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Characteristic Raman Optical Activity Signatures of Protein β‑Sheets Thomas Weymuth and Markus Reiher* Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland

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S Supporting Information *

ABSTRACT: In this study, we compute and analyze theoretical Raman optical activity spectra of large model β-sheets in order to identify reliable signatures for this important secondary structure element. We first review signatures that have already been proposed to be indicative of β-sheets. From these signatures, we find that only the couplet in the amide I region can be regarded as a truly reliable signature. In addition, we propose a strong negative peak at ∼1350 cm−1 to be another good signature for parallel as well as antiparallel β-sheets. We study the robustness of these signatures with respect to perturbations induced by the amino acid side chains, the overall conformation of the sheet structure, and microsolvation. It is found that the latter effects can be very well understood and separated employing the concept of localized modes. Finally, we investigate whether Raman optical activity is capable of discriminating between parallel and antiparallel β-sheets. The amide III region turns out to be most promising for this purpose.

1. INTRODUCTION Together with α-helices, β-sheets belong to the most important and well-known elements of protein secondary structure. While X-ray crystallography and nuclear magnetic resonance (NMR) allow one to elucidate the overall structure of a protein at an atomic level, electronic circular dichroism (CD) spectra provide a simple way to determine the amount of different secondary structure elements present in a given protein.1 Another successful chiroptical technique in this respect is Raman optical activity (ROA),2 which measures the difference of Raman scattering intensity of right and left circularly polarized light (i.e., it is the chiral variant of Raman spectroscopy). Over the past years, both experimental and theoretical studies have established characteristic ROA signatures for many types of secondary structure elements.3−5 In experimental studies, the identification of such signatures is usually based on the comparison of spectra of proteins featuring the same as well as different secondary structure elements. However, most proteins have a rich secondary structure, such that it is difficult to unequivocally establish signatures for the individual secondary structure elements. As an additional challenge, the fact that the normal modes are not directly accessible in experimental studies makes it often very difficult (if not impossible) to assign a given spectral band to a certain vibration. Furthermore, the different factors contributing to the overall spectrum (e.g., molecular structure, conformational dynamics and averaging, solvent effects, etc.) are very difficult to separate experimentally. Here, a theoretical approach can provide additional insight, as one is basically not restricted in the choice of model systems. It is thus possible to study a polypeptide featuring only the secondary structure element of interest, which makes the identification of characteristic © 2013 American Chemical Society

signatures considerably simpler, although it does not guarantee that such a characteristic spectral signature can be detected in a crowded spectrum. Our group has carried out theoretical studies on the signatures of α-helices,6 310-helices,6 and β-turns,7,8 but no theoretical study has addressed the ROA signatures of β-sheets yet. It is the aim of this work to fill this gap. To this end, we have calculated theoretical ROA spectra for various large models of parallel as well as antiparallel β-sheets. A detailed analysis of these, together with a range of experimental spectra published in the literature, should provide us with characteristic signatures of protein β-sheets. We first review the signatures that have already been proposed to be indicative of β-sheets, based on experimental spectra, in section 2. Then, in section 3 we explain our computational procedure as well as the different β-sheet structures we have chosen to investigate. After this, we present the theoretical ROA spectra of these model systems and analyze them in section 4. Finally, we give a conclusion together with a short outlook in section 5.

2. PROPOSED SIGNATURES OF β-SHEETS The first experimental study on ROA signatures of β-sheets was conducted in 1994 by Barron and co-workers.9 They proposed that positive ROA intensity between ∼1000 and 1060 cm−1 originates from β-sheet structures. This assignment is still assumed to hold true.3 However, the experimental spectrum of α-helical poly(L-alanine) in dichloroacetic acid clearly also Received: June 17, 2013 Revised: August 21, 2013 Published: September 10, 2013 11943

