Amide I Infrared Spectral Features Characteristic of ... - ACS Publications

J. Phys. Chem. B 2008, 112, 8737–8743

8737

Amide I Infrared Spectral Features Characteristic of Some Untypical Conformations Appearing in the Structures Suggested for Amyloids Hajime Torii† Department of Chemistry, School of Education, Shizuoka UniVersity, 836 Ohya, Shizuoka 422-8529, Japan ReceiVed: February 15, 2008; ReVised Manuscript ReceiVed: April 24, 2008

Amide I infrared (IR) spectral features are studied, by using the density functional theoretical method, for two untypical (but possibly rather prevalent) structures inspired from those recently suggested for amyloids: a structure consisting of loop regions in the (RL, RR) conformation stacked to form an R-sheet, and a structure involving some main-chain peptide groups (of any residues) and some side-chain amide groups of glutamine and asparagine residues closely located with each other. The amide I vibrational (off-diagonal) coupling constants are examined by extracting them from the calculated Cartesian-based force constants with the average partial vector method and by comparing them with those estimated on the basis of the transition dipole coupling mechanism. It is suggested that the amide I IR band characteristic of the R-sheet conformation in dry environment (without hydrogen bonding to solvent water molecules) is located in a high-frequency region (J1670 cm-1, somewhat higher than that of R-helix), because of the dependence of the diagonal (uncoupled) frequency and the off-diagonal coupling constant on the Φ and Ψ dihedral angles. It is also shown that the amide I vibrations of the closely located peptide and amide groups are strongly coupled through-space with each other, and in the presence of this type of strong vibrational coupling, a noticeable change in the IR intensity upon 13CdO substitution may occur even for a mode that arises mainly from an unsubstituted group and is not much shifted in frequency. The meaning of these results in the interpretation of observed amide I spectral profiles, especially the possible usefulness of IR spectroscopic measurements for detecting those untypical structures in the process of amyloid formation, is also discussed. 1. Introduction It is widely recognized that analyses of amide I infrared (IR) band profiles are useful for structure examinations of polypeptides and proteins.1–5 The origin of the usefulness is considered to be twofold. One is the dependence of the interpeptide (offdiagonal) vibrational coupling on the secondary structures (determined by the Φ and Ψ dihedral angles), which is controlled by the through-space6–14 and through-bond9–11,14–16 interaction mechanisms. The other is the sensitivity of the (diagonal) vibrational frequencies of individual peptide groups to their electrostatic environment,17–25 which depends on both the structure of the peptide chain itself and the configurations of solvent water molecules, as a property of a vibrational mode with a large dipole derivative and a non-negligible mechanical anharmonicity.26 In those analyses, the existence of a weak high-frequency band in the 1695-1670 cm-1 region together with a strong lowfrequency band in the 1640-1620 cm-1 region is considered to be a marker of antiparallel β-sheets. This assignment is based on the large splitting of the two delocalized IR-active modes arising from strong interpeptide vibrational coupling, the vibrational patterns of which are characterized as (π, 0) and (0, π),27,28 and is supported by the observed spectral profiles of polypeptides that are known to be in this conformation. However, in a recent experiment by Paul and Axelsen,29 it has been shown that the spectral profile with a high-frequency shoulder at 1685 cm-1 and a strong band at 1624 cm-1 is observed for an aggregated amyloid β protein Aβ40, which is considered to be in a parallel β-sheet conformation29–33 (although † Phone and Fax: +81-54-238-4624. E-mail: [email protected].

