Infrared and Vibrational CD Spectra of Partially Solvated α-Helices

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Infrared and Vibrational CD Spectra of Partially Solvated r-Helices: DFT-Based Simulations with Explicit Solvent David R. Turner and Jan Kubelka* Department of Chemistry, UniVersity of Wyoming, Laramie, Wyoming 82071 ReceiVed: October 11, 2006; In Final Form: NoVember 10, 2006

Theoretical simulations are used to investigate the effects of aqueous solvent on the vibrational spectra of model R-helices, which are only partly exposed to solvent to mimic R-helices in proteins. Infrared absorption (IR) and vibrational circular dichroism (VCD) amide I′ spectra for 15-amide alanine R-helices are simulated using density functional theory (DFT) calculations combined with the property transfer method. The solvent is modeled by explicit water molecules hydrogen bonded to the solvated amide groups. Simulated spectra for two partially solvated model R-helices, one corresponding to a more exposed and the other to a more buried structure, are compared to the fully solvated and unsolvated (gas phase) simulations. The dependence of the amide I spectra on the orientation of the partially solvated helix with respect to the solvent and effects of solvation on the amide I′ of 13C isotopically substituted R-helices are also investigated. The partial exposure to solvent causes significant broadening of the amide I′ bands due to differences in the vibrational frequencies of the explicitly solvated and unsolvated amide groups. The different degree of partial solvation is reflected primarily in the frequency shifts of the unsolvated (buried) amide group vibrations. Depending on which side of the R-helix is exposed to solvent, the simulated IR band-shapes exhibit significant changes, from broad and relatively featureless to distinctly split into two maxima. The simulated amide I′ VCD band-shapes for the partially solvated R-helices parallel the broadening of the IR and exhibit more sign variation, but generally preserve the sign pattern characteristic of the R-helical structures and are much less dependent on the R-helix orientation with respect to the solvent. The simulated amide I′ IR spectra for the model peptides with explicitly hydrogen-bonded water are consistent with the experimental data for small R-helical proteins at very low temperatures, but overestimate the effects of solvent on the protein spectra at ambient temperatures, where the peptide-water hydrogen bonds are weakened by thermal motion.

Introduction Infrared absorption spectroscopy (IR) is a commonly used experimental technique for probing protein secondary structure and structural changes.1,2 Vibrational circular dichroism (VCD) is a less commonly used method, due to greater experimental difficulty, but provides more distinct structurally characteristic spectral signatures via signed band-shape patterns.3 The sensitivity of the IR and VCD to protein structure arises from couplings between the amide group vibrations that are characteristic of the polypeptide backbone conformation and are most pronounced in the amide I (predominantly amide CdO stretch).4-6 At the same time, amide vibrations are strongly affected by the local environment of the amide groups. In particular, solvent has a dramatic effect on the amide I vibrational frequencies. In the simplest amide, N-methyl acetamide, the amide I frequency shifts nearly 100 cm-1 between the gas phase and aqueous solution and more than 50 cm-1 between acetonitrile and water.7,8 By comparison, the inter-amide vibrational interactions responsible for the characteristic amide I band contours are on the order of 1-10 cm-1.4,5 In model oligo- and polypeptides that are often used to aid interpretation of the vibrational spectra of proteins, all of the amide groups are exposed to solvent. As a result, the vibrational frequencies of the peptide models, such as R-helical alanine rich peptides, are generally lower in water than in non-aqueous * Corresponding author. E-mail: [email protected].

solvents, but the IR and VCD band-shapes remain the same.9-12 By contrast, proteins are not uniformly solvated, but an R-helix in a protein will have one side exposed to the solvent, while the other side will be shielded from solvent by hydrophobic sidechains in contact with sidechains from another helix or structural element. This differential solvation in proteins can affect the amide I spectral band-shapes much more dramatically than just the overall frequency shifts, seen in model R-helical peptides. Experimentally, the main difference between the spectra of the R-helical proteins and model peptides is the higher frequency of the amide I′ (N-deuterated, in D2O) band in proteins (∼1650 cm-1) as compared to the alanine-rich peptides (∼1630 cm-1), which is attributed to more buried R-helices in proteins. However, there is strong experimental evidence that solventinduced frequency shifts give rise to additional amide I′ band components in R-helical proteins. In particular, 1630 cm-1 IR amide I′ component is often found in R-helical proteins and assigned to the solvated R-helix vibrations.13-15 Moreover, DeGrado and co-workers found that, at cryogenic temperatures, amide I′ of an R-helical coiled-coil,16 as well as of a threehelix bundle protein,17 exhibit distinct doublet-like character, in which the low-frequency component was assigned to the amide groups that form hydrogen bonds with water, while the higher frequency component is due to buried amides. These effects were largely diminished at room temperature, where the high (buried)-frequency component was dominant. However,

10.1021/jp0666840 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/26/2007

IR and VCD of Partially Solvated R-Helices selective isotopic labeling of buried and exposed residues exhibited different 13C isotopic shifts at all temperatures. In this report, we use theoretical simulations of the vibrational spectra using DFT vibrational calculations with subsequent transfer of parameters onto larger structures to gain deeper insights into the vibrational states of partially solvated R-helices. A number of research groups have studied the solvent effects on the amide vibrations theoretically, but most work thus far has been concerned with simple amides or oligopeptides that are fully solvated by water.18-24 The effect of solvation on IR and VCD spectra for helical oligopeptides up to 20 residues has been recently studied using density functional theory (DFT) vibrational calculations with explicit solvent in combination with the transfer of the vibrational parameters.25 The transfer of parameters26 allows calculating vibrational spectra at essentially the DFT level of model peptides that are much too large to afford the full DFT treatment. Therefore, DFT vibrational calculations with transfer of parameters provide an independent, non-empirical route for simulating the vibrational spectra for real peptides or small proteins, constrained to desired conformation, which can be directly compared to experiment. The spectral simulations for explicitly solvated oligopeptide helices25 showed that complete solvation of all amide groups, while shifting the vibrational frequency of the amide bands by nearly 50 cm-1, preserves the conformationally sensitive amide vibrational couplings, giving the same normal mode distribution within the band. As a consequence, qualitatively the same characteristic IR and VCD band-shapes were predicted for fully solvated oligopeptides that are calculated for the same model structures in the gas phase, consistently with experiments as well as with other theoretical studies.11,19 By contrast, Bour and Keiderling found that in a model β-hairpin the most pronounced solventinduced changes are predicted for the VCD band-shapes due to differential interactions of amide groups with solvent, which resulted in significant normal mode reordering.27 These authors used the same methodology of transfer of the DFT-level parameters from fragments, but the solvent was approximated by electrostatic field corrections to the vibrational parameters. Simulations of the vibrational spectra of partially solvated R-helices are a continuation of our efforts to provide better understanding of the vibrational spectra of proteins in solution. Independent simulations of the vibrational spectra are important not just for correct interpretation of the experimental data, but may be especially helpful for site-resolved studies using 13C isotopically edited IR spectroscopy. Simulated spectra for 13C labeled proteins can be used in advance for predicting the best residue positions to be labeled so that the 13C signal can be experimentally resolved and detected. In proteins, solvation may be an especially important issue, because the isotopic substitution on the solvent-exposed amides and buried ones may result in very different isotopic frequency shifts.16,17 We use the same methodology and the same model for solvation as in the previous study of the vibrational spectra of explicitly solvated peptide helices.25 Because our objectives are to understand general amide spectral changes due to solvation, without regard to the effects of the particular oligopeptide sequence (amino acid side-chains) or structural variations, we use an alanine R-helix as a model, solvated to a different degree by explicit water, but constrained to the same conformation in all cases. Although the model peptide structure is constrained to a target geometry and therefore not in a true energy minimum, the constraints are applied only to the peptide backbone dihedral angles and do not affect the calculated vibrational spectra of high-frequency stretching and bending amide modes, which do not couple to

