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2009, 113, 1813–1816 Published on Web 01/27/2009
Structurally Sensitive Anharmonic Cr-D Stretch Vibration in Deuterated Peptides Jianping Wang* Beijing National Laboratory for Molecular Sciences, Molecular Reaction Dynamics Laboratory, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China ReceiVed: December 13, 2008; ReVised Manuscript ReceiVed: January 11, 2009
In the present study, vibrational properties of the CR-D stretching mode in deuterated alanine dipeptide are examined by ab initio normal-mode calculations. A backbone conformational scan reveals a quite similar structural sensitivity of the harmonic and anharmonic vibration frequencies for both the fundamental and overtone transitions. The distributions of the frequencies are found to be linearly anticorrelated with that of the CR-D bond length, with the latter being found to be also structurally sensitive. Theory predicts that, as determined by the quantum mechanical anharmonic force field, the highly anharmonic (with a mean diagonal anharmonicity of 48.0 cm-1) and yet highly localized CR-D stretching mode shall be potentially useful in probing peptide local structures and dynamics. 1. Introduction The isotope-edited CR-H, in particular, the CR-D stretch vibration mode in peptides, located in between amide units of the polypeptide chain, has been recognized in recent years as a potentially useful infrared probe for peptide and protein conformations.1-3 Two reasons make the CR-D stretch vibration a candidate for such purposes; for one, the mode is believed to be highly localized and, thus, an ideal local structural reporter; second, the vibrational frequency for the mode is conveniently located near ∼2100 cm-1,4-6 which is an open infrared spectral window for biological systems. The vibrational properties of the C-D stretch mode in general have been found to exhibit structure and microenvironment sensitivities. The C-D stretching vibration (including frequency and line shape) of (methyl-d3)methionine-labeled cytochrome-c was found to be very sensitive to the protein environment in an early FTIR study.4 A very recent theoretical work has shown the sensitivity of the CR-D stretching vibrational frequency to the hydrogen bonding environment of peptides.3 Another study has pointed out the possibility of a split CR-D absorption band structure due to Fermi resonances in deuterium-labeled alanine.6 Further, intermode vibrational couplings and correlations of frequency fluctuation distributions involving the C-D stretch mode in peptide and sugar model compounds have been explored very recently by two-dimensional infrared (2D IR) experiments7 and simulations.8 It is of great interest to explore whether the anharmonic properties, for example, anharmonic frequencies and anharmonicities of the CR-D stretch mode, in peptides are sensitive to backbone conformations. As has been demonstrated recently, there are several anharmonic parameters associated with the amide modes of peptides, namely, the amide-I mode (mainly the carbonyl stretching)9 and the amide-A mode (mainly the N-H stretching).10 Exploring new conformationally sensitive probes shall warrant a flexible choice of probes in proper probing * E-mail:
[email protected]. Tel: +86-010-62656806. Fax: +86-01062563167.
