Structure Analysis of Dipeptides in Water by Exploring and Utilizing

4294

J. Phys. Chem. B 2002, 106, 4294-4304

Structure Analysis of Dipeptides in Water by Exploring and Utilizing the Structural Sensitivity of Amide III by Polarized Visible Raman, FTIR-Spectroscopy and DFT Based Normal Coordinate Analysis Reinhard Schweitzer-Stenner,*,† Fatma Eker,‡ Qing Huang,† and Kai Griebenow† Department of Chemistry and Biology, UniVersity of Puerto Rico, Rı´o Piedras Campus, P.O. Box 23346, San Juan, Puerto Rico 00931-3346

Piotr A. Mroz and Pawel M. Kozlowski Department of Chemistry, UniVersity of LouisVille, LouisVille, Kentucky 40292 ReceiVed: October 4, 2001; In Final Form: January 17, 2002

A series of dipeptides AX and XA (X ) G, K, L, S, and V) were investigated by polarized visible Raman and FTIR-spectroscopy to examine the conformational determinants of the amide III band. A spectral decomposition combined with density functional calculations revealed that the amide III band has a multicomponent structure in that three different modes contribute to amide III vibrations. One of them (amide III2) dominates the Raman spectra particularly of the cationic species. Its normal mode displays an in-phase combination of NH and CR1H in plane bending vibrations, which makes it sensitive to changes of the dihedral angle ψ. Indeed, our Raman data show that amide III2 varies with ψ but remains practically unaffected by variation of φ in the region between -95° and -75°, which is sampled by the investigated AX peptides. Our data support the Lord hypothesis that amide III depends solely on ψ (Lord, R. Appl. Spectrosc. 1977, 31, 187) but specifies to which of the amide III modes this statement applies. Our data further reveal that all amide III modes can interact with side chains vibrations. For some residues this causes a mode delocalization which yields a reduction of the Raman cross section. Amide S, which is a structure sensitive band resonance enhanced with UV-excitation, disappears for ψ-values outside of the β-sheet region due to changes of the normal mode compositions of several modes between 1300 and 1420 cm-1. This explains its absence in the UV-Raman spectra of R-helical structures. Our data suggest that all AX peptides exhibit ψ angles around 150°.

Introduction Twenty-four years ago, Lord published his classical paper3 about “Strategy and Tactics in the Raman Spectroscopy of Biomolecules”, in which he postulated that the frequency of the amide III band in the Raman spectra of peptides and proteins is a well-defined function of the dihedral angle ψ (NCRCN torsion). If this hypothesis is verified, Raman spectroscopy can be used to determine the distribution of ψ angles among the peptides linkages of a protein. Despite its importance for the structure analysis of peptides and proteins in solution significant efforts to check Lord’s hypothesis have been undertaken only recently. Williams and co-workers2 measured the amide III band region in the Raman spectra of a series of AX and XA dipeptides (X labels various amino acid residues). There results lead them to suggest that the amide III frequency depends on the dihedral angle φ rather than on ψ, in contrast to Lord’s proposal. Jordan and Spiro3 investigated various secondary amide derivatives by UV resonance-Raman spectroscopy and found evidence that the bending vibration of the CRH bond adjacent to the carbonyl group is admixed to amide III. They suggested this vibrational mixing * To whom correspondence should be addressed. Phone: (787) 7640000 (2417). Fax: (787) 756-8242. E-mail: [email protected]. † Department of Chemistry, University of Puerto Rico. ‡ Department of Biology, University of Puerto Rico.

as a possible physical source for the ψ-dependence of amide III proposed by Lord.1 Ianoul et al.4 found that the amide III band position in the UV-Raman spectra of a series of acetylated amino acid esters with different side chain derivatives decreases by 7 cm-1 as the preferred φ angle decreases from -75 to -95°.5 This experimental result was reproduced by DFT based normal mode calculations for minimized structures with different constrained φ-angles. Moreover, the authors carried out similar calculations for (blocked) alanylalanine and found a similar though significantly reduced φ-dependence of amide III. In a most recent study, Asher et al.6 investigated in more detail the conformational sensitivity of amide III for alanylalanine, its isotopic derivatives and some acetylated amino acids and found that the NH in-plane bending mode of the peptide group and the respective (C)CRH bending mode are coupled. The eigenvector of amide III exhibits an in-phase combination of (C)CRH and NH in plane bending, in agreement with earlier suggestions by Jordan and Spiro.3 Results of normal mode calculations for minimized structures with different constrained ψ-angles suggest that the coupling between the two bending modes exhibits a sinusoidal dependence on ψ and a linear dependence on the distance between the hydrogen atoms of (C)CRH and NH. The above vibrational mixing is maximal for ψ ≈ 120°, which corresponds to the β-sheet region of the Ramachandran plot and minimal for right-handed R-helical conformations where

10.1021/jp0137118 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/30/2002

Structure Analysis of Dipeptides in Water ψ ≈ 60°. This explains the much higher amide III frequency in the UV-Raman spectrum of the helical structures.7,8 When the present paper was already in preparation, a paper by Mirkin and Krimm9 appeared which reports results from a detailed computational study on N-acetyl-L-alanine-N-methylamide.10 They performed DFT based normal mode calculations for multiple minimized structures with different constrained ψ and φ angles. Their results seem to strongly suggest that the frequency of amide III depends on both dihedral angles, in contrast to Lord’s hypothesis. Taken together, all the results discussed above agree in suggesting that amide III depends on the dihedral angles but several questions listed in the following remain open. 1. None of the above studies addresses the complexity of the amide III band region in the Raman11 and IR-spectra12,13 of dipeptides. Diem and co-workers13 used FTIR spectroscopy to identify three amide III bands resulting from extensive mixing between NH in-plane, (N)CRH and (C)CRH b bending vibrations. Sieler et al.11 identified two amide III bands in the visible and UV resonance Raman spectra of GG. It is not clear which of these amide III bands are sensitive to changes of φ and ψ. 2. It is unclear to what extent side chain vibrations can contribute to the eigenvectors and total energy distributions of amide III modes. Such a mixing would depend on the side chain conformation and would increase the complexity of the conformational space sampled by amide III. 3. All the ab initio based calculations aimed at exploring the conformational sensitivity of amide III were carried out with structures obtained with constrained dihedral angles. Thus, they do not represent a stationary point of the potential energy landscape so that the calculated frequencies might be affected by nonvanishing forces.14 In the present study, we address these points by adopting the following strategy. We have chosen a series of AX (X ) A, G, K, L, S, V) and XA (X ) K, L, S, V) dipeptides, assuming that the C-terminal substitution (AX) changes only φ, whereas the N-terminal substitution (XA) varies ψ. The correctness of this assumption was checked by density functional theory (DFT) calculations. Experimentally, we measured the visible polarized Raman and FTIR spectra of these peptides in water at different pH values and subjected the spectral region between 1200 and 1450 cm-1 to a self-consistent spectral analysis. The assignment of the thus obtained Raman and IR bands was carried out by utilizing results from normal-mode analysis based on the force fields obtained from the above DFT calculations. Thus, we identified three structure sensitive amide III bands among many overlapping Raman and IR-bands. For one of these bands our investigation verifies the ψ-dependence of the frequency positions. We also elucidated the contribution of side chain vibrations to the different amide III modes and estimated the dihedral angles ψ and φ of the investigated peptides from our Raman data. Materials and Methods Materials. Alanylalanine (AA), alanylglycine (AG), alanyllysine (AK), alanylserine (AS), alanylleucine (AL), alanylvaline (AV), glycylalanine (GA), leucylalanine (LA), lysylalanine (KA), serylalanine (SA), and vanylalanine (VA) were purchased from Bachem Bioscience Inc. (>98% purity) and used without further purification. NaClO4 were obtained from Sigma-Aldrich Chemical company (St. Louis, MO). All chemicals were of analytical grade. The peptides were dissolved in H2O at a concentration between 0.3 and 0.5 M. The pH of the solutions was adjusted to 1, 6, and 12 (11 for AA) by adding HCl or

