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Nov 3, 2015 - Understanding the Amide-II Vibrations in β-Peptides. Juan Zhao and Jianping Wang. Beijing National Laboratory for Molecular Sciences; L...
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Understanding the Amide-II Vibrations in β‑Peptides Juan Zhao and Jianping Wang* Beijing National Laboratory for Molecular Sciences; Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China S Supporting Information *

ABSTRACT: In this work, the vibrational characteristics of the amide-II modes in β-peptides in five helical conformations, namely, 8-, 10-, 12-, 14-, and 10/12-helices, have been examined. Remarkable conformational dependence of the amide-II spectral profile is obtained by ab initio computations as well as modeling analysis. Intramolecular hydrogen-bonding interaction and its influence on backbone structure and on the amide-II local-mode transition frequencies and intensities are examined. Through-space and through-bond contributions of the amide-II vibrational couplings are analyzed, and it was found that hydrogen-bonding interaction is not a determining factor for the coupling strength. The results reported here provide useful benchmarks for understanding experimental amide-II infrared spectra of β-peptides and suggest the potential application of this mode on monitoring the structures and dynamics of β-peptides.

I. INTRODUCTION As one type of important unnatural peptide, β-peptides are known to exhibit novel secondary and tertiary structures, and these peptides are potentially applicable in designing new drugs, in fabricating novel materials and biocompatible devices, as well as in solving the puzzle of protein folding.1−3 It is thus of great importance to explore spectroscopic methods that are sensitive to the conformations of β-peptides. Infrared spectroscopy, including linear and nonlinear methods, has been known to be extremely sensitive to structures and structural distributions of α-peptides4−8 and natural proteins that are composed of α-amino acids.9−13 In this regard, the periodically appearing amide units (CONH) in the backbone of α-peptides, which have several infrared-active modes, have been primarily used as a conformational probe. Two of these modes are the amide-I and -II modes, whose vibrational frequencies are located in the 1600−1700 cm −1 and 1500−1600 cm−1 frequency regions, respectively. The amide-I mode is mainly the CO stretching vibration, whereas the amide-II mode is primarily an out-of-phase combination of largely the N−H inplane bending and part of the C−N stretching.14 Their spectral profiles, i.e., frequency, spectral shape and intensity, are known to be conformational dependent and thus can serve as effective structural marker for peptides and proteins.14 The usefulness of the amide-I mode in revealing the secondary and tertiary structures of α-peptides and proteins have been reported extensively.10,15−26 The structural sensitivity of the amide-II mode in α-peptides has also been studied computationally27,28 and experimentally.29−33 Using linear and nonlinear infrared (in particular two-dimensional, 2D) methods, it was found that the amide-II mode is anharmonically coupled to the amide-I mode within the same amide unit,29,30 or across an intramolecular hydrogen bond in the 310-helix.31,32 Using 2D IR cross peak of amide-I © XXXX American Chemical Society

and -II modes in a mode peptide, site-specific hydrogen− deuterium exchange dynamics has also been revealed.33 However, in β-peptides, because there is one extra carbon atom between neighboring amide units, the average interamide distance is generally larger than that in α-peptides. Intuitively, anharmonic vibrational frequency and coupling, mode delocalization, and their dihedral-angle dependences in β-peptides may differ considerably from those in α-peptides. Indeed, a recent computational analysis has showed that interamide-I coupling in β-peptides is generally weaker between nearby amide units than that in α-peptides.34 Experimental and theoretical studies on the amide-I modes of β-peptides have been reported recently.34−40 Our recent computational studies showed that the local-mode frequencies of amide-I modes were determined primarily by peptide backbone and side chain, rather by solvent, exhibiting their local structural sensitivities.39 Intermode vibrational couplings were found to be very sensitive to peptide conformations, and couplings between the amide units forming hydrogen bonding are the strongest for a given conformation. The vibrational properties of the amide-I and amide-II modes in β-peptide in dimer and trimer forms have been investigated recently using gas-phase single-conformational IR spectroscopy.40 This paper is organized as follows. Several typical β-peptide heptamers in perfect helices, namely 8-, 10-, 12-, and 14-helices, and 10/12-hybrid helix were chosen and structurally optimized. Their normal-mode and local-mode frequencies, vibrational coupling, and vibrational transition density for the amide-II modes were obtained using ab initio computations and modeling analysis. Conformational and hydrogen-bonding Received: August 19, 2015 Revised: November 3, 2015

