Characteristic two-dimensional IR spectroscopic features of antiparallel and parallel beta-sheet polypeptides: simulation studies

The antiparallel and parallel beta sheets are two of the most abundant secondary structures found in proteins. Although various spectroscopic methods have been used to distinguish these two different structures, the linear spectroscopic measurements could not provide incisive information for distinguishing an antiparallel beta sheet from a parallel beta sheet. After carrying out quantum-chemistry calculations and model simulations, we show that the polarization-controlled two-dimensional (2D) IR photon echo spectroscopy can be of critical use in distinguishing these two different beta sheets. Particularly, the ratio between the diagonal peak and the cross peak is found to be strongly dependent on the quasi-2D array of the amide I local-mode transition dipole vectors. The relative intensities of the cross peaks in the 2D difference spectrum of an antiparallel beta sheet are significantly larger than those of the diagonal peaks, whereas the cross-peak amplitudes in the 2D difference spectrum of a parallel beta sheet are much weaker than the main diagonal-peak amplitudes. A detailed discussion on the origin of the diagonal- and cross-peak intensity distributions of both the antiparallel and parallel beta sheets is presented by examining vibrational exciton delocalization, relative angles between two different normal-mode transition dipoles, and natures of the cross peaks in the 2D difference spectrum.     

Collective oscillations and the linear and two-dimensional infrared spectra of inhomogeneous beta-sheets

We numerically calculate the collective amide I oscillations and the associated linear and two-dimensional infrared (2DIR) spectra for model antiparallel beta-sheets and study the effect of inhomogeneity. To visualize the collective vibrational exciton states, a new method is introduced, which proves very useful in classifying the optically dominant states with respect to their symmetry properties and phase relations, even in the absence of exact symmetries. We find that energy (diagonal) and interaction (off-diagonal) disorder may have profoundly different effects on the main peaks in the linear spectrum. We also show that in the 2DIR spectra energy disorder leads to diagonal stretching of the diagonal peaks, while the cross-peaks are typically stretched more horizontally. This offers an explanation for the recently observed overall Z-shape in experimental spectra. Finally, we find that the anharmonic splitting between associated positive and negative features in the 2DIR spectra scales inversely proportionally with the exciton delocalization size imposed by the disorder, thus offering a spectroscopic ruler for this size.     

Computational spectroscopy of ubiquitin: comparison between theory and experiments

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.     

Residual native structure in a thermally denatured beta-hairpin

We investigate the thermal denaturation of trpzip2 between 15 and 82 degrees C using two-dimensional infrared (2D IR) vibrational spectroscopy, dispersed vibrational echo (DVE) spectroscopy, and Fourier transform infrared (FTIR) spectroscopy. The FTIR and DVE spectra of trpzip2 show in the amide I region of the spectrum two resonances, which arise primarily from the interstrand coupling between local amide I oscillators along the peptide backbone. The coupling is seen directly in the 2D IR spectra as the formation of cross-peak ridges. Although small shifts of these frequencies occur on heating the sample, the existence of cross-peak ridges at all temperatures indicates that stable hydrogen bond interactions persist between the two beta-strands. These observations indicate a significant amount of native structure in the thermally denatured state of trpzip2.     

Visualization and characterization of the infrared active amide I vibrations of proteins

To facilitate the analysis of frequency-structure correlations in the amide I vibrational spectroscopy of proteins, we investigate visualization methods and spatial correlation functions that describe delocalized vibrations of proteins and protein secondary structures. To study those vibrational modes revealed in infrared spectroscopy, we characterize frequency-dependent bright states obtained from doorway mode analysis. Our visualization methods pictorially color code amplitude and phase of each oscillator within the structure to reveal spatially varying patterns characteristic of excitations within sheets and helices. Spatial correlation functions in the amplitude and phase of amide I oscillators quantitatively address the extent of delocalization and the alpha helical and beta sheet character of these modes. Specifically, we investigate the vibrations of idealized antiparallel beta sheets and alpha helices and perform case studies on three proteins: concanavalin A, myoglobin, and ubiquitin.     

