Toward Detecting the Formation of a Single Helical Turn by 2D IR

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J. Phys. Chem. B 2009, 113, 11775–11786

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Toward Detecting the Formation of a Single Helical Turn by 2D IR Cross Peaks between the Amide-I and -II Modes Hiroaki Maekawa,† Matteo De Poli,‡ Alessandro Moretto,‡ Claudio Toniolo,‡ and Nien-Hui Ge*,† Department of Chemistry, UniVersity of California at IrVine, IrVine, California 92697-2025, and Institute of Biomolecular Chemistry, CNR, PadoVa Unit, Department of Chemistry, UniVersity of PadoVa, 35131 PadoVa, Italy ReceiVed: May 16, 2009; ReVised Manuscript ReceiVed: July 7, 2009

We have combined two-dimensional infrared (2D IR) spectroscopy and isotope substitutions to reveal the vibrational couplings between a pair of amide-I and -II modes that are several residues away but directly connected through a hydrogen bond in a helical peptide. This strategy is demonstrated on a 310-helical hexapeptide, Z-Aib-L-Leu-(Aib)2-Gly-Aib-OtBu, and its 13Cd18O-Leu monolabeled and 13Cd18O-Leu/15NGly bis-labeled isotopomers in CDCl3. The isotope-dependent amide-I/II cross peaks clearly show that the second and fourth peptide linkages are vibrationally coupled as they are in proximity, forming a 310-helical turn. The experimental spectra are compared to simulations based on a vibrational exciton Hamiltonian model that fully takes into account the amide-I and -II modes. The amide-II local mode frequency is evaluated by a new model based on the effects of hydrogen-bond geometry and sites. Ab initio nearest-neighbor coupling maps of the amide-I/I, -I/II, -II/I and -II/II modes are generated by isotopically isolating the local modes of N-acetyl-glycine N′-methylamide (AcGlyNHMe). Longer range couplings are modeled by transition charge interactions. The effects of the capping groups are incorporated and isotope effects are analyzed based on ab initio calculations of six model compounds. The main features of the 2D IR spectra are reproduced by this modeling. The conformational sensitivity of the isotope-dependent amide-I/II cross peaks is discussed in comparison with the calculated spectra for a semiextended structure. Our experimental and theoretical study demonstrates that the combination of 2D IR and 13Cd18O/15N labeling is a useful structural method for detecting helical turn formation with residue-level specificity. I. Introduction Vibrational couplings between the amide modes are fundamental properties keenly dependent on polypeptide structure. The capability of probing vibrational couplings in a site-specific manner with an ultrafast time resolution will be very useful for elucidating the structure evolution during the earliest steps of protein folding. For instance, transient formation of a single helical turn has been proposed as an intermediate step in the helix folding process and requires experimental verification. To fully understand these processes, it is essential to have in hand ultrafast experimental techniques that are capable of detecting couplings between residues that are brought into spatial proximity by intramolecular hydrogen bonds, and distinguishing them from the case of little/no couplings when the conformation is extended. The 2D IR spectroscopy, with its intrinsic picosecond time resolution and high sensitivity to vibrational couplings, is very promising for fulfilling this need. Its applications to the amide-I modes have demonstrated that it is a powerful probe of peptide structures.1–5 We have also recently demonstrated that 2D IR spectral patterns of the unlabeled amide-I mode can reveal the subtle differences in peptide helicity.6–9 The secondary structure sensitivity illustrated in these studies is impressive, but information on local peptide structure is not available because all amide-I local modes contribute to the response of the excitonic states. This difficulty can be circumvented by isotope substitu* To whom correspondence should be addressed. E-mail: [email protected]. Phone: 949-824-1263. Fax: 949-824-8571. † University of California at Irvine. ‡ University of Padova.

tion with amide 13Cd16O or 13Cd18O groups. The 13Cd18O labeling is particularly attractive because it shifts the local amide-I mode frequency by ∼65 cm-1,10 making it possible to fully isolate the labeled amide-I mode from the others. Recent 2D IR studies of isotope-edited amide-I modes have focused on the investigation vibrational couplings within a single helix,11 a hairpin,12,13 amyloid peptides,14,15 between helical dimers,16 and local structure fluctuations.17–20 Expanding the combination of 2D IR spectroscopy and isotope labeling beyond the amide-I to other amide modes can provide unique information. Our strategy21 is to probe the vibrational couplings between the 13Cd18O-labeled amide-I mode and 15N-labeled amide-II mode that are several residues awaybutdirectlyconnectedthroughanintramolecularCdO · · · H-N hydrogen bond. The amide-II mode, mostly composed of the out-of-phase N-H in-plane bending and C-N stretching,22 is a suitable reporter. N-Methylacetamide (NMA) embedded in nitrogen matrix exhibits a 13-15 cm-1 red shift in the amideII frequency upon 15N substitution.23 Comparing to the typical line width of ∼30 cm-1, the sizable isotope shift would allow one to distinguish the labeled amide-II mode from the unlabeled. Although the amide-A mode, predominately N-H stretching, is a more intuitive candidate for the study of isotope substitution, it is impossible to replace the hydrogen atom with deuterium in a site-specific manner. Moreover, the amide-A frequency shift due to 15N labeling is very small (∼8 cm-1)23 compared to the line width of the hydrogen-bonded N-H band (100-300 cm-1), and thus this mode is not a good reporter for local structure information.