J. Phys. Chem. B, Vol. 111, No. 7, 2007 1835 the low-frequency, torsional modes.28 Our solvent model uses only the minimum number of water molecules that form hydrogen bonds with the peptide, and the spectra are calculated for only a single solvent configuration. Such minimal model does not account for the electrostatic effect of the bulk solvent or for the solvent configurational fluctuations, such as molecular mechanics/quantum mechanics (MM/QM) approaches29,30 or combined explicit/implicit solvent calculations.7,18,23 These methods, however, are much more computationally demanding, and taking into account multiple solvent configurations requires approximations, such as empirical corrections based on the solvent electrostatic fileds.19-21 On the other hand, considering only the first hydration layer of water allows DFT-level vibrational calculations for oligopeptides that are large enough that the most important intra-helical interactions are also included. DFT calculations on minimal peptide-water clusters therefore provide realistic vibrational parameters that can be transferred and used for spectral simulations of longer helices. At the same time, hydrogen bonding to water accounts for most of the solvent-induced amide frequency shifts,7 and even a minimal number of water molecules hydrogen bonded to the peptide and “frozen” in a single minimum energy configuration correctly capture some relatively subtle effects on the spectra. Changes from couplet amide I VCD to (-,+,-) sign pattern of amide I′ (N-deuterated) and the enhanced intensities of the 13C IR and VCD amide I′ bands in the isotopically labeled R-helices were reproduced in our simulations with only a minimum number of hydrogen-bonded water molecules with near quantitative accuracy.25 In the following paragraphs, we investigate the effects of solvent on the amide I′ IR and VCD of a model protein R-helix. We focus on the amide I′, because the sensitivity of this band in the IR and VCD to the protein structure is historically best established. Amide I′ also exhibits the largest frequency shifts upon 13C isotopic editing. Consequently, the majority of the protein IR and VCD spectroscopic studies, and all 13C isotopically edited studies, are based on the amide I′ spectra. We compare the spectral simulations for the fully solvated and two partially solvated model R-helices, one corresponding to the more exposed and the other to the more buried structure, as well as for a gas-phase R-helix. We further explore how the simulated vibrational spectra depend on the orientation of the R-helix with respect to the solvent. Finally, we simulate the band-shape changes due to 13C isotopic labeling at solvated as well as buried amide positions. Computational Methods Model Structures. To have a model structure that resembles real protein helices, the geometry of the R-helix used throughout this study is based on the NMR structure of a subdomain of P22 viral coat protein.31 The P22 subdomain is a helix-turnhelix motif with two relatively regular R-helices whose average backbone torsional angles are φ ) -47° ((8°) and ψ ) -59° ((12°). The longer, N-terminal helix is 15 residues long. We chose our model structure to be an L-alanine 15-amide, Ac-(LAla)14-NH-CH3 with the φ ) -47°, ψ ) -59°, and ω ) 180°. An all-L-alanine oligopeptide was used because the focus of this study is on the effects of solvent on the amide backbone vibrations, and not on the effects of the particular amino acid side chains, and because alanine is the smallest L-amino acid (i.e., with a chiral R-carbon), which facilitates the computations. Several states of solvation of the model R-helix are compared, which are illustrated in Figure 1 and summarized in Table 1.

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Figure 1. Model R-helical 15-amide alanine oligopeptides with explicitly hydrogen-bonded water used for simulations of the vibrational spectra. (a) Fully solvated R-helix FS with 20 water molecules, (b) partially solvated R-helix PSA with 9 water molecules, (c) partially solvated R-helix PSB with 7 water molecules, and (d) gas-phase R-helix GP. The bottom panel is a view down the helical axis from the N-terminus.

First, we have computed the vibrational spectra for a fully solvated R-helix, denoted FS (Figure 1a). The fully solvated helix was constructed assuming, as in the previous study,25 a water molecule forming a hydrogen bond to each amide CdO group that is also hydrogen bonded to the peptide N-H; two water molecules hydrogen bonding to the terminal CdO groups; and one water molecule hydrogen bonded to the terminal N-H groups that are not involved in the intrapeptide hydrogen bonds. Second, a partially solvated helix was constructed to approximate the solvation of the N-terminal helix in the P22 subdomain. In the 15-residue stretch of the N-terminal R-helix of P22, a water molecule was added to form a hydrogen bond with each CdO group, which is not shielded by the side-chains in hydrophobic contacts with the opposing helix. This resulted in 9 water molecules hydrogen bonded to amide groups (from the N-terminus) 1, 3, 4, 7, 8, 10, 11, 14, and 15 of the 15amide helix. The partially solvated model 15-amide R-helix, denoted PSA (Figure 1b), was built by adding a hydrogenbonded water to the same amide groups in the regular (φ ) -47°, ψ ) -59°, ω ) 180°) alanine 15-amide. Third, to study the effects of the degree of solvation, we constructed another model for a partially solvated 15-amide R-helix (PSB) with only 7 water molecules hydrogen bonded to amides 1, 4, 7, 8, 11, 14, and 15 (Figure 1c). This model is chosen to most closely resemble the PSA, just with less water. The particular sequence of the solvated and unsolvated amide groups in the PSA and PSB models is only one of many possible. For example, a different orientation of a helix with

respect to the hydrophobic core of a protein will affect which amide groups are exposed and which are buried. To investigate how the exposure of various sides of the model R-helix and, therefore, distributions of solvated and unsolvated amides affect the vibrational spectra, we have constructed additional partially solvated R-helical models. A total of seven different partially solvated variants of PSA and PSB can be obtained by cyclic permutation of the solvated and unsolvated amide groups, which can also be viewed as the helix being rotated along the longitudinal axis with respect to the solvent (Figure 1, Table 1), and allows using the same smaller partially solvated helical models to obtain the vibrational parameters (see below). For brevity, we present the simulated spectra for one additional partially solvated variant of PSA denoted PSA(2) and one corresponding variant of PSB, denoted PSB(2) (Table 1). Finally, for comparison, we computed the vibrational spectra for an isolated (gas phase) 15-amide R-helix, denoted GP (Figure 1d). For calculation of the DFT-level vibrational parameters, all of the model 15-amide R-helices were segmented by amide groups into smaller, 7-amide R-helices Ac-(L-Ala)6-NH-CH3. The 7-amide capped peptide was chosen because it is the smallest R-helix where the central amide is hydrogen-bonded both back and forward in the sequence on its carbonyl and amino groups, respectively. This assures that the model has representation of all types of residues in the helix, central (fully internally hydrogen bonded) and terminal (partially hydrogen-bonded from either N- or C-terminus).10,25 For the fully solvated (FS) and

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TABLE 1: Model 15-Amide Alanine r-Helical Peptides with Explicitly Hydrogen-Bonded Water Molecules

a

Underlined italic residues are explicitly solvated by hydrogen-bonded water on amide CdO. b From N-terminus.