A new perspective on beta-sheet structures using vibrational Raman optical activity: from poly(L-lysine) to the prion protein

The vibrational Raman optical activity (ROA) spectrum of a polypeptide in a model beta-sheet conformation, that of poly(l-lysine), was measured for the first time, and the alpha-helix --> beta-sheet transition monitored as a function of temperature in H(2)O and D(2)O. Although no significant population of a disordered backbone state was detected at intermediate temperatures, some side chain bands not present in either the alpha-helix or beta-sheet state were observed. The observation of ROA bands in the extended amide III region assigned to beta-turns suggests that, under our experimental conditions, beta-sheet poly(L-lysine) contains up-and-down antiparallel beta-sheets based on the hairpin motif. The ROA spectrum of beta-sheet poly(L-lysine) was compared with ROA data on a number of native proteins containing different types of beta-sheet. Amide I and amide II ROA band patterns observed in beta-sheet poly(L-lysine) are different from those observed in typical beta-sheet proteins and may be characteristic of an extended flat multistranded beta-sheet, which is unlike the more irregular and twisted beta-sheet found in most proteins. However, a reduced isoform of the truncated ovine prion protein PrP(94-233) that is rich in beta-sheet shows amide I and amide II ROA bands similar to those of beta-sheet poly(L-lysine), which suggests that the C-terminal domain of the prion protein is able to support unusually flat beta-sheets. A principal component analysis (PCA) that identifies protein structural types from ROA band patterns provides a useful representation of the structural relationships among the polypeptide and protein states considered in the study.     

Conformational preferences and vibrational frequency distributions of short peptides in relation to multidimensional infrared spectroscopy.

Molecular dynamics simulations of the structural distributions and the associated amide-I vibrational modes are carried out for dialanine peptide in water and carbon tetrachloride. The various manifestations in nonlinear-infrared spectroscopic experiments of the distributions of conformations of solvated dialanine are examined. The two-dimensional infrared (2D-IR) spectrum of dialanine exhibits the coupling between the amide oscillators and the correlations of the frequency fluctuations. An internally hydrogen-bonded conformation exists in CCl(4) but not in H(2)O where two externally hydrogen-bonded forms are preferred. Simulations of solvated dialanine show how the 2D-IR spectra expose the underlying structural distributions and dynamics that are not deducible from linear-infrared spectra. In H(2)O the 2D-IR shows cross-peaks from large coupling in the alpha-helical conformer and an elongated higher frequency diagonal peak, reflecting the broader distribution of structures for the more flexible acetyl end. In CCl(4), the computed cross-peak portion of the 2D-IR shows evidence of two amide-I transitions in the high-frequency region which are not apparent from the diagonal peak profile. The vibrational frequency inhomogeneity of the amide-I band arises from fluctuations of the instantaneous normal modes of these conformers rather than the shifts induced by hydrogen bonding. The simulation shows that there are correlations between fluctuations of the acetyl and amino end frequencies in H(2)O that arise from mechanical coupling and not from hydrogen bonding at the two ends of the molecule. The angular relationships between the two amide units which also show up in 2D-IR were computed, and spectral manifestations of them are discussed. The simulations also permit a calculation of the rate of energy transfer from one side of the molecule to the other. From these calculations, 2D-IR spectroscopy in conjunction with simulations is seen to be a promising tool for determining dynamics of structure changes in dipeptides.     

Two-dimensional infrared spectral signatures of 3(10)- and alpha-helical peptides