10.1021/jp8109989 CCC: $40.75
wavelengths, so that the same entity in different molecular surroundings can be characterized using different probes, which may be practically useful in studying intra- and intermolecular interactions in chemical and biological systems. In the present work, by using deuterium-substituted alanine dipeptide at the CR position (denoted as d-ADP), CH3CONHCRDCH3CONHCH3, as a model peptide, we demonstrate the structural sensitivity of the CR-D stretching mode, including its fundamental harmonic frequencies, fundamental and overtone anharmonic frequencies, and frequency and bond length correlations, in the entire peptide backbone conformational space. 2. Computational Methods Harmonic and anharmonic frequencies of fundamental transitions, anharmonic overtone transition frequencies for the 3N 6 () 60) normal modes of d-ADP are obtained by ab initio computations.11 The anharmonic frequencies are evaluated by employing the second-order vibrational perturbation theory based approach,12,13 through which the anharmonic terms in the vibrational potential energy can be obtained perturbatively in terms of the cubic and quartic force constants. Details of the anharmonic frequency computations of peptide oligomers can be found in our recent works.8,14 To explore the conformational dependence of the CR-D vibration in d-ADP, we sample two backbone dihedral angles φ and ψ, defined as as φ )∠CNCRC and ψ )∠NCRCN, respectively, in the range of (-180 e φ e +180°, -180 e ψ e +180°). The sampling grid is a 13 × 13 matrix with ∆φ ) ∆ψ ) 30° intervals; however, since +180° is the same as -180° for each of the dihedral angles, only 144 independent anharmonic frequency computations are required. Each sampling point takes approximately 35 h of wall clock computation time of a quad core computer server (2.33 GHz). During the φ-ψ scan, conformations at certain (φ, ψ) locations were found to be transition states with imaginary low-frequency modes and were subsequently replaced by nearby samplings with φ and/or ψ 2009 American Chemical Society
1814 J. Phys. Chem. B, Vol. 113, No. 7, 2009
Letters
Figure 1. Conformation-dependent vibrational frequency and bond length of the CR-D group in d-ADP. (a) Harmonic frequency (ω0f1). (b) Anharmonic frequency (V0f1). (c) Bond length (rCRD). (d) Anharmonic frequency (V0f2). Color bar: bond length in Å and frequency in cm-1.
values varied by a few degrees. This ensures a more or less evenly spaced grid to cover the entire conformation space. The obtained φ-ψ map of each vibrational parameter is subsequently interpolated by employing a two-dimensional spline method. Calculations are performed using the Hartree-Fock (HF) theory and 6-31+G* basis set. The combination of theory and basis set has been used to predict anharmonic properties of the amide modes in peptides quite satisfactorily.14 3. Results and Discussion The vibrational properties of the CR-D group in d-ADP are found to be very sensitive to the φ-ψ dihedral angles of the peptide backbone. Figure 1a, b, and d show the harmonic frequency of the fundamental transition (denoted as ω0f1), the anharmonic frequency of the fundamental transition (V0f1), and the anharmonic frequency of the overtone transition (ω0f2), respectively, in the φ-ψ space. Clearly, the three frequencies change dramatically as a function of the dihedral angles and exhibit conformational sensitivities that are quite similar to one another. The highest harmonic frequency occurs in the vicinity of (φ ) -120°, ψ ) -60°), whereas the lowest frequency occurs in the vicinity of (φ ) 120°, ψ ) 60°). Similar behaviors are seen in the φ-ψ map of V0f1 and V1f2. However, there is no symmetry in these φ-ψ maps shown in Figure 1. Figure 1c depicts the CR-D bond length (rCRD) as a function of the φ and ψ angles. Overall the φ-ψ map of rCRD is quite similar to those of the frequencies, but with opposite trend. Higher frequencies correspond to shorter bond lengths and vice versa. Further, the similarity between the φ-ψ maps of V0f1 and V0f2 implies an invariant diagonal anharmonicity of the CR-D stretching vibrations throughout the entire conformation space because the diagonal anharmonicity of the ith mode, by definition, is ∆ii ) 2Vi - V2i. Here, Vi is V0f1, and V2i is V0f2 for the ith mode. It is found that the mean value of ∆ii of the CR-D stretching mode is 48.0 cm-1. Similarly, as has been seen for the case of the amide-A mode,10 it is found that there is no clear pattern in the φ-ψ map of the diagonal anharmonicities for the CR-D modes in the entire conformational space (data not shown). Further, it is also noted that the φ-ψ maps of the anharmonic frequencies are not as smooth as that of the harmonic frequencies. Denser samplings may improve the situation but will not change the general profile of these φ-ψ maps.