dx.doi.org/10.1021/jp405981h | J. Phys. Chem. B 2013, 117, 11943−11953

The Journal of Physical Chemistry B

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shows a positive peak at ∼1047 cm−1 (if the solvent is changed to only 30% dichloroacetic acid and 70% chloroform, this peak is found at ∼1044 cm−1).10 We should also note here that Barron et al. explicitly state that this spectral feature of β-sheets can greatly vary in intensity and wavenumber range,3 which might reflect structural variations within the strands. Furthermore, Barron and co-workers also observed a sharp positive peak at ∼1313 cm−1, which they assigned to an antiparallel β-sheet structure. Five years later, the same group observed similar signals in ROA spectra of bovine βlactoglobulin, a protein that is rich in antiparallel β-sheet.11 However, adjacent strands of antiparallel β-sheets are connected by β-turns, and it is thus not a priori clear whether this signal arises from the strands or from the turn structures. In this context it is important to note that our group recently found a similar band in small β-turn model systems.8 Moreover, in experimental spectra of disordered poly(L-lysine) and poly(Lglutamic acid), a positive signal is observed at ∼1320 cm−1.3 It is therefore very likely that a positive signal around ∼1310− 1320 cm−1 is characteristic for turn structures rather than βstrands. Finally, Barron and co-workers found a characteristic couplet, negative at lower and positive at higher wavenumbers and centered around ∼1650−1670 cm−1, to be indicative of βsheets.9 This assignment has been confirmed multiple times since then.3,11−13 Note that the α-helix shows a similar couplet, which is, however, shifted to lower wavenumbers by ∼5−20 cm−1.3,6 As another signature of β-sheets, Blanch et al. proposed a negative band at ∼1248 cm−1.11 In fact, a similar negative peak was observed between ∼1244 and ∼1253 cm−1 in a range of other proteins incorporating β-sheets,3,12,13 such that this signature may also be regarded as being firmly established. We should also note here that intermittently, a negative band around ∼1220 cm−1 was thought to be a signature for β-sheets as well,3,11,12 even though it was originally assigned to β-turns.9 A detailed analysis of the experimental spectra published so far shows that there is no justification for this reassignment,8 which is further confirmed by our theoretical study on model β-turns, which all show negative ROA intensity at ∼1190 cm−1.8 In summary, based on an analysis of the experimental spectra published so far, there are two signatures that can be regarded as being reliable characteristics of β-sheets. First, negative intensity between roughly 1240 and 1255 cm−1, and a −/+ couplet centered around ∼1650−1670 cm−1. Furthermore, positive ROA intensity in the range of ∼1000−1060 cm−1 has also been found in many spectra of proteins featuring β-sheets, although we should recall that this signature is quite variable,3 and does also occur in experimental spectra of α-helical polypeptides.10 All relevant signals are summarized in Table 1.

together by hydrogen bonds. As in the case of the α-helix, all possible backbone hydrogen bonds are formed. One distinguishes two main forms, in which β-sheets occur in proteins; these are denoted as parallel and antiparallel β-sheets.14 The two forms feature distinct hydrogen bonding patterns, as shown schematically in Figure 1. While the hydrogen bonds are spaced

Figure 1. Schematical Lewis structures of a section of two adjacent strands of antiparallel (a) and parallel (b) β-sheets. The two strands of the antiparallel β-sheet are connected by a β-turn, which is drawn in red. The dashed lines at the end of the polypeptide chain denote the continuation of the protein backbone.

evenly in the parallel β-sheet, there is an alternation of narrower and wider spaced hydrogen bond pairs in the antiparallel βsheet. Furthermore, the hydrogen bonds between adjacent strands of an antiparallel β-sheet are almost parallel to each other, while they form significant angles in the case of parallel β-sheets. For our study, we constructed idealized models of both, parallel and antiparallel β-sheets. All models consist of two strands. This will allow us to reproduce generic signatures of βsheets while still maintaining a reasonable size of the models (note also that antiparallel β-sheets are often observed as a twisted ribbon of just two strands14). In analogy to a previous study,6 we employed (S)-alanine as the only residue type, which is the simplest chiral amino acid. In the case of the antiparallel β-sheet, we investigate two models: in the first one, the two strands are connected by a β-turn of type I, whereas we removed the four amino acid residues participating in this turn in a second model. This allows us to study the influence of the turn structure on the overall ROA spectrum. For the parallel βsheet model, the individual strands cannot be connected by short turns, but only by longer loops. These three model systems are depicted in Figure 2. The antiparallel β-sheet with turn consists of a total of 20 (S)-alanine residues, while the other two models feature only 16 amino acids. At their Nterminus, the polypeptides are terminated with an additional

3. METHODOLOGY 3.1. Model Structures. In β-sheets, several almost fully extended strands of the protein polypeptide chain are held Table 1. Summary of ROA Signatures Proposed in the Literature to Be Characteristic of β-Sheets signature

wavenumber range/cm−1

ROA intensity

1 2 3

∼1000−1060 ∼1240−1255 ∼1650−1670

positive negative −/+ couplet 11944



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Figure 2. Model structures investigated in this study: (a) antiparallel β-sheet, the two strands of which are connected by a β-turn; (b) the same antiparallel sheet with the turn removed; (c) parallel β-sheet.