J. Phys. Chem. B, Vol. 106, No. 16, 2002 4295 NaOH to obtain the cationic, zwitterionic and anionic state of the peptide. For the Raman experiments the solvent contained 0.25 M NaClO4 whose 934 cm-1 Raman band was used as an internal standard.15 Methods. Raman Spectroscopy. 457.9 and 488 nm excitation (300 mW, 1W) were obtained from an argon ion laser (Lexel). Laser filters were used to eliminate plasma lines. The polarized exciting laser beam was focused onto the sample with a lens of 100 mm focus length. The Raman scattered light was collected in a 135° backscattering geometry. The scattered radiation was imaged onto the entrance slit (width adjusted to 100 µm) of a triple-grating spectrometer (T64000, Jobin Yvon Inc.). A polarization analyzer followed by a scrambler between collimator and the entrance slit of the spectrometer were employed to measure the Raman intensity polarized parallel (Ix) and perpendicular (Iy) to the scattering plane. The scattering light was dispersed by the spectrometer and then detected by a liquid nirtrogen cooled charge-coupled device (CCD) with 256 × 1024 pixels in the chip. The spectral resolution was about 3.8 cm-1 at 457 nm and 3.2 cm-1 at 488 nm excitation. The frequency calibration of the recorded Raman spectra was checked by means of the 934 cm-1 band of the internal standard, the frequency of which had been determined earlier with high accuracy.15 IR-Spectroscopy. FTIR spectra were measured with a Nicolet Magna-IR System 560 optical bench as described elsewhere.16 A total of 256 scans at 2 cm-1 resolution using Happ-Ganzel apodization were averaged to obtain each spectrum. For all experiments, a Spectra Tech liquid cell equipped with CaF2 windows and 15-µm thick spacers were used. The peptide sample was put between CaF2 windows. Each peptide sample was measured at least four times. Spectra were corrected for the solvent background in an interactive manner using Nicolet OMNIC 3.1 software. Spectral Analysis. All spectra were analyzed using the program MULTIFIT.17 They were normalized to the internal standard, i.e., the ClO4- band at 934 cm-1. To eliminate solvent contributions, we measured the solvent reference spectra for both polarizations, which were then subtracted from the corresponding peptide spectra. The intensities of the normalized polarized Raman bands were derived from their band areas. These and the corresponding IR spectrum were self-consistently analyzed in that they were fitted with a set of identical frequencies, halfwidths, and band profiles. DFT Calculations. Calculations reported in this study were carried out using gradient corrected DFT with the Becke-LeeYoung-Parr composite exchange correlation functional (B3LYP) as implemented in the GAUSSIAN9818 suite of programs for electronic structure calculations. The geometries of AX and XA dipeptides were optimized at B3LYP/6-31g(d,p) level of theory followed by a frequency calculations. All harmonic frequencies at the optimized geometries of dipeptides were real, showing that optimized structures of AX and XA correspond to stable minima. The DFT based Cartesian force constants at the optimized geometry were transformed to natural internal coordinates.14 The set of nonreduntant natural internal coordinates was automatically generated by the TX90 program19 for each dipeptide under consideration and the Scaled Quantum Mechanical (SQM) procedure20 was applied to refine the calculated DFT force constants. The set of transferable scaling factors was used21 to obtain the SQM-DFT force field (FF) for each dipeptide. In the following, we describe the normal mode composition in terms of the contributing natural internal coordinates. To use this end, we use the following abbreviations; s: stretching, ss:

4296 J. Phys. Chem. B, Vol. 106, No. 16, 2002

Schweitzer-Stenner et al.

Figure 1. Schematic representation of the dipeptides structure. R1 and R2 denote the amino acid residues.

TABLE 1: Selected Dihedral Angles of the Dipeptides AX and XA from DFT Optimized Structures AA AG AK AL AS AV GA KA LA SA VA

ψ (NCR1CN)

HCR1NH

φ(CNCR2Cc)

ψ′(NCR2CcO)

-149.0° -148.6° -148.6° -148.5° -148.3° -149.1° 150.0° 135.6° -135.6° -163.5° 145.2°

95.3° 92.7° 92.5° 90.2° 90.4° 94.9°

-157.4° -172.4° -155.6° -153.1° -153.6° -154.1° -158.7° -157.1° -157.4° -153.1° -156.5°

-7.1° 0.5° -18.8° -27.7° -30.4° -15.12° -8.9° -7.7° -6.9° -7.2° -7.3°

21.5° 106.6° 74.3° 31.4°

symmetric stretch, ib: in-plane bending, ob: out-of-plane bending, sb: symmetric bending, d: deformation (asymmetric combination of bending modes), w: wagging, tw: twisting. Results The general structure of the dipeptides investigated in this study is shown in Figure 1. In what follows, we will use the following definitions and notation. (1) We assign all modes as amide III the eigenvectors of which exhibit significant contribution of an in-phase combination of NH ib and CN s.22 (2) With respect to CRH, we distinguish two bending vibrations. One of them designated as CRH ib vibrates in the peptide plane if the latter is coplanar with CRH. The other one designated as CRH ob vibrates orthogonal to CRH ib. To distinguish between the two CRH bonds of the dipeptides, we use CR1H for the N-terminal and CR2H for the C-terminal bond (Figure 1). (3) The strong band at 1400 cm-1 in the UV resonance Raman spectra of many peptides and proteins was earlier designated as amide S by Spiro and co-workers.3,22 Others use the notation CH bending band.7 In view of the existence of four different CR1H bending vibrations and their substantial mixture with peptide vibrations, we consider amide S a more reasonable designation.22 Geometry Optimization. We have performed DFT calculations at the B3LYP/6-31g(d,p) level of theory to obtained structures corresponding to the minimal energy of (nonionic) AX and XA peptides in Vacuo. We would like to emphasize that these calculations were aimed to obtain the structural variation caused by amino acid substitutions rather than the absolute minima, which would have no meaning in the present context because the peptide structure is known to be solvent dependent.23-25 Table 1 lists the angles ψ and φ (NNCRCN and CNCR1CC, Figure 1) extracted from the energy minimum structures of the AX and XA peptides. For the AX-peptides we obtained an average ψ angle of -148.7° with a standard deviation of 0.4°. This strongly indicates that ψ is practically independent of the C-terminal substitution. Interestingly, the latter causes only a moderate variation of φ ( ) -157.7 ( 6.7°), but affects significantly the dihedral angle ψ′ of the carboxylate group (NCR2CO) (Table 1). As expected the XA peptides show different ψ angles between 150° for KA and -149.1° for VA.

