Anharmonic local-mode frequency (ν, in cm-1), anharmonicity (Δ, in cm-1), coupling (β, in cm-1), and wave function mixing angle (ξ, in degree) for two nearest neighboring amide units in various dihedral angles (ϕ and ψ, in degree). The diagonal anharmonicity is obtained from the
1. Introduction
Understanding the structure of proteins is a key to understanding their functions. Infrared (IR) spectroscopy is a very sensitive tool for studying three-dimensional molecular structures of proteins [1,2] in conditions relevant to biology, for example, in solution phase. This is because the vibrational frequency is determined by the chemical structure of the chromophore. However, both intra- and intermolecular force fields are involved. For the intramolecular aspect, the frequency of a specific vibration is influenced by the collective interaction of this mode with the rest 3N-7 (or 3N-6 for linear molecule) modes, where N is the total number of atoms in the molecular system. As for the intermolecular aspect, the frequency of a specific vibration is also influenced by its neighboring solvent molecules. Further, the IR spectroscopy is essentially a label-free method. There are a variety of intrinsic vibrational modes that can be used to characterize protein structures, thus the use of external chromophore, as is obligatory in some other spectroscopic methods, is not absolutely necessary for the IR method.
Commercial Fourier-transform infrared (FTIR) spectrometer allows the measurement of the IR absorption spectra for a large number of vibrational transitions in proteins in the mid-IR frequency range (4000 – 650 cm-1). Certain key vibrational modes are well studied, and empirical relationship between their frequency and protein structure has been established. A well-known example of such is the amide-I mode, which is mainly the C=O stretching vibration. It is usually used as a protein/peptide backbone conformational reporter, because the amide unit is the linkage between amino acid residues and appears periodically on the peptide chain. The well-known linear IR signature of the α-helix, although appears to be a single absorption peak at 1640-1658 cm-1, has a two-component (a low-frequency A-mode and a high-frequency E-mode) band structure [3]. For the anti-parallel β-sheet, there is a major sharp absorption band appearing at 1620-1640 cm-1 and a weak peak at 1680-1696 cm-1 [4-8], while the parallel β-sheet only exhibits a major sharp absorption band at 1620-1640 cm-1 [6,8,9]. Whereas the IR signature of other conformations, such as the β-turn and random coil, usually appears to be a single band at 1640-1658 cm-1 for random coil, or at higher frequency for the β-turn.
Assuming a harmonic potential, quantum chemical calculations can yield a complete set of vibrational frequencies of mid-sized polypeptide molecules. Good performance of the Kohn-Sham formulation of density functional theory (DFT) for predicting molecular geometries and harmonic vibrational frequencies has been established. For example, the fundamental vibrational frequencies for nine amide modes (amide-I to -VII, and amide-A and -B) in simple peptides using the hybrid density functional B3LYP are found to be in reasonable agreement with measurements in the gas phase. In certain cases the results are even better than those from strictly
In reality, molecular vibrations are intrinsically anharmonic. Because of this, experimentally measured IR spectra are often complicated: it contains not only absorption peaks coming from fundamental transitions, but also those from overtone and combination transitions. For a given vibrational chromophore, the frequency difference between its fundamental transition and its overtone transition is known as the (diagonal) anharmonicity. For a pair of vibrational chromophores, the frequency difference between the sum of their fundamental transitions and that of the combinational transition is known as the off-diagonal anharmonicity. The measurement and assignment of overtone and combination bands in conventional linear IR spectroscopy have been known to be trouble some. This is because for the low-frequency modes, their overtone and combination bands fall into the high-frequency region that could be already very crowded; and for the high-frequency modes, their overtone and combination bands will fall into the high-frequency region of the mid-IR or even into the near-IR regime.
Using the two-dimensional infrared (2D IR) spectroscopy developed in recent years, measurement of anharmonic frequencies in the mid-IR region has been made easier. In this method, a typical two-frequency 2D IR spectrum containing a set of anharmonic vibrators can be obtained, and from which the anharmonic frequencies, diagonal- and off-diagonal anharmonicities can be measured.
