 in the other four (pltd, C7, ppII, and α-helix) consecutive conformations (see Figure S1 in the Supporting Information for their structures), (iii) the N-methylacetamided6···water [CD3CONHCD3···H2O] 1:1 complex, (iv) glycine tripeptide-d10 [CD3CO−(NHCD2CO−)2NHCD3] interacting with 2−9 H2O molecules, and (v) the dimer of glycine tripeptide-d10 in the C5 conformation arranged in an antiparallel B


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but this enhancement is smaller than that of C5, because of the strong secondary structure dependence around (Φ, Ψ) = (−180°, 180°).40 It is also recognized that the conformation of a more distant residue is essentially irrelevant to this IR intensity enhancement. An interesting issue with regard to the significant IR intensity enhancement induced by consecutive C5 conformations would be the presence/absence of the cooperative effect. Upon inspection of the result shown in Figure 1, the IR intensity is enhanced by (on average) 197 or 77 km mol−1 if either residue j − 1 or j is in the C5 conformation and the other of these is in the C7, ppII, or α-helix conformation, while it is enhanced by 326 km mol−1 if both of these residues are in the C5 conformation, indicating the presence of a small cooperative effect. The presence of a similar (but different) cooperative effect is also recognized by examining the chain-length dependence of the IR intensity enhancement. The IR intensities of the amide II modes of the individual peptide groups calculated for alanine tripeptide-d14 to hexapeptide-d26 in the consecutive C5 conformation are shown in Figure 2a.

way. All the calculations before the extraction of the vibrational modes of individual peptide groups or molecules by the average partial vector (APV) method52 or its extension were carried out at the B3LYP/6-31+G(2df,p) level using the Gaussian 03 program.53 For i, ii, and v, the C−N−Cα−C and N−Cα−C−N dihedral angles (Φ and Ψ) were fixed at (Φ, Ψ) = (−180°, 180°), (−135°, 135°), (−75°, 145°), and (−57°, −47°) for the residues in the C5, pltd, ppII, and α-helix conformations, while they were optimized without restrictions for the residues in the C7 conformation, resulting in the range −92.4° ≤ Φ ≤ −80.9° and 65.5° ≤ Φ ≤ 82.2°, except for some chains with the C7−C5 or C7−pltd sequence, where the dihedral angles were fixed at (Φ, Ψ) = (−84°, 75°). The other structural parameters (bond lengths, etc.) were optimized before calculating the vibrational frequencies and IR intensities. It is supposed that constraints on softer modes (N−Cα and Cα−C torsions) do not essentially have any harmful effect on the properties of a harder mode (amide II).21 The APV method52 was used to extract the vibrational modes of individual peptide groups. To analyze the origin of the IR intensity enhancement/reduction, the modulations in the electron density induced by the amide II mode were examined by calculating the electron density derivatives ∂ρ(el)(r)/∂QamII or their interaction-induced part δ(∂ρ(el)(r)/∂QamII) [≡(∂ρ(el)(r)/∂QamII)entire_system − (∂ρ(el)(r)/ ∂QamII)isolated] for peptide group 3 of alanine hexapeptide-d26 in the C5 conformation, for peptide group 5 of the same species in the α-helix conformation, and for peptide group 2 in one of the glycine tripeptide-d10 chains in the dimer. The details of the procedure are described in the Supporting Information. For iii, the structure of the complex was optimized with 81 different fixed angular positions (θ and φ, in the range 0° ≤ θ ≤ 90° and 0° ≤ φ ≤ 180°) of the oxygen atom of the water molecule which is hydrogen-bonded to the N−H bond. Here, a spherical polar coordinate system (r, θ, φ) was defined by taking the H(−N) atom as the origin, the N → H direction as the z axis, and the C−N−H···O dihedral angle as φ. The amide II mode of N-methylacetamide-d6 in the complex was extracted from the eigenmodes by using the APV2 method (an extended version of the APV method), which is explained in detail in the Supporting Information. For (θ, φ) = (15°, 0°) and (45°, 180°), the electron density derivatives were also calculated to analyze the origin of the IR intensity enhancement/reduction. For iv, the structures were fully optimized before calculating the vibrational frequencies and IR intensities, and the APV2 method was used to extract the amide II mode from the eigenmodes with rather severe mixing of the amide I and II modes and the HOH bending modes in each system. The structural and other properties are discussed below in section 3.4.