its fragments34,35 and other peptides36 may form aggregates in an antiparallel β-sheet conformation). This observation suggests that there may be some aspects that are not yet well-recognized for the relationship between the structures of peptide chains and their amide I spectral features. In this sense, it will be meaningful to study the amide I spectral features of structures that are considered to be untypical (but may actually be rather prevalent) for globular proteins in their native state and also of some structures suggested for proteins in aggregated forms. In the present paper, the amide I IR spectral features are studied theoretically for two structures inspired from those recently proposed for amyloids. One is a stacked loop structure, which is seen in the aggregated structures of peptide chains with loop regions. In globular proteins, loop regions are considered in many cases to be well-solvated with varying Φ and Ψ dihedral angles, so that the interactions between the peptide chains in this conformation are not usually taken into account. However, in aggregated amyloids, those loops are located close to each other, so that their mutual interactions may be possible. Upon inspection of the structure of the section of residues 26-29 of chains B-D suggested for Aβ42,37 which is shown in Figure 1a, it is recognized that the CdO bonds of all the three peptide groups are oriented in almost the same direction, and the peptide groups of different peptide chains may possibly form hydrogen bonds upon slight structural rearrangement. This structure is reminiscent of the R-sheet conformation,38,39 which is recently suggested40–43 as the origin of self-assembling ability and toxicity of amyloids. Because of the possible importance of this conformation in the amyloid formation, it will be meaningful to clarify whether there are any distinct IR spectral features for this conformation to seek for its appropriate detection methods.

10.1021/jp801364s CCC: $40.75  2008 American Chemical Society Published on Web 06/26/2008

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Figure 1. Drawings of (a) the section of residues 26-29 (or peptide groups 26-28) of chains B-D in the structure suggested for Aβ42 (PDB ID: 2BEG, model 1) (ref 37) and (b) “in-register” double β-sheet suggested for the crystal of the peptide chain GNNQQNY (PDB ID: 1YJP) (ref 44). Carbon, oxygen, nitrogen, and hydrogen atoms are shown with gray, red, blue, and white spheres, respectively. Part of some side chains are omitted in these drawings. The numbering of some peptide and amide groups is shown in panel b.

Another structure that is studied in the present paper is a configuration of peptide chains with a close contact between a main-chain peptide group of one peptide chain and a side-chain amide group of a glutamine or asparagine residue in another peptide chain. This type of close contact is seen in the “inregister” double β-sheet structure suggested for the crystal of the peptide chain GNNQQNY,44 which is shown in Figure 1b. The amide I modes of the main-chain peptide group and the side-chain amide group have similar properties with regard to the frequency positions45 and the through-space coupling ability, as recognized from the spectra of liquid formamide,46,47 where the amide I band is located in the 1700-1600 cm-1 region and exhibits a large noncoincidence effect48 that is induced by strong intermolecular resonant vibrational coupling. As a result, it is expected that those amide I modes are nearly resonantly coupled if the vibrating groups are located close to each other. Supposing that there will be some occasions where the side chain is located at a rather fixed position relative to the main chain (as in the case of the peptide chain GNNQQNY), and taking into account that glutamine and asparagine residues are expected to play an important role in aggregate formation in some cases,49–54 the effect of this vibrational coupling on the spectral features is considered to deserve theoretical analysis. The present study is not aimed at theoretically reproducing the spectral features of some particular samples but at getting further insight into the relationship between the structures of peptide chains and their amide I spectral features from calculations on realistic examples. It is shown below that the IR spectra of R-sheets in dry environment are characterized by a strong band in the higher-frequency amide I region (J1670 cm-1), and the effect of the vibrational coupling between the amide I modes of the main-chain peptide group and the side-chain amide group is seen in the intensity variation upon 13CdO substitution. 2. Computational Procedure The structures of the molecular species for the present calculations were constructed as follows. (1) Upon inspection of the structures of chains B-E suggested for Aβ42 [protein data bank (PDB) ID: 2BEG, model 1],37 the Φ and Ψ dihedral angles of residues Asn27 and Lys28 turned out to be (Φ27, Ψ27, Φ28, Ψ28) ) (62.9°, 69.3°, -73.2°, -95.9°), (80.0°, 68.0°, -64.8°, -101.0°), (78.4°, 76.6°, -67.3°, -92.6°), and (72.2°, 78.1°, -72.2°, -81.2°) for chains B-E, respectively. Taking the averages, we obtained (Φ27 - Φ28)/2 ) 71.4° and (Ψ27 - Ψ28)/2 ) 82.8°. As a result, we constructed a system consisting of three hydrogen-bonded