TABLE 2: Model r-Helical 7-Amides Used for DFT Calculations of the Vibrational Parameters To Be Transferred on the 15-Amide r-Helices transfer to large R-helix FS PSA, PSA(2)

PSB, PSB(2)

GP

sequencea 1 2 3 4 5 6 7 1 2 3 4 5 6 7

Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3 Ac-AAAAAA-NH-CH3

a

Underlined italic residues are explicitly solvated by hydrogenbonded water on amide CdO.

gas phase (GP) helices, only one smaller 7-amide peptide is sufficient to obtain all of the vibrational parameters. For the FS, the R-helical 7-amide cluster with 10 water molecules was calculated, where the water was added using the same rules as for constructing the corresponding large helix (FS). Seven different 7-amide helices were needed to account for all of the combinations of the solvated and unsolvated amide groups in each of the partially solvated models PSA and PSB. For the first partially solvated R-helix PSA, each of the 7-amide helices had 4 water molecules, and 3 water molecules were needed in each 7-amide helical fragment for the less solvated PSB. The sequences of solvated and unsolvated amides in the 7-amide fragments used to obtain the DFT vibrational parameters for PSA and PSB are listed in Table 2.

DFT Calculations. All quantum mechanical calculations were carried out at the DFT level, using the Gaussian 03 program package.32 The BPW91 density functional33 with a 6-31G* basis set34 were used in all cases. The geometries of all small oligopeptide models, including those with explicit water molecules, were fully optimized with the exception of the φ, ψ, ω torsional angles, which were constrained to the target helical conformations. In such optimized peptide-water clusters, the water hydrogen-bond geometries are in a local energy minimum.25 The geometry was considered optimized when all of the default convergence criteria of Gaussian 03 were met. For the optimized structures, analytical harmonic force fields (FF) and the intensity parameters, analytical atomic polar tensors (APT) and atomic axial tensors (AAT), were calculated at the same level of theory. The AAT in Gaussian 03 are implemented according to the magnetic field perturbation (MFP) theory of Stephens35 with gauge-including atomic orbitals (GIAO). The calculations were carried out on the Pittsburgh Supercomputing Center SGI Altix cluster, using 4 CPU, through the kind provision of the NSF Teragrid program. Transfer of the Vibrational Parameters. Vibrational FF and associated APT and AAT intensity parameters for 15-amide R-helices, FS, PSA, PSB, and GP, were obtained by transfer of the Cartesian FF, APT, and AAT matrices calculated at the DFT level for the respective small peptides. As we have demonstrated previously,25 the vibrational parameters for water molecules do not have to be explicitly transferred, because only the effect of water on peptide vibrations is of interest and not the vibrations of water itself. For the fully solvated model helix, FS, all of the amide groups form hydrogen bonds with water, and the FF, APT, and AAT were transferred from a single, fully solvated 7-amide helix. Likewise, for the isolated R-helix GP, all of the parameters can be transferred from a single gas-phase R-helical 7-amide. The procedure used for transfer of Cartesian tensors has been described in detail elsewhere.26 In brief, the short peptide

1838 J. Phys. Chem. B, Vol. 111, No. 7, 2007 fragment for which the FF, APT, and AAT are determined from the DFT calculation is sequentially fitted, amide by amide group, onto all large oligomer segments of the same length. For each such fit, the smaller structure is rotated to the same orientation, and the rotation matrices are used to transform the Cartesian FF, APT, and AAT matrices to the correct coordinate system of the particular large peptide segment. The transformed FF, APT, and AAT are then assigned to the corresponding atoms of the segment. The size of the small fragment (7 amides) and sequential overlap between segments ensures that proper vibrational coupling for each amide group with its neighbors up to six amide groups away is included in the transferred FF. To obtain the FF, APT, and AAT parameters that correctly reflect the solvation state of each amide group and the interactions between the amide groups in different solvation states, seven partially solvated small peptides (Table 2) are needed to reconstruct the vibrational parameters for each of the partially solvated R-helices, PSA and PSB. The transfer algorithm was therefore generalized for transfer of the vibrational parameters from multiple short peptides. The generalized transfer algorithm is a straightforward extension of the algorithm for simultaneous transfer of parameters from two small fragments36 and similar to that used for simulations of the vibrational spectra of irregular peptide structures36,37 and protein structural motifs27,38 from shorter fragments. Simulation of the Vibrational Spectra. The IR and VCD spectra were calculated from the FF, APT, and AAT parameters using a set of programs written in house based on a code kindly provided by Dr. Petr Bour. The Cartesian FF, corrected for translations and rotations and mass weighted, is diagonalized to yield vibrational frequencies, and the normal mode eigenvectors (S-matrices) are contracted with the APT and AAT parameters to produce the resulting dipole (D) and rotational (R) strengths. The spectral band-shapes for IR or VCD simulations are obtained assigning a Lorentzian function to each normal mode with a full width at half-maximum (fwhm) of 15 cm-1, and area proportional to D or R, respectively. Isotopic substitution is implemented by simply changing the masses of atoms to be substituted, such as amide N-deuteration or 13C on amide CdO’s. Experimental IR and VCD measurements typically focus on the amide I′ band measured in D2O, where the amide groups are N-deuterated. For this reason, unless stated otherwise, all of the simulated spectra presented in this study are the amide I′ spectra of the N-deuterated model peptides. Results Extent of Solvation. In Figure 2, we compare the simulated amide I′ (N-deuterated) IR spectra for the model 15-amide R-helix at four levels of solvation that correspond to the models in Figure 1: fully solvated FS, partially solvated PSA and PSB, as well as the gas-phase GP R-helices. The simulation for the fully solvated R-helix FS shows a sharply peaked IR amide I′ (Figure 2a) with maximum computed near 1672 cm-1. The low-frequency sideband is due to the N-terminal amide vibration and is consistently seen in the previous R-helical spectral simulations25,28 as well as in the spectra simulated in this study. In the partially solvated R-helix PSA, the amide I′ IR (Figure 2b) shifts to a higher frequency and becomes substantially broader with much less peak intensity. The broad maximum is calculated between 1678 and 1695 cm-1, with an additional partially resolved shoulder at 1708 cm-1. In the less solvated PSB, the amide I′ IR (Figure 2c) is also broad, but has more resolved structure. The PSB amide I′ peaks toward the higher frequency side of the contour near 1712 cm-1, with

Turner and Kubelka

Figure 2. Simulated amide I′ (N-deuterated) IR absorption spectra for the model 15-amide alanine R-helices with different degrees of solvation: (a) fully solvated R-helix FS, (b) partially solvated R-helix PSA, (c) partially solvated R-helix PSB, and (d) gas-phase R-helix GP. The intensity units are molar extinction coefficients per amide group. The solid vertical bars represent the positions and dipole strengths of the individual amide I′ normal modes.

