Characteristic Raman Optical Activity Signatures of Protein β‑SheetsThomas Weymuth and Markus Reiher*

Laboratorium fur Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland

*S Supporting Information

ABSTRACT: In this study, we compute and analyze theoreticalRaman optical activity spectra of large model β-sheets in order toidentify reliable signatures for this important secondary structureelement. We first review signatures that have already beenproposed to be indicative of β-sheets. From these signatures, wefind that only the couplet in the amide I region can be regarded asa truly reliable signature. In addition, we propose a strongnegative peak at ∼1350 cm−1 to be another good signature forparallel as well as antiparallel β-sheets. We study the robustness ofthese signatures with respect to perturbations induced by theamino acid side chains, the overall conformation of the sheetstructure, and microsolvation. It is found that the latter effects canbe very well understood and separated employing the concept oflocalized modes. Finally, we investigate whether Raman optical activity is capable of discriminating between parallel andantiparallel 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 importantand well-known elements of protein secondary structure. WhileX-ray crystallography and nuclear magnetic resonance (NMR)allow one to elucidate the overall structure of a protein at anatomic level, electronic circular dichroism (CD) spectra providea simple way to determine the amount of different secondarystructure elements present in a given protein.1 Anothersuccessful chiroptical technique in this respect is Raman opticalactivity (ROA),2 which measures the difference of Ramanscattering 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 manytypes of secondary structure elements.3−5 In experimentalstudies, the identification of such signatures is usually based onthe comparison of spectra of proteins featuring the same as wellas different secondary structure elements. However, mostproteins have a rich secondary structure, such that it is difficultto unequivocally establish signatures for the individualsecondary structure elements. As an additional challenge, thefact that the normal modes are not directly accessible inexperimental studies makes it often very difficult (if notimpossible) to assign a given spectral band to a certainvibration. Furthermore, the different factors contributing to theoverall spectrum (e.g., molecular structure, conformationaldynamics and averaging, solvent effects, etc.) are very difficultto separate experimentally. Here, a theoretical approach canprovide additional insight, as one is basically not restricted inthe choice of model systems. It is thus possible to study apolypeptide featuring only the secondary structure element ofinterest, which makes the identification of characteristic

signatures considerably simpler, although it does not guaranteethat such a characteristic spectral signature can be detected in acrowded 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-sheetsyet. It is the aim of this work to fill this gap. To this end, wehave calculated theoretical ROA spectra for various largemodels of parallel as well as antiparallel β-sheets. A detailedanalysis of these, together with a range of experimental spectrapublished in the literature, should provide us with characteristicsignatures of protein β-sheets.We first review the signatures that have already been

proposed to be indicative of β-sheets, based on experimentalspectra, in section 2. Then, in section 3 we explain ourcomputational procedure as well as the different β-sheetstructures we have chosen to investigate. After this, we presentthe theoretical ROA spectra of these model systems andanalyze them in section 4. Finally, we give a conclusion togetherwith a short outlook in section 5.

2. PROPOSED SIGNATURES OF β-SHEETSThe first experimental study on ROA signatures of β-sheets wasconducted in 1994 by Barron and co-workers.9 They proposedthat positive ROA intensity between ∼1000 and 1060 cm−1

originates from β-sheet structures. This assignment is stillassumed to hold true.3 However, the experimental spectrum ofα-helical poly(L-alanine) in dichloroacetic acid clearly also

Received: June 17, 2013Revised: August 21, 2013

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shows a positive peak at ∼1047 cm−1 (if the solvent is changedto only 30% dichloroacetic acid and 70% chloroform, this peakis found at ∼1044 cm−1).10 We should also note here thatBarron et al. explicitly state that this spectral feature of β-sheetscan greatly vary in intensity and wavenumber range,3 whichmight 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 anantiparallel β-sheet structure. Five years later, the same groupobserved similar signals in ROA spectra of bovine β-lactoglobulin, a protein that is rich in antiparallel β-sheet.11

