Two-dimensional infrared spectroscopy as a probe of the solvent electrostatic field for a twelve residue peptide

The linear IR and two-dimensional (2D) IR spectra of the amide-I modes of the 12-residue beta-hairpin peptide tryptophan zipper-2 (SWTWENGKWTWK) and its two 13C isotopomers were simulated, with local mode frequencies evaluated by two solution-phase peptide amide-I frequency maps proposed recently: an electrostatic potential map and an electrostatic field map. Both maps predict a set of nondegenerate local amide-I mode transition energies for the hairpin. Spectral simulations using both maps predict the main spectral features of the linear IR and 2D IR experimental results of the (13)C-labeled and -unlabeled hairpin. The radial distribution functions obtained using trajectories from classical molecular dynamics simulations demonstrate different water distributions at different sites of the hairpin. Our results suggest that the observed difference of the (13)C-shifted band, including its peak position and frequency distributions for different isotopomers, in both linear IR and 2D IR spectra, is likely to be due to the difference in the local environment of the solvated peptide. Ab initio density functional theory calculations show a residue-independent (13)C shift of the amide-I mode, further supporting the result. The variations of these shifts are attributed to the residue level heterogeneity of the electrostatic environment of the peptide. Our results show that 2D IR of peptide with single (13)C isotopic labeling can be used to probe the electrostatic environment of the peptide local structure.     

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.     

Conformations of N-acetyl-L-prolinamide by two-dimensional infrared spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy has been applied to study the conformations of a model dipeptide, N-acetyl-L-prolinamide (AcProNH2) in deuterated chloroform (CDCl3). Spectral features in the amide-I and -II regions are obtained by rephasing (R), nonrephasing (NR), and reverse photon echo (RPE) pulse sequences with two polarization conditions. The 2D spectra obtained by the RPE and NR sequences with (0, 0, 0, 0) polarization reveal new spectral features associated with the multiple conformers of AcProNH2 that are difficult to discern using R sequence and linear-IR spectroscopy. The high resolving power of the RPE sequence comes from destructive interference between the positive and negative peaks of nearby vibrators, similar to the NR sequence. The RPE response functions that are useful for 2D spectral simulations are evaluated, including the effects of vibrational frequency correlations. The 2D spectra obtained with (45, -45, 90, 0) polarization exhibit clear cross-peak patterns in the off-diagonal region for the R and RPE sequences but in the diagonal region for the NR sequence. These patterns, free from strong diagonal contributions, are crucial for structure determination. DFT calculations, normal-mode analysis, Hessian matrix reconstruction, and vibrational exciton Hamiltonian diagonalization yield molecular parameters needed for quantitative simulations of 2D spectra: angles between transition dipoles, coupling constants, and off-diagonal anharmonicities of the amide-I and -II modes are obtained for solvated trans-C7 and cis structures and for gas-phase trans conformers in the region of phi = -120 degrees to 0 degrees and psi = -100 degrees to 180 degrees in the Ramachandran space. Systematic simulations based on a 4:1 population ratio of the solvated trans-C7 and cis structures reproduce well the 2D spectral features obtained at both polarization conditions. However, better agreement between the experimental and simulated cross-peak patterns can be reached if the dihedral angles of the major trans conformer are close to (phi, psi) = (-80 degrees , 100 degrees ). Our results suggest that the major conformer of AcProNH2 in CDCl3 deviates from the gas-phase global minimum, the trans-C7 form, to an extended intermediate between the C7 and polyproline-II structure. These results are discussed in relationship with earlier findings obtained by NMR, transient IR studies, and MD simulations.     

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.     