weaker secondary maximum at 1678 cm-1. The gas-phase R-helix I (Figure 2d) amide I′ is again narrow and virtually identical to that of the FS except at higher frequency (peak at 1725 cm-1) and is somewhat less intense. To better understand the origins of the simulated amide I′ band-shapes, we have analyzed the contributions of the individual amide groups to the amide I′ normal modes. The CdO stretching amplitudes of the most intense amide I′ normal modes for each model R-helix are shown in Figure 3. In Figure 3, the black bars correspond to the solvated amide groups, that is, those with hydrogen-bonded water molecule, while the white bars are unsolvated amides. In FS, most of the amide I′ IR intensity (Figure 2a) comes from the delocalized in-phase vibration of all amide groups computed at 1674 cm-1 (Figure 3a). In PSA (Figure 2b), the presence of both solvated and unsolvated amide groups decouples this dominant normal mode into several components (Figure 3b). As expected, the higher frequency modes (at 1711 and 1706 cm-1) have more contribution from the unsolvated amide groups, while the low frequency ones (1686 and 1678 cm-1) arise predominantly from the solvated groups. However, all of these modes involve to some extent vibrations of both solvated and unsolvated amides. For example, the second most IR intense 1696 cm-1 vibration arises from the C-terminal part of the R-helix and has contribution from

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Figure 3. Normal modes that most significantly contribute to the simulated amide I′ IR spectra of the model R-helices. (a) The most intense amide I′ normal mode for the fully solvated R-helix FS, (b) five most intense amide I′ normal modes for the partially solvated R-helix PSA, (c) five most intense amide I′ normal modes for partially solvated R-helix PSB, and (d) the dominant amide I′ mode for the gas-phase R-helix GP. The vertical bars represent the CdO stretching amplitudes for the individual amide groups. The white bars correspond to the unsolvated amide groups, and the black bars correspond to the amide groups with explicitly hydrogen-bonded water molecules. The frequencies of the normal modes are listed in the upper left corner for each normal mode.

both solvated and unsolvated groups. This shows that residual intra-helical vibrational coupling still plays an important role, despite the solvent-induced frequency shifts. In addition to the overall frequency separation between the solvated and unsolvated amide modes, the vibrations of the solvated amides are also separated into several more localized modes, as are the unsolvated vibrations, in contrast to a single collective normal mode seen in the FS. This can be seen from the two low-frequency vibrations, one at 1686 cm-1, localized near the N-terminus, and the second at 1678 cm-1, the most intense normal mode in PSA, which comes predominantly from the solvated amide groups near the helix center. Both of these modes also contain a small contribution of the neighboring unsolvated amides. In PSB, the decoupling of the solvated and unsolvated amide groups is somewhat more pronounced (Figure 3c). The most IR intense normal mode (1715 cm-1) is an in-phase vibration of the unsolvated groups. The second most intense vibration at 1695 cm-1 is essentially the same as the 1696 cm-1 mode in PSA, arising from the C-terminal part of the model R-helix. The two vibrations responsible for the secondary amide I′ maximum near 1678 cm-1 are mostly due to solvated amide groups, where again the groups at the helix center (1680 cm-1 vibration) are decoupled from the off-center ones (1675 cm-1 mode). For comparison, we also show the most intense amide I′ vibration of the unsolvated R-helix GP (Figure 3d), which is an in-phase collective mode nearly identical to the dominant amide I′ mode in FS. The simulated amide I′ VCDs for the FS, PSA, PSB, and GP model R-helices are shown in Figure 4. The VCD of the FS (Figure 4a) has a positive couplet shape (positive on the low-frequency side, negative on the high-frequency side) characteristic for right-handed helical structures, very similar to that of GP (Figure 4d). A very weak negative component appeared on the low-frequency side of the positive band, suggesting the (-,+,-) pattern that is experimentally observed for N-deuterated R-helices (measured in D2O). As shown

previously,25 and as can also be seen from the absence of this feature in the amide I′ VCD of GP (Figure 4d), this negative feature is reproduced only in simulations that include solvent. The computed amide I′ VCD for the partially solvated helices PSA (Figure 4b) and PSB (Figure 4c) both show more complex (+,-,+,-) sign patterns (from low to high frequency) that might suggest two couplets or even overlapping (-,+,-) shapes. This is evident especially in the PSB (Figure 4c) where the more intense, high-frequency (-,+,-) VCD aligns with the 1712 cm-1 IR peak, while a weaker couplet corresponds to the secondary, lower frequency maximum. The lower frequency negative VCD feature, computed near 1680 cm-1 in both PSA and PSB, is largely due to N-deuteration, as shown in Figure 5, which compares the simulated VCD amide I′ (N-deuterated) and amide I (N-protonated) for PSA and PSB. The N-protonated calculations yield VCD band-shapes for PSA and PSB with a more positive couplet-like character. Aside from these detailed sign variations, overall the amide I′ VCD band-shapes essentially preserve the characteristic R-helical positive couplet shape, with net positive VCD toward the low frequency and negative VCD at the high frequency of the amide I′ contour. Orientation of the r-Helix with Respect to Solvent: Distribution of Solvated and Unsolvated Amide Groups. As the normal-mode analysis above suggests, the coupling between the solvated amide group vibrations is modulated by the intervening unsolvated amides and vice versa. It is therefore interesting to see how the simulated spectra depend on specific distributions of the solvated and unsolvated amide groups within the R-helix, which would result if different sides of the R-helix were exposed to solvent. For this reason, we have simulated the IR and VCD spectra for additional variants of the partially solvated R-helix PSA as well as PSB. The simulated IR and VCD spectra for the PSA(2) and PSB(2) (Table 1) are shown in Figure 6. As compared to PSA (Figure 2b), the simulated amide I′ IR of PSA(2) is distinctly split into two well-resolved maxima at 1708 and 1678 cm-1 with the lower frequency maximum more

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Figure 5. Comparison of the amide I (N-protonated) and amide I′ (N-deuterated) simulated amide I′ (N-deuterated) VCD spectra for the partially solvated model 15-amide alanine R-helices. (a) Amide I (Nprotonated) VCD for the partially solvated R-helix PSA, (b) amide I′ (N-deuterated) VCD for the PSA (same as in Figure 4b), (c) amide I (N-protonated) VCD for the partially solvated R-helix PSB, and (d) amide I′ (N-deuterated) VCD for the PSB (same as in Figure 4c). The intensities are plotted as in Figure 4.

Figure 4. Simulated amide I′ (N-deuterated) VCD spectra for the model 15-amide alanine R-helices with different degrees of solvation: (a) fully solvated R-helix FS, (b) partially solvated R-helix PSA, (c) partially solvated R-helix PSB, and (d) gas-phase R-helix GP. The intensity units are molar differential extinction coefficients per amide group. The vertical lines represent the positions and rotational strengths of the individual amide I′ transitions.

intense, reflecting the proportion of the solvated and unsolvated amide groups. The simulated VCD amide I′ for PSA(2) (Figure 6b) is similar to that computed for PSA (Figure 4b), with a somewhat more intense negative feature near 1680 cm-1 than that in the PSA, corresponding to the stronger IR absorption. The amide I′ IR for PSB(2) (Figure 6c) also shows two maxima: the low-frequency IR amide I′ peak due to the solvated amide groups is computed at 1678 cm-1, the same frequency at which the secondary maximum in PSB (Figure 2c) is predicted. This is also the same frequency as the low-frequency maximum of PSA(2), but is less intense, in accord with less solvation. The high-frequency amide I′ IR peak, arising predominantly from the unsolvated amide vibrations, is predicted at the same frequency as the maximum of PSB, near 1713 cm-1. The simulated amide I′ VCD for the PSB(2) (Figure 6d) is again very similar to that of the original PSB model (Figure 4c) with more intensity shifted toward the lower frequency transitions, following the shift in the IR intensity. Most amide I′ IR intensity of the PSA(2) and, to a slightly less extent, of the PSB(2) is concentrated into two main transitions. These modes are shown in Figure 7. The most intense mode of PSA(2) at 1677 cm-1 arises from an in-phase