10.1021/jp9045879 CCC: $40.75  2009 American Chemical Society Published on Web 07/30/2009

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Figure 1. Molecular formula of the hexapeptides in this study. The carbonyl carbon and oxygen atoms of Leu are isotope labeled with 13 Cd18O in 1* and 1**, and are colored red. The nitrogen atom of Gly is isotope labeled with 15N in 1**, and is colored blue. The ideal 310helical conformation of the peptide is also shown in which the isotope labeled atoms are colored green. The four dashed lines represent intramolecular CdO · · · H-N hydrogen bonds.

As a proof-of-concept study, we focus on a model system of 310-helical peptides. The 310-helix attracts increasing attention because of its essential roles in several dynamical processes. For instance, theoretical studies suggested that picosecond transformation between 310- and R-helix is an intermediate pathway in the helix-coil transition.24 Also, the 310-helical motif is specific and required in some enzymatic reactions.25 The ability to detect the formation of a single helical turn is thus important for studying these processes in detail. Here we report linear and 2D IR spectra of a terminally protected hexapeptide and its isotopomers (Figure 1): unlabeled Z-Aib-L-Leu-(Aib)2-Gly-Aib-OtBu (1, Z, benzyloxycarbonyl; Aib, R-aminoisobutyric acid; OtBu, tert-butoxy), monolabeled peptide with 13Cd18O at the Leu residue (1*), and bis-labeled peptide with 13Cd18O at the Leu residue and 15N at the Gly residue (1**). It is well-known that short peptides with a high fraction of Aib residues tend to form 310-helices.26,27 Following this design principle, we have confirmed that these peptides adopt the 310-helical conformation in CDCl3 based on the characteristic 2D IR doublet cross-peak pattern in the amide-I region measured for 1.21 For the 310-helix, the intramolecular CdO · · · H-N hydrogen-bonding pattern is between i and (i+3)th residues, whereas it is between i and (i+4)th residues for R-helix.27 Therefore, the CdO group of the second peptide linkage in this 310-helical hexapeptide will be hydrogen-bonded with the N-H group of the fourth peptide linkage (the N-terminal Z-Aib is a urethane, not a peptide linkage). The vibrational couplings between them will be revealed by measuring 2D IR cross peaks and their isotope-dependency as we place the 13Cd18O label on the second peptide linkage and the 15N label on the fourth peptide linkage. A preliminary report on some of the experimental results has recently appeared.21 Here we present the complete set of 2D IR spectra that covers the full frequency range for the unlabeled and labeled amide-I and -II modes. Comparing to the many studies focusing on the amide-I mode, the amide-II mode is much less explored both experimentally and theoretically. Only a few recent 2D IR experiments investigated the cross peaks between the amide-I and amide-II modes in NMA,28,29 N-acetyl-L-prolineamide,30,31 and poly-Llysine.32 Theoretical modeling and calculation have been only reported for NMA and small peptides.31,33–35 To interpret our experimental data, we expand the vibrational exciton Hamiltonian model to simulate the full 2D IR spectra including both