Figure 2. IR intensities of the amide II modes of the individual peptide groups (drawn with red, yellow, green, light blue, blue, and purple bars, respectively, for peptide groups 1−6) calculated for (a) alanine tripeptide-d14 to hexapeptide-d26 [CD3CO− (NHCDCD3CO−)nNHCD3, n = 2−5 (labeled on the abscissa)] in the consecutive C5 conformation (for all the residues in a chain), and (b) alanine hexapeptide-d26 in five consecutive conformations [C5, pltd, C7, ppII, or α (labeled on the abscissa)]. The APV method is used to extract the vibrational motions of the individual peptide groups from the amide II eigenmodes calculated for each chain or each conformation. The IR intensity calculated for an isolated Nmethylacetamide-d6 molecule [CD3CONHCD3] is indicated by a dotted line.

3. RESULTS AND DISCUSSION 3.1. Overview of the Secondary Structure Dependence. The IR intensities of the amide II modes of peptide groups 2 and 3 calculated for alanine tetrapeptide-d18 in 125 conformations are shown in Figure 1. It is clearly seen that, for peptide group j, the IR intensity of the amide II mode is most significantly enhanced if both residues j − 1 and j (between which peptide group j is located) are consecutively in the C5 conformation. If only one of these residues is in the C5 conformation, the IR intensity is enhanced also noticeably but to a lesser extent. Among the four conformations other than C5, the pleated β conformation shows clear enhancement,

Excluding the peptide groups at both ends of each peptide chain, it is seen that the IR intensity increases from 538 to (on average) 638 km mol−1 as the peptide chain becomes longer from tripeptide to hexapeptide. Note that this cooperative effect as much as 100 km mol−1 is a significant fraction of the IR C


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Figure 3. Two-dimensional (yz) contour plot of ∫ dxδ(∂ρ(el)(r)/∂QamII), one-dimensional plot of ∫ ∫ dxdzδ(∂ρ(el)(r)/∂QamII) (black line), and its running integral (light blue line) calculated for the amide II mode (QamII, extracted by using the APV method) of peptide group 3 in alanine hexapeptide-d26 [CD3CO(NHCDCD3CO)5NHCD3] in the C5 conformation. The black filled circles stand for the atoms (OCNH from top to bottom) constituting peptide group 3, and the black open circles stand for the other atoms in the chain, which are arranged from left to right for peptide groups 1 to 6. The NH bond of peptide group 3 is taken as the z axis (vertical in this figure), and its carbon atom is placed on the yz plane. The contours in the two-dimensional plot are drawn with the interval of 1.2 × 10−5 a0−3me−1/2 in the range from −30 × 10−5 a0−3me−1/2 to 30 × 10−5 a0−3me−1/2, with the color code shown on the left-hand side. In the one-dimensional plot, the locations of the NH bond of peptide group 3 and the O atom of peptide group 4 are indicated with purple dotted vertical lines, and the H···O center is indicated with a pink dotted vertical line.

Figure 4. (a) Two-dimensional (φZ) cylindrically integrated contour plot of ∫ dr rδ(∂ρ(el)(r,φ,Z)/∂QamII) calculated for the amide II mode (QamII, extracted by using the APV method) of peptide group 5 in alanine hexapeptide-d26 [CD3CO(NHCDCD3CO)5NHCD3] in the α-helix conformation, where Z is the helix axis, and r and φ are the radial and angular coordinates on the XY plane. The black filled circles stand for the atoms (OCNH from top to bottom) constituting peptide group 5, and the black open circles stand for the atoms constituting the other peptide groups in the chain, which are arranged from lower left to upper right for peptide groups 1 to 6. The contours in the two-dimensional plot are drawn with the interval of 2.7 × 10−5 rad−1a0−2me−1/2 in the range from −67.5 × 10−5 to 67.5 × 10−5 rad−1a0−2me−1/2, with the color code shown on the left-hand side. (b) Two-dimensional (yz) contour plot of the same quantity [∫ dxδ(∂ρ(el)(r)/∂QamII)]. The NH bond of peptide group 5 is taken as the z axis (vertical in this figure), and its carbon atom is placed on the yz plane. The black filled and open circles stand for the atoms (O CNH from top to bottom) constituting peptide groups 5 and 2, respectively. The horizontal dotted line indicates the xy plane going through the middle point of the H···O hydrogen bond between the two peptide groups. The contours in the two-dimensional plot are drawn with the interval of 0.9 × 10−5 a0−3me−1/2 in the range from −22.5 × 10−5 to 22.5 × 10−5 a0−3me−1/2, with the color code shown on the left-hand side. (c,d) Onedimensional plots of ∫ ∫ dxdzδ(∂ρ(el)(r)/∂QamII) and their running integrals. The integrals taken in the upper and lower sides of the horizontal dotted line shown in part b and their sum are shown in red, blue, and black lines, respectively. The location of the NH bond of peptide group 5 (y = 0) is indicated with a purple dotted vertical line.

