Theoretical study of internal field effects on peptide amide I modes

Charged terminal groups or polar side chains of amino acids create spatially nonuniform electrostatic potential around intramolecular peptide bonds and induce amide I mode frequency shifts in polypeptides. By carrying out a series of quantum chemistry calculation studies of various ionic di- and tripeptides as well as dipeptides of 20 different amino acids, these internal field effects on vibrational properties are theoretically investigated. The amide I local and normal mode frequencies and dipole and rotational strengths determining IR and vibrational circular dichroism intensities, respectively, are found to depend on the polar nature of side chains, whereas the vibrational coupling strength weakly does so. The empirical correction and fragment analysis methods were used to theoretically calculate the amide I local mode frequencies and dipole and rotational strengths. These values were directly compared with ab initio and density functional theory calculation results, and the agreements were found to be quantitative.     

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.     

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.     

丙氨酸二肽分子二级结构与振动光谱特性

利用从头算方法探索蛋白质模型分子——丙氨酸二肽的二级结构布居特性以及体系势能变化. 引入对分子结构敏感的振动探针(酰胺振动吸收带), 借助其光谱表象, 寻求振动光谱参数与分子结构之间的联系. 研究结果表明: 丙氨酸二肽分子处于C_7eq构型(Φ/Ψ=-80°/80°)时具有最低能量值, 且分子易形成β折叠、PP_II、C₅及C₇等能量较低的稳定构型. 通过简正模式分析, 得到分子3N-6 个振动模式的吸收光谱, 并通过势能分布分析方法对分子骨架上酰胺振动吸收带的特征振动模式进行了指认. 重点考察分子骨架上酰胺-I带振动光谱参数与分子构型变化之间的相关性, 建立振动光谱参数与蛋白质二级结构之间的联系, 为在化学键水平上研究蛋白质的结构及其发挥作用的机制提供科学依据.     

Dipeptide structure determination by vibrational circular dichroism combined with quantum chemistry calculations.

The solution structure and the local solvation environments of alanine dipeptide (AD, 1 a) and its isotopomer (AD*, 1 b, 13C on the acetyl end C==O) are studied by using infrared (IR) spectroscopy and vibrational circular dichroism (VCD). From the amide I IR spectra of AD* in various protic solvents, it is found that each of the two carbonyl groups is fully H-bonded to two water molecules. However, the number of alcohol molecules H-bonded to each C==O varies from one to two, and the local solvation environments are asymmetric around the two peptides of AD* in alcohol solutions. The amide I VCD spectra of AD and AD* in D2O are also measured, and a series of density functional theory (DFT, B3LYP/6-311++G**) calculations are performed to obtain the amide I normal-mode rotational strengths of AD and the intrinsic rotational strengths of its two peptide fragments. By combining the VCD-measurement and DFT-calculation results and employing a coupled oscillator theory, we show that the aqueous-solution structure of the dipeptide can be determined. We believe that the present method will be of use in building up a library of dipeptide solution structures in water.     

Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.     

Two-dimensional circularly polarized IR photon echo spectroscopy of polypeptides: four-wave-mixing optical activity measurement

A coherent two-dimensional (2D) optical spectroscopy utilizing circularly polarized (CP) beams, which was shown to be useful in studying molecular chirality in condensed phases, was theoretically proposed recently [Cho et al. J. Chem. Phys. 2003, 119, 7003]. A photon echo (PE) version of 2D optical activity spectroscopy is discussed in this paper. Considering various dipeptide and polypeptide systems, where the amide I local modes constitute the set of basis modes used to describe exciton and biexciton states as linear combinations of those basis modes, we present numerically simulated 2D circularly polarized IR PE spectra. It is shown that this novel spectroscopic method can provide additional information on the angles between the transition magnetic dipole and the transition electric dipole of two different vibrationally excited states, which are highly sensitive to the 3D structure and chirality of a given polypeptide. Also, a hierarchical relation of IR absorption, vibrational circular dichroism, 2D IR PE, and 2D CP-IR PE is discussed to show advantages of 2D optical activity spectroscopy in general.     