Figure 2. Raman spectra of cationic, zwitterionic and anionic alanylalanine between 400 and 1800 cm-1 measured with 457 nm at the indicated pH. The sample concentration was 0.5 M. The solvent contributions were subtracted as described under Materials and Methods.

Hence, our calculations support the notion that the AX and XA peptides are suitable tools for identifying the influence of ψ on amide III and amide S. This computational result provides the basis for the interpretation of our experimental data. We reiterate once more that these angles cannot be expected to represent the structural reality of these peptides in water. Vibrational Spectra of AA. Figure 2 depicts the visible Raman spectra of the cationic (pH 1), zwitterionic (pH 6), and anionic (pH 11) state of the molecule. All spectra were taken with 457 nm excitation. In principle, they are very similar, but some differences are noteworthy. The pH 1 spectrum displays a band at 1720 cm-1, which results from the CcO s and disappears upon deprotonation of the carboxylate group. It is substituted by a strong band around 1405 cm-1, which overlaps with the amide S band and is assignable to the COO- ss mode.26,27 Amide S can only be identified unambiguously in the spectrum of the cationic species due to the elimination of the overlapping COOss band.11 As observed for GG, amide I appears at a surprisingly high frequency (1686 cm-1) in the spectra of the anionic and zwitterionic states and is significantly downshifted by the N-terminal deprotonation.11 Its band shape is asymmetric and complicated due to vibrational mixing with water and NH3/ NH2 bending vibrations.15 In the amide III region between 1200 and 1350 cm-1, the spectra differ mostly with respect to the relative intensities of the observed bands. In what follows, we confine ourselves on the spectral region between 1200 and 1450 cm-1, which contains all bands relevant for this study. Moreover, we focus on the spectra of the anionic species (pH 11-12) because this allows us the best comparison with the normal modes calculated for nonionic peptides.

Structure Analysis of Dipeptides in Water

J. Phys. Chem. B, Vol. 106, No. 16, 2002 4297 TABLE 2: (a) TED1 of Normal Modes of AA between 1200 and 1410 cm-1 Obtained from DFT Calculations on the Non-ionic State in Vacuo as Described in Material and Methods,d (b) TED1 of normal Modes of AA between 1200 and 1410 cm-1 Obtained from DFT Calculations on the Non-ionic State in Vacuo as Described in Material and Methods (a) νexp [cm-1]

νDFT [cm-1]

νSC [cm-1]

1241

1241

1208

1263

1250

1215

1280

1302

1269

1302 1323 1342

1362 1366 1388

1326 1331 1347

1371

1423

1375

1386 1403

1430 1402

1387 1359

total energy distributiona 0.28 NH2 w, 0.17 NH ib, 0.13 CR1H ib, 0.1 CNs (amide III1) 0.19 CR1H ib, 0.18 NH ib, 0.15 NH2 w, 0.08 CN s, 0.06 NCR2 s, 0.07 CR1H ob (amide III2) 0.31C(CR2)H3 d, 0.07 CN s, 0.03 NH ib, 0.05 CR2H ob, 0.024CR1H ob, 0.02 CR1H ib, 0.014 C(CR2)H3 d (amide III3) 0.5 CR2H ob, 0.26 CR2H ib 0.59 CR1H ob, 0.13 CR1H ib 0.12 CR1H ib, 0.08 NH2 w, 0.41 C(CR2)H3 d 0.84 C(CR1)H3 sb, 0.04 CR1Cβ1 s, 0.03 CR1H ib 0.21 C(CR2)H3 sb, 0.1 CR1C s 0.34 C(CR2)H3 sb, 0.19 CR1H ib, 0.18 NH2 w, 0.04 CR1C s, 0.02 NH ib (amide S) (b)

Figure 3. Upper three panels: Polarized visible Raman and FTIR spectrum of anionic alanylalanin measured at the indicated pH. Lower panel: Unpolarized Raman spectrum of cationic alanylalanine. The Raman spectra were taken with 457 nm excitation. All spectra were corrected for solvent contributions. The peptide concentration was 0.5 M for the Raman and the IR measurements. The band profiles displayed between 1200 and 1350 cm-1 result from a self-consistent spectral decomposition described in Material and Methods.

Comparison with the cationic state is occasionally made to discuss the influence of the carboxylate charge. Figure 3 depicts the polarized Raman spectra and FTIR spectra taken of the anionic and additionally the unpolarized Raman spectrum of the cationic peptide. The band frequencies identified by spectral decomposition were compared with results from normal mode calculations (Table 2a). For the assignment, we made use of the corresponding spectra of AAD (deuterated peptide, data not shown) and normal mode calculations on AA13,28 and related peptides.24 Generally, our assignments and our normal mode descriptions agree with results reported by Weir et al.28 Our results and their results provide considerable evidence for significant vibrational mixing between NH ib, CN s, CR1H ib, CR1H ob, CR2H ib, CR2H ob, and methyl deformation modes. On the basis of the FT-IR spectra of AA and its isotopic derivatives Diem et al.13 designated the bands at 1281, 1325, and 1340 as amide III1, amide III2, and amide III3, respectively (cf. the FTIR spectrum in Figure 3). The results of Weir et al.28 and our calculations agree in indicating that neither the 1323 cm-1 nor the 1342 cm-1 mode exhibits a substantial contribution from NH ib to the Total Energy Distribution (TED, Table 2a), even though our calculations yielded some contributions to the respective eigenvectors (coefficient values 0.12 and 0.15). This notion is corroborated by the fact, that the corresponding bands in the Raman spectrum of deuterated AA appear only slightly (up) shifted (data not shown). Instead, we identified three bands at 1243, 1263, and 1280 cm-1, the corresponding normal modes

νexp [cm-1] AdA

νexp [cm-1] AA

νSC [cm-1]