Figure 6. Simulated amide I′ IR and VCD for the partially solvated R-helices, variants of PSA and PSB, but with different side of the R-helix exposed to solvent. (a) Amide I′ IR for PSA(2), (b) amide I′ VCD for PSA(2), (c) amide I′ IR for PSB(2), and (d) amide I′ VCD for PSB(2). The intensities for the IR spectra are plotted as in Figure 2, and the VCD intensities are as in Figure 4.

vibration of the solvated groups, which, unlike the 1678 cm-1 mode in PSA (Figure 2b), involves the N-terminal (solvated) groups and has less contribution of the unsolvated amide vibrations. The intense 1708 cm-1 mode in PSA(2) responsible for the secondary, high-frequency maximum, is predominantly an in-phase vibration of the unsolvated groups, lacking the outof-phase vibrations of the solvated C-terminus, found in the 1706 cm-1 vibration of PSA. The in-phase combination of vibrations of the individual groups leads to significant intensity enhancement of these two modes. On the other hand, the vibrations close to the center of the amide I′ band, 1680-1695 cm-1, couple mostly out-of-phase and are much less intense than in PSA. By contrast, in PSB(2) the two most intense transitions, at 1676 and 1714 cm-1 (Figure 7b), are rather similar to the corresponding modes in PSB (at 1675 and 1715 cm-1, Figure 2c). In fact, the low-frequency 1676 cm-1 mode, although about 50% more intense than the 1675 cm-1 vibration of PSB, is even more localized, and most of its intensity draws from a large

IR and VCD of Partially Solvated R-Helices

J. Phys. Chem. B, Vol. 111, No. 7, 2007 1841

Figure 7. The most intense normal modes corresponding to the high-frequency and low-frequency maxima in the simulated amide I′ IR of (a) PSA(2) and (b) PSB(2). The normal mode amplitudes are plotted as in Figure 3. The bars represent the relative CdO stretching amplitudes for individual amide groups, the white bars correspond to the unsolvated amide groups, and the black bars represent the explicitly solvated amide groups. The frequencies of the normal modes are listed in the upper left corner for each normal mode.

Figure 8. Simulated amide I′ IR and VCD for two 13C isotopically labeled variants of PSA. (a) Amide I′ IR for PSA labeled on two neighboring solvated amide groups (amides 7 and 8), (b) corresponding amide I′ VCD, (c) amide I′ IR for PSA 13C substituted on two neighboring unsolvated amide groups (amides 5 and 6), and (d) corresponding amide I′ VCD. The intensities for the IR spectra are plotted as in Figure 2, and the VCD intensities are as in Figure 4.

amplitude vibration of a single, solvated amide group. The 1714 cm-1 mode has intensity similar to that of the 1715 cm-1 transition in PSB. The distinct doublet-like shape of the PSB(2) amide I′ IR is in part the result of stronger solvated amide transition, but mainly of the less intense vibration of the groups near the helical C-terminus, which in PSB occurs at 1695 cm-1 (Figure 2c) and is predominantly responsible for the IR intensity near the center of the amide I′ band. In PSB(2), this vibration shifts to 1690 cm-1 and is mostly an out-of-phase mode with much less IR intensity. 13C Isotopic Substitution. The 13C isotopic editing provides means to specifically probe the conformation of the isotopically labeled residues by IR and VCD through the frequency shifts of the 13C labeled amide group vibrations. To take advantage of this method in structural studies of proteins, it is necessary to establish how the solvation or burial of the 13C labeled amide groups affects the isotopically edited IR and VCD spectra. Obviously, there are many possible isotopic substitutions that can be introduced into our model helices. In this paragraph, we show examples of what spectral changes might be expected for a partially solvated helix 13C labeled on the amide groups near the center of the helix that are both solvent exposed and both buried. Figure 8 shows such simulated IR and VCD amide I′ spectra for the PSA model with two 13C-substituted amides near the center of the helix. For PSA 13C labeled on the solvated amides (amide groups 7,8), the isotopic substitution results in the shift of the amide I′ IR (Figure 8a) intensity from 1680 cm-1 to the isotopic side band near 1640 cm-1. The 13C sideband is mainly due to the

in-phase vibration of the (solvated) 13C substituted groups; the weaker, 1625 cm-1 transition arises from the corresponding outof-phase mode. The corresponding simulated amide I′ VCD (Figure 8b) shows an additional couplet below 1650 cm-1 of the 13C labeled groups. The 13C VCD is sharper and rather intense as compared to the 12C VCD, because both 13C groups are hydrogen bonded to water, while by contrast the unlabeled band contains both solvated and unsolvated amide vibrations, which results in broadened shape with less peak intensity. Such band-shape changes upon 13C substitution are expected, because they essentially correspond to what is observed as well as calculated for model R-helical peptides.4 On the contrary, in PSA 13C labeled on the unsolvated amide groups (amides 5,6), there is no distinct 13C IR band simulated toward the low frequency of the main amide I′ contour (Figure 8c). Rather, the unsolvated 13C amide I′ vibrations fall among the 12C solvated group modes and give rise to the amide I′ IR band more sharply peaked near 1680 cm-1. In particular, the in-phase 13C mode is computed at 1676 cm-1, while the weak out-of-phase transition is predicted at 1661 cm-1. The simulated amide I′ VCD (Figure 8d) shows little change from the VCD of the unlabeled PSA model, and more intense negative intensity near 1680 cm-1 corresponds to the IR intensity shift. The simulated 13C isotopically labeled spectra for the less partially solvated R-helix PSB show the same trends as those for PSA and therefore are not presented. Discussion Before discussing the meaning of the above results in greater detail, it is worth pointing out the general limitations of our computational approach. First, our model of the peptide solvation includes only the minimal number of water molecules in the first hydration sphere that form a hydrogen bond with the peptide backbone (CdO groups). One of the consequences of neglecting the bulk solvent is that the computed amide I′ frequencies are higher than those observed experimentally. For example, the peak amide I′ absorption for the model alaninerich R-helical peptides is near 1630 cm-1,9-12 while the computed amide I′ frequency for the fully solvated R-helix is about 40 cm-1 higher. While the explicitly hydrogen-bonded water accounts for most of the solvent-induced frequency shift, the electrostatic field of the bulk solvent results in further red shifts of the amide I′ frequencies.7 The bulk solvent can be taken into account by the implicit reaction field model, point charges, or additional solvent molecules. However, the systematic error in the vibrational frequencies does not negatively affect the normal mode dispersion and ordering and therefore the computed IR and VCD band-shapes. On the other hand, adding more solvent into the model would substantially increase the computational cost. The consistency of the calculated spectral bandshapes has been demonstrated in the previous study of the fully solvated helices25 and is also evident from the agreement