With the aid of modern laser technology, 2D IR spectroscopic studies in the 3-μm wavelength region (frequency = 3300 cm-1) [12], 4-μm (2500 cm-1) [13], 5-μm (2000 cm-1) [14-17], 6-μm (1666 cm-1) [18-20] and 8-μm (1250 cm-1) [21] have been reported. This method is expected to be more powerful with the use of broadband laser sources in the future. Further, the 2D IR spectroscopic method also allows additional anharmonic vibrational parameters to be acquired, for example, diagonal and off-diagonal anharmonicities, and anharmonic couplings. Recent studies have shown that these parameters are also sensitive to molecular structures. In addition, the distributions of these vibrational parameters can also be experimentally determined by 2D IR.
It is of great importance to computationally predict the anharmonic vibrational properties of biomolecules, so that they can be used to interpret experimental IR results. The second-order perturbative vibrational treatment (PT2) [22,23] allows such computations. In this method, a full cubic and a semidiagonal quartic force field is obtained by central numerical differentiation of analytical second derivatives [24]. Un-scaled anharmonic vibrational frequencies of medium size molecules can be obtained quite efficiently. A previous study [25] has shown that the performance of B3LYP functional with reasonable basis sets in computing anharmonic vibrational frequencies of semirigid molecules is quite satisfactory. In addition, high-performance computer clusters can be utilized to compute the cubic and quartic derivatives for a given molecular system so that the anharmonic vibrational frequencies can be obtained efficiently using the DFT/PT2 combination. Very recently, the chain-length dependent anharmonicity and mode-delocalization of the amide-I mode [26], and that of the amide-A mode [27], in typical peptide conformations, have been reported.
In this chapter, we present a review of our recent works in studying the anharmonic vibrations of peptide oligomers. Methods to predict the anharmonic parameters are reviewed followed by results and discussions, mainly on the amide-I modes of peptides. The conformational dependence of the obtained anharmonic parameters is discussed. Results are useful in gaining more insights into the structural basis of the anharmonic vibrations of proteins and peptides.
2. Methods
2.1. Anharmonic vibrational frequency and anharmonicity
In the normal mode picture, the vibrational energy of fundamentals, overtones and combination bands for an
where
The first two terms of equation (2) incorporates exclusively energy derivatives with respect to the
The first bracket contains the interaction between mode
2.2. Anharmonic vibrational coupling and local modes
The through bond and through space interactions amongst vibrational chromophore units cause the anharmonic vibrational excitations to exchange from site to site. This is the physical origin of vibrational coupling. There are several ways to assess the vibrational coupling. The first approach is through
where
The second approach is to use transition multipole interaction. Bilinear term in the expansion of the normal mode displacement of vibrational oscillator is the lowest order of the through space interaction potential [3]. The couplings can be evaluated conveniently either by using an electrostatic transition dipole coupling (TDC) scheme [31,32], or using the transition charge and charge flux interaction [3,33], or using the distributed transition-charge density derivative interaction proposed previously [34]. In these methods, the couplings of different vibrational modes were assumed to depend solely on the molecular structure. For the amide-I mode in peptides, if the two amide units are covalently bonded, the transition charge-based approaches have advantages over the transition dipole approach. However, as the inter unit distance increases, all the approaches tend to give the same answer.
The TDC is computed by using the following formula:
where
The transition charge interaction approach has also been formulated for the amide-I mode in peptides [35]. In this method, atomic partial charge and transition charge are needed, which can be evaluated using the Mulliken charges and charge-fluxes via
In equation (6),
In the TDC approach, the angle between the transition dipole and amide C=O bond is usually set to between 15° and 23° to fit experimental IR spectra. In the TCI approach, the calculated orientation of the transition dipole is found to be ~ 20o with respect to the C=O bond axis and towards the nitrogen atom. This angle falls into the experimentally determined range (15 o to 25o) for the model compound NMA [46]. However, various values of this angle have been obtained theoretically (between -19o and 20o) when using different force fields even for the same model compound [32,47-49].