Two-dimensional infrared (2D IR) spectra of Calpha-alkylated model octapeptides Z-(Aib)8-OtBu, Z-(Aib)5-L-Leu-(Aib)2-OMe, and Z-[L-(alphaMeVal)]8-OtBu have been measured in the amide I region to acquire 2D spectral signatures characteristic of 3(10)- and alpha-helical conformations. Phase-adjusted 2D absorptive spectra recorded with parallel polarizations are dominated by intense diagonal peaks, whereas 2D rephasing spectra obtained at the double-crossed polarization configuration reveal cross-peak patterns that are essential for structure determination. In CDCl3, all three peptides are of the 3(10)-helix conformation and exhibit a doublet cross-peak pattern. In 1,1,1,3,3,3-hexafluoroisopropanol, Z-[L-(alphaMeVal)]8-OtBu undergoes slow acidolysis and 3(10)-to-alpha-helix transition. In the course of this conformational change, its 2D rephasing spectrum evolves from an elongated doublet, characteristic of a distorted 3(10)-helix, to a multiple-peak pattern, after becoming an alpha-helix. The linear IR and 2D absorptive spectra are much less informative in discerning the structural changes. The experimental spectra are compared to simulations based on a vibrational exciton Hamiltonian model. The through-bond and through-space vibrational couplings are modeled by ab initio coupling maps and transition dipole interactions. The local amide I frequency is evaluated by a new approach that takes into account the effects of hydrogen-bond geometry and sites. The static diagonal and off-diagonal disorders are introduced into the Hamiltonian through statistical models to account for conformational fluctuations and inhomogeneous broadening. The sensitivity of cross-peak patterns to different helical conformations and the chain length dependence of the spectral features for short 3(10)- and alpha-helices are discussed.     

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.     

Site-specific vibrational dynamics of the CD3zeta membrane peptide using heterodyned two-dimensional infrared photon echo spectroscopy

Heterodyned two-dimensional infrared (2D IR) spectroscopy has been used to study the amide I vibrational dynamics of a 27-residue peptide in lipid vesicles that encompasses the transmembrane domain of the T-cell receptor CD3zeta. Using 1-(13)C[Double Bond](18)O isotope labeling, the amide I mode of the 49-Leucine residue was spectroscopically isolated and the homogeneous and inhomogeneous linewidths of this mode were measured by fitting the 2D IR spectrum collected with a photon echo pulse sequence. The pure dephasing and inhomogeneous linewidths are 2 and 32 cm(-1), respectively. The population relaxation time of the amide I band was measured with a transient grating, and it contributes 9 cm(-1) to the linewidth. Comparison of the 49-Leucine amide I mode and the amide I band of the entire CD3zeta peptide reveals that the vibrational dynamics are not uniform along the length of the peptide. Possible origins for the large amount of inhomogeneity present at the 49-Leucine site are discussed.     

Signatures of beta-sheet secondary structures in linear and two-dimensional infrared spectroscopy

Using idealized models for parallel and antiparallel beta sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition-dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel beta sheets and between beta hairpins and extended beta sheets.     

Local structure of beta-hairpin isotopomers by FTIR, 2D IR, and ab initio theory

The 12-residue tryptophan zipper beta-hairpin (SWTWENGKWTWK) and two (13)C-isotopomers were examined in the amide-I region using FTIR and femtosecond two-dimensional infrared (2D IR) spectroscopies. Spectroscopic features of the labeled transitions with (13)C-substituted amide unit present in the terminal or turn region of the hairpin, including their frequency shifts and distributions, line broadenings, orientations, and anharmonicities of diagonal peaks, allow the peptide local structure and local environment to be examined. The results suggest a larger structure fluctuation in the terminal region than in the turn region as a result of the side chain effect and solvent-peptide interaction. The results also suggest that the uncoupled amide-I modes are not degenerate and that this is likely to be a common situation for solvated polypeptides. In addition, the amide-I states in the terminal and turn regions were found to be delocalized over several neighboring amide units. Cross-peaks between the various labeled and unlabeled structural regions were clearly observed in the 2D IR correlation spectra, allowing them to be characterized for monitoring structural changes. These results illustrate the sensitivity of 2D IR to the local environment of solvated peptides. The simulated 1D and 2D IR spectra of the hairpin, obtained by using the vibrational exciton model incorporating coupling constants from quantum chemical computations and semiempirical calculations, were found to reproduce the essential features of the experimental results.     