Maekawa et al. the amide-I and amide-II modes. The detailed protocol to calculate the amide-I spectra has already been described in our previous studies.7,8 Here we present a new model for the amideII local mode frequencies based on hydrogen-bond formation energy, devise a new method for calculating the nearest-neighbor coupling maps, and create the coupling maps for the amide-I/I, -I/II, -II/I, and -II/II couplings of N-acetyl-glycine N′-methylamide (AcGlyNHMe). The effects of the capping groups are incorporated, and isotope effects are analyzed. We simulate the amide-I/II 2D IR spectra of an ideal 310-helical structure with the average dihedral angles centered at (φ, ψ) ) (-57°, -30°)27 and a semiextended structure with (-78°, 146°),36 and investigate the conformational sensitivity of the isotope-dependent amide-I/II cross peaks. The assignment of the amide-II band and the strength and conformational sensitivity of the amideII/II couplings are also discussed. II. Experimental Section A. Materials. The syntheses and characterizations of 1, 1*, and 1** have been described previously.21,37 In brief, 1-13C labeled L-Leu (Cambridge Isotope Laboratory, 99%) and 15Nlabeled Gly (CIL, 98%) were used to introduce the 13C and 15N label at the specific positions of the hexapeptides. The carbonyl oxygen atom of 13C-labeled Leu was exchanged with 18O using H218O (CIL, 97%).38 Mass spectrometry showed that 85% of the 13C L-Leu molecules are doubly 18O labeled, while 15% of them remained singly labeled. To measure the vibrational bands from the capping Z and OtBu moieties, Z-Aib-OtBu39 was synthesized and characterized. We also synthesized iPrCO-GlyOtBu (iPrCO, isobutanoyl) and iPrCO-15N-Gly-OtBu to experimentally determine the isotope shift of the amide-II mode due to 15N labeling. iPrCO-15N-Gly-OtBu was synthesized from iPrCOOH and H-15N-Gly-OtBu using 1-(3-dimethylamino)propyl-3-ethylcarbodiimide in the presence of N,N-diisopropyl-Nethylamine and purified by flash chromatography (eluant, 4:6 ethyl acetate/petroleum ether). Yield: 65%. Oil. TLC (7:1 toluene/ethanol): 0.70. IR (CDCl3, 1 mM): 3454, 3424, 1732, 1708, 1668, 1628 cm-1. 1H NMR (CDCl3; 250 MHz): δ (ppm) 6.07 (1H, br s, NH), 3.89 (2H, d, Gly RCH2), 2.40 (1H, m, iPr CH), 1.44 (9H, s, OtBu 3 CH3), 1.14 (6H, m, iPr 2 CH3). When preparing peptide solutions for linear and 2D IR measurements, each peptide was dissolved in CDCl3 (CIL, 99.96 atom % D) with a concentration of ∼5 mM. The solution was held in a 250 µm thick sample cell. B. Linear and 2D IR Measurements. Linear IR spectra of the peptide solutions and neat CDCl3 were recorded using a purged FT IR spectrometer (Perkin-Elmer, Spectrum 2000) with a resolution of 4 cm-1. After subtraction of the solvent spectrum, the spectrum of 1 exhibits the unlabeled amide-I band at around 1666 cm-1 and the amide-II bands at 1480-1560 cm-1 with maximum absorbance of ∼0.25 and ∼0.15, respectively. The 2D IR measurements of the hexapeptides in CDCl3 were conducted using our home-built IR spectral interferometry setup. The details of the setup and the data processing procedure have been described in the previous studies.6–8,31 The center frequency of IR pulses was tuned to ∼1600 cm-1 to excite all of the unlabeled and labeled amide-I and -II modes and observe their cross peaks. We also conducted 2D IR measurements with the IR frequency centered at ∼1550 cm-1 to more clearly investigate cross peaks between the labeled 13Cd18O amide-I mode and the amide-II modes. In this study, the perpendicular polarization configuration, 〈YYZZ〉, was used. To collect rephasing (R) and nonrephasing (NR) spectra, the delay time τ between the first and second incident pulses was scanned from 0 to ∼2.9 ps and

Detecting the Formation of a Single Helical Turn

Figure 2. (a) Measured FT IR spectra of Z-Aib-OtBu (black dashed), 1 (black solid), 1* (red), and 1** (blue) in CDCl3. Each spectrum is normalized by the peak intensity of the urethane/ester CdO band at ∼1716 cm-1 after subtraction of the background spectrum of neat CDCl3. (b) Linear IR spectra simulated for the unlabeled (black), monolabeled (red), and bis-labeled (blue) hexapeptides forming an ideal 310-helix with the average dihedral angles (φ, ψ) ) (-57°, -30°) and the standard deviations σφ ) σψ ) 9.5°. Measured (c) and simulated (d) difference spectra between 1* and 1, 1** and 1, and 1** and 1* in the amide-II frequency region.

0 to ∼2.5 ps, respectively, with a step of 9 fs. Nonresonant solvent response was utilized to find the time zero between the three pulses, and its effects were minimized by setting the waiting time T between the second and third pulses to 200 fs during the data collection of the 2D IR spectra. Spectral interferograms were collected and processed to give data in the ωt-dimension. All of spectral measurements were conducted at ambient temperature (20 ( 1 °C). III. Results A. Linear IR Spectra and Peak Assignments. Figure 2a shows the FT IR spectra of hexapeptides and Z-Aib-OtBu in CDCl3. The spectra have been normalized by the peak intensity of the urethane/ester CdO band at ∼1716 cm-1. The terminally protected mono Aib compound has no peptide bond, and it has the same urethane and ester motifs as those of the hexapeptides. Therefore its spectrum is used to assign the bands originating from the capping groups and to check whether they interfere with the amide-I and -II bands of 1, 1*, and 1**. Z-Aib-OtBu has a band at around 1720 cm-1. It is assignable to the unresolved urethane and ester CdO stretching modes.40 The band at 1505 cm-1 is due to a urethane vibrational mode that is amide-II like,41 and we will hereafter refer to it as the urethaneII mode. No other noticeable bands are present in the frequency region between the two bands. The unlabeled hexapeptide 1 exhibits the urethane/ester CdO band at 1716 cm-1 and the unlabeled amide-I band at 1666 cm-1. Roughly speaking, the two bands at 1528 cm-1 and 1498 cm-1 can be attributed to the vibrational exciton bands of the intramolecularly hydrogen-bonded amide-II modes and the free amide-II mode, respectively,21 with the latter being overlapped with the urethane-II mode. This assignment is based on the fact that the amide-II mode shows a blue frequency shift when the N-H and/or CdO group forms hydrogen bonds with other