peptide chains (CH3CO-Gly-Gly-NDCH3)3, arranged as shown in Figure 1a, with the dihedral angles of (Φ1, Ψ1, Φ2, Ψ2) ) (71.4°, 82.8°, -71.4°, -82.8°). In this structure, (Φ1, Ψ1) and (Φ2, Ψ2) are in the RL and RR regions on the Ramachandran map, so that this system is considered to be in an R-sheet conformation.38–43 This is called R-sheet 1 hereafter. In addition, similar systems with (Φ1, Ψ1, Φ2, Ψ2) ) (60.0°, 60.0°, -60.0°, -60.0°) and (80.0°, 70.0°, -80.0°, -70.0°) were also considered, which are called R-sheets 2 and 3 hereafter. The structure of each of these systems was optimized at the B3LYP/6-31+G(2df,p) level of the density functional theory (DFT) with the constraints of these dihedral angles, the planarity of all the peptide groups, and the same structural parameters for the three peptide chains. The vibrational frequencies and IR intensities were calculated for this optimized structure at the same theoretical level, with all the peptide protons being deuterated, and the frequencies were scaled in a usual way (described below). As a reference, calculations were also carried out for (CH3CO-Gly-Gly-NDCH3)3 in the parallel and antiparallel β-sheet conformations with Φ1 ) Ψ1 ) Φ2 ) Ψ2 ) 180.0°, and for CH3CO-(Gly)8-NDCH3 in the R-helix conformation with (Φ, Ψ) ) (-67°, -37°). Since the amide I mode is a rather highfrequency mode, the problem of spurious mode mixing55 is not expected to be significant even by adopting this kind of computational procedure. However, the calculated vibrational frequencies were adjusted for the effect of interchain hydrogen bonding and the environmental dielectric effect, which are only partially included in the present calculations (described below). (2) To examine the vibrational coupling between some closely located main-chain peptide groups and side-chain amide groups in the structure shown in Figure 1b (3m-4s′, 4m-4s, 5m-6s, 4s-6s, 4s-2s′, and 6s-2s′ according to the numbering shown in this figure), which is derived from the structure suggested for the crystal of the peptide chain GNNQQNY (PDB ID: 1YJP),44 model systems were constructed by placing peptide and amide groups at specified positions, and terminating those groups by methyl groups and/or connecting them by a -(CH2)n- chain. Specifically, the calculated systems were (NMA-d1)2(acetamide-d2)2 as a model of 3m-4s′ (where NMA is the abbreviation of N-methylacetamide), (CH3NDCO(CH2)3 COND2)2 as a model of 4m-4s, (CH3COND(CH2)2COND2)2 as a model of 5m-6s, and (acetamide-d2)4 as models of 4s-6s, 4s-2s′, and 6s-2s′, each of which corresponds to the peptide and amide groups in two layers along the b-axis (which is perpendicular to the plane where the structure is depicted in Figure 1b, and is the direction of interlayer hydrogen-bond chains of the peptide and amide groups) in the structure of 1YJP. The structural parameters

Amide I IR Features of Untypical Conformations

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TABLE 1: Magnitudes, Directions, and Locations of the Vibrational Transition Dipoles Assumed for the Amide I Modes of the Main-Chain Peptide Groups and the Side-Chain Amide Groups for Calculating the Transition Dipole Coupling Constants Å-1

parameter

main chaina

side chainb

-1/2

2.729 16.69 0.7

2.988 10.45 0.7

|∂µ/∂q|/D amu angle between ∂µ/∂q and rOC/deg location of ∂µ/∂q, x for xrO + (1 - x)rC

a Calculated for N-methylacetamide-d1 at the B3LYP/6-31+G(2df,p) level. b Calculated for acetamide-d2 at the B3LYP/6-31+G(2df,p) level.