1842 J. Phys. Chem. B, Vol. 111, No. 7, 2007 between the gas-phase and the fully solvated simulations and, most importantly, between the gas-phase simulations and experimental data for the model oligopeptides in solution. Moreover, the computed frequencies could have been scaled to match the experimental values, as is often done. Another approximation that is dictated by the computational cost is that the above simulations are limited to a single configuration of hydrogen-bonded water molecules around the peptide. All of the explicitly solvated small helical fragments were fully optimized, with the exception of peptide backbone dihedral angles, at the DFT level, so that the peptide-water cluster geometry corresponds to a single local energy minimum. In reality, given the softness of the nonbonded interaction potential between the peptide and water, there would be multiple such local minima with corresponding distribution of the water configurations, and the experimental signals would contain averages over all of these configurations. The effect of such averaging, however, is expected to be mainly in broadening of the spectral components, which is treated in our simulations implicitly, by assigning a width to each transition. To support this argument, we can again invoke the prior simulations of the spectra of fully solvated helical peptides with explicit water in a single, minimum energy configuration.25 The simulated IR and VCD band-shapes were in excellent agreement with the experimental spectra as well as with simulations of Bour and co-workers,19 who accounted for the solvent dynamics by combined molecular dynamics simulations with empirical corrections of the quantum mechanical oligopeptide force field. Aside from the absolute vibrational frequencies, and arbitrarily assigned band widths, the above simulations should reproduce the relative frequency shifts and spectral band-shape changes expected due to hydrogen bonding of water to the amide groups in the partially solvated R-helices. In general, the IR and VCD spectra of the partially solvated R-helices are most affected by the difference in the local vibrational frequencies between the explicitly solvated and unsolvated amide groups. As compared to the fully solvated and gas-phase R-helices, in the partially solvated R-helices the presence of both solvated and unsolvated amide groups results in significantly broader amide I′ bands and even split amide I′ IR into two distinct components. Although the simulations predict substantially different frequencies for vibrations of the explicitly solvated and the buried amide groups, these frequency differences are smaller than those between the amide vibrational frequencies in the fully solvated and gas-phase R-helices. As a consequence, the amide I′ maxima of the partly solvated R-helices fall between those for the fully solvated and gas-phase ones. Interestingly, while the frequencies of the solvated amide groups do not change with the degree of solvation, the unsolvated group vibrations shift higher in the less solvated (PSB) model R-helix as compared to the more partially solvated PSA. These effects are most evident in the PSA(2) and PSB(2) models, where the amide I′ band separates into the distinct absorption maxima of the solvated amide groups and the unsolvated ones. The low-frequency maxima from the solvated group vibrations are 5 cm-1 higher than the FS amide I′ maximum in both PSA and PSB. The frequency shift of the high-frequency maxima as compared to the gas-phase helix GP is ∼17 cm-1 in PSA(2) and ∼12 cm-1 in PSB(2). These shifts in the vibrational frequencies are due to the global effect of the solvent on both explicitly solvated and unsolvated amide vibrations in the partially solvated R-helix. The unsolvated amide groups “feel” the presence of the solvent, which shifts their vibrational frequencies significantly lower, even though they

Turner and Kubelka are not explicitly hydrogen bonded to water. At the same time, the solvated amide group vibrations are less affected by the solvent than in fully solvated R-helix, because there is less water present. The overall frequency shift of the amide I′ depending on the degree of solvation of the R-helix is consistent with the differences in the experimental amide I′ frequencies in proteins (∼1650 cm-1) and fully solvated oligopeptide R-helices (∼1630 cm-1). In addition, the ∼5 cm-1 frequency shift of the unsolvated amide I′ component between the more (PSA) and less (PSB) explicitly solvated models, but no frequency shift of the solvated amide component, has also a parallel in the experimental data on R-helical proteins. In larger helical proteins, where the R-helices are more buried from the solvent, the amide I′ maximum is found typically around 1650 cm-1.1,13,14 In two-helix coiled coils, such as GCN4,16 the amide I′ maximum was reported at 1645 cm-1, and in helix-turn-helix proteins, such as subdomain of P22 viral protein or de-novo designed RtR (K. E. Amunson and J. Kubelka, unpublished), the amide I′ maximum at 273 K is at 1643 cm-1. By contrast, the solvated amide I′ components are generally found at ∼1630 cm-1, independent of the degree of solvation of the constituting R-helices.13,14,16,17 While the overall broadening as a consequence of diminished inter-amide coupling is also reflected in the calculated VCD band-shapes, the simulated VCD amide I′ spectra for the most part retain the characteristic sign pattern common to the righthanded helices. In all cases, predominantly negative VCD is computed at the high frequency and positive toward the low frequency. The relative stability of the VCD band-shapes contrasts with the calculations of Bour and Keiderling,27 who theoretically studied the vibrational spectra of a model β-hairpin and found the most pronounced effects of the nonuniform interaction of the amide groups with solvent on the VCD. This is most likely a consequence of much stronger R-helical VCD, which is dominated by the intra-helical amide interactions and is less sensitive to perturbations as compared to other structures, namely the β-sheets with much weaker intrinsic VCD.39 The details of the VCD band-shapes, however, do reflect the decoupling and enhanced dispersion in the individual vibrational modes in the partially solvated R-helices. In the VCD this increased complexity arises, like in the IR, from more localized normal modes with less overall VCD intensity, but also from cancellations of the oppositely signed VCD transitions. The alternating sign patterns for both PSA and PSB resemble partially overlapping VCD bands of two helices: one to the low and one to the high frequency. All of the simulated amide I′ VCD can be generally characterized as (+,-,+,-) sign bandshapes. These shapes are very well apparent especially for the less solvated PSB models. However, this sign pattern is for a large part a consequence of the N-deuteration, as demonstrated in Figure 5. Experimentally, upon N-deuteration the R-helical VCD changes from a simple couplet (+,- from the low to high frequency) to a three-component (-,+,-) shape.3 This shape is reproduced in the DFT-based VCD simulations for R-helices only when solvent is included.25 The simulated VCD for FS shows very weak negative VCD, much weaker than that previously computed for a longer 21-amide R-helix. The shorter R-helix used in this study is the most likely reason for this difference, because no negative low-frequency VCD was predicted for a short N-deuterated, fully solvated 7-amide R-helix.25 In the partially solvated helices, the N-deuteration results in an additional, relatively intense negative VCD around 1680 cm-1, although they are of the same length as FS. This suggests that partial solvation may result in more pronounced