However, adjacent strands of antiparallel β-sheets areconnected by β-turns, and it is thus not a priori clear whetherthis signal arises from the strands or from the turn structures. Inthis context it is important to note that our group recentlyfound a similar band in small β-turn model systems.8 Moreover,in experimental spectra of disordered poly(L-lysine) and poly(L-glutamic acid), a positive signal is observed at ∼1320 cm−1.3 Itis therefore very likely that a positive signal around ∼1310−1320 cm−1 is characteristic for turn structures rather than β-strands.Finally, Barron and co-workers found a characteristic couplet,

negative at lower and positive at higher wavenumbers andcentered around ∼1650−1670 cm−1, to be indicative of β-sheets.9 This assignment has been confirmed multiple timessince then.3,11−13 Note that the α-helix shows a similar couplet,which is, however, shifted to lower wavenumbers by ∼5−20cm−1.3,6

As another signature of β-sheets, Blanch et al. proposed anegative band at ∼1248 cm−1.11 In fact, a similar negative peakwas observed between ∼1244 and ∼1253 cm−1 in a range ofother proteins incorporating β-sheets,3,12,13 such that thissignature 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-sheetsas well,3,11,12 even though it was originally assigned to β-turns.9

A detailed analysis of the experimental spectra published so farshows that there is no justification for this reassignment,8 whichis 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 spectrapublished so far, there are two signatures that can be regardedas being reliable characteristics of β-sheets. First, negativeintensity 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 hasalso 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-helicalpolypeptides.10 All relevant signals are summarized in Table 1.

3. METHODOLOGY

3.1. Model Structures. In β-sheets, several almost fullyextended strands of the protein polypeptide chain are held

together by hydrogen bonds. As in the case of the α-helix, allpossible backbone hydrogen bonds are formed. One distin-guishes two main forms, in which β-sheets occur in proteins;these are denoted as parallel and antiparallel β-sheets.14 Thetwo forms feature distinct hydrogen bonding patterns, as shownschematically in Figure 1. While the hydrogen bonds are spaced

evenly in the parallel β-sheet, there is an alternation of narrowerand wider spaced hydrogen bond pairs in the antiparallel β-sheet. Furthermore, the hydrogen bonds between adjacentstrands of an antiparallel β-sheet are almost parallel to eachother, while they form significant angles in the case of parallelβ-sheets.For our study, we constructed idealized models of both,

parallel and antiparallel β-sheets. All models consist of twostrands. This will allow us to reproduce generic signatures of β-sheets while still maintaining a reasonable size of the models(note also that antiparallel β-sheets are often observed as atwisted ribbon of just two strands14). In analogy to a previousstudy,6 we employed (S)-alanine as the only residue type, whichis the simplest chiral amino acid. In the case of the antiparallelβ-sheet, we investigate two models: in the first one, the twostrands are connected by a β-turn of type I, whereas weremoved the four amino acid residues participating in this turnin a second model. This allows us to study the influence of theturn structure on the overall ROA spectrum. For the parallel β-sheet model, the individual strands cannot be connected byshort turns, but only by longer loops. These three modelsystems are depicted in Figure 2. The antiparallel β-sheet withturn consists of a total of 20 (S)-alanine residues, while theother two models feature only 16 amino acids. At their N-terminus, the polypeptides are terminated with an additional

Table 1. Summary of ROA Signatures Proposed in theLiterature to Be Characteristic of β-Sheets