To further examine the conformational dependence of the CR-D stretching modes, we analyzed the correlation of distributions of frequency and bond length. The results are given in Figure 2. A linear correlation between the distributions of ω0f1 and V0f1 is found (panel a, the correlation coefficient is 0.95), indicating a more or less constant red shift (∼90 cm-1) of the fundamental transition energy over the entire conformational space. Panels b and c show linearly anticorrelated distributions of the harmonic frequencies and anharmonic frequencies for the fundamental and overtone transitions with respect to the distribution of the CR-D bond lengths sampled in the φ-ψ space. It is found that the correlation coefficients between ω0f1 and rCRD, between V0f1 and rCRD, and between V0f2 and rCRD are -0.96, -0.92, and -0.95, respectively. Note that we plot 0.5V0f2 against rCRD in panel c, so that the energy difference between the two straight lines for a given CR-D bond length is approximately half of the diagonal anharmonicity. The predicted frequency red shift (∼90 cm-1) from the harmonic to anharmonic picture shown in Figure 2a is due to the anharmonic correction that is a sum of the diagonal anharmonicity and half of the off-diagonal anharmonicities (∆ij)
ωi - Vi ) ∆ii +
1 ∑∆ 2 j*i ij
Here the sum runs over the entire 3N - 6 normal modes. Since the mean value ∆ii for CR-D stretching is 48.0 cm-1, the collective contribution of ∆ij accounts for the remaining ∼50% of the red shift. For a local mode like the CR-D stretching, the diagonal anharmonicity ∆ii is dominated by the contribution from the diagonal cubic and quartic anharmonic terms in the potential energy function 2 δii ) -Φiiii /8 + 5Φiii /ωi /24
where Φiiii and Φiii are the diagonal quartic and cubic force constants. To shows this effect, we list the computed diagonal cubic and quartic force constants and frequencies for 10 typical second structures, namely, the RL2-helix (φ ) +90°, ψ ) -90°), π-helix (-57°, -70°), PPII structure (-75°, +135°), RL1-helix (+60°, +60°), C7 structure (+82°, -69°), extended structure (180°, -180°), R-helix (-58°, -47°), 310-helix (-50°, -25°), antiparallel β-sheet (-139°, +130°), and parallel β-sheet (-119°, +113°). The results are given in Table 1. The off-
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J. Phys. Chem. B, Vol. 113, No. 7, 2009 1815
Figure 2. Frequency and bond length correlations of CR-D stretching vibrations in d-ADP. (a) Harmonic frequency (ω0f1) versus anharmonic frequency (V0f1) of the fundamental transition. (b) Fundamental harmonic frequency versus bond length (rCRD). (c) Fundamental anharmonic frequency (circles) and overtone anharmonic frequency (V0f2/2, triangles) versus bond length.
TABLE 1: Harmonic Frequency for the Fundamental Transition (ωi, in cm-1), Anharmonic Frequencies for the Fundamental and Overtone Transitions (Wi and W2i, in cm-1), Quartic (Φiiii, in cm-1) and Cubic (Φiii, in cm-1) Force Constants, and Their Contribution (δii, in cm-1) to the Diagonal Anharmonicity (∆ii, in cm-1) for the Cr-D Stretching Mode in 10 Representative Peptide Conformations
a
(φ, ψ)
ωi
Vi
V2i
Φiiii
Φiii
δiia
∆iia
PEDb
(+90°, -90°) (-57°, -70°) (-75°, +135°) (+60°, +60°) (+82°, -69°) (+180°, -180°) (-58°, -47°) (-50°, -25°) (-139°, +130°) (-119°, +113°)
2433.1 2404.6 2430.1 2407.8 2426.5 2354.5 2407.9 2404.6 2433.9 2446.7
2368.5 2318.7 2336.4 2323.5 2336.5 2253.8 2329.6 2299.7 2372.9 2370.9
4655.3 4597.0 4639.7 4606.0 4626.8 4459.3 4615.2 4570.1 4661.5 4686.0
584.2 584.4 578.4 589.1 581.0 591.2 583.6 586.3 577.3 574.5
-1255.0 -1257.0 -1251.9 -1257.3 -1252.6 -1262.0 -1256.8 -1260.4 -1248.3 -1244.6
61.9 63.8 62.1 63.1 62.1 67.0 63.7 64.4 61.2 60.1
81.7 40.4 33.1 41.0 46.2 48.3 44.0 29.3 84.3 55.8
0.9978 0.9977 0.9975 0.9980 0.9977 0.9979 0.9978 0.9980 0.9976 0.9975
2 ∆ii ) 2Vi-V2i; δii ) -Φiiii/8 + 5Φiii /ωi/24. b Cartesian-coordinate-based potential energy distribution (PED).