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between peptide groups j and j + 1 in α-helix, the electron density is not significantly modulated around the CO bond of peptide group j + 1 (j = 5 for the case shown in Figure 4) as compared with the case of C5 (j = 3 for the case shown in Figure 3). (2) Instead, because of the hydrogen bonding between peptide groups 5 and 2, electron density is noticeably modulated around the CO bond of peptide group 2. (3) Electron density modulation is delocalized to some extent also to other peptide groups. The second point is more clearly recognized in the ordinary two-dimensional plot shown in Figure 4b, where the vibrating N−H bond of peptide group 5 is taken along the z axis (y = 0). Around this vibrating N−H bond, δ(∂ρ(el)(r)/∂QamII) is negative on the +y side and positive on the −y side. However, its sign is opposite around the O atom of peptide group 2. This is most probably because of the electrostatic polarization of this O atom induced by the +y displacement of the positively charged H(−N) atom. This mutually compensating behavior of δ(∂ρ(el)(r)/∂QamII) around the NH···OC hydrogen bond is clearly seen also in the one-dimensional plot and its running integral shown in Figure 4c,d, where the plots for the upper (+z) and lower (−z) sides are shown separately. The positive peak of the running integral around y = 0 obtained for the upper side (i.e., around the N−H bond) is mostly canceled by the negative feature obtained for the lower side (i.e., around the O atom), suppressing the IR intensity enhancement. The third point raised above should also be examined. Because of the conformational difference, the rather long-ranged interpeptide charge flux along the y axis (perpendicular to the vibrating N− H bond) obtained for the C5 conformation (shown in Figure 3) is not possible for the α-helix conformation. As a result, the negative feature of δ(∂ρ(el)(r)/∂QamII) around the N−H bond in the peptide group on the adjacent N terminus side along the peptide chain (peptide group j − 1) affects the total behavior more significantly, and hence, the running integral (total value) is negative in the whole range along the y axis. The electronic contribution of the dipole derivative ∂μ(el)/∂QamII related to this total δ(∂ρ(el)(r)/∂QamII) is calculated as (∂μy(el)/∂QamII, ∂μz(el)/ ∂QamII) = (−0.343, 0.199) D Å−1 amu−1/2, which partially cancels the dipole derivative of an isolated peptide group of (∂μy/∂QamII, ∂μz/∂QamII) = (2.346, −0.613) D Å−1 amu−1/2. This partial cancellation explains the IR intensity reduction from 248.4 km mol−1 (an isolated N-methylacetamide-d6 molecule) to 174.1 km mol−1 (peptide group 5 in alanine hexapeptide-d26) obtained for the α-helix conformation. Note that the latter value (or the value averaged over peptide groups 3−5, 171 km mol−1) is in reasonable agreement with the observed value of 1.3−1.6 × 102 km mol−1 reported in a previous study.47 Therefore, this polarization-induced reduction of IR intensity obtained for the α-helix conformation is another important factor of the secondary structure dependence. 3.3. Water Angular Position Dependence in the Hydration Effect. The dependence of the vibrational frequency and IR intensity of the amide II mode of the Nmethylacetamide-d6···H2O 1:1 complex on the angular position [θ and φ of the spherical polar coordinate system around the H(N) atom] of the hydrating water molecule is shown as two-dimensional contour plots in Figure 5. As shown in part a, the frequency is highest at θ ≅ 0° (linear NH···O) and shifts significantly to the low frequency side as θ increases, but does not depend much on the φ angle. In fact, this behavior is natural for a bending mode of a hydrogen-bond donating atom, in that the vibrational frequency shifts to the higher-frequency