Amide I vibrational circular dichroism of dipeptide: Conformation dependence and fragment analysis

The amide I vibrational circular dichroic response of alanine dipeptide analog (ADA) was theoretically investigated and the density functional theory calculation and fragment analysis results are presented. A variety of vibrational spectroscopic properties, local and normal mode frequencies, coupling constant, dipole, and rotational strengths, are calculated by varying two dihedral angles determining the three-dimensional ADA conformation. Considering two monopeptide fragments separately, we show that the amide I vibrational circular dichroism of the ADA can be quantitatively predicted. For several representative conformations of the model ADA, vibrational circular dichroism spectra are calculated by using both the density functional theory calculation and fragment analysis methods.     

Determination of conformational preferences of dipeptides using vibrational spectroscopy

The NMR coupling constants ((3)J(H(N), H(alpha))) of dipeptides indicate that the backbone conformational preferences vary strikingly among dipeptides. These preferences are similar to those of residues in small peptides, denatured proteins, and the coil regions of native proteins. Detailed characterization of the conformational preferences of dipeptides is therefore of fundamental importance for understanding protein structure and folding. Here, we studied the conformational preferences of 13 dipeptides using infrared and Raman spectroscopy. The main advantage of vibrational spectroscopy over NMR spectroscopy is in its much shorter time scale, which enables the determination of the conformational preferences of short-lived states. Accuracy of structure determination using vibrational spectroscopy depends critically on identification of the vibrational parameters that are sensitive to changes in conformation. We show that the frequencies of the amide I band and the A12 ratio of the amide I components of dipeptides correlate with the (3)J(H(N), H(alpha)). These two infrared vibrational parameters are thus analogous to (3)J(H(N), H(alpha)), indicators for the preference for the dihedral angle phi. We also show that the intensities of the components of the amide III bands in infrared spectra and the intensities of the skeletal vibrations in Raman spectra are indicators of populations of the P(II), beta, and alpha(R) conformations. The results show that alanine dipeptide adopts predominantly a PII conformation. The population of the beta conformation increases in valine dipeptides. The populations of the alpha(R) conformation are generally small. These data are in accord with the electrostatic screening model of conformational preferences.     

Vibrational dynamics of DNA. II. Deuterium exchange effects and simulated IR absorption spectra

In Paper I, we studied vibrational properties of normal bases, base derivatives, Watson-Crick base pairs, and multiple layer base pair stacks in the frequency range of 1400-1800 cm(-1). However, typical IR absorption spectra of single- and double-stranded DNA have been measured in D(2)O solution. Consequently, the more relevant bases and base pairs are those with deuterium atoms in replacement with labile amino hydrogen atoms. Thus, we have carried out density functional theory vibrational analyses of properly deuterated bases, base pairs, and stacked base pair systems. In the frequency range of interest, both aromatic ring deformation modes and carbonyl stretching modes appear to be strongly IR active. Basis mode frequencies and vibrational coupling constants are newly determined and used to numerically simulate IR absorption spectra. It turns out that the hydration effects on vibrational spectra are important. The numerically simulated vibrational spectra are directly compared with experiments. Also, the (18)O-isotope exchange effect on the poly(dG):poly(dC) spectrum is quantitatively described. The present calculation results will be used to further simulate two-dimensional IR photon echo spectra of DNA oligomers in the companion Paper III.     

A short synthesis of bicyclic dipeptides corresponding to Xxx-L-Pro Xxx-D-Pro having constrained trans-proline amides

[formula: see text] A short synthesis that generates two isomeric bicyclic dipeptides having constrained, trans-proline amide bonds has been developed. One of these bicyclic dipeptides corresponds to an Xxx-L-Pro dipeptide (4), while the other isomer corresponds to an Xxx-D-Pro dipeptide (5). The two isomers are readily distinguished by their 1H NMR spectra.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

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.     