IR and VCD of Partially Solvated R-Helices low-frequency negative amide I′ VCD in the protein R-helices, and, because this feature is computed only for R-helices with solvent, the negative low-frequency VCD observed experimentally may be a signature of the solvated R-helical vibrations. Although we compute an additional positive VCD even lower in frequency than the N-deuteration induced negative band, which is not experimentally observed, this feature may be resolved in the simulations due to the overestimated spread of the amide modes, discussed in more detail below. In our simulations, the computed amide I′ IR band-shapes strongly depend on which particular amide groups are in contact with solvent. We have presented only two examples out of seven differently solvated variants of each PSA and PSB. The two variants shown represent the limiting cases: the PSA exhibits the most uniform amide I′ IR, while the PSA(2) amide I′ IR is most distinctly split into the solvated and unsolvated contributions. The same trends were calculated for the PSB models, which differ from the PSA only by the different number of water molecules, but correspond to each other in terms of along which side the R-helix is in contact with water. Despite the differences in the simulated band-shapes for different solvated faces of the model R-helix, all variants of PSA have in common relatively intense transitions near 1708 and 1678 cm-1, which in PSA(2) give rise to the two amide I′ maxima. Similarly, the less solvated PSB-derived models all exhibit relatively intense modes at 1712 and 1678 cm-1, which in PSB(2) correspond to the resolved amide I′ IR peaks. In all cases, these transitions can be assigned primarily to the unsolvated (the high frequency) and solvated (the low frequency) amide vibrations (Figure 3b,c and Figure 7). The overall shape of the amide I′ IR band is given by the relative intensities of these transitions with respect to other modes near the center of the band (1690-1700 cm-1). In PSA(2), the solvated groups are coupled into an intense collective mode and so are the unsolvated groups (Figure 7a), resulting in a sharp, doublet-like amide I′. By contrast, in PSA both the solvated and the unsolvated modes are relatively isolated on few explicitly neighboring groups and are therefore less intense, and the modes near the band center (Figure 3b), which involve both solvated and unsolvated amides, are more intense. In PSB(2), the solvated and unsolvated modes are not enhanced by coupling, but the distinct double maximum amide I′ in PSB(2) is predominantly due to much less intensity near the center of the amide I′ contour, which is due to the vibration from both solvated and unsolvated amides near the C-terminus of the helix. It should be noted that the mixed solvated-unsolvated amide modes largely involve the helical termini. The termini of the helix tend to naturally vibrate higher (the C-terminus) or lower (N-terminus) in frequency than the dominant helical modes. As a consequence, these central modes may be significantly diminished in longer helices or in proteins. The intensity redistributions among the individual normal modes are a consequence of the predominantly local nature of the vibrational couplings.4 Because the neighboring amides couple most strongly, the efficiency of the overall coupling is affected by the inter-dispersed solvated and unsolvated groups. This is reminiscent of the anomalous 13C isotopic band intensities in large peptide β-sheets.40 In these intermolecular sheets, although only two amide groups were labeled out of 13, certain spatial distribution of the 13C labeled amides in the antiparallel β-sheet efficiently decoupled the 12C vibrations so that the IR intensity of the coupled 13C modes appeared greatly enhanced over the intensity of local 12C vibrations. These significant changes in the inter-amide vibrational coupling and, therefore, in the IR intensities were computed even though the

J. Phys. Chem. B, Vol. 111, No. 7, 2007 1843 inter-amide coupling constants remained unchanged, because the force fields were not affected by the isotopic substitutions. The dependence of the IR amide I′ spectra on which particular amide groups are solvated, rather than just on how much the R-helix is exposed to solvent, illustrates the potential complexity of the solvent effects on the vibrational spectra of protein structures. The solvent-induced frequency shifts combine with intra-helical vibrational coupling and may give rise to different spectral signatures depending on the details of the interaction of the particular protein R-helix with solvent. The simulated broad and multicomponent amide I′ bandshapes are not typical in the experimental spectra of R-helical proteins. Both amide I′ IR and VCD are similar to those found in the model R-helical peptides: relatively narrow, sharply peaked amide I′ IR, and (-,+,-) VCD bands.3 The main difference between the IR spectra of proteins and model oligopeptides is the change in the vibrational frequencies. In R-helical proteins, the amide I′ IR maximum occurs near 1650 cm-1, as compared to ∼1630 cm-1 amide I′ IR maximum in the alanine-rich peptides. However, the evidence for different solvation states of protein helices is often found as additional low-frequency amide I′ IR bands. The ∼1630 cm-1 amide I′ component can often be resolved in the R-helical protein IR spectra and is typically assigned to the solvated R-helix.13-17 These low-frequency bands are typically much weaker than the main, higher-frequency ones, as to give rise to a substantially broader or even a two-component amide I′ IR spectrum. A notable exception is the R-helical coiled-coil protein tropomyosin,15 which exhibits an intense component at 1630 cm-1 that has been assigned to amides hydrogen bonded to water, in addition to the higher frequency bands at 1639 and 1650 cm-1. The reason for this discrepancy stems in large part from our model of solvation as rigidly hydrogen-bonded water molecules. Effectively, our solvated R-helix models represent “frozen” peptide-water clusters. In this respect, the simulated spectra much better correspond to the experimental data at cryogenic temperatures of DeGrado and co-workers.16,17 These authors measured the amide I′ spectra of a coiled coil16 as well as of a three-helix bundle protein17 at a wide range of temperatures from ambient to 10 K, and showed that the amide I′ spectra of proteins in water change significantly within this temperature range. While at ambient temperatures the amide I′ of the GCN4 coiled coil was a uniform band, peaked near 1645 cm-1, when cooled to 10 K, a second, low-frequency maximum appeared below 1630 cm-1, resulting in a distinct two-component band-shape.16 Very similar results were observed for the three-helix bundle R3D, although the amide I′ IR at 13 K was not split into two distinct maxima, but rather a broad band with a flat maximum between 1625 and 1650 cm-1.17 The intense low-frequency bands at low temperatures were assigned to solvated amide groups and attributed to much stronger hydrogen bonding between the peptide and water, which above the glass transition temperature of water is weakened by the thermal motion. Our simulations are consistent with this argument, because with tightly hydrogen-bonded solvent molecules, we predict broad and split amide I′ band-shapes similar to those experimentally observed at very low temperatures. At ambient temperatures, where the amide I′ spectra of proteins are more uniform, the hydrogen bonds between water and protein amide groups must be significantly weaker. Quantitatively, however, the simulations overestimate the splitting between the solvated and unsolvated amide I′ bands. For the GCN4 coiled-coil experimentally at 10 K, the two bands were separated by ∼20 cm-1,16 while in our simulations the

1844 J. Phys. Chem. B, Vol. 111, No. 7, 2007 separation is 30-35 cm-1. These effects are again most evident in the PSA(2) and PSB(2) models with distinctly split amide I′ bands. The overestimation of the experimentally seen splitting may be due to the frequency of the solvated amide groups being computed too low, but this is not likely the case. In the cryogenic experiments, the low-frequency band was found even lower than the typical R-helical maxima for the fully solvated helices at ambient temperatures.16,17 By contrast, in our simulations, the solvated amide vibrations are higher, by ∼5 cm-1, than in the fully solvated R-helix (Figure 2). Furthermore, if we identify the high-frequency amide I′ IR component with the buried R-helix amide I′ band in proteins, from our simulations the frequency of this band would be shifted by 35-40 cm-1, depending on the degree of solvation, as compared to the amide I′ of a fully solvated helix FS. Considering that the R-helical alanine-rich peptides have the amide I′ maxima at ∼1630 cm-1, this would put the protein amide I′ maxima at 1665-1670 cm-1, which is higher than that experimentally observed, again overestimated by ∼10-15 cm-1. The reason for the splitting between the solvated and unsolvated band components being computed too high is therefore most likely an overestimation of the vibrational frequencies of the high-frequency, unsolvated amide I′ components. Even when buried inside a protein, the amide groups would be influenced by the environment. Although in general the interior of a protein is expected to be a low dielectric constant medium, it is still not a vacuum. The sensitivity of the amide vibrational frequencies to the polarity of the environment has been demonstrated.7,41,42 Comparison of the simulated amide I′ band-shapes for 13C substituted model R-helices to the cryogenic experiments reflects the larger computed splitting between the solvated and unsolvated group frequencies. Isotopic labeling of two solvent exposed amide groups results in a distinct isotopic sideband almost 50 cm-1 below the 12C main band, which agrees with experiment.16,17 On the other hand, substitution of the unsolvated groups does not show any low-frequency 13C sideband. Rather, the intensity is shifted more into the ∼1680 cm-1 component from the solvated, unlabeled amide groups, resulting in a sharper low-frequency IR maximum. While the experimental spectra for both GCN4 and R3D with 13C labels at buried residue positions exhibited more sharply peaked 12C bands toward the lower frequency, this was most likely due to the reduced intensity of the high-frequency, buried amide band. The 13C sideband was observed in all cases, in R3D at least partially resolved.17 This disagreement may in part be a consequence of different isotopic substitution, for in the experiments all of the buried amide groups were 13C labeled, while in our simulation only two were labeled, near the center of the helix. However, it is mostly due to the unsolvated amide frequencies being calculated too high, as was already discussed above. For practical purposes of 13C isotopic labeling, it is therefore desirable to label exposed groups, because those will shift furthest in frequency, but also decouple most efficiently from the rest of the protein vibrations to best reflect the local structural information.4 Substitution of the buried groups that does not give rise to a separate 13C band, even if it causes observable changes to the amide I′ IR band-shape, is likely to be much less useful for site-specific structural studies. Although, if the 13C isotopic editing is used to monitor unfolding, and buried residues are labeled, the isotopic sideband may become more resolved as the protein unfolds and the isotopically substituted groups become exposed to solvent. Such isotopically edited spectra may therefore report on structural changes indirectly, through solvation of the labeled residues.