of the peptide and amide groups were taken from isolated molecules of NMA and acetamide, with the location of the carbonyl carbon atom, the direction of the CdO bond, and the orientation of the peptide plane being determined by the coordinates of the corresponding C, O, and N atoms in 1YJP. The structural parameters of the -(CH2)n- backbone were also taken from this PDB file. The vibrational frequencies and IR intensities were calculated at the B3LYP/6-31+G(2df,p) level, and the frequencies were adjusted for the environmental dielectric and hydrogen-bonding effects and scaled (described below). For the first three model systems, the frequencies and IR intensities of the 13CdO substituted species were also calculated. The coupling constants between the amide I vibrations of peptide and amide groups were extracted from the calculated Cartesian-based force constants by using the average partial vector (APV) method, which was developed in our previous study.21 Those coupling constants constitute the off-diagonal terms of the vibrational Hamiltonian in the amide I vibrational subspace,8 and hence, they are classified as “off-diagonal”, in contrast to the (uncoupled) vibrational frequencies of individual peptide or amide groups, which are classified as “diagonal”. The coupling constants thus extracted were compared with those calculated according to the transition dipole coupling (TDC) mechanism,6–12 which is considered to be the main mechanism of the through-space vibrational coupling of the amide I vibrations. The magnitudes and directions of the dipole derivatives needed for calculating the TDC constants were obtained from the calculations on isolated molecules of NMA-d1 and acetamide-d2, and the locations of those dipole derivatives were assumed to be at r ) xrO + (1 - x)rC with x ) 0.7, where rC and rO represent the locations of the carbonyl carbon and oxygen atoms, as shown in Table 1. As shown in the previous studies,21,22 formation of a hydrogen-bond chain has a significant effect on the electrostatic environment of the peptide groups and, hence, their amide I diagonal vibrational frequencies. In the present study, to include this effect, the calculated frequencies were adjusted by referring to the hydrogen-bond chain length dependence of the amide I diagonal force constants found for (NMA-d1)n with n ) 3-8, which was calculated also at the B3LYP/6-31+G(2df,p) level. As shown in Figure 2, the amide I diagonal force constant of the center molecule (extracted by using the APV method) depends on the hydrogen-bond chain length, and the limiting value is estimated as 1.659 mdyn Å-1 amu-1 (unscaled) according to the fit by a second-order polynomial of n-1. As a result, the adjustments were done by using this limiting value, together with the (average) amide I diagonal force constant(s) calculated for (NMA-d1)n with n ) 1 and 3. The calculated vibrational frequencies were further scaled in a usual way, with the scale factor of 0.9850 (its square for the force constants) obtained by comparing the frequencies calculated for an isolated NMA molecule (1744.1 cm-1) and observed56 for this molecule in the gas phase (1718 cm-1).

Figure 2. Mass-weighted force constant of the amide I mode of the center molecule in the (N-methylacetamide-d1)n clusters, calculated at the B3LYP/6-31+G(2df,p) level and by using the average partial vector (APV) method (ref 21), plotted against the inverse of the number of molecules (n ) 3-8). Filled circles, n ) 3, 5, 7; open squares, n ) 4, 6, 8, where the average over the two center molecules is taken; dotted line, fit by a linear function; solid line, fit by a second-order polynomial.