signature wavenumber range/cm−1 ROA intensity

1 ∼1000−1060 positive2 ∼1240−1255 negative3 ∼1650−1670 −/+ couplet

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

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hydrogen atom, leading to an NH2 group, while at the C-terminus, the carboxy group was replaced by an acetyl moiety.These terminal groups will introduce vibrations that are notfound in β-sheets present in proteins. As a result, we will seesome artifacts in the amide I region, which, however, have noadverse 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 Figure3. We introduced perturbations to the idealized β-sheet modelsof Figure 2; in one case, we change either one or all amino acidresidues from (S)-alanine to glycine (Figure 3a,b), while in thesecond case, we study microsolvation by adding one and twowater molecules to one and two peptide units, respectively(Figure 3c). Finally, we also consider the typical twist found inmost β-sheets in order to study the robustness of the signatureswith respect to large-scale conformational changes. To this end,we extracted two strands of antiparallel β-sheet fromconcanavalin A (residues 60−66 and 73−79). In order toguarantee consistency with the rest of our study, we changed allamino acids to (S)-alanine in this model system (see Figure 3d)and optimized the whole model in an unconstrainedoptimization.3.2. Computational Details. All structures were fully

optimized (i.e., without any constraints) with the BP86exchange−correlation functional15,16 and Ahlrichs’ valencetriple-ζ basis set with one set of polarization functions17

(dubbed def-TZVP) on all atoms as implemented in theTURBOMOLE program package (version 5.10).18 Furthermore, inall calculations, advantage was taken of the resolution-of-the-identity (RI) approximation with the auxiliary basis sets

corresponding to def-TZVP. During the structure optimization,electronic energies were converged to 10−6 hartree, while themaximum norm of the Cartesian electronic energy gradient wasconverged to 10−4 hartree/bohr. It was ensured by vibrationalanalysis that all structures correspond to true minima on thepotential energy surface.The harmonic wavenumbers, normal modes, and the

derivatives of the polarizability tensors necessary for theevaluation of the ROA backscattering intensity were calculatedin a seminumerical fashion using the program SNF19 of thepackage MOVIPAC,20 employing a stepsize of 0.01 bohr (thisreduces the numerical error in the frequencies to about 1 cm−1;this is small compared to the error introduced by the harmonicapproximation, which can be expected to be generally smallerthan 20 cm−1 for the methodology employed here19,21−25). Forthe individual distorted structures, analytical energy gradientsand polarizability tensors were computed with our local versionof TURBOMOLE’s escf module,26 utilizing the same densityfunctional and basis sets as described above. Electronic energieswere tightly converged to 10−8 hartree for the distortedstructures using the dense m4 grid of TURBOMOLE from whichthe properties (i.e., frequencies and intensities) are calculated.The vibrational frequencies obtained were not scaled since it isknown that BP86 due to a fortunate error cancellation yieldsharmonic frequencies that are already in good agreement withmeasured fundamental ones.19,21−25 The velocity representa-tion of the electric dipole operator was applied in order toensure gauge invariance. The ROA backscattering intensitieswere obtained for a wavelength of 799 nm and it was ensured inall cases that the energy corresponding to this wavelength is far

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 sameantiparallel sheet with the turn removed; (c) parallel β-sheet.

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

4. RESULTS AND DISCUSSION

4.1. Proposed Signatures. We first investigate the ROAspectra of the three idealized model systems of antiparallel andparallel β-sheets (Figure 2) for the existence of the signaturesproposed in the literature. The three ROA spectra are shown inFigure 4 with the three regions where signatures are expectedhighlighted in blue. Concerning the first signature (positiveintensity between ∼1000 and 1060 cm−1), we identify a weak

positive peak in the ROA spectrum of the antiparallel β-sheetcontaining a turn, while the other two spectra do not showpositive ROA intensity in this range. However, in these lattercases, there are always several normal modes associated withpositive intensity in the relevant spectral range, but they arealways annihilated by near-lying normal modes that areassociated with negative ROA intensity. This signature thusdoes not appear to be a sufficiently reliable general signature forβ-sheets, which is in line with the experimental observation thatit 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 threespectra in Figure 4. However, this signature is found in allexperimental spectra published so far, except in the spectra ofpoly(L-lysine) in water at 50 °C, which also features a β-sheet

Figure 3. Second set of model systems studied: (a) parallel β-sheet with one residue changed to glycine; (b) antiparallel β-sheet with all residueschanged 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.