1235c

1241

1197

1330c

1263

1222

1274b

1280

1266

1311b

1329

1346b

1302 1323 1342

1376b

1371

1374

1386

1386

1403

1316

1330c

1353

total energy distributiona 0.14 NH ib, 0.1 CNs, 0.2 NCR2 s (amide III1) 0.18 NH ib, 0.07 CN s, 0.05 CR1H ob, 0.075 CR2H ib (amide III2) 0.06 CNs, 0.02 NH ib, 0.05 CR2H ob, 0.051CR1H ob, 0.3 CR1H ib, 0.08 NH2 w amide III3) 0.43 CR2H ob, 0.23 CR2H ib 0.59 CR1D ob, 0.13 CR1D ib 0.07 CR1H ob, 0.03 NH2 w, 0.71 C(CR2)H3 d 0.83 C(CR1)H3 sb, 0.03 C(CR2)H3 d 0.23 C(CR2)H3 sb, 0.01 CR1C s 0.04 CR1D ib, 0.06 CR2H ob, 0.45 NH2 w 0.06 CR1C s, 0.04 NH ib (amide S)

a TED ) Total Energy Distribution defined as participation of n-normal coordinate in m-normal mode. C(CR2)H3 d, C(CR2)H3 d: d represents all nonsymmetric combinations of bending vibrations. b Taken from ref 5. c Taken from ref 13. d ν : experimental waveexp numbers obtained from Raman and FTIR spectra, νDFT: wavenumbers directly obtained from the DFT calculation, νSC: wavenumbers obtained by scaling the force constants as described in Material and Methods.

of which exhibit substantial contributions from an in-phase combination of NH ib and CN s. We designate them as amide III1, amide III2, and amide III3, respectively. The calculated NH ib coefficients of their eigenvectors are 0.55, 0.54, and 0.2. The band at 1263 cm-1 is very weak in the IR-spectrum but like amide III3 relatively intense in the Raman spectrum (Figure 3). Figure 4 shows the eigenvectors of the three amide III modes calculated for nonionic AA in vacuo. The main difference between the modes concerns the mixing with the CR1H bending



Figure 5. Comparison of unpolarized Raman spectra of anionic alanylalanine measured with 457 nm excitation. Both spectra were normalized onto the internal standard band at 934 cm-1 and corrected for difference in sample concentration.

Figure 4. Eigenvectors of amide III1, amide III2 and amide III3 of nonionic alanyl-alanine obtained from DFT-calculations described in Material and Methods.

modes. Amide III2 exhibits an in-phase combination between NH ib and CR1H ib, whereas amide III3 depicts a out-of-phase mixing with CR1H ib and CR1H ob and additionally an in-phasemixing with CR2H ib. Amide III1 shows contributions from all four CRH bending modes. Amide III1 and III2 also depict NH2 wagging (w) vibrations. We have further checked the validity of our vibrational analysis by calculating the normal modes for the isotopic derivative AdA, for which CR1H is replaced by CR1D. Table 2b lists the calculated frequency values of all modes between 1200 and 1400 cm-1. The modes were assigned to bands observed in the IR13 and UV resonance Raman spectra of AdA.6 In agreement with these experimental data, our calculations yielded slight frequency upshifts of the modes, which are mainly combinations of CR2H ib, CR2H ob and Cβ2H d (observed at 1302 and 1342 cm-1 for AA, Table 2a). As expected, another deformation mode describable as mixture of CR2H ib and CR2H ob (observed at 1323 cm-1 for AA, Table 2a) is downshifted out of the spectral region. The slight experimentally obtained

downshifts of amide III1 and III3 are well reproduced by our calculation. For amide III2, it is more difficult to compare experiment and theory. Our calculation suggest only a modest upshift (7 cm-1) of this mode, but the UV resonance Raman spectrum of AdA exhibits a very strong band at 1330 cm-1.6 If it is amid III2, its upshift is 67 cm-1. The main reason for this discrepancy between calculation and experiment could be the neglect of hydrogen bonding between NH and a H2O molecule of the solvation shell, which significantly increases the force constant of NH ib.22,32 Moreover, the large bandwidth of the 1330 cm-1 band suggests that it is composed of more than one band. Indeed, our calculation predicts an additional mode at 1316 cm-1, which substitutes amide S. It is a mixture of NH2 w, NH ib, CR2H ib, CR2H ob, CR1D ib, and CR1C s (Table 2b). The latter is well-known to cause UV-resonance enhancement.29 Hence, it is very likely that the intense band at 1330 cm-1 in the UV-Raman spectrum of AdA is constituted by overlapping amide III2 and amide S. The UV resonance enhancement of amide III mostly results from the CN s contribution to its eigenvector, because the π f π* at 190 nm causes a significant extension of this internal coordinate.29,32 For dipeptides with a deprotonated carboxylate group, additional enhancement is provided by vibronic coupling to COO- f π* charge-transfer transitions.11,26,27 The enhancement due to CN s part of amide III is so strong that it dominates its intensity even with visible excitation. As shown by Shorygin, this preresonance amplification for very large differences between resonance and excitation wavenumbers is characteristic for organic molecules with π conjugation.30,31 It is demonstrated in Figure 5, which displays the 1200-1550 cm-1 of the x-polarized 457 and 488 nm Raman spectra of the anionic AA. The two spectra were normalized onto the 934 cm-1 band of NaCCl4 to eliminate the nonresonant dependence on the excitation wavelength. Amide III2 and III3 are clearly more intense with 457 nm excitation, whereas the remaining Raman bands display practically identical intensities. This suggests that amide III2 and III3 are both coupled to the far-UV transitions and that they contribute nearly equally to the overall band shape measured with UV-excitation. The use of the apparent (UVRaman) peak frequency of amide III for determining ψ as suggested by Asher et al.6 is only justified if the overall band shape is dominated by amide III2. The above results suggest that this requirement might not be generally fulfilled. However, the Raman spectra of the cationic state shows a significantly reduced intensity of amide III3 (Figure 3, lower panel). The


J. Phys. Chem. B, Vol. 106, No. 16, 2002 4299

Figure 6. Spectral decomposition of unpolarized Raman spectra of the indicated AX (6a)-peptides and XA (6b)-peptides between 1200 and 1450 cm-1 measured at alkaline pH. The spectra of AA, AG, AS, SA, and VA were measured with 457 nm, those of AK, AL, KA, LA, and VA with 488 nm excitation. Reference spectra were used to correct for solvent contributions. The solute concentration was 0.5 M for AA, AG, and SA and 0.3 M for the remaining peptides.