corresponding to def-TZVP. During the structure optimization, electronic energies were converged to 10−6 hartree, while the maximum norm of the Cartesian electronic energy gradient was converged to 10−4 hartree/bohr. It was ensured by vibrational analysis that all structures correspond to true minima on the potential energy surface. The harmonic wavenumbers, normal modes, and the derivatives of the polarizability tensors necessary for the evaluation of the ROA backscattering intensity were calculated in a seminumerical fashion using the program SNF19 of the package MOVIPAC,20 employing a stepsize of 0.01 bohr (this reduces the numerical error in the frequencies to about 1 cm−1; this is small compared to the error introduced by the harmonic approximation, which can be expected to be generally smaller than 20 cm−1 for the methodology employed here19,21−25). For the individual distorted structures, analytical energy gradients and polarizability tensors were computed with our local version of TURBOMOLE’s escf module,26 utilizing the same density functional and basis sets as described above. Electronic energies were tightly converged to 10−8 hartree for the distorted structures using the dense m4 grid of TURBOMOLE from which the properties (i.e., frequencies and intensities) are calculated. The vibrational frequencies obtained were not scaled since it is known that BP86 due to a fortunate error cancellation yields harmonic frequencies that are already in good agreement with measured fundamental ones.19,21−25 The velocity representation of the electric dipole operator was applied in order to ensure gauge invariance. The ROA backscattering intensities were obtained for a wavelength of 799 nm and it was ensured in all cases that the energy corresponding to this wavelength is far

hydrogen atom, leading to an NH2 group, while at the Cterminus, the carboxy group was replaced by an acetyl moiety. These terminal groups will introduce vibrations that are not found in β-sheets present in proteins. As a result, we will see some artifacts in the amide I region, which, however, have no adverse effect on our investigation and conclusions. In order to further analyze ROA signatures of β-sheets, we also set up a second series of model systems, depicted in Figure 3. We introduced perturbations to the idealized β-sheet models of Figure 2; in one case, we change either one or all amino acid residues from (S)-alanine to glycine (Figure 3a,b), while in the second case, we study microsolvation by adding one and two water molecules to one and two peptide units, respectively (Figure 3c). Finally, we also consider the typical twist found in most β-sheets in order to study the robustness of the signatures with respect to large-scale conformational changes. To this end, we extracted two strands of antiparallel β-sheet from concanavalin A (residues 60−66 and 73−79). In order to guarantee consistency with the rest of our study, we changed all amino acids to (S)-alanine in this model system (see Figure 3d) and optimized the whole model in an unconstrained optimization. 3.2. Computational Details. All structures were fully optimized (i.e., without any constraints) with the BP86 exchange−correlation functional15,16 and Ahlrichs’ valence triple-ζ basis set with one set of polarization functions17 (dubbed def-TZVP) on all atoms as implemented in the TURBOMOLE program package (version 5.10).18 Furthermore, in all calculations, advantage was taken of the resolution-of-theidentity (RI) approximation with the auxiliary basis sets 11945



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Figure 3. Second set of model systems studied: (a) parallel β-sheet with one residue changed to glycine; (b) antiparallel β-sheet with all residues changed to glycine; (c) parallel β-sheet with one and two amino-acid residues microsolvated by one and two water molecules, respectively; (d) twisted antiparallel β-sheet, extracted from concanavalin A.

positive peak in the ROA spectrum of the antiparallel β-sheet containing a turn, while the other two spectra do not show positive ROA intensity in this range. However, in these latter cases, there are always several normal modes associated with positive intensity in the relevant spectral range, but they are always annihilated by near-lying normal modes that are associated with negative ROA intensity. This signature thus does not appear to be a sufficiently reliable general signature for β-sheets, which is in line with the experimental observation that it varies in both intensity and wavenumber range.3 The second signature, namely, a positive peak between ∼1240 and 1255 cm−1, cannot be identified in any of the three spectra in Figure 4. However, this signature is found in all experimental spectra published so far, except in the spectra of poly(L-lysine) in water at 50 °C, which also features a β-sheet

below any electronic excitations. The line spectra resulting from this methodology were finally broadened by means of a convolution with a Lorentzian line shape featuring a full width at half-maximum (fwhm) of 15 cm−1. This line broadening as well as the analysis and graphical representation of all spectra were produced with the program MATHEMATICA (version 7.0).27