When the through bond interaction is important, the
2.3. Potential energy distribution
To evaluate how much a normal mode is delocalized onto its neighboring unit of the same kind, the potential energy distribution (PED) analysis can be carried out on the basis of the internal coordinates. This method has been recognized for some time [32]. The obtained PED value can be used to describe the relative contributions of various displacement coordinates to the total change in potential energy during a specific vibrational motion. When a normal mode Q
where
Here
2.4. Simulation of 1D IR spectra
In the following, we introduce two simple frequency-domain methods for simulating 1D IR spectra of peptides. First, for the entire 3
The excitonic modeling, on the other hand, is particularly useful for simulating the linear IR spectra of a set of identical vibrational modes in the frequency domain. It has been used effectively to the amide-I mode of peptides. The excitonic band structure is illustrated in Figure 1, in which site states and excitonic states are shown. A set of coupled anharmonic oscillators, i.e., the site states
In equation (9),
The strength of the transition dipole of each eigenmode gives the total linear IR spectrum, as shown previously [3]:
where
3. Results and discussion
3.1. Conformation dependent amide-I normal mode vibration in peptide oligomers
First we examine the anharmonic parameters of the amide-I mode of a model dipeptide. The molecular structure of the glycine dipeptide (Ac-Gly-NMe, or CH3CONHCαH2CONHCH3) is shown in Figure 2, in which backbone dihedral angles are defined to be ϕ (CNCαC) and ψ (NCαCN). Here ten well-known secondary conformations are chosen, namely αL2-helix (ϕ = +90°, ψ = -90°); π-helix (-57°, -70°); polyproline-II (PPII, -75°, +135°); αL1-helix (+60°, +60°); C7 conformation (+82°, -69°); extended structure (180°, -180°); α-helix (-58°, -47°); 310-helix (-50°, -25°); anti-parallel β-sheet (-139°, +135°); and parallel β-sheet (-119°, +113°). Harmonic and anharmonic frequencies of the two amide-I modes in these dipeptides are evaluated using the density functional theory and Hartree-Fock (HF) methods. The results from the two methods are found to be highly correlated, as shown in Figure 3. Two amide-I normal modes in these dipeptides are linear combinations of the two amide-I local modes, which are dominated by the C=O stretching vibration. In the left column of Figure 3, two amide-I normal mode frequencies (harmonic picture) are shown: one is the symmetric stretching and has a relatively higher frequency (panel A) and the other is the asymmetric stretching whose frequency is lower (panel C). In order to better compare the HF frequencies (squares) and DFT frequencies (circles), the HF results are subtracted by 150 cm-1. The results show that the calculated normal-mode harmonic frequencies at the level of Hartree-Fock theory have the same trend as those obtained at the level of the density functional theory. One can also draw the same conclusion from the anharmonic frequencies that are given in the right column of Figure 3 (panel B and D). In addition, the frequency difference between the high- and low-frequency modes in the harmonic picture (panel E) and in the anharmonic picture (panel F) are also meaningful to compare, because the frequency separation is closely related to the inter-mode coupling. Clearly the frequency separations obtained by the HF and DFT methods are also in good agreement, for both the harmonic and anharmonic cases. Further more, for the ten conformations the averaged DFT anharmonic frequency of the high-frequency mode is found to be 31.7 cm-1 lower than that of the harmonic frequency, indicating the effect of considering the anharmonic potential. Similarly, the lowered value is 28.7 cm-1 for the low-frequency mode. On the other hand, for the HF results, the anharmonic frequency drops 29.0 cm-1 for the high-frequency mode, and 26.0 cm-1 for the low-frequency mode. This indicates a similar anharmonic energy decrease using the two different methods. However, it is also noted that for some typical structures the frequency splitting show method-dependence, which will result in method-dependent inter-mode coupling, as discussed below. The performance of the DFT (B3LYP) and HF methods in computing the anharmonicities of the amide-I modes of peptide oligomers has been examined previously [29] and it was shown that the two methods were able to provide an optimum compromise between reliability and computer time.