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Figure 1. Skeleton structures of helical β-peptide heptamers (8H, 10H, 12H, 14H, 10/12H). Dashed line indicates hydrogen bond. Amide units are numbered from the N-terminus to C-terminus. The 10-element hydrogen-bonding starts from the N-terminus in the 10/12H conformation. Amide oxygen atoms are in red, hydrogen atoms are in light gray, nitrogen atoms are in blue, and backbone carbon atoms are in gray. Lower-right corner shows a general structure of a β-peptide heptamer with backbone dihedral angles (ϕ, θ, ψ) shown. N

dependences of these vibrational parameters were examined and discussed, aiming to gain more insights into the structure− spectrum relationship of the β-peptides.

Qa =

∑ qiUia i=1

(1)

where Uia is the reduced eigenvector (or called wave function) of the ath normal mode in the amide-II subspace containing N amide units. Note that Uia is not the ab initio calculated eigenvector but is computed from the eigenvector in the following way. It is known that the amide-II mode is mainly a combination of the C−N stretching and N−H in-plane bending. For an isolated β-peptide model compound, Nethylpropionamide (NEPA), the PED values of these two components are estimated to be 0.22 and 0.51, respectively. To use the N−H bending contribution, we set Uia to be proportional to the magnitude of the ith N−H bending in the ath amide-II normal mode. Similarly, to use the C−N stretching contribution, we also set Uia to be proportional to the magnitude of the ith C−N bond length change in the ath amide-II normal mode. By normalizing the eigenvector matrix U composed of a collection of Uia, the magnitude and phase of eigenvector element Uia were determined. Then a wave function demixing procedure can be done by

II. COMPUTATIONAL METHODS A. Ab Initio Calculations. β-Peptide heptamers consisting of β3-Ala amino acid in five different helical conformations were considered in this work, which are 8-helix (8H), 10-helix (10H), 12-helix (12H), 14-helix (14H), and 10/12-helix (10/ 12H), respectively. Schematic diagrams of these five helical conformations are shown in Figure 1. Vibrational properties of the amide-II bands were analyzed for these peptides in gas phase. Geometry optimization and normal-mode analysis of these heptamers were carried out using the density functional theory (DFT) at the level of B3LYP/6-31+G*, using Gaussian09.41 No scaling factor was applied for the calculated vibrational frequencies. The backbone dihedral angles (ϕ, θ, ψ, shown in Figure 1) were fixed during the geometry optimization, which are −111.5°, 68.6°, 13.9° for the 8H conformation; 73.5°, 51.3°, 73.6°for 10H; −88.5°, 89.3°, −111.4° for 12H; −141.6°, 59.9°, −133.3° for 14H; 89.5°, 65.9°, −110.6° for the first, third, and fifth amino acids, and −99.3°, 61.3°, 89.9° for the second, fourth, and sixth amino acids for the 10/12H conformation.42,43 Infrared spectra of these peptides in the amide-II mode regions were simply simulated by broadening their transition intensities using a Lorentzian line shape with the full width at half-maximum (fwhm) setting to 16 cm−1. Note that such simulation is only for illustration purpose, more complicated protocol can be used if one desired more realistic line shape.44 B. Local-Mode Frequency and Vibrational Coupling. The local-mode frequencies and vibrational couplings of the amide-II modes were obtained by the wave function demixing (WFD) method, which has been used to evaluate the vibrational couplings of the amide-I modes of both α- and βpeptides.34,45 Ab initio vibrational computation provides the eigenvalues (vibrational transition frequencies) and eigenvectors (or normal coordinates) for each normal mode. These computational outputs were used to decouple the amide-II normal modes. Here, a given amide-II normal coordinate (Qa) is assumed to be a linear combination of N reduced amide-II local coordinates (qi):