Turner and Kubelka From the above comparisons with the experimental data, it is apparent that the explicitly hydrogen-bonded water to the amide groups on the exposed face of the R-helix is not an adequate model for simulation of the vibrational spectra of the partially buried R-helices in proteins in solution at ambient temperatures. At room temperature, due to the thermal motion, the water appears to form hydrogen bonds to the protein amide groups transiently, with overall occupancy significantly less than 100%.17 Taking into account the solvent dynamics would require calculations of the spectra for a large number of configurations of the solvent molecules. For all but the smallest peptides, such calculations are too expensive at the fully quantum mechanical level. A much less computationally demanding approach is the use of molecular dynamics simulations to generate multiple solvent configurations that are subsequently combined with empirical corrections for the frequency shifts caused by the electrostatic field due to the solvent molecules.19,27,41,42 Such methodology is useful not just for approximating the effects of the solvent, but it could also take into account the electrostatic field of the protein side-chains and model the effect of the “interior” of the protein on the vibrational frequencies of the buried amides.41 This may be equally important, because the above simulations seem to overestimate the (relative) frequencies of the unsolvated amide groups, with respect to those of the fully solvated peptides and solvated amide groups, as compared to the experimental frequency differences. Amino acid sidechains may represent another important factor that may have to be taken into account for realistic simulations of protein vibrational spectra, because especially polar and charged sidechain groups can have significant effects on the amide I vibrational frequencies.41,43 The frequency and intensity corrections in the empirical models, however, have to be calibrated by fitting the parameters of the model to the fully quantum mechanical calculations of the vibrational spectra for peptidewater clusters. Therefore, in addition to illustrating the effects of the directly hydrogen-bonded water on the vibrational spectra of partially buried peptide helices, the non-empirical, fully quantum mechanics-based calculations presented above may serve as important benchmarks for the development of new approximate approaches for accurate simulation of the vibrational spectra of proteins in solution. Conclusion The DFT-based simulations demonstrate the effects of hydrogen bonding of the amide groups in model protein-like R-helices on the amide I′ IR and VCD spectra. The simulated spectra for the partially solvated helices are significantly different from those for the fully solvated R-helix, whose amide I′ IR and VCD are, aside from the overall frequency shift, essentially the same as the gas-phase R-helical spectra. The presence of both solvated and unsolvated amide groups results in much broader amide I′ IR and VCD bands. The varying degree of solvation of the R-helix is reflected in the overall frequency shift of the amide I′ bands and predominantly in the shift in the vibrational frequency of the unsolvated amide groups. The VCD band-shapes are generally less affected by the solvent than the IR, in agreement with the previous simulation studies as well as with experiment. The VCD exhibits additional sign variations due to the N-deuteration, suggesting that the lowfrequency negative VCD intensities, typical for the N-deuterated R-helices, arise from the solvated amide group vibrations. The amide I′ band-shapes, especially the IR, depend not only on how much the helix is solvated (or buried), but also along which side the R-helix makes contact with the solvent. This shows

IR and VCD of Partially Solvated R-Helices that the effects of solvation on the partially buried R-helices can be rather complex and vary from case to case and that solvation must be taken into account for accurate simulations of the vibrational spectra of proteins in solution. The simulated amide I′ IR band-shapes are in agreement with the experimental spectra for R-helical proteins in solution at very low temperatures, but not at room temperature, where the thermal fluctuations weaken the peptide-water hydrogen bonds. For more realistic simulations of the protein vibrational spectra at ambient temperatures, the solvent dynamics must be taken into account. In addition, in quantitatively comparing the frequencies of the solvated and unsolvated groups with experiments at cryogenic temperatures, the simulations overestimated the frequency splitting, most likely due to the frequency of the unsolvated groups being computed too high. Therefore, the influence of the surrounding environment on the buried amide group vibrations has to be taken into account as well. The results of the above simulations are important for further theoretical studies of the solvent effects on the vibrational spectra of peptides and proteins as well as for further development of theoretical methods for simulations of the vibrational spectra of proteins in solution. Acknowledgment. This work was supported by a Faculty Grant-in-Aid program of the University of Wyoming and by the national Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF), and Terascale Extensions: Enhancements to the Extensible Terascale Facility. We also wish to thank Dr. Petr Bour for sharing his programs for parameter transfer and vibrational analysis. References and Notes (1) Barth, A.; Zscherp, C. Q. ReV. Biophys. 2002, 35, 369. (2) Krimm, S.; Bandekar, J. AdV. Protein Chem. 1986, 38, 181. (3) Keiderling, T. A. Peptide and protein conformational studies with vibrational circular dichroism and related spectroscopies. In Circular Dichroism: Principles and Applications, 2nd ed.; Nakanishi, K., Berova, N., Woody, R. A., Eds.; Wiley: New York, 2000; p 621. (4) Huang, R.; Kubelka, J.; Barber-Armstrong, W.; Silva, R.; Decatur, S. M.; Keiderling, T. A. J. Am. Chem. Soc. 2004, 126, 2346. (5) Choi, J. H.; Ham, S. Y.; Cho, M. J. Phys. Chem. B 2003, 107, 9132. (6) Krimm, S. Interpreting Infrared Spectra of Peptides and Proteins. In Infrared Analysis of Peptides and Proteins: Principles and Applications; ACS Symposium Series; Singh, B. R., Ed.; American Chemical Society: Washington, DC, 2000; p 38. (7) Kubelka, J.; Keiderling, T. A. J. Phys. Chem. A 2001, 105, 10922. (8) Torii, H.; Tatsumi, T.; Kanazawa, T.; Tasumi, M. J. Phys. Chem. B 1998, 102, 309. (9) Huang, C. Y.; Klemke, J. W.; Getahun, Z.; DeGrado, W. F.; Gai, F. J. Am. Chem. Soc. 2001, 123, 9235. (10) Silva, R. A. G. D.; Kubelka, J.; Decatur, S. M.; Bour, P.; Keiderling, T. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 8318. (11) Yoder, G.; Pancoska, P.; Keiderling, T. A. Biochemistry 1997, 36, 15123.

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