intensity of an isolated peptide group (calculated for an isolated N-methylacetamide-d6 molecule,40 248.4 km mol−1). Calculations on alanine hexapeptide-d26 in five different consecutive conformations shown in Figure 2b indicate more clearly the secondary structure dependence of the IR intensity. In the case of the C5 conformation, because of the cooperative effect discussed above, the IR intensity is enhanced by as much as 2.57 times (averaged over peptide groups 2−5) compared to an isolated peptide group (i.e., from 248.4 to 638 km mol−1). The pleated β conformation also shows clear enhancement, but to a lesser extent (1.81 times averaged over peptide groups 2− 5, i.e., from 248.4 to 451 km mol−1). In contrast, it is recognized that, in the case of the α-helix conformation, the IR intensities calculated for peptide groups 3−6 are reduced significantly as compared to that of an isolated peptide group. That is, the intensity value averaged over peptide groups 3−5 (i.e., excluding the peptide group at the end) is 171 km mol−1, which is 0.69 times the intensity of an isolated peptide group. For the other two conformations (C7 and ppII), this kind of significant enhancement/reduction of the IR intensity is not obtained. 3.2. Electron Density Analysis on the Origin of the Secondary Structure Dependence. The interaction-induced electron density derivative δ(∂ρ(el)(r)/∂QamII) calculated for the amide II mode (QamII, extracted by using the APV method) of peptide group 3 in alanine hexapeptide-d26 in the C5 conformation is shown in Figure 3. It is recognized from the two-dimensional plot that the modulation of the electron density is significant not only in the spatial region around the vibrating N−H bond but also around the CO bond of peptide group 4 that interacts directly with the vibrating N−H bond (as CO···HN of the C5 ring). This delocalized nature of δ(∂ρ(el)(r)/∂QamII) is clearly recognized also from the one-dimensional running integral. It is positive in the whole range along the y axis (taken as perpendicular to the vibrating NH bond) and especially at the O···H center between peptide groups 3 and 4, indicating that a partial but significant transfer of electron density occurs between peptide groups (called interpeptide charge f lux,40 after the notion of charge flux developed in other studies54−58) from the C terminus side [right side (+y) in the figure] to the N terminus side upon atomic displacements in the +QamII direction [+y displacement of the H(N) atom]. The electronic contribution of the dipole derivative ∂μ(el)/∂QamII related (as shown in eq 1) to this δ(∂ρ(el)(r)/∂QamII) is calculated as (∂μy(el)/∂QamII, ∂μz(el)/ ∂QamII) = (1.586, −0.424) D Å−1 amu−1/2, which reasonably explains the IR intensity enhancement from 248.4 km mol−1 (an isolated N-methylacetamide-d6 molecule, corresponding to |∂μ/∂QamII| = 2.425 D Å−1 amu−1/2) to 661.6 km mol−1 (peptide group 3 in alanine hexapeptide-d26, corresponding to |∂μ/∂QamII| = 3.957 D Å−1 amu−1/2). In other words, the rather long-ranged interpeptide charge flux shown in Figure 3 is the major reason for the significant IR intensity enhancement. The interaction-induced electron density derivative δ(∂ρ(el)(r)/∂QamII) calculated for the amide II mode of peptide group 5 in alanine hexapeptide-d26 in the α-helix conformation is shown in Figure 4. Upon inspection of the cylindrically integrated two-dimensional contour plot shown in part a, some similarities and differences with the case of the C5 conformation shown in Figure 3 are noticeable. (1) The modulation of the electron density is similar within the vibrating peptide group, but is totally different on its C terminus side along the peptide chain. Because there is no direct NH···OC interaction E


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intensity changes, the magnitude of the induced dipole derivative [|δ(∂μ/∂QamII)|, defined as δ(∂μ/∂QamII) ≡ (∂μ/ ∂QamII)complex − (∂μ/∂QamII)isolated] is always larger than 0.12 D Å−1 amu−1/2 and is typically ∼0.2 D Å−1 amu−1/2 (see Figure S2 in the Supporting Information). To analyze the mechanisms of those IR intensity enhancement and reduction, the interaction-induced electron density derivatives δ(∂ρ(el)(r)/∂QamII) are calculated for the complexes at (θ, φ) = (15°, 0°) and (45°, 180°). The former is selected because the calculated IR intensity (205.9 km mol−1) is almost the same as that calculated for (θ, φ) = (15°, 30°), and for this type of analysis, a planar N−H···O configuration is convenient. The result is shown in Figure 6. As shown in part a, the situation obtained for (θ, φ) = (15°, 0°) is quite similar to that shown in Figure 4b calculated for peptide group 5 in alanine hexapeptide-d26 in the α-helix conformation. That is, around the vibrating N−H bond (located at y = 0), δ(∂ρ(el)(r)/∂QamII) is negative on the +y side and positive on the −y side, but the sign is opposite around the hydrogen-bond accepting O atom, so that these two factors severely cancel each other. This mutual cancellation is also clearly seen in the one-dimensional plot and its running integral shown in Figure 6b,c; the positive peak around y = 0 obtained for the upper side (i.e., around the N−H bond) in the one-dimensional running integral is mostly canceled by the negative feature obtained for the lower side (i.e., around the O atom), suppressing the IR intensity enhancement. Because the hydrogen bonding is intermolecular in this case, it is possible to quantitatively estimate the contribution of the electrostatic polarization by replacing the Nmethylacetamide-d6 molecule by a set of CHelpG59 atomic partial charges on the atomic sites.44 As shown with a green line in Figure 6c, the overall negative feature of the one-dimensional running integral is primarily determined by the electrostatic polarization effect. (The corresponding two-dimensional contour plot is shown in Figure S3b in the Supporting Information.) In fact, the electronic contribution of the dipole derivative ∂μ(el)/∂QamII related to this electrostatic polarization effect is calculated as (∂μy(el)/∂QamII, ∂μz(el)/∂QamII) = (−0.094, 0.060) D Å−1 amu−1/2, and explains about a half of the difference in ∂μ/∂QamII between the complex and an isolated molecule [(2.142, −0.536) and (2.346, −0.613) D Å−1 amu−1/2, respectively]. The other half arises from the slight difference in the vibrational amplitudes of individual atoms between the two species. The situation obtained for (θ, φ) ≅ (45°, 180°) is quite different. As shown in Figure 6d,e, although we can recognize a rather common feature of δ(∂ρ(el)(r)/∂QamII) around the vibrating N−H bond, which is located (at y = 0) on the upper side, there is no compensating feature at around y = 0 on the lower side. As a result, the positive peak of the onedimensional running integral at y = 0 obtained for the upper side (shown in red in Figure 6f) mostly survives in the total value (black). The effect of electrostatic polarization (green) looks rather insignificant in the whole range along the y axis. The electronic contribution of the dipole derivative ∂μ(el)/ ∂QamII related to the total δ(∂ρ(el)(r)/∂QamII) is calculated as (∂μy(el)/∂QamII, ∂μz(el)/∂QamII) = (0.194, −0.344) D Å−1 amu−1/2, which reasonably explains the difference in ∂μ/ ∂QamII between the complex and an isolated molecule [(2.543, −0.946) and (2.346, −0.613) D Å−1 amu−1/2, respectively], while the electrostatic polarization effect (its two-dimensional contour plot is shown in Figure S3e in the Supporting