H = U −1ΛU

(2)

where Λ is the eigenvalue matrix obtained by the ab initio vibrational calculations. The diagonal elements of matrix H are the local-mode frequencies of amide-II modes, whereas the offdiagonal elements are the intermode coupling constants. The method to decouple the amide-II modes and to extract the local-mode frequencies and couplings simultaneously described here is thus denoted as the WFD method hereafter. C. Vibrational Transitional Density Cubes. The firstorder vibrational transition (charge) density cubes (VTDCs) describes how the electron density of a molecule changes with respect to its vibrational motion,46,47 which can be used to reveal the delocalization extent of vibrational modes. The firstorder VTDC for the ath mode on a given molecule can be calculated as46 P(δQ a) − P( −δQ a) ∂P = ∂Q a 2δQ a B

(3) DOI: 10.1021/acs.jpcb.5b08070 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B where P is the electronic density cube, Qa is the normal coordinate of the ath mode. Geometric optimization and frequency analysis were performed to obtain the equilibrium structure and normal coordinates. Then the equilibrium coordinate was varied by two small steps (δQa and −δQa) separately, and the electro density cube P(δQa) and P(−δQa) at the two new structures were computed. VTDC was then calculated using eq 3. In this work, the vibrational step was set to 0.01 Å anu1/2 for the amide-II normal modes. The electronic density cubes were computed using Multiwfn.48 The VTDCs are created on grids with 100 points on each side of electronic density cube. Additionally, the delocalization of the amide-II normal-mode was evaluated using the potential energy distribution (PED).49

complex due to additional mixed-helical interamide interaction. Clearly, dramatic differences in the amide-II band are seen for these five helices, suggesting a structural sensitivity of this mode. Such spectral characteristics remain to be consistent as the chain-length increases. Systematic variations of band intensity and band positions are seen in a chain-length-dependent calculation (Figure 2 left panel). As the chain length increases, band intensity generally increases due to increased number of amide units; band position generally blue shifts due to increased number of hydrogen bonds. Here, in the frequency domain the high-frequency side is the “blue-end”, whereas the low-frequency side is the “red-end”. However, because the conformation and hydrogen-bonding interaction vary from case to case in the helical β-peptides, the IR absorption transition frequency and its distribution exhibit conformational dependence. It is also interesting to see that for amide-II bands, the frequency position of the high-frequency component in the 8H conformation is the highest among the five helices, and that in 14H is the lowest. However, the peak position of the amide-I band in the 8H conformation is the lowest among the five helices, and that of 14H is the highest (Figure S1 in Supporting Information, SI). This reflects a well-known phenomenon (e.g., in a model α-peptide29) that the amide-II and amide-I vibrational frequencies are anticorrelated. A simple explanation is as follows. The amide-II vibration partially contains the C−N stretching, whereas the amide-I vibration mainly contains the CO stretching. Once a hydrogen-bond is formed on the C O side, its bond length will increase, and the amide-I frequency will be lowered; at the same time, the bond length of the C−N will decrease so as to cause an increase in the amide-II frequency. Such an anticorrelated bond length and frequency of the amide-I and II modes are given in Figure S2 of the SI. The anticorrelated vibrational frequency of the amide-II and -I modes shows a similar behavior of the amide group in βpeptides and in α-peptides. Note that because the amide-II mode also contains significant contribution of the N−H inplane bending. A hydrogen-bonded NH group will also have an increased amide-II frequency (Figure S2 of the SI). More discussion on the amide-II frequency and its influencing factors are given in a later section. Localization of the Amide-II Modes. To dissect the IR signature of the computed normal-mode spectra of these heptamers in various conformations, we carried out the VTDC calculation. VTDCs visually quantify atomic charge redistribution during a specific normal-mode vibration. Thus, the VTDCs can serve as a measure of vibrational delocalization, playing a similar role as the well-known potential energy distributions,14 but showing the mode delocalization in a straightforward three-dimensional visualization. The results of VTDC are given in Figure 3. Only the results of representative modes (a typically localized mode, one or two typically delocalized modes) are shown. The frequency positions of these modes are marked in Figure 2. A complete plot of the VTDCs in each heptameric conformation is given in Figure S3 of the SI. From Figure 3, it can be seen that first, in all cases, the highfrequency absorption bands are mainly the vibrations of the amide-II modes with amino hydrogen atoms participating in the formation of hydrogen bonds, whereas the low-frequency band are mainly the vibrations of the amide-II modes with hydrogen atoms free of hydrogen bonds. Note that for a given