J. Phys. Chem. B, Vol. 113, No. 34, 2009 11777 residues or solvent molecules,35,42 contrary to the red shift of the amide-I mode upon hydrogen bonding. If the hexapeptide forms a complete 310-helix, the amide N-H groups of the second to fifth peptide linkages will be involved in intramolecular CdO · · · H-N hydrogen bonds whereas the N-H group of the first peptide linkage is exposed to solvent. Our FT IR measurements of the 310-helical peptides, Z-(Aib)n-OtBu (n ) 2, 3, 5, 8 and 10), in CDCl3 support this picture.21 This series of spectra clearly shows that one broad peak appears at ∼1497 cm-1 for n ) 2, and a new band is observed at 1518 cm-1 for n ) 3. The latter band continues to blue shift by 15 cm-1 as the chain length increases up to n ) 10. Also, the integrated intensity of the high frequency band becomes higher with n. These features are consistent with the picture that the number of hydrogenbonded amide-II modes increases with the helical length, hence the high frequency band grows. The intensity ratio of the two amide-II bands in 1 is in-between those of the Z-(Aib)5-OtBu and Z-(Aib)8-OtBu, and thus is in agreement with the trend. The picture that the hexapeptide forms a 310-helix is also corroborated by the observation that the 2D IR cross-peak pattern of 1 exhibits a clear doublet in the amide-I region.21 The isotope labeled peptides 1* and 1** have very similar line shape to that of 1 in the frequency region higher than 1640 cm-1. The 13Cd18O substitution on Leu leads to a decrease in the intensity of the unlabeled amide-I band and the shifted band appears at ∼1598 cm-1. Its peak position is the same for 1* and 1**, independent of the 15N label on the Gly residue. The frequency shift by ∼68 cm-1 is close to the theoretically calculated value for a CdO harmonic oscillator. The labeled amide-I mode is fully isolated from the other modes. Other differences between the unlabeled and labeled peptides are found in the amide-II bands. The hydrogen-bonded amide-II band of 1* red shifts and is less resolved from the free amide-II band. With the addition of 15N-labeling, the higher frequency amideII band of 1** further red shifts by ∼4 cm-1 from that of 1*. To see the effects of isotope labeling more clearly, the difference spectra between two peptides were taken (Figure 2c). The difference between 1* and 1 shows increased and decreased absorbance at ∼1514 cm-1 and ∼1536 cm-1, respectively. Because the 13C- and 18O-labeled NMA exhibit, respectively, red frequency shifts of 15 and 9 cm-1 from the unlabeled NMA in gas phase,43 we can expect that the 13Cd18O-labeled Aib-LLeu local peptide unit will also exhibit a red shift which in turn results in an overall frequency shift of excitonic amide-II bands. Because the isotope substitution is on the second peptide linkage that involves an intramolecular hydrogen bonding, the major change is observed in the high frequency amide-II band. The spectral change between 1** and 1 is more complicated; one increased absorbance at ∼1517 cm-1 and two decreased absorbances at ∼1532 cm-1 and 1546 cm-1 are observed. Once again the major change is observed in the high frequency amideII band because the 15N-Gly substitution is on the fourth peptide linkage which is also involved in intramolecular hydrogen bonding. The difference spectrum between 1** and 1* reveals the complicated reorganization of the amide-II excitonic states upon 15N-labeling the fourth amide-II local mode. The two model compounds iPrCO-Gly-OtBu and iPrCO-15NGly-OtBu in CDCl3 exhibit a single peak of the amide-II mode at 1514 cm-1 and 1498 cm-1, respectively, but there is no difference in their peak positions for the amide-I mode (1669 cm-1) and the ester CdO stretching mode (1733 cm-1) (data not shown). Therefore, the 15N label decreases only the frequency of the amide-II mode by 16 cm-1 with no effects on the amide-I mode. This experimentally measured amide-II

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Figure 3. Absolute magnitude 2D R spectra of 1 (a), 1* (b), and 1** (c) in CDCl3 measured with the perpendicular polarization configuration and the IR pulses tuned to ∼1600 cm-1. Each experimental spectrum is plotted with 40 equally spaced lines after being normalized by the maximum intensity of the unlabeled amide-I band. Simulated spectra for the unlabeled (d), monolabeled (e), and bis-labeled (f) hexapeptides forming the ideal 310-helix structure with the average dihedral angles (φ, ψ) ) (-57°, -30°) and the standard deviations σφ ) σψ ) 9.5°. The same color scale is used to plot the simulated spectra in d-f, and the number of contour lines is increased to 80 to more clearly exhibit the weak cross peaks.