The vibrational frequencies calculated in this way do not include part of the environmental dielectric effect on the diagonal terms, which arises, in the case of an R- or β-sheet, from the through-space interactions with the solvent water molecules or some atomic groups located above and below the sheet. Considering that the amide I frequency of NMA in nonhydrogen-bonding polar solvents is lower than that of an isolated NMA molecule by about 40 cm-1,57 all the vibrational frequencies calculated in the present study were shifted down by half of this difference (20 cm-1). The amount of this adjustment is supported empirically from the fact that the vibrational frequency of the strongly IR-active mode of an R-helix [(Φ, Ψ) ) (-67°, -37°)] is calculated as 1662 cm-1 by adopting this procedure (adjustment for the dielectric and hydrogen-bonding effects and scaling) as shown below, which is close to (but still slightly higher than) the empirically known frequency region of the amide I IR band of an R-helix (1660-1650 cm-1). All the calculations at the B3LYP/6-31+G(2df,p) level of the DFT method were performed by using the Gaussian 03 program.58 The calculations based on the APV method and the TDC mechanism were carried out with our original programs or procedures. 3. Results and Discussion The IR spectra in the amide I frequency region calculated for (CH3CO-Gly-Gly-NDCH3)3 in the R-sheet conformations 1-3 are shown on the left-hand side of Figure 3, which are compared with those calculated for CH3CO-(Gly)8-NDCH3 in the R-helix conformation and (CH3CO-Gly-Gly-NDCH3)3 in the parallel and antiparallel β-sheet conformations shown on the right-hand side. It is recognized that, in the spectra of R-sheets, there is a strong band in a high-frequency region (J1670 cm-1, somewhat higher than that of R-helix), in contrast to those of β-sheets where a strong band appears in a low-frequency region (j1620 cm-1). There are two factors that should be considered for the highfrequency position obtained for the R-sheets. One is the dependence of the diagonal force constants (the calculated values of which are shown in Table 2) on the Φ and Ψ dihedral angles. As stated in section 1, because the amide I mode has a large dipole derivative, the amide I frequency is sensitive to the electrostatic environment of the peptide group. The electrostatic environment originates partly from the charge distributions in the covalently bonded neighboring peptide groups, so that it is

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Figure 3. Infrared spectra in the amide I region calculated at the B3LYP/6-31+G(2df,p) level for (CH3CO-Gly-Gly-NDCH3)3 in the R-sheet conformations 1-3 and in the parallel and antiparallel β-sheet conformations, and for CH3CO-(Gly)8-NDCH3 in the R-helix conformation. The structure of each conformation is defined as R-sheet 1, (Φ1, Ψ1, Φ2, Ψ2) ) (71.4°, 82.8°, -71.4°, -82.8°); R-sheet 2, (Φ1, Ψ1, Φ2, Ψ2) ) (60.0°, 60.0°, -60.0°, -60.0°); R-sheet 3, (Φ1, Ψ1, Φ2, Ψ2) ) (80.0°, 70.0°, -80.0°, -70.0°); β-sheets, Φ1 ) Ψ1 ) Φ2 ) Ψ2 ) 180.0°; R-helix, (Φ, Ψ) ) (-67°, -37°). The diagonal force constants are adjusted for the effects of interchain hydrogen bonding and for the dielectric effects (as described in the text), and the frequencies are scaled by 0.9850.

TABLE 2: Calculated Amide I Diagonal Force Constants of Individual Peptide Groups and Off-Diagonal Vibrational Coupling Constants between the Covalently-Bonded and Hydrogen-Bonded Peptide Groups in r- and β-Sheetsa off-diagonal coupling/ mdyn Å-1 amu-1 diagonal/mdyn Å-1 amu-1

covalently bonded

sheet

DFTb,c

DFTb

R2f R3g parallel βh antiparallel βh

1.6679 1.6480 1.6401 1.5635 1.5529

0.0335 0.0215 -0.0085 0.0248 0.0186 -0.0062 0.0267 0.0189 -0.0087 0.0124 -0.0015 -0.0066 0.0123 -0.0016 -0.0116