Next, the full conformation space (-180° ≤ ϕ ≤ +180°, -180° ≤ ψ ≤ +180°) for peptide backbone is explored with total 169 samplings of partially optimized structures (∆ϕ = ∆ψ = 30°). The partial optimization is performed at the HF level of theory by fixing ϕ and ψ to desired values each time, to sample the entire conformational space. The result is given in Figure 4. The two amide-I normal-mode frequencies (panel A and B) show significant conformation sensitivity, with different dependences on the two dihedral angles. In panel A, the harmonic high-frequency component exhibits a low-frequency region that is anti-diagonally arranged (from lower right to upper left). In panel B, the harmonic low-frequency component, however, exhibits a similarly arranged low-frequency region, but in much smaller area. The conformational dependences of the anharmonic normal-mode frequencies, which are given in panel C and D respectively, resemble those of their harmonic counterparts (panel A and B respectively). However, a detailed analysis shows subtle difference in mean value and distribution of the harmonic and anharmonic frequencies: on average the anharmonic frequency drops
3.2. Conformation dependent amide-I local mode vibration in peptide oligomers
Local-mode frequencies can be obtained by decoupling the two amide-I normal modes in either the harmonic or anharmonic picture. The results are shown in Figure 5. In the harmonic picture, the obtained zero-order amide-I vibration frequency (denoted as
In the anharmonic picture, the conformational dependence of the local-mode frequencies differs slightly from that in the harmonic picture. The results are shown in Figure 5, C and D panels. In panel C, the conformational dependence of the zero-order vibrational frequency (
Thus the computation results shown in Figure 5 indicate a generally non-degenerate zero-order frequency picture under both the harmonic and anharmonic approximations. Such a non-degeneracy is believed to be an intrinsic property of polypeptides. For example, in a 13C labeled β-hairpin two amide-I modes on the same peptide chain are found to have different zero-order frequencies by both 1D and 2D IR studies [59]. The non-degeneracy of the local states is believed to be due to the variation of local chemical and solvent environment of peptide amide group (-CONH-) [60]. Such a non-degenerate local-mode picture should be taken into account during empirical modeling of the 1D and 2D IR spectra of peptides and proteins. In particular, a set of zero-order transition energies can be initialized as the diagonal elements of the one-exciton Hamiltonian. Because these local-mode frequencies are backbone dihedrals (ϕ, ψ) dependent, they bear site-specific local structure characteristics and are also sensitive to solvent environment. On the other hand, the normal modes in peptides do not carry direct local-structure identities because of the mode delocalization. Under such circumstances the IR frequency and peptide structure relationship cannot be established in a straightforward way. It is for these reasons that peak assignment in conventional IR spectroscopy could be troublesome.
Further, because the amide-I local-mode frequency in the conformational space in the anharmonic picture appears to be quite similar to that in the harmonic picture one may scale the frequency from the latter to the former. This suggests a simple way to approximately obtain the anharmonic frequencies. However, care should be taken when the scaling method is utilized, because it is well known that the frequency scaling is not applicable simultaneously to all the 3
3.3. Anharmonicity, coupling and mode delocalization
In this work the diagonal anharmonicity is defined as the decrease of the energy gap between the first excited state and its overtone state (
We first discuss the anharmonicity of a single vibrator case. In an isolated peptide unit, for example,
As shown in equation (4), the wave function mixing angle is determined by the coupling and transition energy gap of two local modes. Large mixing angle means large mode delocalization. The results of the mixing angle and inter-mode coupling for several dipeptides are listed in Table 1. For alanine dipeptide in the α-helical conformation (ϕ, = –58°, ψ = –47°), the mixing angle between two local states is
The term
Further, the degree of mode delocalization can be characterized by using the potential energy distribution that describes the relative contributions of various displacement coordinates to the total change in potential energy during the vibration. Here we examine the mode delocalization in gas-phase and in explicit solvent environment. We carry out computations at the harmonic level for alanine dipeptide systems in either α-helical or β-sheet conformation, with four water molecules included in each case. The results are given below (Figure 6 and Table 2). Similar short peptide systems were examined previously to study the hydration effect of peptides [68]. The solution-phase local-mode frequencies are found to red shift from those in the gas-phase because the two amide units are both H-bonded with solvent molecules (Table 2). However, it is clear the frequency separations between the high-frequency mode and low-frequency mode for ADP in gas and in solution phases are quite similar. So it is expected that the decoupled local mode frequency separations are similar too. In other words, solvent effect on frequency separation (and mode localization caused by that) is not significantly affected by the first hydration layer in this case.
|
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|||
(ϕ, ψ) | (–58, –47) | (–75, +135) | (–50, –25) | (–83, +71) | ||
|
1734.2 | 1714.0 | 1734.8 | 1711.4 | 1704.2 | |
|
1729.3 | 1675.0 | 1748.7 | 1660.5 | 1698.6 | |
|
11.5 | 21.3 | 14.9 | 19.9 | 8.7 | |
|
11.7 | 19.3 | 21.9 | 17.3 | 13.3 | |
|
4.9 | –0.1 | 6.0 | –8.2 | –3.1 | |
|
31.8 | 0.1 | 69.5 | 8.9 | 24.2 | |
|
1.0 | 2.5×10-3 | 0.4 | 0.2 | 0.6 |
One sees that the PED values of the two modes decrease similarly (with a few percent variation). This is found to be the case for both conformations. Here the decreased PED indicates more mode delocalization, reaching over water bending modes through hydrogen-bonding interactions. This hydration picture is reasonable for short peptides because one can hardly have one amide unit hydrogen-bonded with solvent and another not, in a solvated short peptide. This suggests that given a homogeneous solvent environment, the amide-I mode-delocalization in short peptide would probably change similarly for each amide unit. Note that for longer peptides containing different side chains and forming intramolecular hydrogen-bonds, it might be true that only some of the amide-I frequencies would be red-shifted due to hydrogen-bonding interaction, but certainly this is a case-dependent story.