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conformation.12 In this spectrum, one can only see a broadnegative peak at 1218 cm−1, which rises to a strong positivepeak 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 peaknearby. Hence, we are left with a clear contradiction ofexperimental and theoretical results. For this to resolve, weneed to investigate the calculated results in more detail. In fact,further investigations (see Section 4.3.1) give some evidencethat this signature could be dependent on the amino acid sidechains.Finally, a −/+ couplet in the amide I region is proposed to be

characteristic for β-turns. Indeed, we find such a couplet onlysomewhat above the proposed spectral region, namely,centered around roughly 1700 cm−1. Note that the strongpositive peak at ∼1650 cm−1 is partially an artifact of the modelsystems, as NH2 distortion vibrations also occur in thiswavenumber range. However, in a protein-embedded β-sheetsuch an amino group would not be present. If we would discardthe normal modes associated with these distortion vibrations,this peak would be somewhat less prominent, but still clearlyvisible (most of the normal modes in this region are associatedwith vibrations delocalized over the entire turn structure). Thenormal modes building up the characteristic couplet representthe typical amide I vibrations, i.e., C−O stretching vibrations,with some admixture of N−H in-plane bending. All vibrationsare usually delocalized over the entire sheet structure, as can beseen in the top panel of Figure 5, which depicts a typical normalmode found in this spectral range.4.2. Additional Signatures. When comparing the three

spectra in Figure 4, we note that they are very similar, despitethe fact that the three model systems locally feature quitedifferent structural elements. For example, one antiparallelsheet involves a β-turn, while the other does not. However, thepresence (or absence) of this turn cannot be unequivocallyconcluded simply based on the two ROA spectra. Therefore,

we conclude that the ROA signals stemming from the turn8 aresimply covered by the signals arising from the rest of the β-sheet models.Due to the similarity of the three spectra, we recognize many

spectral regions where all spectra show either positive ornegative ROA intensity. However, not all of these regionsshould be regarded as true signatures. To be considered as areliable signature, we should identify a significantly strong peak,the normal modes of which are associated with the peptidebackbone of the sheet structure. One peak that is particularlystrong and almost identical in all three spectra is the negativeband at ∼1350 cm−1. It is the strongest peak in the spectra ofthe two antiparallel β-sheet models, and, although somewhatweaker, 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 andCH3 deformation vibrations (see Figure 5, middle). Thespectral range of this characteristic signature is highlighted inred in Figure 4. It can also be found in all experimental spectraof β-sheet models and proteins incorporating a significantamount of β-sheets,3,9,11,12 and can thus be considered as beinga reliable signature of β-sheets.

4.3. Robustness of β-Sheet Signatures. Of course, oneimportant issue to clarify is how robust these signatures are, i.e.,how strongly do they depend on the exact conformation of theβ-sheet model, the particular type of side chain employed, andthe environment such as solvent molecules? To investigaterobustness against perturbations, we study the second set ofmodel systems of Figure 3.

4.3.1. Influence of Side Chain. In order to investigate towhich extent the characteristic β-sheet signatures depend onthe actual amino acid side chain, we changed a single residue toglycine. The resulting ROA spectrum is shown in the middlepanel of Figure 6. When comparing this spectrum to the one ofthe original, all-(S)-alanine parallel β-sheet (top panel of Figure6), we find that the two spectra are very similar, and allsignatures proposed above can be found in the spectrum of themodified β-sheet. This is not very surprising, since the originalstructure is only slightly changed. Nevertheless, there is oneparticular band that allows one to unequivocally distinguish thetwo spectra from each other, namely, a negative peak at 1246cm−1 (highlighted in red in Figure 6). This band is caused by asingle normal mode, which represents a bending vibration ofthe two hydrogen atoms of the glycine residue, coupled withN−H in-plane bending motions of the two neighboring peptideunits (bottom panel of Figure 5). Interestingly, this negativeband lies exactly in the region where Barron and co-workersproposed a signature of β-sheets, which, however, could nothave been found in our all-(S)-alanine model systems (seeabove).To replace only a single amino-acid residue is certainly a

small perturbation. Clearly, we need to study a largermodification 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, allROA signals stem from the chirality of the β-sheet structureand can thus be taken as an ultimate fingerprint of a sheetstructure. The resulting ROA spectrum is shown in the lowerpanel of Figure 6. As can be seen, the overall intensity of allsignals is diminished, which is due to the fact that all elementsof local chirality are eliminated for the achiral amino acid. FromFigure 6 it can be concluded that the resulting ROA spectrum