R1e

TDCd

hydrogenbonded DFTb

TDCd -0.0113 -0.0091 -0.0113 -0.0085 -0.0109

a (Average of) the constants involving the center peptide group in (CH3CO-Gly-Gly-NDCH3)3 are shown. b Calculated at the B3LYP/ 6-31+G(2df,p) level, scaled by 0.9703. c Adjusted for the effects of interchain hydrogen bonding and for the dielectric effects, as described in the text. d Calculated with the parameters shown in Table 1. e (Φ1, Ψ1, Φ2, Ψ2) ) (71.4°, 82.8°, -71.4°, -82.8°). f (Φ1, Ψ1, Φ2, Ψ2) ) (60.0°, 60.0°, -60.0°, -60.0°). g (Φ1, Ψ1, Φ2, Ψ2) ) (80.0°, 70.0°, -80.0°, -70.0°). h Φ1 ) Ψ1 ) Φ2 ) Ψ2 ) 180.0°.

dependent on the Φ and Ψ dihedral angles. Since the CdO bonds (and hence the group dipole moments) are arranged in a parallel side-by-side fashion in an R-strand, the peptide groups are in a “repulsive” electrostatic environment. Therefore, as shown in previous studies,12,16,59 if the amide I diagonal vibrational frequency is mapped as a function of the Φ and Ψ dihedral angles, R-strands are located close to the ridge [Ψ = -180° - Φ, with a peak at (Φ, Ψ) = (0°, -180°)], in contrast to β-strands, which are located close to the valley (Ψ = -Φ). This effect is considered to be one of the factors that generate an IR band in a high-frequency amide I region. The other factor is the dependence of the off-diagonal vibrational coupling constants between covalently bonded

peptide groups on the Φ and Ψ dihedral angles and the relationship among the vibrational coupling, the vibrational patterns, and the direction of the CdO bonds. The vibrational coupling of the amide I mode is controlled by the through-space and through-bond interaction mechanisms as stated also in section 1, and the TDC is recognized as the main mechanism of the through-space coupling. The equation for the TDC is in a form of an electrostatic interaction between dipole derivatives, so that the coupling according to this mechanism tends to be large for the amide I mode because it has a large dipole derivative. Since the dipole derivative of the amide I mode is almost parallel to the permanent dipole of the peptide group, as recognized from the parameters shown in Table 1, the dependence of the TDC constant on the Φ and Ψ dihedral angles is quite similar to that of the diagonal force constant affected by the electrostatic environment. This means that positive values are expected for the coupling between covalently bonded peptide groups in R-strands, and this is indeed the case for the R-sheets treated in the present calculations as shown in Table 2. The actual coupling constants are even larger by ∼0.01 mdyn Å-1 amu-1 because of the through-bond coupling, as shown also in Table 2, and this result is consistent with that obtained in our previous study.9 Because the CdO bonds are oriented in almost the same direction in an R-strand, the in-phase mode (where all the CdO bonds stretch in phase) is strongly IR active, and because the coupling is positive, this in-phase mode is shifted up in frequency. This effect is considered to be another factor that generate an IR band in a high-frequency amide I region. In the case of β-sheets, the coupling between the amide I vibrations of covalently bonded peptide groups is also positive but smaller, and this is due to the through-bond coupling, as shown in Table 2. [Note that the through-bond coupling is also dependent on the secondary structure,9 although it may look rather constant (with the difference between “DFT” and “TDC” being 0.010 ( 0.004 mdyn Å-1 amu-1) in Table 2.] Since the

Amide I IR Features of Untypical Conformations

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TABLE 3: Calculated Amide I Vibrational Coupling Constants Involving Glutamine and Asparagine Side Chains in the Structure Suggested for the “In-Register” Double β-Sheet vibrational coupling/mdyn Å-1 amu-1 peptide or amide groupsa

DFTb

TDCc

3m-4s′ 4m-4s 5m-6s 4s-6s 4s-2s′ 6s-2s′

-0.0148 0.0092 0.0181 -0.0233 -0.0077 0.0221

-0.0164 0.0087 0.0146 -0.0153 -0.0061 0.0214

a Numbering of the peptide and amide groups is shown in Figure 1b. b Calculated at the B3LYP/6-31+G(2df,p) level, scaled by 0.9703. c Calculated with the parameters shown in Table 1.