isotope shift will be utilized in our model calculation as described in section IV.A. B. 2D IR Spectra. Absolute magnitude 2D R and NR spectra collected with the IR pulses tuned to ∼1600 cm-1 are shown in Figures 3a-c and 4a-c, respectively. Because of the finite bandwidth of the IR pulses, the peaks near the center frequency are strongly enhanced. The R spectrum of 1 in Figure 3a exhibits a strong unlabeled amide-I peak (A), a urethane/ester CdO peak (B) and the amide-II peaks (C and D) on the diagonal, corresponding to the prominent features in its linear spectrum. The hydrogen-bonded amide-II band (C) at (ωt, -ωτ) ∼ 1520-1550 cm-1 appears to be formed by several components as implied from a weak shoulder on the higher frequency side of the diagonal line. This shoulder is only a hint in the linear IR at ∼1540 cm-1. Cross peaks between these components are evident. The free amide-II band (D) is a weak shoulder to the red side of the hydrogen-bonded amide-II band and cannot be resolved. We can see weak cross peaks between the amide-I and hydrogen-bonded II modes at ωt ) 1525 cm-1 (E) and 1548 cm-1 (F) along ωτ ) -1673 cm-1, but the cross peak between the amide-I and free amide-II modes is not discernible. For 1* and 1**, an additional peak, due to the 13Cd18O-labeled amide-I mode, appears on the diagonal. It is, however, hard to clearly discern whether cross peaks exist between this labeled amide-I mode and other amide-I or -II modes. On the contrary, NR spectra in Figure 4a-c manifest better resolved diagonal peaks and more distinct cross peaks than the R spectra. The NR sequence has higher resolving power due to destructive interference effects.31 The nonrephasing nature of this pulse sequence is particularly useful for line-narrowing cross peaks between anticorrelated vibrators,44 such as hydrogen-

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Figure 4. Absolute magnitude 2D NR spectra of 1 (a), 1* (b), and 1** (c) in CDCl3 measured with the perpendicular polarization configuration and the IR pulses tuned to ∼1600 cm-1. Simulated spectra for the unlabeled (d), monolabeled (e), and bis-labeled (f) hexapeptides. See the caption of Figure 3 for other details.

bonded amide-I and -II modes. For 1, many cross peaks among the unlabeled amide-I, amide-II and the capping CdO stretching modes are observed. The clear two cross peaks between the amide-I and -II modes at (ωt, ωτ) ) (1525, 1664) cm-1 (G) and (1549, 1660) cm-1 (H) implicate that the hydrogen-bonded amide-II band has two components, and each of them is coupled with the unlabeled amide-I modes. The free amide-II mode diagonal peak (I) now clearly appears at (ωt, ωτ) ) (1493, 1497) cm-1, and its cross peaks to the hydrogen-bonded amide-II modes and amide-I modes are also more clearly seen. We also observe the cross peaks that indicate the couplings between the urethane-II and urethane CdO stretching modes at (ωt, ωτ) ) (1496, 1711) cm-1. In the NR spectra of 1*, cross peaks between the 13Cd18O amide-I mode and the unlabeled amide-I or amideII modes are also easily observed. The cross peaks along ωτ ) 1598 cm-1 are indicative of the couplings between the labeled amide-I mode and amide-II modes in the hexapeptide. In the spectra of 1** in which the 15N label is incorporated, one of the significant differences from 1* is that the position of the cross peak between the 13Cd18O-labeled amide-I mode and hydrogen-bonded amide-II modes is slightly shifted to a lower frequency. Also, the intensity pattern of the diagonal and cross peaks in the amide-II frequency region changes upon 15N substitution. To focus on these important features, we investigate the spectra collected with the IR pulses tuned to center at ∼1550 cm-1 (Figures 5 and 6). The R spectrum of 1 in Figure 5a shows strong amide-II peaks with structured lobes, which could be assigned to the cross peaks between different amide-II exciton states. A subtle difference between the R spectrum of 1* and 1** (Figures 5b and 5c) is a slight shift of the strongest diagonal amide-II peak as well as the cross peak between the labeled amide-I and amide-II modes. As discussed earlier in comparing Figures 3 and 4, the NR spectra (Figure 6a-c) reveal cross peaks in this frequency region more clearly than the R spectra (Figure 5a-c). We can notice several cross peaks between the amide-II modes in the spectrum

Detecting the Formation of a Single Helical Turn

Figure 5. Absolute magnitude 2D R spectra of 1 (a), 1* (b), and 1** (c) in CDCl3 measured with the perpendicular polarization configuration and the IR pulses tuned to ∼1550 cm-1. Simulated spectra for the unlabeled (d), monolabeled (e), and bis-labeled (f) hexapeptides forming the ideal 310-helix structure with the average dihedral angles (φ, ψ) ) (-57°, -30°) and the standard deviations σφ ) σψ ) 9.5°. Each spectrum is plotted with 40 equally spaced lines after being normalized by the strongest peak intensity.