Figure 4. ROA spectra of the first set of (unperturbed) modelstructures shown in Figure 2. Highlighted in blue are the spectralregions in which characteristic signatures of β-sheets have beenproposed in the literature, whereas the red region marks a signatureidentified in this work.

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specifically shows the intrinsic features of the β-sheet structure.However, we can expect that the overall chirality of the β-sheetstructure also dominates the spectra of the all-(S)-alaninemodel systems. In fact, for large helical systems, it has beenfound that the helical chirality dominates over the local chiralityof the individual amino acids,28 even though for smallersystems, the configuration of individual residues plays animportant role.29

Concerning the β-sheet signatures, we see that both thecouplet in the amide I region as well as the negative peak at∼1350 cm−1 can clearly be recognized. In addition, we also findnegative intensity in the range between 1240 and 1255 cm−1.These observations can be considered as evidence that thislatter signature depends on the side chains within the sheetstructure, being not present when only (S)-alanine builds upthe strands, but being already clearly visible when only a singleresidue is changed to glycine. We should emphasize again that anegative peak at ∼1250 cm−1 is not visible in the spectrum of amodel β-sheet consisting of (S)-lysine only (see above).4.3.2. Twisted β-Sheets. The idealized structures of the β-

sheet models investigated above is often not found as such inprotein structures. A characteristic structural distortion ofprotein-building β-sheets is that their strands are usuallytwisted. In order to examine the effect of such large-scaleconformational changes, we extracted a twisted β-sheet from

the structure of the protein concanavalin A, and calculated itsROA spectrum (all residues were changed to (S)-alanine, andthe structure was then fully optimized), which is shown in thelower 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 specificspectral regions where the two spectra of Figure 7 differsignificantly. For example, the characteristic −/+ couplet in theamide I region is no longer visible in the spectrum of thetwisted structure, but only the positive part of it is.Nevertheless, also in this spectrum there are some normalmodes that are associated with negative ROA intensity justbelow the positive peak, but these modes cannot build up anegative band since they are canceled by close-lying normalmodes associated with positive backscattering intensity. Thestrong negative peak at ∼1350 cm−1, however, is clearly presentin the spectrum of the twisted β-sheet.

4.3.3. Microsolvation. Another important issue of concern isthe influence of the environment as, e.g., exerted by solventmolecules. Unfortunately, a full-fledged solvation study (ascarried out for a sugar molecule recently by Cheeseman et al.30)of the β-sheet models is beyond the scope of this work andcomputationally very demanding. However, we can selectivelyadd only a few water molecules to the sheet structure and studythe resulting microsolvation effects. Surely, this will not yield a

Figure 5. Typical normal modes of characteristic signatures of β-sheets, taking the parallel β-sheet model as an example: (a) amide I vibration at1676 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.

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spectrum resembling a fully solvated case, but it will allow us tounderstand solvation in a stepwise fashion. In this work, weonly consider adding one and two water molecules to one andtwo peptide units, respectively (Figure 3c). The spectrum ofthese microsolvated parallel β-sheet models are shown in Figure8 and compared to their unsolvated counterpart (Figure 8,top). Clearly, the addition of one and two water moleculesconstitutes a very small perturbation of the overall structure.Still, the local effect and its spread among the normal modescan provide insights into the change of the ROA spectrumupon hydration. For instance, a full-fledged molecular dynamicsstudy of the solvated sheets would provide an enormousamount of information, which can then be rationalized bycomparison to the results seen for the effect of a few watermolecules studied here.