III. RESULTS AND DISCUSSION Amide-II Absorption Characteristics. The simulated amide-II IR spectra of the five different helical conformations with varying chain length are shown in Figure 2 (left panel).

Figure 2. (Left) Simulated amide-II normal-mode IR spectra of βpeptide heptamer in five helical conformations. Conformation and chain-length dependences are shown. (Right) Computed normalmode transition intensities versus frequencies for heptamers in sticks, with picked-out modes marked (*) for VTDC analysis. Dashed line indicates average transition intensity in each case, while dotted line indicates the transition intensity of NEPA (219.8 km/mol).

Take the spectra of heptamers in the 8H, 10H, and 12H conformations for example, there are mainly two separated absorption bands. For the 14H conformation, a seemingly structure-less IR spectrum is predicted, whose behavior is consistent in the chain-length-dependent computation. For the 10/12H conformation, the IR absorption profile exhibits features alike those from 10H (two closely located peaks) and 12H (two further separated peaks) but appear to be more C

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Figure 3. Computed VTDCs of the representative amide-II modes (with vibrational frequency given in cm−1) in each helical conformation. The modes are marked in Figure 2. Color code for VTDCs: magenta for positive and cyan for negative charge variations. Color code for structures: amide oxygen atoms are in red, hydrogen atoms are in light gray, nitrogen atoms are in blue, and backbone carbon atoms are in gray. The N-terminus is at the bottom.

(1622.5 cm−1 for 8H, 1584.7 cm−1 for 10H, and 1609.9 cm−1 for 12H). Transition Intensity of the Amide-II Modes. The amideII normal-mode transition intensities from tetrameric to heptameric β-helices were computed, and the results of heptamers are compared with the monopeptide case (NEPA) in Figure 2 (right panel). First of all, the average transition intensity in the case of 10H is higher than that of NEPA, whereas those of the remainders are lower, and in certain cases significantly lower, than that of NEPA. The average intensity as a function of chain length and its comparison with that of NEPA is given in Figure S4 of the SI. These results suggest that amide-II intensity of β-peptides is conformation dependent. An interesting connection between a conformational-dependent interpeptide charge flux (similar to the VTDC defined in this work) through hydrogen bond and an enhanced amide-II transition intensity has been established recently in α-peptide oligomers.50 The enhancement was found to be structural dependent; for example, it presents in the C5 (β-strand) conformation but not in C7 (intramolecular hydrogen-bonded) conformation, due to the geometrical relation between the dipole derivative induced by the interpeptide interaction with respect to the intrinsic transition dipole derivative of the amideII mode.50 As discussed in the work, such a finding is significant because experimentally it was observed that the amide-II/ amide-I intensity ratio is higher in β-sheets than in α− helices.51,52 Thus, a similar enhancement behavior in certain βhelices (particularly 10H) is of significance. However, to visualize the net charge flux, charge density difference between a peptide oligomer and peptide monomer has to be considered, which is beyond the scope of this work. Nevertheless, the computed overall intensity enhancing in 10H conformation (as well as an overall intensity diminishing in other conformations) can be explained by the proposed charge flux effect.50 Local-Mode Frequencies of the Amide-II Modes. After decoupling the amide-II normal modes, the local-mode vibrational frequencies and couplings were obtained. This allows one to examine the chemical environment effect on the amide-II vibrational frequency. The results of local-mode