reason for this is revealed by our preliminary normal mode calculation on the zwitterionic AA-(H2O)n [n ) 2-4] complexes (Mroz, Kozlowski, Eker, Schweitzer-Stenner, unpublished), which yields a significant COO- ss contribution to the eigenvector so that the mode can vibronically couple to the charge-transfer transitions from the carboxylate to the lowest π*-orbital of the peptide.26 This transition is eliminated in the cationic state, and it is not of great relevance for the spectra of longer peptides and proteins. Altogether, our results therefore suggest that the overall amide III band shape is dominated by amide III2 with visible and also with UV excitation. In the following, we investigate whether this is the case irrespective of the amino acid residues framing a given peptide group. Vibrational Spectra of AX Peptides. Figure 6a exhibits the visible, unpolarized Raman spectra of the AX peptides measured at alkaline pH. These spectra were self-consistently analyzed together with the corresponding x- and y-polarized Raman and FTIR-spectra. For the sake of simplicity and to reduce the number of fitting parameters, we assumed Gaussian profiles for all Raman and IR bands. Earlier investigations on N′-methylacetamide (NMA) and GG showed that the bands are Voigtian with a dominant Gaussian contribution.11,32 In a second step, we carried out normal mode calculations for the optimized structures of the above peptides. We reiterate that they do not necessarily represent the most stable structure in aqueous solution and that we are solely interested in changes rather in absolute values of frequencies. Frequencies of modes with a significant NH ib contribution can be expected to be underestimated by our calculations due to the absence of

TABLE 3: Calculated Frequencies (cm-1) of AX Vibrations with Significant Contributions from In-Phase or Out-ofPhase Mixing between CA1H ib and NH ib Normal Modesa

peptide

amide III2 (CR1H ib, NH ib, CN s)

amide III3 (CR1H ib, CR1H ob, NH ib, CR2H ib, CR2H ob, CN s)

amide S (CR1H ib, NH ib, CRC s)

AA AG AK AL AS AV

1215(1263) 1217(1261) 1213(1261) 1213(1261) 1215(1262) 1212(1261)

1269(1280) 1289(1270) 1282(1281) 1289(1279) 1280(1276) 1299(1276)

1359(1402) 1355(1398) 1355(1412) 1358(1402) 1356(1404) 1355(1405)

a

Experimental Values Are Given in Parenthesis.

hydrogen bonding. Table 3 lists the calculated and measured frequencies of amide III modes and of amide S. The data obtained for the AX-peptides reveal a quite clear picture. They exhibit two modes with strong in-phase coupling between NH ib and CR1H ib, namely, amide III2 and III3 (only AA shows an out-of-phase combination for III3). Additionally, amide III3 exhibits admixtures from CR1H ob and CR2H ib, so that its frequency can be expected to depend on ψ and φ. A single amide S mode with a significant contribution from outof-phase vibrating CR1H ib and NH ib was obtained. As expected, neither amide III2 nor amide S change their frequency significantly with C-terminal substitution (1212-1216 cm-1, 1355-1357 cm-1, Table 3). Correspondingly, all Raman spectra in Figure 5a depict the amide III2 band between 1261 and 1264 cm-1. It is the band with the highest (integrated) intensity between 1200 and 1300 cm-1. The amide S band, which is



Figure 7. Unpolarized Raman spectra of the indicated cationicAX (7a)-peptides and XA (7b)-peptides between 1200 and 1450 cm-1. The spectra of AA, AG, AS, SA, and VA were measured with 457 nm, those of AK, AL, KA, LA, and VA with 488 nm excitation. Reference spectra were used to correct for solvent contributions. The solute concentration was 0.5 M for AA, AG, and SA and 0.3 M for the remaining peptides.

TABLE 4: Calculated Frequencies (cm-1) of XA Vibrations with Significant Contributions from In-Phase Mixing between CA1H ib and NH ib Normal Modes. Experimental Values Are Given in Parenthesis

Figure 8. FTIR-spectra of anionic alanylalanine, alanyllysine, and leucylalanine. The background contribution was subtracted as described in Material and Methods. The solute concentration was 0.5 M for AA and 0.25 M for AL and KA. The position of AIII2 is indicated.

unambiguously detectable only in the spectra of the cationic species (Figure 7a), exhibits also practically identical frequencies for all AX-peptides. The frequency of amide III3 appears somewhat affected by the C-terminal substitution in that it varies between 1270 (AG) and 1281 cm-1 (AA). Its relative intensity, however, varies significantly. The intensity ratio amide III3/amide III2 is lowest for AS and AV. For all AX, we obtain a significant reduction of the amide III3 intensity in the cationic state (Figure 7a). Vibrational Spectra of XA Peptides. Figure 6b displays the unpolarized Raman spectra of the anionic XA peptides. The spectrum of AA was included for comparison. Again, the spectral decomposition was self-consistently carried out by

peptide

amide III2 (CR1H ib, NH ib, CN s)

AA KA LA SA VA

1215(1263) 1190(1278) 1221(1276) 1231(1280) 1191(1256)

amide III3 (CR1H ib, CR1H ob, NH ib, CR2H ib, CR2H ob, CN s) 1269(1280) 1294(1270) 1297(1281) 1222(1276)

simultaneous fits to the polarized Raman and FTIR spectra. Figure 8 shows the spectral decomposition of the FTIR spectra of AA, AK, and LA (again for alkaline pH). Amide III2 can clearly be identified as the most intense band between 1200 and 1300 cm-1 in the spectra of KA and SA. The assignment is less clear for LA and VA due to the overlap of many bands of intermediate intensity. Fortunately, the corresponding spectra of the cationic species (Figure 7b) resolve the issue since they display amide III2 more isolated. Together, the spectra in Figs. 6b and 7b clearly show that amide III2 is affected by the N-terminal substitution. The shifts are more pronounced for the anionic species. For KA, LA, and SA, amide III2 appears 1015 cm-1 upshifted with respect to the frequency position of AA. On the contrary, the substitution with valine causes a downshift of approximately 5 cm-1. The corresponding band is weak in the FTIR-spectrum, but it can be identified by comparison with the Raman spectrum. The normal mode calculations for the XA peptides also yielded significant changes of the amide III2 frequency (Table 4). As obtained for the AX series we obtain two modes exhibiting an in-phase mixture of CR1H ib and NH ib for KA


J. Phys. Chem. B, Vol. 106, No. 16, 2002 4301

Figure 10. φ-dependence of amide III2. Upper panel: theoretically obtained frequencies of amide III1 (blue-9); amide III2 (b), and amide III3 (red-9); lower panel: experimentally obtained frequencies of amide III2 (b) and amide III3 (red-9), amide III band frequency of acetylated amino acid esters as reported by Ianoul et al.4

Discussion

Figure 9. Eigenvectors of the amide III2a and amide III3 modes of nonionic leucylalanin obtained from DFT calculations described in Material and Methods.