4. RESULTS AND DISCUSSION 4.1. Proposed Signatures. We first investigate the ROA spectra of the three idealized model systems of antiparallel and parallel β-sheets (Figure 2) for the existence of the signatures proposed in the literature. The three ROA spectra are shown in Figure 4 with the three regions where signatures are expected highlighted in blue. Concerning the first signature (positive intensity between ∼1000 and 1060 cm−1), we identify a weak 11946



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we conclude that the ROA signals stemming from the turn8 are simply covered by the signals arising from the rest of the βsheet models. Due to the similarity of the three spectra, we recognize many spectral regions where all spectra show either positive or negative ROA intensity. However, not all of these regions should be regarded as true signatures. To be considered as a reliable signature, we should identify a significantly strong peak, the normal modes of which are associated with the peptide backbone of the sheet structure. One peak that is particularly strong and almost identical in all three spectra is the negative band at ∼1350 cm−1. It is the strongest peak in the spectra of the two antiparallel β-sheet models, and, although somewhat weaker, is also pronounced in the case of the parallel β-sheet. Furthermore, the shape of this peak is the same in all spectra, being constituted of only a few very close-lying normal modes. These normal modes are associated with Cα−H bending and CH3 deformation vibrations (see Figure 5, middle). The spectral range of this characteristic signature is highlighted in red in Figure 4. It can also be found in all experimental spectra of β-sheet models and proteins incorporating a significant amount of β-sheets,3,9,11,12 and can thus be considered as being a reliable signature of β-sheets. 4.3. Robustness of β-Sheet Signatures. Of course, one important issue to clarify is how robust these signatures are, i.e., how strongly do they depend on the exact conformation of the β-sheet model, the particular type of side chain employed, and the environment such as solvent molecules? To investigate robustness against perturbations, we study the second set of model systems of Figure 3. 4.3.1. Influence of Side Chain. In order to investigate to which extent the characteristic β-sheet signatures depend on the actual amino acid side chain, we changed a single residue to glycine. The resulting ROA spectrum is shown in the middle panel of Figure 6. When comparing this spectrum to the one of the original, all-(S)-alanine parallel β-sheet (top panel of Figure 6), we find that the two spectra are very similar, and all signatures proposed above can be found in the spectrum of the modified β-sheet. This is not very surprising, since the original structure is only slightly changed. Nevertheless, there is one particular band that allows one to unequivocally distinguish the two spectra from each other, namely, a negative peak at 1246 cm−1 (highlighted in red in Figure 6). This band is caused by a single normal mode, which represents a bending vibration of the two hydrogen atoms of the glycine residue, coupled with N−H in-plane bending motions of the two neighboring peptide units (bottom panel of Figure 5). Interestingly, this negative band lies exactly in the region where Barron and co-workers proposed a signature of β-sheets, which, however, could not have been found in our all-(S)-alanine model systems (see above). To replace only a single amino-acid residue is certainly a small perturbation. Clearly, we need to study a larger modification of the model-sheet primary structure. Therefore, we changed all residues in the antiparallel β-sheet model from (S)-alanine to glycine (Figure 3b). Since glycine is achiral, all ROA signals stem from the chirality of the β-sheet structure and can thus be taken as an ultimate fingerprint of a sheet structure. The resulting ROA spectrum is shown in the lower panel of Figure 6. As can be seen, the overall intensity of all signals is diminished, which is due to the fact that all elements of local chirality are eliminated for the achiral amino acid. From Figure 6 it can be concluded that the resulting ROA spectrum

Figure 4. ROA spectra of the first set of (unperturbed) model structures shown in Figure 2. Highlighted in blue are the spectral regions in which characteristic signatures of β-sheets have been proposed in the literature, whereas the red region marks a signature identified in this work.