For this, the analysis of the spectra in terms of localizedmodes is a suitable way to dissect the microsolvation effects.The concept of localized modes31,32 allows us to spatiallylocalize selected vibrations, which are usually delocalized overthe entire polypeptide chain in the basis of normal modes. Thisis achieved by a suitably chosen unitary transformation of theHessian matrix (see ref 31 for details on the approach and refs20 and 33 for publicly available implementations). In our case,we localized all 16 amide I vibrations, i.e., all normal modesbetween 1630 and 1720 cm−1. The resulting coupling matrix,i.e., the Hessian matrix in the basis of localized modes, is showngraphically in Figure 9.In this representation, we color-code the value of the

coupling constants (i.e., the off-diagonal elements of thecoupling matrix). When first investigating the coupling matrixof the unsolvated β-sheet (see the left-hand side of Figure 9),we see that all adjacent residues within one strand (i.e., residues1−8 for the first strand, and residues 9−16 for the secondstrand), couple strongly to each other with coupling constantsof approximately 8 cm−1. Interactions of a given residue with itssecond-nearest neighbor are much less pronounced and onlyslightly positive. All other couplings are almost zero, indicatingthat such long-range interactions can be neglected. However,the two strands are held together by hydrogen bonds, andaccordingly there is a strong negative coupling constantbetween residues that are bound by hydrogen bonds (cf., theoff-diagonal blue squares in Figure 9).We found that neglecting any coupling constants smaller

than 2.5 cm−1 yields vibrational frequencies in close agreementwith the reference values from the full coupling matrix; that is,the mean absolute deviation is only 1.2 cm−1 (see Table 2). Asonly the coupling between adjacent residues and residues thatare bound by hydrogen bonds is larger than 2.5 cm−1, thisshows that even the interactions between second-nearestneighbor residues may be neglected without introducing alarge error.Comparing the coupling pattern of the unsolvated β-sheet to

the one of the microsolvated β-sheet (top right-hand side of

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 anantiparallel all-glycine β-sheet. The blue marks highlight thecharacteristic signatures established in section 4.1, while the redmark shows the spectral region with which the all-(S)-alanine β-sheetcan be distinguished from both other structures.

Figure 7. ROA spectra of the idealized antiparallel β-sheet (top panel),and the same structure in the twisted conformation depicted in Figure3 at the bottom.

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

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Figure 9), we see that it does not change much. The largestdifferences can be seen for the coupling of residue five (the onethat has been microsolvated) to its neighbors. Therefore, wecan conclude that the microsolvation has only a minor effect onthe coupling pattern. Still, small changes can have unexpectedstrong effects on the normal mode spectrum.Apart from the coupling constants, the localized frequencies

(i.e., the main diagonal elements of the coupling matrix) areimportant for the normal mode spectrum. In the couplingmatrix of the microsolvated β-sheet (right-hand side of Figure9), we show the difference between the localized frequencies ofthe solvated structure and the one of the unsolvated β-sheet areshown in a grayscale. We see that the localized frequencies donot change much between the two coupling matrices, with theexception of the localized frequency of residue five, which isshifted by almost 30 cm−1 to lower wavenumbers in thesolvated case.An interesting question is whether this general pattern will

change in a fundamental way if more than one residue ismicrosolvated. In order to study this issue within our simplebottom-up approach, we also microsolvated a second peptideunit. Note that the microsolvation of a unit directly adjacent tothe one already microsolvated is impossible, as the C−O andN−H bonds of this peptide unit are oriented toward the insideof the β-sheet. Therefore, we added a second water molecule to

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

Table 2. Comparison of Frequencies Obtained by NeglectingAny Coupling between Non-Adjacent Residues As Well Asbetween Resdiues Not Bound by Hydrogen Bonds (So-Called Strong-Coupling Frequencies) with Their ReferenceValuesa

strong-coupling frequencies reference frequencies error

1638.5 1641.8 3.351641.6 1642.6 1.071645.6 1644.8 0.771648.1 1646.3 1.751648.8 1647.3 1.421650.2 1648.7 1.521654.8 1653.4 1.381669.9 1669.7 0.151671.8 1672.3 0.451674.1 1673.2 0.911674.1 1675.8 1.641677.5 1676.9 0.541680.1 1680.3 0.181683.3 1684.8 1.451708.7 1707.3 1.391710.6 1712.2 1.67

aAll values are given in cm−1.