Figure 6. Absolute magnitude 2D NR spectra of 1 (a), 1* (b), and 1** (c) in CDCl3 measured with the perpendicular polarization configuration and the IR pulses tuned to ∼1550 cm-1. Simulated spectra for the unlabeled (d), monolabeled (e), and bis-labeled (f) 310-helical hexapeptides. See the caption of Figure 5 for other details. Horizontal slices of the experimental and simulated 2D spectra along the dashed line at ωτ ) 1598 cm-1 are shown in Figures 7a and 7b, respectively.

of 1, for example, at (ωt, ωτ) ) (1489, 1541) cm-1 (J) and (1544, 1531) cm-1 (Κ). The cross peaks between the labeled amide-I mode and amide-II modes are also clearly observed in the NR

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Figure 7. (a) Slices of the experimental absolute magnitude 2D NR spectra of 1 (black), 1* (red), and 1** (blue) along the horizontal dashed line at ωτ ) 1598 cm-1 in Figure 6a-c. (b) Slices of the simulated 2D NR spectra (Figure 6d-f) at ωτ ) 1598 cm-1 for the unlabeled (black), monolabeled (red), and bis-labeled (blue) hexapeptides forming the ideal 310-helix structure with the average dihedral angles (φ, ψ) ) (-57°, -30°). (c) Slices of the simulated 2D NR spectra (Figure 11b-d) at ωτ ) 1602 cm-1 for the unlabeled (black), monolabeled (red), and bislabeled (blue) hexapeptides forming the ideal semiextended conformation with the average angles (φ, ψ) ) (-78°, 146°). All 2D spectra were normalized by the strongest peak intensity of diagonal amide-II bands before slicing.

spectra of 1* and 1**. As shown by the vertical dashed lines in Figures 6b and 6c, the cross peak observed at (1527, 1598) cm-1 for 1* (L) is shifted to (1518, 1598) cm-1 for 1** (M), while the strongest amide-II diagonal peak position also red-shifted along ωt. The shift of the cross peak is represented in Figure 7a that shows slices of the NR spectra along ωτ ) 1598 cm-1 (indicated by the horizontal lines in Figure 6a-c). The slice of 1 (black line) has a peak at 1524 cm-1, coming from the vertically elongated lobe of the diagonal amide-II as seen in Figure 6a. The peak at ωt ∼ 1593 cm-1 in the slices of 1* and 1** is from the diagonal 13Cd18O labeled amide-I mode. The 1* and 1** traces in the region between 1500 and 1560 cm-1 are clearly different. The peak maxima of 1* and 1** in this region differ by 9 cm-1, and 1** has an additional peak at ωt ∼ 1541 cm-1. IV. Theoretical Calculations A. Vibrational Exciton Hamiltonian Model for Coupled Amide-I and -II Modes. In contrast to the vast efforts on developing simulation protocols for linear and 2D IR spectra of the amide-I mode,7,8,13,33,45–49 few studies have been done on the amide-II mode.33–35 It is quite useful to expand the capability of 2D IR spectroscopic techniques toward other modes, like the amide-A and, as this study demonstrates, amide-II mode. This development necessitates a generalized theoretical framework which can describe the experimental results well. Our previous model calculation has successfully simulated the amide-I modes of the 310-helical conformation.7,8 Here we expand it to simulate the linear and 2D IR spectral patterns of the coupled amide-I and -II modes in the hexapeptides. Our new calculation continues to base on the vibrational exciton model. The diagonal elements of the Hamiltonian correspond to the amide-I and -II local mode frequencies. The off-diagonal elements of the Hamiltonian describe the vibrational couplings between the amide-I/I, -II/II, -I/II, and -II/I modes. First, we describe how the amide-I and -II local mode frequencies are evaluated in our model calculation. There are

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currently three methods for calculating the frequency shift of the amide-I mode from the value in gas phase (δωI). One is to make use of the correlation between δωI and the electrostatic properties, such as the potentials or electric fields created by the peptide atoms and solvent molecules surrounding the amide-I local mode.33,45–48 Recently this method has been combined with MD simulation results to simulate 2D IR spectra of peptides and proteins.9,19,50 The second method is to explicitly take into account the molecules that form hydrogen bonds with the CdO or N-H group of a local peptide unit.42,51,52 The normal-mode frequencies of the complexes with different hydrogen-bonding configurations were estimated from quantum mechanical calculations. In the third model,7,8 the electrostatic energy of intramolecularly hydrogen-bonded CdO · · · H-N groups (EKS), as defined by Kabsch and Sander,53 is correlated to the frequency shift at the carbonyl oxygen site (δωICO) and the amide hydrogen I ). The correlation coefficients were obtained by site (δωNH matching the model frequency shift to the results obtained from quantum mechanical calculations of NMA-water clusters.42 Here we applied the same principle to the amide-II mode and obtained relationships as follows: II δωCO ) 0.7 cm-1 mol/kJ × EKS II δωNH ) 2.9 cm-1 mol/kJ × EKS