conformation.12 In this spectrum, one can only see a broad negative peak at 1218 cm−1, which rises to a strong positive peak at 1260 cm−1. It might thus be that also in this spectrum, there could actually be a somewhat weaker negative band at ∼1240 cm−1, which is simply annihilated by the negative peak nearby. Hence, we are left with a clear contradiction of experimental and theoretical results. For this to resolve, we need to investigate the calculated results in more detail. In fact, further investigations (see Section 4.3.1) give some evidence that this signature could be dependent on the amino acid side chains. Finally, a −/+ couplet in the amide I region is proposed to be characteristic for β-turns. Indeed, we find such a couplet only somewhat above the proposed spectral region, namely, centered around roughly 1700 cm−1. Note that the strong positive peak at ∼1650 cm−1 is partially an artifact of the model systems, as NH2 distortion vibrations also occur in this wavenumber range. However, in a protein-embedded β-sheet such an amino group would not be present. If we would discard the normal modes associated with these distortion vibrations, this peak would be somewhat less prominent, but still clearly visible (most of the normal modes in this region are associated with vibrations delocalized over the entire turn structure). The normal modes building up the characteristic couplet represent the typical amide I vibrations, i.e., C−O stretching vibrations, with some admixture of N−H in-plane bending. All vibrations are usually delocalized over the entire sheet structure, as can be seen in the top panel of Figure 5, which depicts a typical normal mode found in this spectral range. 4.2. Additional Signatures. When comparing the three spectra in Figure 4, we note that they are very similar, despite the fact that the three model systems locally feature quite different structural elements. For example, one antiparallel sheet involves a β-turn, while the other does not. However, the presence (or absence) of this turn cannot be unequivocally concluded simply based on the two ROA spectra. Therefore, 11947



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Figure 5. Typical normal modes of characteristic signatures of β-sheets, taking the parallel β-sheet model as an example: (a) amide I vibration at 1676 cm−1, which is responsible for the negative part of the couplet in Figure 4, bottom; (b) mode leading to the sharp negative peak at 1347 cm−1 in Figure 4, bottom; (c) CH2 deformation vibration of the glycine residue responsible for the band at 1246 cm−1 in Figure 6, middle.

specifically shows the intrinsic features of the β-sheet structure. However, we can expect that the overall chirality of the β-sheet structure also dominates the spectra of the all-(S)-alanine model systems. In fact, for large helical systems, it has been found that the helical chirality dominates over the local chirality of the individual amino acids,28 even though for smaller systems, the configuration of individual residues plays an important role.29 Concerning the β-sheet signatures, we see that both the couplet in the amide I region as well as the negative peak at ∼1350 cm−1 can clearly be recognized. In addition, we also find negative intensity in the range between 1240 and 1255 cm−1. These observations can be considered as evidence that this latter signature depends on the side chains within the sheet structure, being not present when only (S)-alanine builds up the strands, but being already clearly visible when only a single residue is changed to glycine. We should emphasize again that a negative peak at ∼1250 cm−1 is not visible in the spectrum of a model β-sheet consisting of (S)-lysine only (see above). 4.3.2. Twisted β-Sheets. The idealized structures of the βsheet models investigated above is often not found as such in protein structures. A characteristic structural distortion of protein-building β-sheets is that their strands are usually twisted. In order to examine the effect of such large-scale conformational changes, we extracted a twisted β-sheet from

the structure of the protein concanavalin A, and calculated its ROA spectrum (all residues were changed to (S)-alanine, and the structure was then fully optimized), which is shown in the lower panel of Figure 7. We see that the two spectra in Figure 7 are again quite similar from a global perspective, but there are some specific spectral regions where the two spectra of Figure 7 differ significantly. For example, the characteristic −/+ couplet in the amide I region is no longer visible in the spectrum of the twisted structure, but only the positive part of it is. Nevertheless, also in this spectrum there are some normal modes that are associated with negative ROA intensity just below the positive peak, but these modes cannot build up a negative band since they are canceled by close-lying normal modes associated with positive backscattering intensity. The strong negative peak at ∼1350 cm−1, however, is clearly present in the spectrum of the twisted β-sheet. 4.3.3. Microsolvation. Another important issue of concern is the influence of the environment as, e.g., exerted by solvent molecules. Unfortunately, a full-fledged solvation study (as carried out for a sugar molecule recently by Cheeseman et al.30) of the β-sheet models is beyond the scope of this work and computationally very demanding. However, we can selectively add only a few water molecules to the sheet structure and study the resulting microsolvation effects. Surely, this will not yield a 11948



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Figure 6. ROA spectra of the idealized parallel β-sheet consisting of (S)-alanine only (top panel) and with one residue changed to glycine (middle panel); the bottom panel shows the ROA spectrum of an antiparallel all-glycine β-sheet. The blue marks highlight the characteristic signatures established in section 4.1, while the red mark shows the spectral region with which the all-(S)-alanine β-sheet can be distinguished from both other structures.

Figure 8. ROA spectra of the idealized parallel β-sheet (top panel), and the same structure microsolvated with one and two water molecules, respectively (cf. Figure 3c).