φ-Dependence of Amide III Modes. Figure 10a depicts the theoretically obtained amide III2 and III3 frequencies of AX as a function of φ between -175 and 150°. As mentioned above essentially no φ-dependence is obtained for amide III2, whereas amide III3 shows some pretty scattered variation indicating a tendency toward higher frequencies with increasing φ. A somewhat clearer picture is obtained by correlating the amide III frequencies with the side chain preferences of the C-terminal residue. The latter can be obtained from a paper by Serrano33 who used a broad protein database to determine the statistical distributions of φ for all natural amino acids, which reflect their intrinsic structural propensity. Following Ianoul at al.,4 we calculate the first moment of these distribution, i.e.

ni

N

and LA. For SA and VA, only amide III2 exhibits this pattern. Figure 9 shows the eigenvectors of these modes for KA. The mode with the lower frequency is amide III2, the other one is amide III3. Both modes exhibit substantial CN s contributions to their eigenvectors. Because the minimized structure of the peptide in vacuo is not necessarily that adopted in water, the frequency shifts cannot be directly compared with our experimental values. Differences between calculations and experiment are most pronounced for KA, for which the theoretical amide III2 frequency is dramatically downshifted with respect to AA, whereas the corresponding experimental value appears upshifted (Figures 6b and 7b). For LA, SA, and VA, however, the experimental shifts are at least qualitatively reproduced. Altogether, the data show that a change of ψ causes have a major impact on amide III2.

〈φ〉 )

∑ i)1

φi

N

(1)

where N is the number of ∆φ ) 10° intervals, ni/N is the probability for an amino acid to adopt an angle in the interval φi ( ∆φ/2. Figure 10b displays the experimental amide III2 and III3 frequencies of the AX peptides as a function of their values which lie between -98 and -78°. Of course, Amide III2 is again φ independent. The tendency of the amide III3 frequency to shift up with increasing φ is now apparent due to the absence of data scattering. Ianoul et al.4 obtained a similar φ dependence of the peak frequency of the amide III band in the UV-Raman spectra of acetylated amino acid esters (red data points in Figure 10b). These peptides do not have a N-terminal CRH group and their amide III frequencies are at much higher values, comparable with NMA.32 This might



Figure 11. ψ-dependence of amide III2 (1) as obtained from the DFT calculations on the AX peptides (≤) (2) as derived from an analysis of the experimentally observed frequencies of amide III2 (b). The solid line results from a fit of eq 2 to the data points, the dashed line was obtained by shifting the solid line so that the data point of AA could be reproduced.

suggest that the strongest contribution to the amide III band results from a amide III3 like mode which is sensitive to changes of φ. In this context, we emphasize once again that the dihedral angles obtained from the energy minimization are unlikely to represent the real solution structure of the investigated peptides. This explains the differences between the values obtained from the Serrano study33 and the corresponding φ values obtained from the energy minimization. Taken together our experimental data show that there is no detectable φ-dependence of amide III2 in a range between 75 and 100°, which represents the region of highest propensity for all natural amino acid residues.33 Our theoretical results suggest something similar for the extended region between -150 and -175°. On the contrary, amide III3 show some φ-dependence due to the admixture of CR2H bending vibrations. ψ-Dependence of Amide III Modes. Figure 11 (lower data points) depicts the theoretically obtained ψ-dependence of amide III2 of the XA peptides. The structure obtained from energy minimization sample the (extended) region around ψ ) (180° with KA, SA in the β-sheet and AA, LA, and VA in the socalled -region, which for proteins is only accessible to glycine containing peptides.34 To estimate the ψ angle of the AX-peptides, we have modeled our experimental data as follows. First, we assume that the ψ-dependence of amide III2 can be described by a periodic function, which is minimal at ψ ) 120° and maximal at 30° corresponding to a parallel and an antiparallel orientation of CR1H, respectively. Making use of the UV-amide III frequencies of various secondary structures observed by Chi et al.,7 we estimate a difference of 60 cm-1 between the highest and the lowest possible amide III frequency. Thus, we obtain the equation

(

ν˜ AIII ) νAIII0 + 30 cm-1‚cos ψ +

π 3

)

(2)

The solid line in Figure 11 was obtained by fitting eq 2 to the theoretically calculated data points. This yielded a satisfactory fit with νAIII0 ) 1220 cm -1. Next, we employed the result of a recent study, which exploits the excitonic coupling of amide I to determine the dihedral angles of the tripeptides AAA.35,36 For the anionic state of the former, we found ψ ) 165°. Because amide III appears nearly at the same wavenumber for AAA and AA (126037 and 1263 cm-1) one can assume that the ψ values of the two peptides are practically identical so that the coordinate of AA in Figure 11 is νAIII ) 1263 cm-1, ψ ) 165°. The solid curve in Figure 11 was shifted up to reproduce these data point.

Figure 12. Representation of the AX and XA structures in the Ramachandran space defined by the dihedral angles φ and ψ.

This yielded the dashed curve in Figure 11, which we used to estimate the ψ-values of the XA peptides from the experimental amide III2 frequencies. The following emerges from this analysis. VA has a ψ-angle of 130° close to a conformation which allows optimal coupling between NH ib and CR1H ib. Two solutions are consistent with the frequency values of KA, LA, and SA., i.e., ψ ≈ 50° or an extended structure with ψ values between -160° and -170°. The latter is much more likely because the former does not correspond to an allowed region of the Ramachandran plot. Interestingly, this result suggests a much closer correspondence between the minimized structure of the DFT calculations and the real structure in water for SA, LA, and VA (cf. Figure 11) than one might intuitively expect. Only for AA and KA, the respective structures are significantly different. This suggests that the structure of the investigated AX peptides are differently affected by the solvent. For AA, the very strong solvent dependence was recently demonstrated by DFT calculations.25 The results of the above analysis is summarized by the Ramachandran like plot in Figure 12 which displays the ψ and φ coordinates of the investigated AX and XA peptides. For AX, the dihedral angles suggest a extended β-helix conformation. This is in close to what has been obtained for all protonation states of AAA.35 VA is close to a 31-helix conformation. KA, LA, and SA are all in the so-called -region which is normally only sampled by glycine containing peptides. In agreement with recent studies on tripeptides,35,24,38,39 our results strongly indicate that even very short peptides adopt a pretty well defined structure in water, at least with respect to their dihedral angles. If different conformers of the investigated dipeptides coexisted we would obtain substantial broader and asymmetric amide III bands, and differences between the frequency positions of the XA dipeptides would most likely be insignificant. In agreement with the present results, a stable structure was recently derived for tri-alanine in D2O by different spectroscopic techniques.35,39 All this does not rule out conformational heterogeneity with respect to side chain conformations and the C-terminal carboxylate group.11 Conformational SensitiVity of Amide S. In UV-resonance Raman spectroscopy, amide S has been used as another structural marker band. It appears only in the spectra of socalled random coil and β-sheet structures, but is completely absent in those of right-handed R-helices.3,7 Mix et al.37 have recently shown that due to the absence of interpeptide vibrational mixing the intensity of amide S is describable as a superposition of the contribution from the individual peptide CRH-peptide


Figure 13. Comparison of normalized unpolarized Raman spectra of alanylalanine, alanyllysine, lysylalanine, and leucylalanine between 1200 and 1450 cm-1 taken with 488 nm excitation. The spectra were corrected for different concentrations.