Figure 5. Two-dimensional contour plots of the (a) vibrational frequency and (b) IR intensity of the amide II mode calculated for the N-methylacetamide-d6···H2O 1:1 complex optimized with a fixed angular position (θ and φ) of the oxygen atom of the water molecule which is hydrogen-bonded to the N−H bond. The APV2 method is used to extract the vibrational motions of the amide II mode (i.e., to separate it from the amide I mode and the HOH bending mode). The spherical polar coordinate system (r, θ, φ), which is used exclusively in this figure, is defined by taking the H(−N) atom as the origin, the N → H direction as the z axis, and the C−N−H···O dihedral angle as φ. The calculated configurations of the complex are indicated with black filled circles. The red crosses indicate the angular positions where hydrogen-bonded optimized structures could not be obtained, and the gray crosses indicate those where the absence of hydrogen-bonded optimized structures is assumed on the basis of the calculations indicated by red crosses. The contours are drawn with the interval of 5 cm−1 (for part a) and 10 km mol−1 (for part b), with the color code shown on the left-hand side. The values in parentheses in part a are the scaled (by 0.9860) frequencies.

side as the hydrogen bond becomes stronger. As shown in Figure S2 in the Supporting Information, the vibrational frequencies obtained here are well-correlated to the hydrogenbond distances r(H···O), in contrast to the case of the effect of hydration (on OC) on the amide I′ frequency of the Nmethylacetamide-d1···2H2O 1:1 complex21 where there is essentially no correlation between the vibrational frequency and the hydrogen-bond distance. The water angular position dependence of the IR intensity shown in Figure 5b looks quite different. The IR intensity is strongest at (θ, φ) ≅ (45°, 180°) and weakest at (θ, φ) ≅ (15°, 30°), meaning that it depends significantly on the φ angle as well as on the θ angle. Compared with the IR intensity calculated for an isolated N-methylacetamide-d6 molecule (248.4 km mol−1), the intensity of 311.1 km mol−1 calculated at (θ, φ) = (45°, 180°) means an enhancement by 63 km mol−1, while the intensity of 205.5 km mol−1 calculated at (θ, φ) = (15°, 30°) means a reduction by 43 km mol−1. In fact, the IR intensity is not well-correlated to the hydrogen-bond distance, and including the angular positions with essentially no F


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Figure 6. (a, d) Two-dimensional (yz) contour plots of ∫ dxδ(∂ρ(el)(r)/∂QamII) calculated for the amide II mode (QamII, extracted by using the APV2 method) of the N-methylacetamide-d6···H2O 1:1 complex optimized with fixed angular positions of the oxygen atom of the water molecule, at (θ, φ) = (15°, 0°) for part a and at (45°, 180°) for part d. The N−H bond is taken as the z axis (vertical in this figure), and the peptide group (OC NH) is placed on the yz plane. The black filled circles stand for the positions of all the atoms. (Note that some hydrogen atoms are mutually eclipsed.) The horizontal dotted line indicates the xy plane going through the 1:2 (for part a) or 1:3 (for part d) dividing point of the H···O hydrogen bond. The contours in the two-dimensional plot are drawn with the interval of 0.56 × 10−5 a0−3me−1/2 in the range from −14 × 10−5 to 14 × 10−5 a0−3me−1/2, with the color code shown on the left-hand side. (b, c, e, f) One-dimensional plots of ∫ ∫ dxdzδ(∂ρ(el)(r)/∂QamII) and their running integrals. The integrals taken in the upper and lower sides of the horizontal dotted line shown in part a and d and their sum are shown in red, blue, and black lines, respectively. The values calculated by replacing the N-methylacetamide-d6 molecule by a set of CHelpG atomic partial charges on the atomic sites are shown in green lines (labeled as polarization effect). The location of the NH bond (y = 0) is indicated with a purple dotted vertical line.