For this, the analysis of the spectra in terms of localized modes is a suitable way to dissect the microsolvation effects. The concept of localized modes31,32 allows us to spatially localize selected vibrations, which are usually delocalized over the entire polypeptide chain in the basis of normal modes. This is achieved by a suitably chosen unitary transformation of the Hessian matrix (see ref 31 for details on the approach and refs 20 and 33 for publicly available implementations). In our case, we localized all 16 amide I vibrations, i.e., all normal modes between 1630 and 1720 cm−1. The resulting coupling matrix, i.e., the Hessian matrix in the basis of localized modes, is shown graphically in Figure 9. In this representation, we color-code the value of the coupling constants (i.e., the off-diagonal elements of the coupling matrix). When first investigating the coupling matrix of the unsolvated β-sheet (see the left-hand side of Figure 9), we see that all adjacent residues within one strand (i.e., residues 1−8 for the first strand, and residues 9−16 for the second strand), couple strongly to each other with coupling constants of approximately 8 cm−1. Interactions of a given residue with its second-nearest neighbor are much less pronounced and only slightly positive. All other couplings are almost zero, indicating that such long-range interactions can be neglected. However, the two strands are held together by hydrogen bonds, and accordingly there is a strong negative coupling constant between residues that are bound by hydrogen bonds (cf., the off-diagonal blue squares in Figure 9). We found that neglecting any coupling constants smaller than 2.5 cm−1 yields vibrational frequencies in close agreement with the reference values from the full coupling matrix; that is, the mean absolute deviation is only 1.2 cm−1 (see Table 2). As only the coupling between adjacent residues and residues that are bound by hydrogen bonds is larger than 2.5 cm−1, this shows that even the interactions between second-nearest neighbor residues may be neglected without introducing a large error. Comparing the coupling pattern of the unsolvated β-sheet to the one of the microsolvated β-sheet (top right-hand side of

Figure 7. ROA spectra of the idealized antiparallel β-sheet (top panel), and the same structure in the twisted conformation depicted in Figure 3 at the bottom.

spectrum resembling a fully solvated case, but it will allow us to understand solvation in a stepwise fashion. In this work, we only consider adding one and two water molecules to one and two peptide units, respectively (Figure 3c). The spectrum of these microsolvated parallel β-sheet models are shown in Figure 8 and compared to their unsolvated counterpart (Figure 8, top). Clearly, the addition of one and two water molecules constitutes a very small perturbation of the overall structure. Still, the local effect and its spread among the normal modes can provide insights into the change of the ROA spectrum upon hydration. For instance, a full-fledged molecular dynamics study of the solvated sheets would provide an enormous amount of information, which can then be rationalized by comparison to the results seen for the effect of a few water molecules studied here. 11949



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Figure 9. Coupling matrices of the localized amide I vibrations of the unsolvated parallel β-sheet (top left), and its microsolvated counterparts with one (top right) and two water molecules (bottom). The colored squares represent the coupling constants, ranging from −7 to 9 cm−1, while the grayscale squares on the main diagonal of the right coupling matrices represent the difference between the localized frequencies of the solvated structures with the one of the unsolvated β-sheet (also given in wavenumbers).

Figure 9), we see that it does not change much. The largest differences can be seen for the coupling of residue five (the one that has been microsolvated) to its neighbors. Therefore, we can conclude that the microsolvation has only a minor effect on the coupling pattern. Still, small changes can have unexpected strong effects on the normal mode spectrum. Apart from the coupling constants, the localized frequencies (i.e., the main diagonal elements of the coupling matrix) are important for the normal mode spectrum. In the coupling matrix of the microsolvated β-sheet (right-hand side of Figure 9), we show the difference between the localized frequencies of the solvated structure and the one of the unsolvated β-sheet are shown in a grayscale. We see that the localized frequencies do not change much between the two coupling matrices, with the exception of the localized frequency of residue five, which is shifted by almost 30 cm−1 to lower wavenumbers in the solvated case. An interesting question is whether this general pattern will change in a fundamental way if more than one residue is microsolvated. In order to study this issue within our simple bottom-up approach, we also microsolvated a second peptide unit. Note that the microsolvation of a unit directly adjacent to the one already microsolvated is impossible, as the C−O and N−H bonds of this peptide unit are oriented toward the inside of the β-sheet. Therefore, we added a second water molecule to

Table 2. Comparison of Frequencies Obtained by Neglecting Any Coupling between Non-Adjacent Residues As Well As between Resdiues Not Bound by Hydrogen Bonds (SoCalled Strong-Coupling Frequencies) with Their Reference Valuesa

a

strong-coupling frequencies

reference frequencies

error

1638.5 1641.6 1645.6 1648.1 1648.8 1650.2 1654.8 1669.9 1671.8 1674.1 1674.1 1677.5 1680.1 1683.3 1708.7 1710.6

1641.8 1642.6 1644.8 1646.3 1647.3 1648.7 1653.4 1669.7 1672.3 1673.2 1675.8 1676.9 1680.3 1684.8 1707.3 1712.2

3.35 1.07 0.77 1.75 1.42 1.52 1.38 0.15 0.45 0.91 1.64 0.54 0.18 1.45 1.39 1.67

All values are given in cm−1.