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mode |
|
|
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ω |
PED | ω |
PED | ω |
PED | ω |
PED | |
|
1771.1 | 0.57 | 1733.7 | 0.53 | 1749.4 | 0.56 | 1716.3 | 0.36 |
|
1758.0 | 0.58 | 1721.7 | 0.46 | 1733.3 | 0.60 | 1694.0 | 0.41 |
3.4. Simulated 1D IR spectra of peptides
The simulated 1D IR spectra of two typical turn conformations (Table 3) employing the vibrational exciton model in the frequency domain are shown in Figure 7. More details can be found in a recent work [3]. Discernable conformational-dependent spectral features are seen in simulated 1D IR spectra of these peptide structures. The spectral features include absorption peak positions and line width profiles. For the γ–turn, two amide-I local modes are coupled and transition intensities are not equal. For the β–turn, three coupled local transitions form excitonic band structure (normal modes) that differs from that of the γ–turn. In Figure 7, stick spectrum are also given in each panel. Inhomogeneous distribution of the transition energies are clearly shown in each case [69]. Further, because of transition intensity transfer, a direct result of vibrational coupling, the computed 1D IR spectra show patterns that significantly different from the local-mode picture with three independent bands.
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||||||
γ–turn | ω1 | ϕ2 | ψ2 | ω2 | ||||
classic | +172.6 | 74.9 | -75.0 | −170.8 | C7 | |||
β–turn | ω1 | ϕ2 | ψ2 | ω2 | ϕ3 | ψ3 | ω3 | |
type I | +175.3 | −60.0 | −30.0 | −177.1 | −90.0 | +0.0 | −171.2 | C10 |
4. Conclusions
This chapter discusses the methods and application of anharmonic vibration parameters for the purpose of connecting the secondary structure of proteins and peptides to their IR spectra. Using the amide-I mode in particular, the usefulness of the methods is clearly demonstrated. The performance of the DFT and HF theories in predicting the anharmonic frequencies are compared and the conformational dependence of the obtained parameters are examined. The methods to compute vibrational coupling are also reviewed and examples are discussed. The coupled nature of the amide-I band for typical secondary structures is analyzed using the potential energy distribution function, and the local-mode properties (frequency and coupling) are discussed. Since the solvent effect on these parameters is unavoidable, as has shown for PED analysis, solvent molecules must be taken into account in assessing the vibrational properties of solute. Polarizable continuum method [70] for solvent model can be used for such purposes. In addition, site-dependent dynamical interactions between peptide and water molecules in the hydration shells needs to be examined by molecular dynamics simulations employing proper molecular mechanical force fields, so that the statistical distributions and correlations of the transition frequencies can be computed. This can be done by carrying our instantaneous normal mode analysis, for example. Time-dependent vibrational couplings can also be computed based on the molecular dynamics trajectories. Nevertheless, simultaneous assessment of vibrational parameters of multiple vibrational modes shall prove useful in understanding the characteristics of linear and nonlinear infrared spectra of both static and equilibrium dynamical structures of proteins, peptides and other biomolecules [71].
Acknowledgments
I would like to thank my students in the Quantum Multidimensional Infrared Spectroscopy group in the Molecular Reaction Laboratory of the Institute of Chemistry, for their contributions to this work.
This work was supported by the National Natural Science Foundation of China (20773136, 30870591 and 21173231), and by the Chinese Academy of Sciences (Hundred Talent Fund).
References
- 1.
Mantsch HH, Chapman D. Infrared spectroscopy of biomolecules, Wiley-Liss, New York, 1996. - 2.
Barth A, Zscherp C. What vibrations tell us about proteins. Quarterly Reviews of Biophysics 2002;35:369-430. - 3.
Wang J, Hochstrasser RM. Characteristics of the two-dimensional infrared spectroscopy of helices from approximate simulations and analytic models. Chemical Physics 2004;297:195-219. - 4.
Miyazawa T. Perturbation treatment of the characteristic vibrations of polypeptide chains in various configurations. The Journal of Chemical Physics 1960;32:1647-52. - 5.