Information) contributes only by (0.025, −0.128) D Å−1 amu−1/2 to this difference. The difference in ∂μ(el)/∂QamII between the total and electrostatic polarization component of δ(∂ρ(el)(r)/∂QamII) is (∂μy(el)/∂QamII, ∂μz(el)/∂QamII) = (0.169, −0.216) D Å−1 amu−1/2 [0.274 D Å−1 amu−1/2 in magnitude], and since it is nearly parallel to the H···O hydrogen bond (making an angle of only 7°), it will be most reasonable to expect that it arises from the intermolecular charge flux through this hydrogen bond, similarly to the interpeptide charge flux occurring in a peptide chain in the C5 conformation discussed in section 3.2. In fact, upon division of the whole space by the plane perpendicular to the H···O hydrogen bond passing through the hydrogen-bond center, and integration of δ(∂ρ(el)(r)/∂QamII) in each of these divided subspaces, the water molecule side is calculated to have a total loss of electron density derivative, amounting to 1.259 × 10−4 a0−1me−1/2 or 1.016 × 10−2 Å−1 amu−1/2 in magnitude, and the peptide side is calculated to have a total gain of the same amount. If we take the hydrogen-bond distance (2.321 Å) as the distance over which the electric charge is transferred in the charge flux, the dipole derivative induced by this charge flux is estimated as |∂μ/∂QamII| = 0.113 D Å−1 amu−1/2 in magnitude. The actual situation is more complex, and the electron density modulation is delocalized also to the spatial regions of the two molecules, as clearly seen in the one-dimensional plot shown in Figure S4d and its running integral shown in Figure S4e in the Supporting Information, to give rise to ∂μ(el)/∂QamII of the magnitude of 0.274 D Å−1 amu−1/2. 3.4. Effect of Hydrogen Bonding on the IR Intensity Enhancement of the C5 Conformation. The vibrational frequencies and IR intensities of the amide I and II modes

calculated for peptide group 2 in some complexes (structures 1−6 in Figure 7) of glycine tripeptide-d10 and a few water molecules are shown in Table 1. All of these are obtained as fully optimized structures. In these cases, the amide I and II modes are rather close to each other in frequency, so that the use of the APV2 method is essential to extract the vibrational motions of those modes. The results shown in Table 1 indicate that this method works well in a stable way. Structures 1 and 2 are C5 for both residues 1 and 2, and peptide group 2 (located between these two residues) has one water molecule on CO and no water molecule on N−H. It is recognized from the results shown in Table 1 that the IR intensity of the amide II mode is significantly enhanced (to 533.5 and 514.3 km mol−1) in these cases, to the same extent as peptide group 2 in alanine tripeptide-d14 (to 538.4 km mol−1) shown in Figure 2a. Structures 3 and 4 are also C5 for both residues 1 and 2, but differently from structures 1 and 2, peptide group 2 has two water molecules on CO and one water molecule on NH. The latter is located at the angular position of (θ, φ) = (20.7°, 12.7°) in structure 3 and (19.7°, 10.9°) in structure 4 (indicated by the spherical polar coordinate system used in Figure 5). As a result, with consultation of the results shown in section 3.3, it is most reasonable to expect that this water molecule gives rise to some reduction of the IR intensity of the amide II mode. The results shown in Table 1 suggest that this is indeed the case; the IR intensity is calculated as 370.1 and 373.1 km mol−1, smaller than the value calculated for structures 1 and 2. However, even with this reduction, the IR intensity is still larger than those calculated for the conformations sufficiently far from C5 (i.e., C7, ppII, or α-helix on both sides of the vibrating peptide G