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Furthermore, all four secondary structure elements can be distinguished from each other by relying on the band shape of the amide I region. In the case of the β-turn, we find only positive ROA intensity in this spectral range, while the 310-helix produces a characteristic −/+ couplet. Both α-helix as well as (parallel and antiparallel) β-sheets feature a −/+ couplet in the amide I region, but these two secondary structure elements can also be distinguished from each other, as the couplet is shifted approximately 20 cm−1 to lower wavenumbers in the case of the α-helical model system (upon solvation, it is shifted to even lower wavenumbers35). Note that this very finding is also experimentally confirmed.3 4.5. Differentiating Parallel and Antiparallel β-Sheets. The discrimination of parallel and antiparallel β-sheets is a very important topic that has already been addressed in infrared and vibrational circular difference spectroscopy.36−38 We are therefore advised to analyze the data presented in this work with respect to the question of whether one can distinguish these two types of secondary structure by ROA spectroscopy. It is known that the extended amide III region, i.e., the spectral region between roughly 1200 and 1400 cm−1, is especially sensitive to secondary structure.39 Therefore, it comes as no surprise that we find a difference between parallel and antiparallel β-sheets exactly in this region. In fact, when closely analyzing the spectra depicted in Figures 4, 6, 7, and 8, we see that all parallel β-sheets exhibit only positive ROA intensity around ∼1275 cm−1, while we find weakly negative peaks for all antiparallel β-sheet structures. All of the perturbations considered above (different residue(s), twisted conformation, solvent molecule) have no influence on this spectral feature. Therefore, it appears to be quite robust and would thus be very well suited to differentiate parallel from antiparallel β-sheet structure. When analyzing the experimental ROA spectra of jack bean concanavalin A, human immunoglobulin G, and bovine β-lactoglobulin (which all contain significant amounts of antiparallel β-sheet), we identify a characteristic feature at about 1250 cm−1, which might correspond to the feature we proposed above.3 However, the spectrum of rabbit aldolase apparently shows a negative peak at ∼1253 cm−1,3 and it has been suggested that this band originates from the parallel β-sheet structure found in this protein. Therefore, further investigations are necessary to clarify whether the negative peak at ∼1275 cm−1 can be used as a reliable indicator of antiparallel β-sheets. Apart from the feature in the amide III region, we find one additional difference between the spectra of parallel and antiparallel sheets, namely, a peak at ∼1525 cm−1. This peak is negative in the case of parallel β-sheets, and positive for antiparallel sheets. However, this feature appears not to be very reliable. It vanishes when we add a single water molecule to the parallel β-sheet (cf., Figure 8). Moreover, the spectrum of the antiparallel all-glycine β-sheet shows only (weak) negative ROA intensity in this range, and not a positive peak as expected. Therefore, this feature is not consistent across all of our calculated spectra. Hence, one should not regard it as a diagnostic band to differentiate generic parallel β-sheet from antiparallel β-sheet structures.

the peptide unit of residue three in the same fashion as we treated residue five. The resulting coupling matrix is shown at the bottom of Figure 9. Again, the coupling pattern between the unsolvated and the microsolvated case does not change very much. Also for the localized frequencies, we make the same observation as above. All localized frequencies remain essentially unchanged, except the one of the two residues that are microsolvated. These frequencies are shifted by almost 30 cm−1 to lower wavenumbers. 4.4. Comparison to Other Secondary Structure Elements. After having established the −/+ couplet in the amide I region as well as the sharp negative peak at about 1350 cm−1 to be truly characteristic for β-sheets, we shall now investigate the ROA spectra of other secondary structure elements for an interference of these signatures with vibrations characteristic for, e.g., helices. We have already carried out theoretical studies on α- and 310-helices6 (see also refs 34 and 35), as well as on β-turns.8 The resulting ROA spectra are reproduced in Figure 10, together with the spectrum of the