CdO bonds are oriented alternately along a β-strand, this positive coupling shifts down the frequency of the IR-active mode. In contrast, the vibrational coupling between hydrogenbonded peptide groups is negative for all the five conformations shown in Table 2, and it is reasonably explained by the TDC mechanism (the difference between “DFT” and “TDC” being smaller than 0.003 mdyn Å-1 amu-1). This negative coupling induces a lower-frequency shift of the IR-active mode, because the CdO bonds of hydrogen-bonded peptide groups are oriented in almost the same direction. As recognized from the result shown in Figure 3, the calculated frequency position of the strong IR band is different by more than 10 cm-1 even among the three R-sheet conformations. This suggests a rather high sensitivity of the frequency position of the amide I band to the Φ and Ψ dihedral angles in the R-strand region on the Ramachandran map. However, this frequency position is sufficiently distinct from that of β-sheets, so that IR spectroscopic measurements may be useful for detecting R-sheets in the process of amyloid formation. In a previous study,60 an IR spectrum with bands at 1633, 1690, and 1730 cm-1 in the amide I region was measured for alternating poly(D,L-peptides), and a question was raised as to whether it is consistent with an R-sheet (polar pleated sheet) conformation. Considering the results obtained in the present study, the conformation corresponding to this spectrum will deserve further examination. It should also be remarked that frequency positions of the strong IR bands calculated for the parallel and antiparallel β-sheets shown in Figure 3 are lower than those usually seen for β-sheets in globular proteins (1640-1620 cm-1), because the diagonal force constants are adjusted for the effect of hydrogen bonding of an infinite hydrogen-bond chain as stated in section 2. This is considered to be related to the observation61–64 of the amide I IR bands at rather low frequency positions for many amyloid samples. The amide I vibrational coupling constants calculated for the model species of some closely located pairs of peptide and amide groups appearing in the “in-register” double β-sheet structure are shown in Table 3. It is seen that they all have magnitudes similar to those between hydrogen-bonded peptide groups shown in Table 2, suggesting that these couplings will also induce some effects on the spectral profiles if the side chains are located at rather fixed positions relative to the main chain. It is also recognized that the signs and the magnitudes of the coupling constants are reasonably explained by the TDC mechanism, except for the case of 4s-6s (the reason not yet known). The IR spectra in the amide I frequency region calculated for the first three species, which involve both a main-chain

Figure 4. Infrared spectra in the amide I region of (N-methylacetamided1)2(acetamide-d2)2 as a model of 3m-4s′, (CH3NDCO(CH2)3COND2)2 as a model of 4m-4s, and (CH3COND(CH2)2COND2)2 as a model of 5m-6s, calculated at the B3LYP/6-31+G(2df,p) level. The diagonal force constants are adjusted for the effects of interchain hydrogen bonding and for the dielectric effects (as described in the text), and the frequencies are scaled by 0.9850: red, 12C species; blue, 13CdO substituted in the main chain; green, 13CdO substituted in the side chain.

peptide group and a side-chain amide group, are shown with red sticks in Figure 4. It is seen that strongly IR-active modes appear at ∼1650 and ∼1630 cm-1. (Note that there are additionally two modes with very weak IR intensities, because each calculated species corresponds to two layers as explained in section 2, and hence, there are four amide I oscillators in total.) The mode at ∼1650 cm-1 mainly arises from the vibrations of the side-chain amide groups, whereas the mode at ∼1630 cm-1 mainly arises from those of the main-chain peptide groups. However, because of the vibrational coupling discussed above, these vibrations are slightly mixed with each other, inducing intensity redistribution. In the case of the model of 3m-4s′, the vibrational coupling is negative as shown in Table 3, so that the vibrations of the main-chain peptide groups are mixed in the opposite phase into the ∼1650 cm-1 mode, whereas those of the side-chain amide groups are mixed in phase into the ∼1630 cm-1 mode. Because the CdO bonds of the side-chain amide groups are oriented in the opposite direction to those of the main-chain peptide groups, this vibrational mixing gives rise to intensity redistribution to the high-frequency side, as shown in the top panel of Figure 4. In the cases of the models of 4m-4s and 5m-6s, the vibrational coupling is positive, so that the vibrational mixing occurs in the opposite sign to the case of 3m-4s′. However, since the CdO bonds of the main-chain peptide groups and the side-chain amide groups are oriented in almost the same direction, the vibrational mixing induces intensity redistribution to the high-frequency side also in these cases, as shown in the middle and bottom panels of Figure 4.