Miyazawa T, Blout ER. The infrared spectra of polypeptides in various conformations: amide I and II bands. Journal of the American Chemical Society 1961;83:712-19. - 6.
Chirgadze YN, Nevskaya NA. Infrared spectra and resonance interaction of amide-I vibration of the antiparallel-chain pleated sheet. Biopolymers 1976;15:607-25. - 7.
Mukherjee S, Chowdhury P, Gai F. Effect of dehydration on the aggregation kinetics of two amyloid peptides. The Journal of Physical Chemistry B 2008;113:531-35. - 8.
Cerf E, Sarroukh R, Tamamizu-Kato S, Breydo L, Derclaye S, Dufrêne YF, Narayanaswami V, Goormaghtigh E, Ruysschaert JM, Raussens V. Antiparallel β-sheet: a signature structure of the oligomeric amyloid β-peptide. Biochemical Journal 2009;421:415-23. - 9.
Goormaghtigh E, Cabiaux V, Ruysschaert JM. Determination of soluble and membrane protein structure by Fourier transform infrared spectroscopy. I. Assignments and model compounds. Subcellular Biochemistry 1994;23:329-62. - 10.
Watson TM, Hirst JD. Density functional theory vibrational frequencies of amides and amide dimers. The Journal of Physical Chemistry A 2002;106:7858-67. - 11.
Merrick JP, Moran D, Radom L. An evaluation of harmonic vibrational frequency scale factors. The Journal of Physical Chemistry A 2007;111:11683-700. - 12.
Cowan ML, Bruner BD, Huse N, Dwyer JR, Chugh B, Nibbering ETJ, Elsaesser T, Miller RJD. Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O. Nature 2005;434:199-202. - 13.
Asbury JB, Steinel T, Stromberg C, Corcelli SA, Lawrence CP, Skinner JL, Fayer MD. Water dynamics: vibrational echo correlation spectroscopy and comparison to molecular dynamics simulations. The Journal of Physical Chemistry A 2004;108:1107-19. - 14.
Lee K-K, Park K-H, Park S, Jeon S-J, Cho M. Polarization-angle-scanning 2D IR spectroscopy of coupled anharmonic oscillators: A polarization null angle method. The Journal of Physical Chemistry B 2011;115:5456-64. - 15.
King JT, Kubarych KJ. Site-specific coupling of hydration water and protein flexibility studied in solution with ultrafast 2D-IR spectroscopy. Journal of the American Chemical Society 2012;134:18705-12. - 16.
Li D, Yang F, Han C, Zhao J, Wang J. Correlated high-frequency molecular motions in neat liquid probed with ultrafast overtone two-dimensional infrared spectroscopy. The Journal of Physical Chemistry Letters 2012;3:3665-70. - 17.
Yu P, Yang F, Zhao J, Wang J. Hydration dynamics of cyanoferrate anions examined by ultrafast infrared spectroscopy. The Journal of Physical Chemistry B 2014;118:3104-14. - 18.
Hochstrasser RM. Two-dimensional spectroscopy at infrared and optical frequencies. Proceedings of the National Academy of Sciences of the United States of America 2007;104:14190-96. - 19.
Maekawa H, Ballano G, Toniolo C, Ge N-H. Linear and two-dimensional infrared spectroscopic study of the amide I and II modes in fully extended peptide chains. The Journal of Physical Chemistry B 2010;115:5168-82. - 20.
Middleton CT, Marek P, Cao P, Chiu C-c, Singh S, Woys AM, de Pablo JJ, Raleigh DP, Zanni MT. Two-dimensional infrared spectroscopy reveals the complex behaviour of an amyloid fibril inhibitor. Nature Chemistry 2012;4:355-60. - 21.
Costard R, Heisler I, A., Elsaesser T. Structural dynamics of hydrated phospholipid surfaces probed by ultrafast 2D spectroscopy of phosphate vibrations. The Journal of Physical Chemistry Letters 2014;5:506-11. - 22.
Nielsen HH. The vibration-rotation energies of molecules. Reviews of Modern Physics 1951;23:90-136. - 23.
Califano S: Vibrational states, John Wiley and Sons, London, New York, Sydney, Toronto, 1976. - 24.
Barone V. Anharmonic vibrational properties by a fully automated second-order perturbative approach. The Journal of Chemical Physics 2005;122:014108/1-08/10. - 25.