Figure 10. Comparison of the ROA spectra of a model α-helix (top panel), the antiparallel β-sheet model investigated in this work, a type I β-turn, and a 310-helix (bottom panel; all structures composed from (S)-alanine residues). The data for the helical systems have been reproduced according to ref 6 and those for the β-turn according to ref 8.

antiparallel β-sheet model. Again, the two β-sheet signatures mentioned above are highlighted in blue. We can see that these signatures can well serve to distinguish the β-sheet from the other secondary structure elements. The sharp negative peak at ∼1350 cm−1 does not exist in the spectra of the helical polypeptides. Also in the case of the small β-turn, such a peak is not visible, even though there is a single normal mode which is associated with negative ROA intensity in this spectral region.

5. CONCLUSIONS AND OUTLOOK We have calculated ROA spectra of a range of antiparallel and parallel β-sheet model polypeptides in search for characteristic signatures. The stability of these fingerprints against structural and electronic perturbations has been investigated for (1) a 11951



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Regarding the question of whether parallel and antiparallel βsheets can be distinguished from each other by means of ROA spectroscopy, we found only one diagnostic spectral feature that would allow for such a discrimination of all our parallel βsheet models from their antiparallel counterparts. This spectral feature is a small peak at ∼1275 cm−1 in the amide III region, which is negative for antiparallel β-sheets, but positive for parallel β-sheet structures. However, whether this feature is as robust as needed for practical applications needs to be established by further theoretical and experimental studies.

replacement of a single (S)-alanine residue of one of the original all-(S)-alanine sheets by a glycine residue, (2) a replacement of all (S)-alanine residues by glycine, which allowed us to study the β-sheet specific ROA features, (3) the addition of a single water molecule, and (4) the twisting of the sheet structure. From the three signatures that have been proposed so far in the literature to be indicative for sheet structures (see Table 1), the first signaturepositive intensity between ∼1000 and 1060 cm−1could not be found in our theoretical spectra. This is in accord with experimental findings.3 A second signature, namely, a negative peak between ∼1240 and 1255 cm−1, cannot be found in the all-(S)-alanine model systems, but is clearly visible when glycine is present in the sheet structure. Therefore, our work gives some evidence that this signature is rather dependent on the amino acid side chains. The third signature, a −/+ couplet in the amide I region, could be fully confirmed in this study. This couplet is also particularly well suited to distinguish the β-sheet structure from other secondary structure elements, such as α- and 310-helices. In addition, we were able to propose another signature characteristic for parallel as well as antiparallel β-sheets, namely, a sharp negative peak at approximately 1350 cm−1. This band is very robust with respect to large-scale conformational changes of the sheet structure and can also be identified in all experimental spectra of β-sheet structures (or proteins incorporating a significant amount of this secondary structure element). In order to obtain transferable knowledge on microsolvation effects, we investigated the addition of a single water molecule. While the resulting ROA spectrum is almost identical to the unsolvated reference, the concept of localized modes allowed us to gain additional insight. For the amide I region, we found that the coupling pattern does not change significantly upon microsolvation. Adjacent amino acids couple quite strongly, while interactions between second-nearest neighbors are already much weaker, and any further interactions can be neglected (except residues that are bound by hydrogen bonds). Hydrogen bonds lead also to a significant coupling of amino acids, which are, however, negative (as opposed to the coupling within one strand). The only significant change introduced by the microsolvation is the localized frequency of the solvated residue, which is shifted almost 30 cm−1 to lower wavenumbers. We should explicitly state here that the addition of a single water molecule, although providing valuable insight, cannot account for all effects of a full solvation model. Therefore, further analysis of extended microsolvation patterns and molecular dynamics trajectories of solvated sheets is required for a complete understanding of the changes in the coupling matrix, such that the ROA spectrum of a solvated polypeptide chain might be constructed from the local-mode model. Work along these lines is currently carried out in our laboratory. Already at this stage, our simple solvation attempts provide a clear picture of the action of one (or two) solvent molecule(s), and this knowledge may become useful when results from molecular dynamics are to be interpreted. Such comparisons will then be useful to understand whether it might eventually be possible to estimate solvation effects of biomolecules from microsolvated and unsolvated reference structures. Clearly, this would provide access to solvation effects at dramatically less computational cost than required for a full-fledged quantum mechanics/molecular mechanics (QM/MM) approach.30

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates and Raman spectra of all structures investigated in this work. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the Swiss National Science Foundation SNF (Project 200020_144458/1). REFERENCES

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