8742 J. Phys. Chem. B, Vol. 112, No. 29, 2008 The effect of this intensity redistribution is reduced by shifting down the frequency of the amide I vibration of the main-chain peptide groups by 13CdO substitution. As shown with blue sticks in Figure 4, while the ∼1630 cm-1 mode moves down to ∼1585 cm-1, the ∼1650 cm-1 mode remains almost at the same frequency by this isotopic substitution. However, because the effect of the intensity redistribution is reduced, the IR intensity of the ∼1650 cm-1 mode becomes weaker. A more pronounced change is seen by the 13CdO substitution of the side-chain amide groups. In this case, as shown with green sticks in Figure 4, the ∼1650 cm-1 mode moves down to ∼1605 cm-1, while the ∼1630 cm-1 mode remains almost at the same frequency. However, since the frequency sequence is reversed, the ∼1630 cm-1 mode becomes much stronger than the ∼1605 cm-1 mode. This result points out that, in the presence of strong vibrational coupling, there is a high possibility that, upon 13CdO substitution, the IR intensity changes to a noticeable extent even for a mode that is not directly related to the isotopic substitution and is, therefore, not much shifted in frequency. This point may lead to a slightly complicated situation in the interpretation of the IR spectra observed for 13CdO substituted species of peptide chains and proteins, but it also means that, in the presence of strong vibrational coupling, spectral data obtained from this type of isotopic substitution may contain rich structural information. In this sense, IR spectroscopic measurements of samples with selective 13CdO isotopic substitution will be useful for detecting close contacts (close enough to produce large vibrational couplings) between main-chain peptide groups and side-chain amide groups in the process of amyloid formation. 4. Concluding Remarks In the present paper, to get further insight into the relationship between the structures of peptide chains and their amide I spectral features, the IR spectra in the amide I frequency region have been calculated by using the DFT method for two untypical (but possibly rather prevalent) structures inspired from those recently suggested for amyloids. The amide I vibrational (offdiagonal) coupling constants have been examined by extracting them from the calculated Cartesian-based force constants by using the APV method.21 From the calculations on the structure consisting of loop regions in the (RL, RR) conformation stacked to form an R-sheet, it has been suggested that the amide I IR band characteristic of this structure is located in a high-frequency region (J1670 cm-1, somewhat higher than that of R-helix). The dependence of both the diagonal amide I frequency and the off-diagonal coupling constant on the Φ and Ψ dihedral angles is important in this regard. From the calculations on the structure involving some closely located main-chain peptide groups and side-chain amide groups, it has been shown that the amide I vibrations of those closely located groups are strongly coupled through-space with each other by the TDC mechanism. It has also been shown that, in the presence of this type of strong vibrational coupling, a noticeable change in the IR intensity upon 13CdO substitution may occur even for a mode that arises mainly from an unsubstituted group and is not much shifted in frequency. Since the TDC is in a form of an electrostatic interaction between dipole derivatives,48 and in this sense is a general vibrational coupling mechanism, the latter result will be applicable also to the cases of peptide groups in different environment (e.g., those in R- and β-strands) strongly coupled with each other. In those cases, upon 13CdO substitution, the IR intensities of the modes of the peptide groups that are strongly

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