diagonal cubic force constant, for example, Φiij, was found to be at least an order of magnitude smaller than Φiiii (data not shown). It is seen that the Φiiii and Φiii force constants and their contribution (δii) to the diagonal anharmonicity for the CR-D stretching mode in the 10 conformations are quite similar. Further, δii is found to be significant and has the same sign as ∆ii in all cases, meaning the diagonal anharmonicity of the CR-D mode is largely determined by the mode itself. However, interactions with other modes also have contributions to ∆ii. This reveals the incomplete localization nature of the CR-D mode in terms of its anharmonic properties. In other words, the CR-D mode is not as highly localized as expected simply by the potential energy distribution (PED) analysis performed on the basis of the Cartesian coordinate (shown in Table 1). Quite convincingly, the conformationally dependent CR-D bond length shown in this work is the structural basis of the conformationally sensitive harmonic and anharmonic frequencies. It was first proposed by Krimm and his co-workers1,2 that the CR-D stretching frequency in peptides could be used to determine the φ-ψ conformation. The structural sensitivity of the CR-D stretching frequency was believed to be due to the major factor in determining the frequency, that is, the bond length.2 An inverse relationship between the harmonic CR-D stretching frequency and the CR-D bond length ωC-D and rCRD has been demonstrated previously for several peptide conformations such as RR, β, and polyproline-II.2 The φ-ψ map of the bond length obtained in the present study indeed shows a similar
conformationally sensitive pattern to that of the harmonic frequency and to that of the anharmonic frequency as well. The picture can be understood since the CR-D bond length is determined by the electronic structure of the peptide, which is influence by the chemical environment and nonbonded interactions as well. These interactions are perhaps the most influential ingredients in the ab initio anharmonic force fields that determine the vibrational parameters. Further, being located in the middle of two amide units, the CR-D species has a structurally asymmetric environment, causing the observed asymmetry of the φ-ψ maps in Figure 1. Along this line, it is expected that side chains in different amino acid residues may further influence the conformational dependence of the CR-D stretching frequency by exerting additional electrostatic and mechanical influences on the CR-D bond length. Located in high-frequency region, the CR-D and N-H (and N-D) stretching modes share quite a few similarities. For example, both modes are highly anharmonic with large diagonal anharmonicities (mean value is 142.8 cm-1 for N-H, 72.4 cm-1 for N-D,10 and 48.0 cm-1 for CR-D in the entire φ-ψ space obtained at the same level of theory), and both show insignificant conformational dependence of the diagonal anharmonicities. However, the CR-D and N-H modes have different conformational dependences of frequency. The φ-ψ map of frequencies of the N-D mode is more or less C2 symmetric in the φ-ψ space, as shown previously,10 while those of the CR-D mode are not (Figure 1). Further, the conformational dependence
1816 J. Phys. Chem. B, Vol. 113, No. 7, 2009 of the anharmonic parameters of the CR-D stretch is also significantly different from what was reported for the amide-I modes.10 As a delocalized mode, the amide-I mode has conformationally dependent diagonal and off-diagonal anharmonicities.9 For a localized mode such as the CR-D stretch, one expects to see weak couplings and thus insignificant conformational dependence of the off-diagonal anharmonicities between two adjacent CR-D modes presented in larger systems such as the alanine tripeptide. Our current work involves investigation of the anharmonic properties of the CR-D stretching mode in other amino acid residues with larger side chain groups as the alkyl group in alanine is quite small (-CH3). Presumably, the CR-D bond length will be