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the peptide unit of residue three in the same fashion as wetreated residue five. The resulting coupling matrix is shown atthe bottom of Figure 9. Again, the coupling pattern betweenthe unsolvated and the microsolvated case does not change verymuch. Also for the localized frequencies, we make the sameobservation as above. All localized frequencies remainessentially unchanged, except the one of the two residuesthat are microsolvated. These frequencies are shifted by almost30 cm−1 to lower wavenumbers.4.4. Comparison to Other Secondary Structure

Elements. After having established the −/+ couplet in theamide I region as well as the sharp negative peak at about 1350cm−1 to be truly characteristic for β-sheets, we shall nowinvestigate the ROA spectra of other secondary structureelements for an interference of these signatures with vibrationscharacteristic for, e.g., helices. We have already carried outtheoretical studies on α- and 310-helices

6 (see also refs 34 and35), as well as on β-turns.8 The resulting ROA spectra arereproduced in Figure 10, together with the spectrum of the

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

Furthermore, all four secondary structure elements can bedistinguished from each other by relying on the band shape ofthe amide I region. In the case of the β-turn, we find onlypositive ROA intensity in this spectral range, while the 310-helixproduces a characteristic −/+ couplet. Both α-helix as well as(parallel and antiparallel) β-sheets feature a −/+ couplet in theamide I region, but these two secondary structure elements canalso be distinguished from each other, as the couplet is shiftedapproximately 20 cm−1 to lower wavenumbers in the case of theα-helical model system (upon solvation, it is shifted to evenlower wavenumbers35). Note that this very finding is alsoexperimentally confirmed.3

4.5. Differentiating Parallel and Antiparallel β-Sheets.The discrimination of parallel and antiparallel β-sheets is a veryimportant topic that has already been addressed in infrared andvibrational circular difference spectroscopy.36−38 We aretherefore advised to analyze the data presented in this workwith respect to the question of whether one can distinguishthese 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, isespecially sensitive to secondary structure.39 Therefore, itcomes as no surprise that we find a difference between paralleland antiparallel β-sheets exactly in this region. In fact, whenclosely analyzing the spectra depicted in Figures 4, 6, 7, and 8,we see that all parallel β-sheets exhibit only positive ROAintensity around ∼1275 cm−1, while we find weakly negativepeaks for all antiparallel β-sheet structures. All of theperturbations considered above (different residue(s), twistedconformation, solvent molecule) have no influence on thisspectral feature. Therefore, it appears to be quite robust andwould thus be very well suited to differentiate parallel fromantiparallel β-sheet structure. When analyzing the experimentalROA spectra of jack bean concanavalin A, human immunoglo-bulin G, and bovine β-lactoglobulin (which all containsignificant amounts of antiparallel β-sheet), we identify acharacteristic feature at about 1250 cm−1, which mightcorrespond to the feature we proposed above.3 However, thespectrum of rabbit aldolase apparently shows a negative peak at∼1253 cm−1,3 and it has been suggested that this bandoriginates from the parallel β-sheet structure found in thisprotein. Therefore, further investigations are necessary to clarifywhether the negative peak at ∼1275 cm−1 can be used as areliable indicator of antiparallel β-sheets.Apart from the feature in the amide III region, we find one

additional difference between the spectra of parallel andantiparallel sheets, namely, a peak at ∼1525 cm−1. This peakis negative in the case of parallel β-sheets, and positive forantiparallel sheets. However, this feature appears not to be veryreliable. It vanishes when we add a single water molecule to theparallel β-sheet (cf., Figure 8). Moreover, the spectrum of theantiparallel all-glycine β-sheet shows only (weak) negative ROAintensity in this range, and not a positive peak as expected.Therefore, this feature is not consistent across all of ourcalculated spectra. Hence, one should not regard it as adiagnostic band to differentiate generic parallel β-sheet fromantiparallel β-sheet structures.