Barone V. Accurate vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: The case of azabenzenes. The Journal of Physical Chemistry A 2004;108:4146-50. - 26.
Zhao J, Wang J. Chain-length and mode-delocalization dependent amide-I anharmonicity in peptide oligomers. The Journal of Chemical Physics 2012;136:214112. - 27.
Wang J. Conformational dependence of anharmonic NH stretch vibration in peptides. Chemical Physics Letters 2009;467:375-80. - 28.
Zheng ML, Zheng DC, Wang J. Non-native side chain IR probe in peptides: Ab initio computation and 1D and 2D IR spectral simulation. The Journal of Physical Chemistry B 2010;114:2327-36. - 29.
Wang J, Hochstrasser RM. Anharmonicity of Amide Modes. The Journal of Physical Chemistry B 2006;110:3798-807. - 30.
Wang J. Conformational dependence of anharmonic vibrations in peptides: amide-I modes in model dipeptide. The Journal of Physical Chemistry B 2008;112:4790-800. - 31.
Cheam TC, Krimm S. Transition dipole interaction in polypeptides: ab initio calculation of transition dipole parameters. Chemical Physics Letters 1984;107:613-16. - 32.
Krimm S, Bandekar J. Vibrational spectroscopy and conformation of peptides, polypeptides, and proteins. Advances in Protein Chemistry 1986;38:181-364. - 33.
Hamm P, Lim M, DeGrado WF, Hochstrasser RM. The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure. Proceedings of the National Academy of Sciences of the United States of America 1999;96:2036-41. - 34.
Moran A, Mukamel S. The origin of vibrational mode couplings in various secondary structural motifs of polypeptides. Proceedings of the National Academy of Sciences of the United States of America 2004;101:506-10. - 35.
Hamm P, Hochstrasser RM, in M.D. Fayer (Ed.), Ultrafast Infrared and Raman Spectroscopy. Marcel Dekker Inc., New York, 2001, p. 273-347. - 36.
Dybal J, Cheam TC, Krimm S. Carbonyl stretch mode splitting in the formic acid dimer: electrostatic models of the intermonomer interaction. Journal of Molecular Structure 1987;159:183-94. - 37.
Torii H, Tasumi M. Infrared intensitites of vibrational modes of an -a-helical polypeptide: calculations based on the equilibrium charge/charge flux (ECCF) model. Journal of Molecular Structure 1993;300:171-79. - 38.
Hamm P, Woutersen S. Coupling of the amide I modes of the glycine dipeptide. Bulletin of the Chemical Society of Japan 2002;75:985-88. - 39.
Qian W, Krimm S. Origin of the C=O stretch mode splitting in the formic acid dimer. The Journal of Physical Chemistry 1996;100:14602-08. - 40.
Yokoyama I, Miwa Y, Machida K. Extended molecular mechanics calculations of thermodynamic quantities, structures, vibrational frequencies, and infrared absorption intensities of formic acid monomer and dimer. Journal of the American Chemical Society 1991;113:6458-64. - 41.
Yokoyama I, Miwa Y, Machida K. Simulation of Raman spectra of formic acid monomer and dimer in the gaseous state by an extended molecular mechanics method. The Journal of Physical Chemistry 1991;95:9740-46. - 42.
Besler BH, Merz KMJ, Kollman PA. Atomic charges derived from semiempirical methods. Journal of Computational Chemistry 1990;11:431-39. - 43.
Chirlian LE, Francl MM. Atomic charges derived from electrostatic potentials: A detailed study. Journal of Computational Chemistry 1987;8:894-905. - 44.
Breneman CM, Wiberg KB. Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis. Journal of Computational Chemistry 1990;11:361-73. - 45.
Reed AE, Weinstock RB, Weinhold F. Natural population analysis. The Journal of Chemical Physics 1985;83:735-46. - 46.
Bradbury EM, Elliott A. The infrared spectrum of crystalline N-methylacetamide. Spectrochimica Acta 1963;19:995-1012. - 47.
Torii H, Tasumi M. Model calculations on the amide-I infrared bands of globular proteins. The Journal of Chemical Physics 1992;96:3379-87. - 48.
Dwivedi AM, Krimm S. Vibrational analysis of peptides, polypeptides, and proteins. X. Poly(glycine I) and its isotopic derivatives. Macromolecules 1982;15:177-85. - 49.