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A peptide chain in the consecutive C5 conformation may alternatively be hydrogen-bonded to (an)other peptide chain(s) to form a sheet. To examine the situation in this case, the interaction-induced electron density derivative δ(∂ρ(el)(r)/∂QamII) is calculated for the amide II mode of peptide group 2 in the antiparallel dimer of glycine tripeptided10 in the C5 conformation. The result is shown in Figure 8a−c. It is recognized that, in the spatial region of the peptide chain on the upper side (in which the NH bond of peptide group 2 is vibrating), the electron density is modulated in the same way as in an isolated peptide chain in the consecutive C 5 conformation, such as alanine hexapeptide-d26 shown in Figure 3. (A similar result is obtained also for the parallel dimer, as shown in Figure S5 in the Supporting Information.) That is, the electron density modulation is delocalized over the peptide chain, most noticeably to the spatial region around the CO bond on the C terminus side [right side (+y) in the figure] of the vibrating NH bond (directly interacting as CO···H N), with a partial transfer of electron density from CO to NH upon atomic displacements in the +QamII direction [+y displacement of the H(N) atom]. This is partially canceled by the electron density modulation around the hydrogen-bond accepting O atom on the lower side, in the same way as in an αhelical peptide chain shown in Figure 4 and a peptide−water complex at (θ, φ) = (15°, 0°) shown in Figure 6a−c. However, the extent of this partial cancellation is less significant in the glycine tripeptide-d10 dimer, so that the positive peak of the one-dimensional running integral around the vibrating N−H bond survives in the plot of the total value (black) shown in Figure 8c, and the IR intensity (calculated as 405.9 km mol−1) is significantly larger than that of an isolated peptide group. In other words, hydrogen bonding between peptide chains only partially cancels the IR intensity enhancement of the C5 conformation. The dipole derivative ∂μ/∂QamII is calculated as (∂μy/∂QamII, ∂μz/∂QamII) = (3.106, 0.084) D Å−1 amu−1/2 (represented with the coordinate system adopted in Figure 8).60 The electronic contribution of the dipole derivative ∂μ(el)/ ∂QamII related to δ(∂ρ(el)(r)/∂QamII) shown in Figure 8, which amounts to (∂μy(el)/∂QamII, ∂μz(el)/∂QamII) = (0.754, 0.320) D Å−1 amu−1/2, explains most of the part of the difference in ∂μ/ ∂QamII [(0.712, 0.468) D Å−1 amu−1/2] between the glycine tripeptide-d10 dimer and an isolated peptide group.

Figure 7. Structures of glycine tripeptide-d 10 [CD 3 CO− (NHCD2CO−)2NHCD3] interacting with a few H2O molecules: 1, 2, in the C5 conformation interacting with two H2O molecules on the CO bonds of peptide groups 1 and 2; 3, 4, in the C5 conformation interacting with one H2O molecule on the NH bond of peptide group 2 and other five or six H2O molecules (for 3 and 4, respectively) on some other hydrogen-bonding sites; 5, 6, in a conformation close to ppII or pltd interacting with one H2O molecule on the NH bond of peptide group 2 and other seven or eight H2O molecules (for 5 and 6, respectively) on some other hydrogen-bonding sites. All the structures are fully optimized at the B3LYP/6-31+G(2df,p) level. The Φ and Ψ dihedral angles of the peptide chain are shown in Table 1.

group) shown in Figures 1 and 2 and also for structures 5 and 6 in Table 1, indicating that the water molecule hydrogen-bonded to the N−H bond only partially cancels the IR intensity enhancement arising from the interpeptide charge flux in the C5 conformation. This partial cancellation arising from hydration, as well as the strong secondary structure dependence around the C5 conformation40 (giving rise to the difference between C5 and pltd discussed in section 3.1), of the IR intensity enhancement may be a reason for the varying degrees of changes in the amide II/amide I IR intensity ratio observed in previous studies.5,31,33,46−51

4. CONCLUDING REMARKS In the present study, the effects of secondary structure variations and hydration on the IR intensity of the amide II mode of peptide chains have been examined theoretically. The APV method51 or its newly developed extension (APV2) has

Table 1. Vibrational Frequencies and the IR Intensities of the Amide I and II Modes of Peptide Group 2 in Some Complexes of Glycine Tripeptide-d10 and Water Molecules Calculated with the APV2 Methoda dihedral angleb/deg structure 1 2 3 4 5 6

c

amide I of peptide group 2

Φ1

Ψ1

Φ2

Ψ2

−186.9 −180.0 −172.0 −178.6 −115.8 −94.3

185.4 180.2 182.7 189.1 136.6 126.6

−178.7 −179.6 −181.9 −180.9 −80.5 −80.9

178.6 180.1 180.3 179.9 150.6 149.8

freq/cm

−1

1702.9 1693.8 1655.1 1655.1 1662.4 1659.1

amide II of peptide group 2 −1

IR int/km mol 354.5 316.0 475.3 473.9 409.2 413.8

freq/cm−1

IR int/km mol−1

1530.0 1539.7 1579.6 1581.7 1641.3 1629.1

533.5 514.3 370.1 373.1 195.0 224.5

a Calculated at the B3LYP/6-31+G(2df,p) level. bThe Φ and Ψ dihedral angles for residue n are indicated as Φn and Ψn, respectively. cShown in Figure 7.