somewhat different from residue to residue. Interesting systems also include peptide-water clusters to mimic solvent effect in the first hydration layer. Solvent hydrogen bonding effects on the harmonic CR-D stretching frequency have been illustrated in a very recent work,3 in which a hydrogen-bonded water with both CR-D and CdO groups in deuterated alanine dipeptide blue shift the CR-D stretching frequency by 8 cm-1. Interaction between C-D and other modes is also an interesting subject. The CdO/C-D interaction in the deuterated formamide has been studied by 2D IR experiments7 and by ab initio computations in the deuterated glycolaldehyde as well.8 Further, it should be pointed out that the intensity of the CR-D stretching mode is typically 50 times weaker than that of the amide-I mode, as predicted at the HF/6-31+G* level, meaning that a higher sample concentration might be needed experimentally in order to make use of the CR-D absorption band in structure and dynamics studies of peptides. As shown in a recent study,6 the weak CR-D stretching peak may be accompanied by Fermi resonances, making spectral interpretation further complicated. However, one expects to see intensified peaks, for example, in the hydrogen-bonded complexes. In summary, we have found that the anharmonic frequencies of fundamental and overtone transitions of the CR-D stretching mode in dipeptide are conformationally dependent, even though the modes are highly localized. We have also confirmed the conformational dependence of the harmonic frequency of its fundamental transition proposed by Krimm and his co-workers.1,2 Further, the φ-ψ maps of these parameters obtained at the level of HF/6-31+G* are found to be highly anticorrelated with the CR-D bond length. It is also found that the diagonal anharmonicity of the CR-D stretching mode, although being significant and measurable by nonlinear infrared spectroscopy such as 2D IR,15 does not exhibit clear conformational dependence. As a case study of deuterated alanine-based dipeptides, the structural sensitivity of the CR-D stretch mode as a local structural probe
Letters in a polypeptide chain is revealed in the entire backbone conformational space. It is expected that neutral or charged side chains and a hydrophilic or hydrophobic local environment all will affect the frequencies and line shapes of this vibrational mode. Therefore the CR-D stretch mode shall prove potentially useful in reporting the local conformation and local structural environment of peptide and proteins in condensed phases. Acknowledgment. This work was supported by the National Natural Science Foundation of China (20773136, 30870591), by the National High-Tech Research and Development Program of China (2007AA02Z139), and by the Chinese Academy of Sciences through the Hundred Talent Fund. References and Notes (1) Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2004, 108, 10923– 10924. (2) Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2007, 111, 5300–5303. (3) Mirkin, N. G.; Krimm, S. J. Phys. Chem. B 2008, 112, 15267– 15268. (4) Chin, J. K.; Jimenez, R.; Romesberg, F. E. J. Am. Chem. Soc. 2001, 123, 2426–2427. (5) Chin, J. K.; Jimenez, R.; Romesberg, F. E. J. Am. Chem. Soc. 2002, 124, 1846–1847. (6) Kinnaman, C. S.; Cremeens, M. E.; Romesberg, F. E.; Corcelli, S. A. J. Am. Chem. Soc. 2006, 128, 13334–13335. (7) Kumar, K.; Sinks, L. E.; Wang, J.; Kim, Y. S.; Hochstrasser, R. M. Chem. Phys. Lett. 2006, 432, 122–127. (8) Wang, J. J. Phys. Chem. B 2007, 111, 9193–9196. (9) Wang, J. J. Phys. Chem. B 2008, 112, 4790–4800. (10) Wang, J. Chem. Phys. Lett. 2008, doi:10.1016/j.cplett.2008.11.031. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003. (12) Barone, V. J. Chem. Phys. 2005, 122, 014108/014101–014110. (13) Califano, S. Vibrational States; John Wiley and Sons: London, New York, Sydney, Toronto, 1976. (14) Wang, J.; Hochstrasser, R. M. J. Phys. Chem. B 2006, 110, 3798– 3807. (15) Asplund, M. C.; Zanni, M. T.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 8219–8224.
JP8109989