5. CONCLUSIONS AND OUTLOOKWe have calculated ROA spectra of a range of antiparallel andparallel β-sheet model polypeptides in search for characteristicsignatures. The stability of these fingerprints against structuraland electronic perturbations has been investigated for (1) a

Figure 10. Comparison of the ROA spectra of a model α-helix (toppanel), the antiparallel β-sheet model investigated in this work, a type Iβ-turn, and a 310-helix (bottom panel; all structures composed from(S)-alanine residues). The data for the helical systems have beenreproduced according to ref 6 and those for the β-turn according to ref8.

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replacement of a single (S)-alanine residue of one of theoriginal all-(S)-alanine sheets by a glycine residue, (2) areplacement of all (S)-alanine residues by glycine, whichallowed us to study the β-sheet specific ROA features, (3) theaddition of a single water molecule, and (4) the twisting of thesheet 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 signaturepositive intensity between ∼1000 and 1060cm−1could not be found in our theoretical spectra. This is inaccord with experimental findings.3 A second signature, namely,a negative peak between ∼1240 and 1255 cm−1, cannot befound in the all-(S)-alanine model systems, but is clearly visiblewhen glycine is present in the sheet structure. Therefore, ourwork gives some evidence that this signature is ratherdependent on the amino acid side chains. The third signature,a −/+ couplet in the amide I region, could be fully confirmed inthis study. This couplet is also particularly well suited todistinguish the β-sheet structure from other secondary structureelements, 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 isvery robust with respect to large-scale conformational changesof the sheet structure and can also be identified in allexperimental spectra of β-sheet structures (or proteinsincorporating a significant amount of this secondary structureelement).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 theunsolvated reference, the concept of localized modes allowed usto gain additional insight. For the amide I region, we found thatthe coupling pattern does not change significantly uponmicrosolvation. Adjacent amino acids couple quite strongly,while interactions between second-nearest neighbors arealready much weaker, and any further interactions can beneglected (except residues that are bound by hydrogen bonds).Hydrogen bonds lead also to a significant coupling of aminoacids, which are, however, negative (as opposed to the couplingwithin one strand). The only significant change introduced bythe microsolvation is the localized frequency of the solvatedresidue, which is shifted almost 30 cm−1 to lower wavenumbers.We should explicitly state here that the addition of a singlewater molecule, although providing valuable insight, cannotaccount for all effects of a full solvation model. Therefore,further analysis of extended microsolvation patterns andmolecular dynamics trajectories of solvated sheets is requiredfor a complete understanding of the changes in the couplingmatrix, such that the ROA spectrum of a solvated polypeptidechain might be constructed from the local-mode model. Workalong these lines is currently carried out in our laboratory.Already at this stage, our simple solvation attempts provide aclear picture of the action of one (or two) solvent molecule(s),and this knowledge may become useful when results frommolecular dynamics are to be interpreted. Such comparisonswill then be useful to understand whether it might eventually bepossible to estimate solvation effects of biomolecules frommicrosolvated and unsolvated reference structures. Clearly, thiswould provide access to solvation effects at dramatically lesscomputational cost than required for a full-fledged quantummechanics/molecular mechanics (QM/MM) approach.30

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

■ ASSOCIATED CONTENT*S Supporting InformationCartesian coordinates and Raman spectra of all structuresinvestigated in this work. This information is available free ofcharge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: markus.reiher@phys.chem.ethz.ch.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work has been supported by the Swiss National ScienceFoundation SNF (Project 200020_144458/1).

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