H


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the C5 conformation. This is another important factor of the secondary structure dependence of the IR intensity. The reduced IR intensity (∼170 km mol−1) is in reasonable agreement with the observed value of 1.3−1.6 × 102 km mol−1 reported in a previous study.47 (3) Hydration of the N−H bond induces enhancement/reduction of the IR intensity depending on the angular position of the hydrating water molecule as shown in Figure 5, and it is related to the presence/ absence of the intermolecular charge flux and the polarization effect as shown in Figure 6. (4) Hydrogen bonding between peptide chains in the C5 conformation reduces the IR intensity, but this reduction is less significant than the enhancement arising from the interpeptide charge flux, as discussed in relation to the result shown in Figure 8. The same is true also for the effect of hydration on a peptide chain in the C5 conformation shown in Table 1. Taking into account also the results obtained in the previous study,40 the occurrence/nonoccurrence of the interpeptide or intermolecular charge flux in the above cases is most probably related to the geometrical relation between the H···O interaction (of the C5 ring and/or the hydrogen bond) and the displacement direction of the H(−N) atom in the amide II mode. The extent of partial charge transfer between the H and O atoms in the H···O interaction depends on the H···O distance,61,62 and hence, a charge flux is induced as this distance is modulated by a molecular vibration. In the present cases, the displacement direction of the H(−N) atom in the amide II mode is almost perpendicular to the N−H bond within the peptide plane, so that it modulates the H···O distance of the C5 ring shown in Figures 3 and 8 and of an in-plane peptide−water hydrogen bond with a large θ angle such as the case shown in Figure 6d, but not the H···O distance of a rather linear N−H··· O structure such as the cases shown in Figures 4 and 6a. In the latter cases, instead of a charge flux, a partially canceling polarization effect appears, giving rise to a reduction of the IR intensity. It is expected that the results obtained in the present study are helpful for our better understanding of the relations between the spectral features of the amide II mode and the structural, dynamical, and/or interaction properties of peptide chains, and for better utility of the amide II band in the analyses of those properties.

Figure 8. (a) Two-dimensional (yz) contour plot of ∫ dxδ(∂ρ(el)(r)/ ∂QamII) calculated for the amide II mode (QamII, extracted by using the APV method) of peptide group 2 in glycine tripeptide-d10 [CD3CO− (NHCD2CO−)2NHCD3] in the C5 conformation interacting with another chain of glycine tripeptide-d10 in the same conformation arranged in an antiparallel way. The black filled circles stand for the atoms (OCNH from top to bottom) constituting peptide group 2 in the first chain, and the black open circles stand for the other atoms. The NCαC bisection of residue 2 (which connects peptide groups 2 and 3) is taken as the z axis (vertical in this figure), with these three atoms being placed on the yz plane. The contours in the twodimensional plot are drawn with the interval of 1.2 × 10−5 a0−3me−1/2 in the range from −30 × 10−5 to 30 × 10−5 a0−3me−1/2, with the color code shown on the left-hand side. The horizontal dotted line indicates the xy plane going through the middle point of the H···O hydrogen bond in the center of this complex. (b,c) One-dimensional plot of ∫ ∫ dxdzδ(∂ρ(el)(r)/∂QamII) and its running integral. The integrals taken in the upper and lower sides of the horizontal dotted line shown in part a and their sum are shown in red, blue, and black lines, respectively. The locations of the H(N) and O atoms of residue 2 are indicated with purple dotted vertical lines, and the center between these two atoms is indicated with a pink dotted vertical line.

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ASSOCIATED CONTENT

S Supporting Information *

been used as a tool for extracting the vibrational modes of individual peptide groups or molecules from delocalized eigenmodes, and the modulations in the electron density induced by the amide II mode have been calculated and analyzed in the form of the electron density derivatives ∂ρ(el)(r)/∂QamII. The main conclusions obtained in the present study may be summarized as follows. (1) The IR intensity of the amide II mode is enhanced for the C5 conformation because of the interpeptide charge flux40 through the H···O interaction of the C5 ring as shown in Figure 3, and there is a small cooperative effect, giving rise to chain-length dependence and a larger enhancement for a consecutive C5 conformation as shown in Figures 1 and 2. This is one of the important factors of the observed5,31,33,46−51 secondary structure dependence of the IR intensity. (2) In contrast, the IR intensity is reduced for the α-helix conformation as also shown in Figure 2b, because there is a partially canceling polarization effect in the electron density modulations around the hydrogen-bond accepting O atom in the NH···OC hydrogen bond as shown in Figure 4, and there is no interpeptide charge flux of the kind seen for

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b08258.

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Detailed procedures, additional structures, and relation between vibrational and structural properties (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone and fax: +81-54-238-4624. E-mail: torii.hajime@ shizuoka.ac.jp. Notes

The authors declare no competing financial interest.

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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. I


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