linkages. A conclusive explanation for the disappearance of amide S in the UV-Raman spectra of R-helical structures has not yet been presented. In this context, the behavior of amide S in the spectra of the cationic XA peptides (Figure 7b) is illuminating. Apparently, amide S band is nearly absent in the spectra of KA, LA, and SA. For VA, it appears broadened compared with AA but still clearly detectable. As argued above, KA, LA, and SA sample the conformational space in the ψ interval around -165°. The detuning from the optimal ψ-value for CR1H-NH coupling is 75°, which is much less than the 170° in R-helices. Apparently, this is sufficient to eliminate amide S. Correspondingly, we observed a significant intensity redistribution among the bands between 1300 and 1350 cm-1. This leads us to suggest that CR1H ib is now coupled to several modes in this frequency range. In fact, our mode calculations for some XA peptides reveal several modes which depict an out-of-phase combination of CR1H ib and NH ib. Side Chain Effects. A use of amide III for a detailed analysis of secondary structures requires the clarification of important issue, namely the dependence of intensity and frequency on the amino acid residues adjacent to a given peptide group. The successful correlation of the XA’s amide III2 frequencies with ψ argues against a major influence on the frequency of this mode. With respect to the intensity, however, the situation is different. This is demonstrated in Figure 13, which compares the x-polarized Raman spectra of AA, AK, KA and LA between 1200 and 1500 cm-1 as measured with 488 nm at alkaline pH. All these spectra were normalized by scaling their internal standard line at 934 cm-1 to the same intensity. AA and LA show different intensity distributions but are comparable in terms of absolute intensities, but AK and KA exhibit much less Raman scattering in the entire spectral region. For the amide III modes this observation is reproduced by our DFT calculations, which reveal significantly smaller CN s contributions to the eigenvectors. The reason for this is the strong mixing with the methylene deformation modes of the lysine residue (Figure 9). This gives rise to a delocalization of the vibrational energy and thus to smaller contributions of individual internal coordinates. This certainly holds for the visible as well as for UV-resonance Raman spectra, because both depend on the contribution of CN s to the eigenvector. Further experiments are necessary to clarify in detail how the amide III Raman cross-section depends on the choice of the amino acid residue and to evaluate the consequences for the secondary structure determination. Comparison with Theoretical Studies. Very recently, Mirkin and Krimm reported results from a theoretical of the amide III

J. Phys. Chem. B, Vol. 106, No. 16, 2002 4303 dependence on φ and ψ.9 They selected the blocked tri-alanine analogue N-acetyl-L-alanine-N-methylamide for their analysis. DFT calculations were carried out on the same level of theory as used in the present study. To identify the influence of the dihedral angles on the amide III frequency the authors calculated the minimum energy structure for different constrained values of ψ and φ. Their results seem to clearly indicate that the amide III frequency depends strongly on both coordinates, in contrast to Lord’s hypothesis. A comparison with results from our study, however, renders difficult for three reasons delineated in the following. First, we think that the general approach employed by Mirkin and Krimm9 is problematic from a physical point of view because their calculations were carried out for nonstationary geometries. Constrains imposed on dihedral angles introduce nonvanishing forces along these coordinates yielding a force field which is rotationally and translationally noninvariant.14,40 This gives rise to coordinate dependent frequencies. Hence, it is in principle impossible to define vibrational frequencies at nonstationary geometries. Possible strategies to overcome this problem have been outlined by Pulay and associates.14 Second, Mirkin and Krimm do not distinguish explicitly between different amide III modes, which, as shown in the present study, depend differently on the dihedral angles. It is therefore unclear to which of our three amide III modes the results of their studies can be compared. Third, the two peptide groups of the molecule investigated by the authors are linked only to a single CRH group, in contrast to our more biologically realistic peptides. Irrespective of the above concerns we like to emphasize that the results reported by Mirkin and Krimm9 indicate a very weak φ dependence for the region around ψ ) 165°, in full agreement with our results obtained from our AX spectra. In an earlier study, Ianoul et al.4 carried out DFT calculations for different acetylated amino acid esters to reproduce the experimentally determined φ-dependence of the corresponding amide III band. These calculations were also performed with constrained angular coordinates but only for a restricted conformational space (-95° e φ e -75°, ψ ) -21°) around the minimum so that the nonvanishing forces might not be as relevant as they certainly are for the calculations by Mirkin and Krimm.9 Ianoul et al.4 reproduced the experimentally obtained φ dependence amide III. This is not in contrast to our results because amide III of the peptides investigated by Ianoul et al.4 can be expected to have another normal mode composition than the amide III modes of the dipeptides dealt with in the present study. Indeed, a DFT calculation carried out by Ianoul et al. for di-alanine suggests a significantly reduced φ-dependence of the amide III frequency in the above conformational interval. Summary and Outlook In this study we have investigated a series of AX and XA dipeptides by combining polarized visible Raman and FTIR spectroscopy with DFT calculations to investigate the conformational sensitivity of amide III. We identified three modes designated as amide III1, III2, and III3 in the spectra of AX and XA dipeptides (X ) G, K, S, V), based on the criteria that amide III is constituted by an in-phase mixing between NH ib and CN s.22,32 From the normal-mode analysis, we obtain that amide III2 contains a significant contribution from an in-phase combination of NH ib and CR1H ib, which is a necessary requirement for making it sensitive to changes of ψ. The mode shows only weak coupling to bending modes of CR2H so that a dependence on φ is not expected. Indeed, our experimental data confirm that the frequency of amide III2 remains nearly