amide unit, the amide-II frequency is also moderately blueshifted when its CO group forms hydrogen bond with the N−H group from a neighboring amide. When such a hydrogen bond is formed, the C−N bond-order decreases and its stretching frequency increases, leading to the blue-shift of the amide-II mode. For the 8H conformation, there is only one amide group on the acetyl side that does not form hydrogen bond with its NH group, which is the reason for the only one low-frequency transition shown in Figure 2f. This transition is highly localized on the acetyl amide unit, which can be seen clearly from its VTDC profile (Figure 3, 1554.9 cm−1 mode). However, for the 10H and 12H conformations, there are two amide-II modes in the low-frequency absorption band. From the VTDCs, it is clear that for 10H conformations, the two low-frequency modes are mainly the vibrations of the two amide units on the NHmethyl side. One of which, with frequency of 1565.8 cm−1, is localized on the second amide unit (Figure 3). For the 12H conformation, the two low-frequency modes are mainly the vibrations of the two amide units on the acetyl side (one of them is the 1568.7 cm−1 mode). For the 14H conformation, there is no obvious grouping in the stick transitions in Figure 2i; however, there are three major components in the amide-II frequency region. Similar to the 10H conformation, the three low-frequency modes are mainly the vibrations of the amide units on the NH-methyl side (for example, the 1545.8 cm−1 mode). Other modes, being mostly delocalized, are the vibrations of the amide units on the acetyl side (for example, the 1581.7 cm−1 mode). For the 10/12H conformation, the stick transitions are generally divided into three groups, so there are three obvious separated absorption peaks in Figure 2j. From its VTDCs, one sees that the amide-II modes are highly localized in this conformation, and each normal mode mainly contain one amide group vibration. Three examples are given in Figure 3, which are the 1564.7, 1605.4, and 1624.5 cm−1 modes. In addition, the high-frequency amide-II component observed in the 8H, 10H, and 12H conformations, are moderately delocalized. One example is given for each case in Figure 3 D

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that a hydrogen-bonded NH will have a restrained geometry, a strained bending force constant, and an increased N−H bond length (Figure S2 of the SI), which will cause a blue shift to the amide-II modes. This further explains why the amide units with free NH groups would have a lowered local-mode frequency (Figure 4). Further, for a given amide unit, if both its oxygen and hydrogen atoms participate in hydrogen bonds, the amide-II local-mode frequency will further increase. On the contrary, its amide-I local-mode frequency will decrease.34 Take the 10/12H conformation as one example, for the fourth amide group, both oxygen and hydrogen atoms are involved in a 12-membered hydrogen-bonding ring, whereas for the sixth amide group, only hydrogen atom is involved in a 12-membered hydrogenbonding ring. This causes the amide-II local-mode frequency of the fourth amide group to be higher than that of the sixth amide group. This phenomenon can also be seen in the homogeneous helical conformation (8H, 10H, 12H, and 14H). Coupling Constants for the Amide-II Modes. Vibrational couplings are very important interamide interaction terms that link the local modes together to form a normalmode picture. The WFD couplings of the amide-II modes in the five helical conformations are given in Figure 5. The results using the N−H in-plane bending and C−N stretching local modes are computed separately and are shown in Figure 5 for comparison. It is convenient to denote pairwise coupling in terms of βi,i+n, for the ith and (i+n)th amide units. Overall, the magnitude and sign of the couplings for the local amide-II

frequency are given in Figure 4. It is seen that the local-mode frequencies of the amide-II modes whose amide NH are

Figure 4. Local-mode frequencies of the amide-II modes of the five helical β-peptide conformations. Amide-unit number n is numbered from the N-terminus to C-terminus.