Simulation studies of amide I IR absorption and two-dimensional IR spectra of beta hairpins in liquid water

Amide I IR absorption and two-dimensional (2D) IR photon echo spectra of a model beta hairpin in aqueous solution are theoretically studied and simulated by combining semiempirical quantum chemistry calculations and molecular dynamics simulation methods. The instantaneous normal-mode analysis of the beta hairpin in solution is performed to obtain the density of states and the inverse participation ratios of the one-exciton states. The motional and exchange narrowing processes are taken into account by employing the time-correlation function theory for the linear and nonlinear response functions. Numerically simulated IR absorption and 2D spectra are then found to be determined largely by the amide I normal modes delocalized on the peptides in the two strands. The site-specific isotope-labeling effects on the IR and 2D IR spectra are discussed. The simulation results for the ideal (A17) beta hairpin are directly compared with those of the realistic 16-residue (GB1) beta hairpin from an immunoglobulin G-binding protein. It was found that the characteristic features in IR and 2D spectra of both the ideal (A17) beta hairpin and the GB1 beta hairpin are the same. The simulated IR spectrum of the GB1 beta hairpin is found to be in good agreement with experiment, which demonstrates that the present computational method is quantitatively reliable.     

Onset of 3(10)-helical secondary structure in aib oligopeptides probed by coherent 2D IR spectroscopy

We have investigated the onset of the secondary structure and the evolution of two-dimensional infrared (2D IR) spectral patterns as a function of chain length with a study of 3(10)-helical peptides. The results show that 2D IR is highly sensitive to peptide conformation, disorder, and size. An extensive set of 2D IR spectra of C (alpha)-methylated homopeptides, Z-(Aib) n -O tBu ( n = 3, 5, 8, and 10), in CDCl 3 was measured in the amide-I region. The 2D spectral patterns of the tripeptide are quite different from those of the longer peptides. The spectral signatures begin to converge at the pentapeptide and become almost the same for the octa- and decapeptide. Simulations employing a vibrational exciton model were performed, with the local mode frequency shifts estimated from the intramolecular hydrogen bond electrostatic energies. The 2D spectra are well simulated using dihedral angle distributions around the average values (phi, psi) approximately (-57 degrees , -31 degrees) with a width of approximately 21 degrees. The simulated site-dependent amide-I local mode frequencies are in agreement with those from scaled semiempirical AM1 calculations. The tripeptide exhibits a more noticeable discrepancy between the experimental and simulated cross-peak patterns. This behavior suggests the presence of a peptide population outside the single beta-turn conformation. The onset of the 3(10)-helical secondary structure appears to already occur at the pentapeptide level.     

Amide I two-dimensional infrared spectroscopy of beta-hairpin peptides

In this report, spectral simulations and isotope labeling are used to describe the two-dimensional IR spectroscopy of beta-hairpin peptides in the amide I spectral region. 2D IR spectra of Gramicidin S, PG12, Trpzip2 (TZ2), and TZ2-T3(*)T10(*), a dual (13)C(') isotope label, are qualitatively described by a model based on the widely used local mode amide I Hamiltonian. The authors' model includes methods for calculating site energies for individual amide oscillators on the basis of hydrogen bonding, nearest neighbor and long-range coupling between sites, and disorder in the site energy. The dependence of the spectral features on the peptide backbone structure is described using disorder-averaged eigenstates, which are visualized by mapping back onto the local amide I sites. beta-hairpin IR spectra are dominated by delocalized vibrations that vary by the phase of adjacent oscillators parallel and perpendicular to the strands. The dominant nu(perpendicular) band is sensitive to the length of the hairpin and the amount of twisting in the backbone structure, while the nu(parallel) band is composed of several low symmetry modes that delocalize along the strands. The spectra of TZ2-T3(*)T10(*) are used to compare coupling models, from which we conclude that transition charge coupling is superior to transition dipole coupling for amide groups directly hydrogen bound across the beta strands. The 2D IR spectra of TZ2-T3(*)T10(*) are used to resolve the redshifted amide I band and extract the site energy of the labeled groups. This allows the authors to compare several methods for calculating the site energies used in excitonic treatments of the amide I band. Gramicidin S is studied in dimethyl sulfoxide to test the role of solvent on the spectral simulations.     

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.     