Impact of four (13)C-proline isotope labels on the infrared spectra of ribonuclease T1

Ribonuclease T1 was biosynthesized, with all four prolines (13)C-labeled in the peptide C[double bond]O bond, using a proline auxotrophic yeast strain of Saccharomyces cerevisiae. The (13)C- and (12)C-proline isotopomers of ribonuclease T1 were investigated by infrared spectroscopy in the thermally unfolded and natively folded state at 80 and 20 degrees C, respectively. In the thermally unfolded state, both proteins established almost indistinguishable spectral features in the secondary structure sensitive amide I region. In contrast, the spectra measured at 20 degrees C revealed substantial qualitative and quantitative differences, though parallel analysis by circular dichroism suggested identical native folds for both isotopomers. Major spectral differences in the infrared spectra were detected at 1626 and 1679 cm(-1), which are diagnostic marker bands for antiparallel beta-sheets in ribonuclease T1 and at 1645 cm(-1), a region that is characteristic for the infrared absorption of irregular structures. Starting with the known three-dimensional structure of ribonuclease T1, the observed effects of the isotope labeling are discussed on the basis of transition dipole coupling between the (12)C[double bond]O and (13)C[double bond]O groups. The experimental results were confirmed by transition dipole coupling calculations of the amide I manifold of the labeled and unlabeled variant.     

Two-dimensional infrared spectra of the 13C=18O isotopomers of alanine residues in an alpha-helix

The parameters needed to describe the two-dimensional infrared (2D IR) spectra of the isotopically labeled alpha-helix are presented. The 2D IR spectra in the amide-I' spectral region of a series of singly 13C=18O-labeled 25-residue alpha-helices were measured by three-pulse heterodyned spectral interferometry. The dependence of the spectra on the population time was measured. Individual isotopomer levels (residues 11-14) were clearly identified in 2D IR, downshifted by approximately 61 cm(-1) from the main helical band. By analyzing the line shapes of the 13C=18O diagonal peaks that appeared at approximately 1571.3 +/- 0.8 cm(-1) for all four labeled samples, we observed wider structural distributions for residues 14 and 11 than those for 12 and 13. A small fast component in the correlation function was used to estimate the dynamics of these distributions. In all cases, the v = 1 --> 2 transition showed a more Lorentzian-like line shape and also decayed faster than the v = 0 --> 1 transition, indicating that the population relaxation time of the v = 2 state was significantly faster than the v = 1 state. The amide transitions with naturally abundant 13C=16O appeared at approximately 1594 cm(-1), forming very weak and blurred cross-peaks with 13C=18O isotopomer modes. The effects of spectral interferences on the coherence time dependence of the detection frequency spectrum were also investigated. The methods of first moments and Wigner analysis were developed to circumvent the interference effects on the weak isotopomer transitions. The structural origin of the distributions for individual isotopomers was proposed to be an effect of nearby lysine residues on the intrahelical hydrogen-bond network.     

2D IR photon echo of azido-probes for biomolecular dynamics

The vibrations in the azido-, N(3), asymmetric stretching region of 2'-azido-2'-deoxyuridine (N(3)dU) are examined by two-dimensional infrared spectroscopy. In water and tetrahydrofuran (THF), the spectra display a single sharp diagonal peak that shows solvent sensitivity. The frequency-frequency correlation time in water is 1.5 ps, consistent with H-bond making and breaking dynamics. The 2D IR spectrum is reproduced for N(3)dU in water based on a model correlation function and known linear response functions. Its large extinction coefficient, vibrational frequency outside the protein and nucleic acid IR absorption, and sensitivity to water dynamics render -N(3) a very useful probe for 2D IR and other nonlinear IR studies: its signal is ca. 100 times that of nitriles.     

Different spectral signatures of octapeptide 3(10)- and alpha-helices revealed by two-dimensional infrared spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy is applied to the amide I modes of the terminally protected homo-octapeptide Z-[L-(alphaMe)Val](8)-OtBu in CDCl(3), 2,2,2-trifluoroethanol (TFE), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) solutions to acquire 2D spectral signatures that distinguish between 3(10)- and alpha-helix structures. Suppression of diagonal peaks by controlling polarizations of IR pulses clearly reveals cross-peak patterns that are crucial for structural determination. A doublet feature is observed when the peptide ester forms a 3(10)-helix in CDCl(3) and TFE and when it is at the initial stage of 3(10)- to alpha-helix transition in HFIP. In contrast, the 2D IR spectrum shows a multiple peak pattern after the peptide ester has acidolyzed and become an alpha-helix in HFIP. Electronic circular dichroism spectra accompanying the acidolysis-driven conformational change are also reported. This is the first report on the experimental 2D IR signature of a 3(10)-helical peptide. These results, using a model octapeptide, demonstrate the powerful capability of 2D IR spectroscopy to discriminate between different helical structures.     