hydrogen bonded are generally higher for those whose amide NH are not hydrogen bonded (see Figure 1). For example, in the 8H conformation, except one amide group on the acetyl side whose hydrogen atom is free of hydrogen bond, all the remainder’s local-mode frequency are far higher than that mode. In the 10H conformation, starting from the N-terminus, the amide groups have their NH groups form hydrogen bonds with amide CO groups so their amide-II local-mode frequencies are higher, except the last two amide groups on the NH-methyl side. In the 12H conformation, the two amide groups on the acetyl end are free from hydrogen bonds, so their amide-II frequencies are lower than those who are hydrogen-bonded. In the 10/12H conformation, there are two types of hydrogen bonds involved in this hybrid structure, so the local-mode picture is somewhat complicated. However, in general, the local-mode picture of the 10/12H exhibits the feature of a combined 10H and 12H: both peptide ends have a lowfrequency site. These low-frequency modes are due to amide groups (namely, the second and seventh) whose hydrogen atoms are not involved in hydrogen bond. In addition, the local amide-II mode frequencies of the amide groups forming the 12membered hydrogen bond ring are generally lower than those of amide groups in the 10-membered ring. For example, the fourth amide unit that forms a 12-membered ring is lower in frequency than both the third and fifth amide units that each forms a 10-membered ring. The dependence of the amide-II frequency on the hydrogen bond of the NH group is closely related to the N−H in-plane bending contribution to the amide-II mode. It is conceivable

Figure 5. Pair-wise WFD coupling constants among the amide-II local modes of the five helical β-peptide conformations. Black: βi,i+1; red: βi,i+2; green: βi,i+3; blue: βi,i+4; magenta: βi,i+5; cyan: βi,i+6. The values of βi,i+n are listed starting from the acetyl end. The dotted line indicates zero coupling. HB denotes hydrogen-bonded amide pairs. Solid dots: using the N−H bending as reduced amide-II local coordinate; hollow dots: using the C−N stretching as reduced amide-II local coordinate. E

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The Journal of Physical Chemistry B modes are conformational dependent. Furthermore, the results using the N−H in-plane bending and C−N stretching local modes are in reasonable agreement (except a few nearest neighboring couplings in the 10/12H conformation), showing that both can be used to assess the coupling. As the interamide separation increases, the pairwise coupling gradually decreases. The couplings are strong and negative in most cases, only being weakly positive in certain cases. Significant coupling terms are found to be between the nearest-neighbored and also the nextnearest-neighbored amide pairs. Figure 5 shows that the nearest neighbor couplings (βi,i+1) are the strongest in each helix except 10H. In the 10H conformation, the next nearest neighbored couplings (βi,i+2) are the strongest instead. It is likely that this is due to hydrogen-bonding interactions between the next nearest amide pairs, which favors both transition dipole interaction (through space) and also through-bond interaction. In the 10/ 12H hybrid conformation, βi,i+1 varies more or less periodically along the peptide chain, because the backbone dihedral angle varies periodically for the two nearest amide groups along the peptide chain. A much better structure−coupling correlation was observed in the amide-I coupling for the same hybrid conformation.34 To further understand the origin of the amide-II coupling, we first compute the transition dipole coupling (TDC),14,34 which is the through-space contribution of the total vibrational coupling (i.e., the WFD coupling), using the following equation: ⎯⇀ ⎯ ⎯⇀ ⎯

βij =

1 μi ·μj − · 4π ·ε0

Figure 6. Absolute value of averaged coupling constants as the function of the distance between pairwise C−N bond central points (r). Black dashed line is obtained by a simplified TDC modeling (see text for details).

⎯ ⎯ ⇀ ⎯⇀ ⇀ ⎯⇀ 3(nij ·μi )(nij ·μj )

rij3

(4)