Two-dimensional infrared investigation of N-acetyl tryptophan methyl amide in solution

The linear infrared and two-dimensional infrared (2D IR) spectra in the amide-I region of N-acetyl tryptophan methyl amide (NATMA) in solvents of varying polarity are reported. The two amide-I transitions have been assigned unambiguously by using 13C isotopic substitution of the carbonyl group. The amide unit at the amino end shows a lower transition frequency in CH2Cl2 and methanol, while the acetyl end has a lower transition frequency in D2O. Multiple conformers exist in CH2Cl2 and methanol, but only one conformer is evident in D2O. The 2D IR cross peaks from the intermode coupling yield off-diagonal anharmonicities 2.5 +/- 0.5, 3.25 +/- 0.5, and 3.0 +/- 0.5 cm(-1) in CH2Cl2, methanol, and D2O, respectively, which by simple matrix diagonalization yield the coupling constants 8.0 +/- 0.5, 8.0 +/- 1.0, and 5.5 +/- 1.0 cm(-1). The major conformer in CH2Cl2 corresponds to a C7 structure, in agreement with that found in the gas phase [Dian, B. C.; Longarte, A.; Mercier, S.; Evans, D. A.; Wales, D. J.; Zwier, T. S. J. Chem. Phys. 2002, 117, 10688-10702] with intramolecular hydrogen bonding between the acetyl end C=O and the amino end N-H. The backbone dihedral angles (phi, psi) are determined to be in the ranges of (-55 +/- 5 degrees , 30 +/- 5 degrees ), (120 +/- 10 degrees , -20 +/- 10 degrees ), and (+/-160 +/- 10 degrees , +/-75 +/- 10 degrees ) in CH2Cl2, methanol, and D2O, respectively.     

Two-dimensional infrared spectroscopy of antiparallel beta-sheet secondary structure

We investigate the sensitivity of femtosecond Fourier transform two-dimensional infrared spectroscopy to protein secondary structure with a study of antiparallel beta-sheets. The results show that 2D IR spectroscopy is more sensitive to structural differences between proteins than traditional infrared spectroscopy, providing an observable that allows comparison to quantitative models of protein vibrational spectroscopy. 2D IR correlation spectra of the amide I region of poly-l-lysine, concanavalin A, ribonuclease A, and lysozyme show cross-peaks between the IR-active transitions that are characteristic of amide I couplings for polypeptides in antiparallel hydrogen-bonding registry. For poly-l-lysine, the 2D IR spectrum contains the eight-peak structure expected for two dominant vibrations of an extended, ordered antiparallel beta-sheet. In the proteins with antiparallel beta-sheets, interference effects between the diagonal and cross-peaks arising from the sheets, combined with diagonally elongated resonances from additional amide transitions, lead to a characteristic "Z"-shaped pattern for the amide I region in the 2D IR spectrum. We discuss in detail how the number of strands in the sheet, the local configurational disorder in the sheet, the delocalization of the vibrational excitation, and the angle between transition dipole moments affect the position, splitting, amplitude, and line shape of the cross-peaks and diagonal peaks.     

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.     

Calculations of intermode coupling constants and simulations of amide I,II, and III vibrational spectra of dipeptides

Amide I, II, and III vibrations of polypeptides are important marker modes whose vibrational spectra can provide critical information on structure and dynamics of proteins in solution. The extent of delocalization and vibrational properties of amide normal mode can be described by the amide local mode frequencies and intermode coupling constants between a pair of amide local modes. To determine these fundamental quantities, the previous Hessian matrix reconstruction method has been generalized here and applied to the density functional theory results for various dipeptide conformers. The calculation results are then used to simulate IR absorption, vibrational circular dichroism, and 2D IR spectra of dipeptides. The relationships between dipeptide backbone conformations and these vibrational spectra are discussed. It is believed that the present computational method and results will be of use to quantitatively simulate vibrational spectra of complicated polypeptides beyond simple dipeptides     

Infrared and vibrational CD spectra of partially solvated alpha-helices: DFT-based simulations with explicit solvent

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

Utilizing Lifetimes to Suppress Random Coil Features in 2D IR Spectra of Peptides

We report that the waiting time delay in 2D IR pulse sequences can be used to suppress signals from structurally disordered regions of amyloid fibrils. At a waiting time delay of 1.0 ps, the random coil vibrational modes of amylin fibrils are no longer detectable, leaving only the sharp excitonic vibrational features of the fibril β-sheets. Isotope labeling with (13)C(18)O reveals that structurally disordered residues decay faster than residues protected from solvent. Since structural disorder is usually accompanied by hydration, we conclude that the shorter lifetimes of random-coil residues is due to solvent exposure. These results indicate that 2D IR pulse sequences can utilize the waiting time to better resolve solvent-protected regions of peptides and that local mode lifetimes should be included in simulations of 2D IR spectra.     