Side chain dependence of intensity and wavenumber position of amide I' in IR and visible Raman spectra of XA and AX dipeptides

A series of AX and XA dipeptides in D2O have been investigated by FTIR, isotropic, and anisotropic Raman spectroscopy at acidic, neutral, and alkaline pD, to probe the influence of amino acid side chains on the amide I' band. We obtained a set of spectral parameters for each peptide, including intensities, wavenumbers, half-widths, and dipole moments, and found that these amide I' parameters are indeed dependent on the side chain. Side chains with similar characteristic properties were found to have similar effects on the amide I'. For example, dipeptides with aliphatic side chains were found to exhibit a downshift of the amide I' wavenumber, while those containing polar side chains experienced an increase in wavenumber. The N-terminal charge causes a substantial upshift of amide I', whereas the C-terminal charge causes a moderate decrease of the transition dipole moment. Density functional theory (DFT) calculations on the investigated dipeptides in vacuo yielded different correlations between theoretically and experimentally obtained wavenumbers for aliphatic/aromatic and polar/charged side chains, respectively. This might be indicative of a role of the hydration shell in transferring side chain-backbone interactions. For Raman bands, we found a correlation between amide I' depolarization ratio and wavenumber which reflects that some side chains (valine, histidine) have a significant influence on the Raman tensor. Altogether, the obtained data are of utmost importance for utilizing amide I as a tool for secondary structure analysis of polypeptides and proteins and providing an experimental basis for theoretical modeling of this important backbone mode. This is demonstrated by a rather accurate modeling for the amide I' band profiles of the IR, isotropic Raman, and anisotropic Raman spectra of the beta-amyloid fragment Abeta(1-82).     

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.     

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.     

Vibrational dynamics of DNA. I. Vibrational basis modes and couplings

Carrying out density functional theory calculations of four DNA bases, base derivatives, Watson-Crick (WC) base pairs, and multiple-layer base pair stacks, we studied vibrational dynamics of delocalized modes with frequency ranging from 1400 to 1800 cm(-1). These modes have been found to be highly sensitive to structure fluctuation and base pair conformation of DNA. By identifying eight fundamental basis modes, it is shown that the normal modes of base pairs and multilayer base pair stacks can be described by linear combinations of these vibrational basis modes. By using the Hessian matrix reconstruction method, vibrational coupling constants between the basis modes are determined for WC base pairs and multilayer systems and are found to be most strongly affected by the hydrogen bonding interaction between bases. It is also found that the propeller twist and buckle motions do not strongly affect vibrational couplings and basis mode frequencies. Numerically simulated IR spectra of guanine-cytosine and adenine-thymine bases pairs as well as of multilayer base pair stacks are presented and described in terms of coupled basis modes. It turns out that, due to the small interlayer base-base vibrational interactions, the IR absorption spectrum of multilayer base pair system does not strongly depend on the number of base pairs.     

Theoretical calculations of infrared absorption, vibrational circular dichroism, and two-dimensional vibrational spectra of acetylproline in liquids water and chloroform

Infrared absorption, vibrational circular dichroism, and two-dimensional infrared pump-probe and photon echo spectra of acetylproline solutions are theoretically calculated and directly compared with experiments. In order to quantitatively determine interpeptide interaction-induced amide I mode frequency shifts, high-level quantum chemistry calculations were performed. The solvatochromic amide I mode frequency shift and fluctuation were taken into account by carrying out molecular dynamics simulations of acetylproline dissolved in liquids water and chloroform and by using the extrapolation method developed recently. We first studied correlation time scales of the two amide I vibrational frequency fluctuations, cross correlation between the two fluctuating local mode frequencies, ensemble averaged conformations of the acetylproline molecule in liquids water and chloroform. The corresponding conformations of the acetylproline in liquids water and chloroform are close to the ideal 3(10) helix and the C(7) structure, respectively. A few methods proposed to determine the angle between the two transition dipoles associated with the amide I vibrations were tested and their limitations are discussed.