Rey-Lafon M, Forel MT, Garrigou-Lagrange C. Study of normal modes of cis- and trans-amide groups using force fields of d-valarolactam and N-methylacetamide. Spectrochimica Acta, Part A 1973;29:471-86. - 50.
Torii H, Tasumi M. Ab initio molecular orbital study of the amide I vibrational interactions between the peptide groups in di- and tripeptides and considerations of the conformation of the extended helix. Journal of Raman Spectroscopy 1998;29:81-86. - 51.
la Cour Jansen T, Dijkstra AG, Watson TM, Hirst JD, Knoester J. Modeling the amide I bands of small peptides. The Journal of Chemical Physics 2006;125:044312/1. - 52.
Gorbunov RD, Kosov DS, Stock G. Ab initio-based exciton model of amide I vibrations in peptides: Definition, conformational dependence, and transferability. The Journal of Chemical Physics 2005;122:224904-12. - 53.
Kim YS, Wang J, Hochstrasser RM. Two-dimensional infrared spectroscopy of the alanine dipeptide in aqueous solution. The Journal of Physical Chemistry B 2005;109:7511-21. - 54.
Jamróz MH. Vibrational energy distribution analysis VEDA 4, Warsaw, 2004. - 55.
Mukamel S: Principles of nonlinear optical spectroscopy, Oxford University Press, 1995. - 56.
Cho M: Two-dimensional optical spectroscopy, CRC Press, Boca Raton, London, New York, 2009. - 57.
Hamm P, Zanni M: Concept and methods of 2D infrared spectroscopy, Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Tokyo, Mexico City, 2011. - 58.
Jansen TL, Knoester J. A transferable electrostatic map for solvation effects on amide I vibrations and its application to linear and two-dimensional spectroscopy. The Journal of Chemical Physics 2006;124:044502/1-02/11. - 59.
Wang J, Chen J, Hochstrasser RM. Local structure of β-hairpin Isotopomers by FTIR, 2D IR, and ab initio theory. The Journal of Physical Chemistry B 2006;110:7545-55. - 60.
Wang J, Zhuang W, Mukamel S, Hochstrasser RM. Two-dimensional infrared spectroscopy as a probe of the solvent electrostatic field for a twelve residue peptide. The Journal of Physical Chemistry B 2008;112:5930-37. - 61.
Schmidt JR, Corcelli SA, Skinner JL. Ultrafast vibrational spectroscopy of water and aqueous N-methylacetamide: comparison of different electronic structure/molecular dynamics approaches. The Journal of Chemical Physics 2004;121:8887-96. - 62.
Hayashi T, Zhuang W, Mukamel S. Electrostatic DFT map for the complete vibrational amide band of NMA. The Journal of Physical Chemistry A 2005;109:9747-59. - 63.
Hamm P, Lim M, Hochstrasser RM. Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared spectroscopy. The Journal of Physical Chemistry B 1998;102:6123-38. - 64.
Fang C, Wang J, Kim YS, Charnley AK, Barber-Armstrong W, Smith AB, III, Decatur SM, Hochstrasser RM. Two-dimensional infrared spectroscopy of isotopomers of an alanine rich alpha-helix. The Journal of Physical Chemistry B 2004;108:10415-27. - 65.
Rubtsov IV, Hochstrasser RM. Vibrational dynamics, mode coupling and structure constraints for acetylproline-NH2. The Journal of Physical Chemistry B 2002;106:9165-71. - 66.
Ham S, Cha S, Choi J-H, Cho M. Amide I modes of tripeptides: Hessian matrix reconstruction and isotope effects The Journal of Chemical Physics 2003;119:1451-61. - 67.
Lim M, Hochstrasser RM. Unusual vibrational dynamics of the acetic acid dimer. The Journal of Chemical Physics 2001;115:7629-43. - 68.
Bohr HG, Frimand K, Jalkanen KJ, Nieminen RM, Suhai S. Neural-network analysis of the vibrational spectra of N-acetyl L-alanyl N8-methyl amide conformational states. Physical Review E 2001;64:021905-1. - 69.
Wang J. Assessment of the amide-I local modes in gamma- and beta-turns of peptides, Physical Chemistry and Chemical Physics 2009;11:5310-5322. - 70.
Cances E, Mennucci B, Tomasi J. A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics. The Journal of Chemical Physics 1997;107:3032-41. - 71.
Wang J. Ab initio-based all-mode two-dimensional infrared spectroscopy of a sugar molecule. The Journal of Physical Chemistry B 2007;111:9193-96.