Differentiation of beta-sheet-forming structures: ab initio-based simulations of IR absorption and vibrational CD for model peptide and protein beta-sheets.

Ab initio quantum mechanical computations of force fields (FF) and atomic polar and axial tensors (APT and AAT) were carried out for triamide strands Ac-A-A-NH-CH(3) clustered into single-, double-, and triple-strand beta-sheet-like conformations. Models with phi, psi, and omega angles constrained to values appropriate for planar antiparallel and parallel as well as coiled antiparallel (two-stranded) and twisted antiparallel and parallel sheets were computed. The FF, APT, and AAT values were transferred to corresponding larger oligopeptide beta-sheet structures of up to five strands of eight residues each, and their respective IR and vibrational circular dichroism (VCD) spectra were simulated. The antiparallel planar models in a multiple-stranded assembly give a unique IR amide I spectrum with a high-intensity, low-frequency component, but they have very weak negative amide I VCD, both reflecting experimental patterns seen in aggregated structures. Parallel and twisted beta-sheet structures do not develop a highly split amide I, their IR spectra all being similar. A twist in the antiparallel beta-sheet structure leads to a significant increase in VCD intensity, while the parallel structure was not as dramatically affected by the twist. The overall predicted VCD intensity is quite weak but predominantly negative (amide I) for all conformations. This intrinsically weak VCD can explain the high variation seen experimentally in beta-forming peptides and proteins. An even larger variation was predicted in the amide II VCD, which had added complications due to non-hydrogen-bonded residues on the edges of the model sheets.     

Dual-frequency 2D IR on interaction of weak and strong IR modes

Dual-frequency 2D IR heterodyne photon-echo spectroscopy of C[triple bond]N and C=O stretching vibrational modes in 2-cyanocoumarin is reported. We have shown that the interaction among these modes provides convenient and useful structural constraints for molecules. Implementation of two pulse sequences, 4, 4, and 6 microm and 6, 6, and 4 microm, allowed the clear determination of contributions caused by vibrational relaxation. Positive correlation between C[triple bond]N and C=O frequency distributions was observed in 2-cyanocoumarin. Because C[triple bond]N modes are highly localized and have frequencies in a spectral region with minimal water absorption, the C[triple bond]N/C=O interactions have a strong potential for use as structural reporters in proteins. In addition to CN/CO peaks, the cross-peaks responsible for the C[triple bond]N/C=C interaction are also observed in the 2D IR spectra, where C=C is a coumarin ring stretching mode. We have demonstrated that 2D IR spectroscopy can utilize interactions of strong IR modes with weak local modes as structural reporters.     

Cross-strand coupling of a beta-hairpin peptide stabilized with an Aib-Gly turn studied using isotope-edited IR spectroscopy

Isotope-edited IR spectroscopy was used to study a series of singly and doubly 13C=O-labeled beta-hairpin peptides stabilized by an Aib-Gly turn sequence. The double-labeled peptides have amide I' IR spectra that show different degrees of vibrational coupling between the 13C-labeled amides due to variations in the local geometry of the peptide structure. The single-labeled peptides provide controls to determine frequencies characteristic of the diagonal force field (FF) contributions at each position for the uncoupled 13C=O modes. Separation of diagonal FF and coupling effects on the spectra are used to explain the cross-strand labeled spectral patterns. DFT calculations based on an idealized model beta-hairpin peptide correctly predict the vibrational coupling patterns. Extending these model results by consideration of frayed ends and the hairpin conformational flexibility yields an alternate interpretation of details of the spectra. Temperature-dependent isotopically labeled IR spectra reveal differences in the thermal stabilities of the individual isotopically labeled sites. This is the first example of using an IR-based isotopic labeling technique to differentiate structural transitions at specific sites along the peptide backbone in model beta-hairpin peptides.