Dynamics of amide-I modes of the alanine dipeptide in D2O

The equilibrium dynamics of the acetyl and amino amide-I groups of the alanine dipeptide were examined separately using (13)C isotopic selection and 2D IR. The population relaxation times of the amide transitions were measured to be in the range 500 fs by means of heterodyne transient grating methods. The vibrational frequency correlation functions consisted in all cases of a motionally narrowed part, a component near 800 fs, and a constant part representing a distribution of structures that is static on the few ps time scale. The intermediate time scale is attributed to fluctuations in the stretching and bending of hydrogen bonds between the carbonyl and water.     

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.     

Ab initio-based all-mode two-dimensional infrared spectroscopy of a sugar molecule

To construct two-dimensional infrared (2D IR) spectra having all vibrational modes of a molecule included is still quite challenging, both experimentally and theoretically. Here we report an ab initio-based all-mode 2D IR spectra simulation approach. Using deuterated glycolaldehyde (CH2OHCDO), the smallest sugar as a model molecule, we have calculated correlation 2D IR spectrum of its entire 3N-6 (N=8) normal modes in the mid-to-far-IR region (4000-0 cm(-1)), using quantum chemical anharmonic frequency and anharmonicity computations in conjunction with time-domain third-order nonlinear response functions. The calculated 2D IR spectra were found to contain a network of structural and dynamical parameters of the molecule. It is found that certain spectral regions, once enlarged, show features that are in reasonable agreement with limited but already available single- and dual-frequency 2D IR experimental results. The extension of narrow-band 2D IR spectroscopy into the full mid-to-far-IR regime would allow us to characterize the structural distributions and dynamics of molecular complexes in condensed phases with sufficient number of parameters.     

Gas‐Phase Peptide Structures Unraveled by Far‐IR Spectroscopy: Combining IR‐UV Ion‐Dip Experiments with Born–Oppenheimer Molecular Dynamics Simulations

Vibrational spectroscopy provides an important probe of the three‐dimensional structures of peptides. With increasing size, these IR spectra become very complex and to extract structural information, comparison with theoretical spectra is essential. Harmonic DFT calculations have become a common workhorse for predicting vibrational frequencies of small neutral and ionized gaseous peptides. ¹ Although the far‐IR region (<500 cm^?1) may contain a wealth of structural information, as recognized in condensed phase studies, ² DFT often performs poorly in predicting the far‐IR spectra of peptides. Here, Born–Oppenheimer molecular dynamics (BOMD) is applied to predict the far‐IR signatures of two γ‐turn peptides. Combining experiments and simulations, far‐IR spectra can provide structural information on gas‐phase peptides superior to that extracted from mid‐IR and amide A features.     

Temperature-Dependence of the Amide-I Frequency Map for Peptides and Proteins

In our recent work [Phys. Chem. Chem. Phys. 11, 9149 (2009)], a molecular-mechanics force field-based amide-I vibration frequency map (MM-map) for peptides and proteins was constructed. In this work, the temperature dependence of the MM-map is examined based on high-temperature molecular dynamics simulations and infrared (IR) experiments. It is shown that the 298-K map works for up to 500-K molecular dynamics trajectories, which reasonably reproduces the 88 oC experimental IR results. Linear IR spectra are also simulated for two tripeptides containing natural and unnatural amino acid residues, and the results are inreasonable agreement with experiment. The results suggest the MM-map can be used to obtain the temperature-dependent amide-I local mode frequencies and their distributions for peptide oligomers, which is useful in particular for understanding the IR signatures of the thermally unfolded species.