where ε0 is the dielectric constant (set to 1 for gas phase), μi is the transition dipole of the ith amide-II mode, nij is the unit vector connecting the ith and jth transition dipole centers, and rij is the distance between the ith and jth transition dipole centers (see Table S1 in the SI). Here the value of the transition dipole was set to 2.4 D·Å−1·amu−1/2, and the direction of the dipole is 17° with respect to the C−N bond direction (pointing from C to N). These parameters were obtained by a DFT calculation at the level of B3LYP/6-31+G*, using an isolated single β-peptide (NEPA). For the local amideII modes, the direction of the transition dipole moment was almost parallel to the direction of the C−N bond in the amide unit of an isolated α-peptide amide unit.29 The absolute values of the computed TDC are shown in Figure 6 (black dot). The results of the WFD couplings are also shown in Figure 6 (red dot) for comparison. Here we simply assume that the transition dipole centers at the middle point of the C−N bond. Besides this strict TDC scheme, a simplified TDC modeling is also applied, in which two parallel C−N bonds in a plane are separated by a varying distance r. Assuming the transition dipole is also along the C−N bond and pointing from C to N, the TDC is computed and also shown in Figure 6 (dashed line). This simple computation illustrates a reverse cubicdistance dependence of the TDC in an ideal case. Generally, the WFD and two TDC results agree with one another at medium to long distances. A nearly perfect situation is shown in the case of the 8H conformation. However, significant variation between WFD and two TDC results appear at shorter distance. Their difference indicates the contribution of through-bond coupling. At r ≤ 6 Å, large deviation between TDC and WFD begins to show. A representative example is the 10H conformation. In addition, in the case of 10H

conformation, the nearest neighbor TDC agreeing reasonably with the total coupling (WFD) suggests that the through-bond contribution is almost negligible. For the rest cases shown in Figure 6, the TDC values more or less follow the trend of WFD values, also suggesting an insignificant through-bond contribution. Further, the simplified TDC results show a rough fit to both the WFD and strict TDC results, for the 8H conformation in particular, indicating an insignificant angular dependence of the coupling in this case. For the remaining conformations, acceptable fitting is seen at long distances. This result can be understood easily because in the 8H conformation, the interamide distance is generally larger than others (see Figure 1, and also Table S1 of SI). Also, in the TDC scheme, at longer distance, the coupling becomes smaller, and the angular factor naturally becomes less important. How strong are the amide-II intermode couplings? As shown above, the couplings between the nearest neighbor amide units are the strongest except the 10H conformation, indicating an insignificant impact of the hydrogen bond on the coupling in amide-II modes. This differs from the situation of the amide-I modes. Our recent work has shown that for amide-I modes, the couplings between the amide groups connected by hydrogen bonds are always the strongest in the same set of helical βpeptides.34 Structural and Spectral Relationship. The local-mode frequencies and intermode couplings are important factors determining the band structure of the amide-II IR absorption spectra. Due to the variation of local-mode frequencies and interamide couplings, the IR spectra of the amide-II modes are conformational dependent. In the β-peptides, the amide units are generally divided into two types: the amino hydrogen atom forms hydrogen bond, or not. The averaged local-mode F

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NH group is hydrogen-bonded or not. This is different from the case of the amide-I modes, where the couplings between the amide units forming hydrogen bonds are the strongest. This is because the amide-I mode is mostly CO stretching, which is of course sensitive to whether the CO group involves a hydrogen bond or not. The couplings obtained by the TDC model are generally follow the trend of the WFD values at medium to long distances, suggesting a significant throughspace contribution. In addition, for the 8H, 10H, and 10/12H conformations, the couplings obtained by the WFD method show a rough fit to a simplified TDC scheme without angular factor, indicating an insignificant angular dependence of the coupling. Nevertheless, because of the intramolecular hydrogen-bonding interactions, the local-mode frequencies and intermode coupling exhibit conformational dependences, which are the reasons for different helices to show different amide-II spectra. In summary, because of the unique conformations and structural stabilities of β-peptides, it is very critical to understand their structural and spectral relationship using a structural sensitive method such as linear and/or nonlinear infrared spectroscopy. The basis structural and spectroscopic parameters derived from this work shall allow one to use the amide-II mode as a structural probe for the β-peptides. This work paves the way toward further understanding the amide-II spectra of β-peptides in various conformations. Future work may include solvent effect on the amide-II vibrational properties, which can be done by using implicit (PCM solvent model),53 or even by introducing explicit solvent layers. It should be pointed out that the implicit solvent model does not take into account solvent−solute hydrogen bonding interactions. The effect of solvent is realized through the change of dielectric constant. However, intramolecularly hydrogenbond free amide unit can form hydrogen bond with solvent molecules. This may change the local-mode picture quite substantially. In addition, in explicit solvent environment, solute−solvent interaction will change a perfect helix into an imperfect one, which will also change the amide-II local-mode structure. This effect can be accounted for using solute−solvent clusters extracted from, for example, molecular dynamics simulations. Further, frequency maps for the amide-II vibration in β-peptides, like those developed for the amide-I modes, shall be developed in order to quickly predict local-mode frequencies for a sizable β-peptide in a given conformation.