4304 J. Phys. Chem. B, Vol. 106, No. 16, 2002 unaffected by changes of φ in a range between -75° and -95° but varies significantly as a function of ψ. Therefore, our results support the hypothesis of Lord. With respect to the conformation of the investigated dipeptides our analysis reveals that all AX peptides exhibit ψ angles around 150°, whereas most of the XA dipeptides (KA, LA, SA) prefer a very extended structure with ψ values between -160° and -170°. VA is an exception from the rule in that it exhibits a ψ-value of around 130°. Our results suggest further that an amino acid substitution has generally a much greater impact on ψ than on φ. Finally, we found evidence that a well-defined amide S band assignable to a mode with an out-phase-combination of CR1H ib and NH ib does only exist within a small range of ψ values in the β-sheet region for which the coupling between these local vibrations is maximal. Outside of this region this pattern can be found in many modes between 1300 and 1400 cm-1. Our finding explains the absence of amide S in the spectra of R-helical structures. The question arises whether the findings reported in this paper are applicable for the structure analysis of longer peptides or even proteins, which can be expected to give rise to even more complex spectra in the amide III region. Fortunately, some recent results indicate that the situation is less complicated than one might expect. First, a UV-resonance Raman study on a representative set of tripeptides in H2O/D2O have shown that all modes in the amide III region including amide S are rather localized due to the absence of significant interpeptide coupling.37 This result suggests that the Raman and IR-spectra in this region can be understood as a superposition of spectra from the individual peptide groups. Asher et al.6 recently showed that the UV-resonance Raman intensity of amide S in the spectra of di-, tri-, tetra, and penta-alanine increases linearly with the number of peptide groups. A comparison of this and the present study strongly suggests that AIII2 is dominant with UVresonance Raman, so that the spectral complexity is significantly reduced. The amide III bands in the UV-resonance Raman spectra of polypeptides and proteins are broad and asymmetric.7 If they result predominantly from amide III2, their band profile can be considered as reflecting the distribution of ψ-angles. Indeed, Mix has recently shown that the peak position of amide III bands in the spectra of various proteins can be correlated with the average ψ-value in a given secondary structure motif.41 Altogether, these results suggest that amide III can be used as a marker band for ψ in larger, biologically relevant systems, but further studies have to be carried out to sustain this view. Acknowledgment. Financial support for R.S.S. was provided by NSF (PR EPSCOR) Grant No. OSR-9452893 and from the Fondos Institucionales para la Investigacio´n of the University of Puerto Rico (20-02-2-78-514). We thank Dr. Brad Weiner for allowing us to build up a temporary set up for Raman experiments in his laboratory. References and Notes (1) Lord, A. C. Appl. Spectrosc. 1977, 31, 187. (2) Williams, R. W.; Weaver, J. L. and Lowrey, A. H. Biopolymers 1990, 30, 599. (3) Jordan, T.; Spiro, T. G. J. Raman Spectrosc. 1994, 25, 537. Lord, A. C. Appl. Spectrosc. 1977, 31, 187. Williams, R. W.; Weaver, J. L.; Lowrey, A. H. Biopolymers 1990, 30, 599.

Schweitzer-Stenner et al. (4) Ianoul, A.; Boden, M. N.; Asher, S. A. J. Am. Chem. Soc. 2001, 123, 7433. (5) The φ-values were obtained by calculating the respective side chain average φ-angle propensity by utilizing the study of Serrano, L. J. Mol. Biol. 1995, 254, 322. (6) Asher, SA.; Ianoul, A.; Mix, G.; Boyden, M. N.; Karnoup, AQ.; Diem, M.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 2001, 123, 11 775. (7) Chi, Z.; Chen, X. G.; Holtz, J. S. W.; Asher, S. A. Biochemistry 1998, 37, 2854. (8) Chi, Z, Asher, SA. Biochemistry 1998, 37, 2865. (9) Mirkin, N.; Krimm, S. J. Phys. Chem B 2001, in press. (10) In agreement with earlier studies we use the term dipeptides, tripeptides, etc, for molecules containing two, three, etc. amino acid residues. (11) Sieler, G.; Schweitzer-Stenner, R.; Holtz, J. S. W.; Pajcini, V.; Asher, S. A. J. Phys. Chem. B 1999, 103, 372. (12) Oboodi, M. R.; Alva, C.; Diem, M. J. Phys. Chem. 1984, 88, 501. (13) Diem, M.; Lee, O.; Roberts, G. M. J. Phys. Chem. 1992, 96, 548. (14) Fogarasi, G.; Zhou, X.; Taylor, P. W.; Pulay, P. J. Am. Chem. Soc. 1992, 114, 8191. (15) Sieler, G.; Schweitzer-Stenner, R. J. Am. Chem. Soc. 1997, 119, 1720. (16) Griebenow, K.; Diaz Laureano, Y.; Santos, A. M.; Montan˜ez Clemente, I.; Rodriguez, L.; Vidal, M.; Barletta, G. J. Am. Chem. Soc. 1999, 121, 8157. (17) Jentzen, W.; Unger, E.; Karvounis, G.; Shelnutt, J. A.; Dreybrodt, W.; Schweitzer-Stenner, R. J. Phys. Chem. 1996, 100, 14 184. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zarzewski, V. G.; Montgomery, J. A., Jr.; Stratman, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo C.; Clifford, S.; Ochterski, J.; Peterson, J. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Ragvachakari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkare, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzales, C.; HeadGordon, M.; Replodge, R. S.; Pople, J. A. Gaussian; Inc.: Pittsburgh, PA, 1998. (19) Pulay, P., Fayetteville, AR 1990; Theor. Chim. Acta 1979, 50, 229. (20) Pulay, P.; Gogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037. (21) Rauhut, G.; Pulay, P. J. Phys. Chem. 1995, 99, 3093. (22) Schweitzer-Stenner, R. J. Raman Spectrosc. 2001, 32, 711. (23) Shang, H. S.; Head-Gordon, T. J. Am. Chem. Soc. 1994, 116, 1528. (24) Han, W,-G.; Jakanen, K. J.; Elstner, M.; Suhai, S. J. Phys. Chem. B 1998, 102, 2587. (25) Knapp-Mohammady, M.; Jalkanen, K. J.; Nardi, F.; Wade, R. C.; Suhai, S. Chem. Phys. 1999, 240, 63. (26) Chen, X. G.; Li, P.; Holtz, J. S. W.; Chi, Z.; Pajcini, V.; Asher, SA.; Kelly, L. A. J. Am. Chem. Soc. 1996, 118, 9705. (27) Pajcini, V.; Chen, X. G.; Bormett, W.; Geib, S. J.; Asher, SA. J. Am. Chem. Soc. 1996, 118, 9716. (28) Weir, A. F.; Lowrey, A. H.; Williams, R. W. Biopolymers 2001, 58, 577. (29) Chen, X. G.; Asher, S. A.; Schweitzer-Stenner, R.; Mirkin, N. G.; Krimm, S. J. Am. Chem. Soc. 1995, 117, 2884. (30) Shorigyn, P. P. Usp. Khim. 1971, 40, 694. (31) Leites, L. A.; Bukalov, S. S. J. Raman Spectrosc. 2001, 32, 413. (32) Chen, X. G.; Schweitzer-Stenner, R.; Asher, SA.; Mirkin, N. G.; Krimm, S. J. Phys. Chem. 1995, 99, 3074. (33) Serrano, L. J. Mol. Biol. 1995, 254, 322. (34) Karplus, M. A. Protein Science 1996, 5, 1406. (35) Schweitzer-Stenner, R.; Eker, F.; Huang, Q.; Griebenow, K. J. Am. Chem. Soc. 2001, 123, 9628. (36) Schweitzer-Stenner, R. Biophys. J. 2002, in press. (37) Mix, G.; Schweitzer-Stenner, R.; Asher, SA. J. Am. Chem. Soc. 2000, 132, 9028. (38) Ford, S. J.; Wen, Z. Q.; Hecht, L.; Barron, L. D. Biopolymers 1994, 34, 303. (39) Woutersen, S.; Hamm, P. J. Phys. Chem B 2000, 104, 11 316. (40) Pulay, P. In Applications of Electronic Structure Theory; Schaefer, H. F., IIII.; Ed.; Plenum Press: New York, 1977; p 153. (41) Mix, G. Doctoral Thesis, Universita¨t Bremen, 2000.

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