where δωIICO(NH) is the frequency shift of the amide-II mode due to the presence of hydrogen bonding at the CdO (N-H) group. In addition to intramolecular hydrogen-bonding effects, if the CdO or N-H group is exposed to solvent, it is necessary to consider the additional decrease (increase) of the amide-I (II) mode due to the effects of solvation (δωsolvent). In the past studies, this was empirically included as a constant shift of 10-20 cm-1 for the amide-I mode.7,8,13 In our case, we also need to include the solvent effects on the amide-II mode when the CdO groups are exposed to chloroform. Therefore, we set I II ) 10 cm-1 and δωsolvent ) -5 cm-1. The amide-I and δωsolvent -II local mode frequencies that constitute the diagonal elements 0,II of the vibrational exciton Hamiltonian (ω0,I p and ωp , p ) 1-5) are thus represented as I(II) I(II) I(II) ω0,I(II) ) ωI(II) - δωsolvent - δωCO - δωNH p 0

where the unperturbed local mode frequencies of the amide-I and -II modes (ω0I and ω0II) were set to 1680 cm-1 and 1505 cm-1, respectively. Second, we describe how to calculate the vibrational couplings between the amide-I/I, -I/II, -II/I, and -II/II modes. It is well-known that the couplings between the amide-I/I modes are categorized into two cases depending on whether the two modes are nearest neighbors or not. For non-nearest neighbors, the vibrational coupling can be well approximated by the transition dipole coupling (TDC),22,54 or transition charge coupling (TCC) to include multipole interactions.13,55,56 However, these electrostatic interactions cannot properly describe the nearest-neighbor coupling, for which the through-bond effects need to be included.55 Several groups estimated the coupling from quantum mechanical calculations of AcGlyNHMe and mapped out the coupling as a function of the dihedral angles φ and ψ.33,55–59 However, these maps report quite different coupling strengths that are strongly dependent on the calculation method, basis set, how the dipeptide structure is optimized, and how the

Maekawa et al.

Figure 8. Nearest-neighbor coupling maps calculated for AcGlyNHMe at the B3LYP/6-31+G(d) level with fixed dihedral angles (φ, ψ). Coupling between the amide-I and -I modes (top left); N-terminal amide-I and C-terminal amide-II modes (top right); N-terminal amideII and C-terminal amide-I modes (bottom left); amide-II and -II modes (bottom right). All four maps are plotted in a single color scale and the unit of the couplings is cm-1.

amide-I local modes are defined. Because none of the existing nearest-neighbor coupling maps take into account simultaneously the couplings between the amide-I/I, -I/II, -II/I, and -II/ II modes, we newly created these four maps for our purpose. Using the Gaussian 03 package,60 AcGlyNHMe was fully optimized with fixed φ and ψ at the B3LYP/6-31+G(d) level, and the Hessian matrix with respect to the mass-weighted Cartesian coordinates was obtained. To define the amide-I and amide-II local modes on the peptide unit at the N (C)-terminus, three isotope labels (13C, 18O, and D) were substituted at the other unit at the C (N)-terminus. The isotope labeling leads to a large frequency difference between the two local modes, making it possible to substantially weaken the mixing of the two modes and retrieve the local mode coordinates on each peptide unit. After the amide-I and -II local modes were obtained, the system energy was calculated for four structures distorted along each local mode by (0.01 Å amu1/2. The vibrational couplings at a given fixed φ and ψ set were obtained by taking the finite difference of these energies.57,59 We repeated this procedure for φ and ψ sets from -180° to 180° with a step of 30° and interpolated the values between the calculated points to generate the nearest-neighbor coupling maps shown in Figure 8. The pattern of the amide-I/I map qualitatively agrees with those obtained in the past33,55–59 but the magnitudes are different. The maps of the amide-II/II and -II/I couplings exhibit very similar patterns to those recently calculated by Hayashi and Mukamel,33 although they did not report the map for I/II coupling. The coupling strength between the amide-I/II modes in the same peptide unit was also calculated in the same way, and it is (33 cm-1 at (φ, ψ) ) (-60°, -30°). The intrapeptide-unit coupling between the amide-I and -II modes has been experimentally determined for two model peptides, NMA (27-29 cm-1)28,29 and N-acetyl-L-prolineamide (29.6-32 cm-1).61 For the latter, the coupling strength has also been theoretically calculated to be 23.8 cm-1 for the trans-C7 conformer and 30.6 cm-1 for the cis conformer, using the Hessian matrix reconstruction method.31 Our calculated coupling is similar to these values. In general, the sign of amide-I/II coupling and amide-II/I coupling cannot be determined from the calculation and also they are not independent from each other. Although the sign of

Detecting the Formation of a Single Helical Turn

J. Phys. Chem. B, Vol. 113, No. 34, 2009 11781

TABLE 1: Partial Charges and Charge Derivatives along the Amide-I and Amide-II Modes of NMA, along the Urethane CdO Stretching Mode and Urethane-II (Amide-II-like) Mode of Dimethylurethane, and along the Ester CdO Stretching Mode of Methylacetate partial chargea amide-I amide-II urethane CdO urethane-II

charge derivativea

C

O

N

H

C

O

N

H

direction

magnitude

0.496

-0.542

-0.336

0.383

0.592

-0.567

-0.428

0.404

0.062 -0.054 -0.033 0.036

0.198 0.064 0.267 -0.007

-0.269 0.041 -0.232 -0.049

0.009 -0.051 -0.002 0.020

22 (14) 68 (70) 5 (13) 86 (88)