frequency difference between the two type amide-II modes is about 46, 25, 40, 22 cm−1 in the 8H, 10H, 12H, and 14H structures, respectively. The value is the largest in the 8H conformation, which is the main reason that the frequency difference of the two absorption peaks shown in Figure 2a is the largest (ca. 67 cm−1). On the contrary, the averaged frequency difference in the 14H conformation is the smallest, while the couplings in this conformation are also relatively small (Figure 5d), which is why this conformation shows a basically structureless IR spectrum (Figure 2d). For the 10/12H conformation, there are two types of hydrogen bonds involved in the amide units: with both the carbonyl oxygen and amino hydrogen atoms forming hydrogen-bonded ring, or with only amino hydrogen atom forming 10- or 12-membered hydrogen-bonded ring. The high-frequency groups are due to the amide units with both the carbonyl oxygen atom and amino hydrogen atom forming the 10-membered hydrogen bonds. The middle groups are due to those with only amino hydrogen atom forming the 10- or 12-membered hydrogen bonds. Although the lowestfrequency groups are mainly due to the amide units with amino hydrogen atom having no hydrogen bond. The distributed local-mode frequency is the main reason for the multipeak normal-mode picture of this hybrid conformation. On the basis of these discussions, one can safely conclude that because of the intramolecular hydrogen-bonding interactions, the local-mode frequencies and intermode coupling exhibit conformational dependences.

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SUMMARY AND OUTLOOK In this work, the vibrational properties of the amide-II band in five heptameric β-peptide helical conformations were examined. It was found that the amide-II modes are conformational dependent. The normal-mode picture shows that amide-II modes are divided into two groups of bands in 8-, 10-, and 12helical conformations because of local-mode frequency distributions and vibrational couplings. Substantial transition intensity variation was predicted for the amide-II band for certain conformations (for example, enhancement in 10H and diminishment in 8H), due to conformation-induced vibrational transition density charge flux, agreeing with what was observed previously in α-peptide oligomers.50 The localization and delocalization of the amide-II modes can be effectively viewed by the vibrational transition charge density presentations. The low-frequency modes are generally localized because of free NH groups in the terminal amide units, which may occur on the acetyl end or on the NH-methyl end, depending on the helical conformation. The highfrequency modes, on the other hand, are generally delocalized mainly due to intramolecular hydrogen-bonding connections. The local-mode frequencies and intermode couplings for the amide-II modes were also analyzed. The amide-II local-mode frequencies of the amide units in the terminal region are generally lower than those in the middle, when the terminal amide hydrogen atoms form no hydrogen bond. The couplings between the nearest neighbor amide units are the strongest in the helices considered in this work except the 10H conformation. This suggests that hydrogen-bonding interaction is not a determining factor for the coupling strength of the amide-II modes. The insensitivity of the amide-II coupling to the NH hydrogen bonding is mainly because the amide-II mode also involves a significant portion the C−N stretching motion (PED = 0.22), which is not too sensitive to whether the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b08070. Additional data including complete IR spectra simulated in the amide-II and amide-I frequency region; normalmode VTDCs for five β-peptide helices; correlations between the local-mode frequencies and bond lengths; interamide distances using C−N bond middle point; and computed average amide-II normal-mode transition intensity for β-peptide helices (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (+86)-010-62656806. Fax: (+86)-010-62563167. G

DOI: 10.1021/acs.jpcb.5b08070 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Nature Science Foundation of China (21173231 and 91121021), and by the Chinese Academy of Sciences (Hundred Talent Program).

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