3.16 (2.70) 1.73 (1.93) 3.68 (3.00) 1.52 (2.53)

partial chargea ester CdO

transition dipole derivativeb

charge derivativea

transition dipole derivativeb

C

O()C)

O

C

O()C)

O

direction

0.518

-0.478

-0.040

-0.002

0.211

-0.209

21 (13)

a

magnitude 3.01 (2.59) -1

-1/2 b

The partial charge is represented as a fraction of elementary charge (e), and the unit of the charge derivative is e Å amu . The angles between the transition dipole derivative of the amide-I (II) mode and the CdO (N-H) bond axis are given in degrees, and the magnitudes are presented in D Å-1 amu-1/2. For comparison, the angle and magnitude directly obtained from the DFT calculation and vibrational analysis at the B3LYP/6-31+G(d) level are in parentheses.

Figure 9. Vibrational couplings for the network of amide-I and amideII modes in an ideal 310-helix with (φ, ψ) ) (-57°, -30°). (a) For the amide-I mode at the ith peptide unit, the amide-I/I and -I/II couplings are denoted in red and blue, respectively. (b) For the amide-II mode at the ith peptide unit, the amide-II/I and -II/II couplings are denoted in red and blue, respectively.

the coupling constant between 13Cd16O and 13Cd18O-labeled amide-I modes has been previously determined from their linear or 2D IR peak intensity ratio,11 the simplified expression in the previous work cannot be applied to vibrators with different transition dipole strength nor to labeled vibrators when the isotope shifts are not sufficient to fully isolate them from the unlabeled vibrators. We found that flipping the signs of the amide-I/II and -II/I couplings resulted in different linear and 2D IR spectral patterns, and the sign was treated as one variable in the simulation. The final simulations were carried out by setting a negative sign to the amide-I/II coupling for the modes within the same peptide unit. The signs of other amide-I/II and -II/I couplings were then chosen to be consistent with this setting. All of the non-nearest-neighbor couplings in this study were modeled with TCC, and the transition charge parameters were obtained from DFT calculation of NMA at the B3LYP/631+G(d) level. As in the literature,55 the Mulliken partial charges and charge derivatives of the methyl groups were added to those of the connected C and N atoms. The values used in our calculation are listed in Table 1. Figure 9 illustrates the coupled networks of amide-I and -II modes in an ideal 310-helix with (φ, ψ) ) (-57°, -30°). For the amide-I mode at the ith peptide unit, the amide-I/I and -I/II couplings are denoted in red and blue, respectively, in Figure 9a. For the amide-II mode at the ith peptide unit, the amide-II/I and -II/II are denoted in red and blue, respectively, in Figure

9b. Although the coupling strength between the amide-I and -II modes within the same unit (-33 cm-1) is the largest in the exciton Hamiltonian, this is not the only coupling which induces the cross peak. For example, the amide-I at the ith peptide unit and the amide-II mode at the (i+2)th peptide unit are connected through an intramolecular hydrogen bond and they have a TCC of -11.6 cm-1. The nearest-neighbor amide-I/II coupling of -8.3 cm-1 between the ith and (i+1)th peptide units is also considerable. These couplings will all contribute to the generation of cross peaks. Therefore, the cross peaks in the NR spectra of 1* in Figure 6 manifest the complicated couplings between the labeled amide-I mode and many amide-II modes. The 15N labeling is required to distinguish between different contributing amide-II modes, as demonstrated in 1**. The transition dipole derivatives along the amide-I and -II local modes (µI and µII) have been calculated using the partial charges and charge derivatives. Table 1 lists the magnitudes and directions, and the latter is represented as an angle between µI(II) and the CdO (N-H) bond axis. The angles are quite close to those used in the TDC calculation.62 In our spectral simulations, we have set the transition dipole directions of the amide-I and -II local modes to these calculated angles. To model the isotope effects on the vibrational properties of the amide-I and -II modes, we performed DFT calculations and normal-mode analysis on NMA and its 13Cd18O and 15N labeled isotopomers at the B3LYP/6-311++G(d,p) level. We also calculated the frequencies and transition dipole derivatives of N-t-butyl-2,2-dimethyl-propionamide (NBDMPA), (CH3)3CCONHC(CH3)3, that serves as a model for a single peptide unit with a peptide backbone consisting of Aib residues. The results are summarized in Table 2. It should be noted that these isotope labels hardly affect the atom displacements along the mode. The 13Cd18O label decreases the amide-I and -II frequencies by 70 and 6-7 cm-1, respectively. The 15N label causes an isotope shift in the amide-II mode by 8-13 cm-1 but not in the amide-I mode. The isotope effects on the directions of the transition dipole moments are negligible. Transition dipole strength changes