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Two-dimensional infrared measurements of the coupling between amide modes of an α-helix
Chemical Physics Letters 382 (2003) 586–592 www.elsevier.com/locate/cplett
Two-dimensional infrared measurements of the coupling between amide modes of an a-helix C. Fang a, J. Wang a, A.K. Charnley a, W. Barber-Armstrong b, A.B. Smith III a, S.M. Decatur b, R.M. Hochstrasser a,* a
Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, PA 19104-6323, USA b Department of Chemistry, Mount Holyoke College, South Hadley, MA 01075, USA Received 8 September 2003; in final form 14 October 2003
Published online:
Abstract The 2D IR spectra of doubly isotopically substituted a-helices with 13 C@16 O and 13 C@18 O labels enabled the couplings between amide-I modes separated by one, two and three residues to be measured. The magnitudes and signs of couplings between the isotopomers and between them and the helix exciton band states confirm that the states of the helix and isotopomers are delocalized. The results are compared with simulations. The off-diagonal anharmonicities agree reasonably with a set of couplings that derive from transition charge interactions except for nearest neighbors for which the coupling is modified by through bond interactions. Ó 2003 Published by Elsevier B.V.
1. Introduction The IR spectra of proteins are intimately connected with their complete three dimensional structures on the length scale of chemical bonds. However, their vibrational transitions are not spectrally resolved. Our strategy is to insert both 13 C@16 O and 13 C@18 O labels into secondary structures. Since their isotope shifts are different, a pair of isotopic peaks are created and 2D IR spectroscopic methods can then be used to analyze
*
Corresponding author. Fax: +1-215-8980590. E-mail address: [email protected] (R.M. Hochstrasser). 0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.cplett.2003.10.111
the coupling between those specific pairs of molecular transitions. The development of methods to obtain structural changes in proteins is an important experimental challenge to which 2D IR [1–8] can contribute significantly. The photon echo is an essential component of 2D IR [9]. The earliest echoes on molecules were in the infrared [10], soon followed by nanosecond two pulse echoes in the visible [11]. As optical lasers improved, measurements were extended to faster responding liquids and glasses [12], to heterodyning, gating and three pulse methods (see e.g., [13]) and meanwhile the IR echo was extended to the picosecond regime [14]. Femtosecond infrared experiments on proteins and aqueous systems [15] evolved to femtosecond three pulse echoes of
C. Fang et al. / Chemical Physics Letters 382 (2003) 586–592
ions in water [16], peptides and proteins [17], and finally to heterodyning of phase locked IR echoes which enabled the assembly of complex multidimensional vibrational spectra [2]. Earlier, pump– probe 2D IR spectra on peptides and proteins [1], which relate to the real part of the heterodyned 2D IR experiment [18], had been reported. Recently, dual frequency 2D IR was accomplished [8] and 2D IR spectroscopy of vibrators [18,19] is currently expanding in the study of liquids [20,21], glasses and biological systems [22]. In this work, the labels are inserted into residues of an a-helix and the 2D IR is used to determine the couplings. Also the population times, the inhomogeneous distributions and the correlations of the fluctuations of the vibrational frequencies at the various sites can be measured. We also simulate the complete 2D IR spectra neglecting through bond [23,24] and polarizability [25] effects and calibrate the method from known helix properties [6,26–28].
2. Methods and experimental results More details of the methods and results will be given in a future publication.
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2.2. Linear spectroscopy Fig. 1 presents the linear IR data for each of the compounds studied with the main helix peak fitted to two gaussian contributions, one from helical and the other from more random structures. Another gaussian centered at 1596 cm1 accounted for the 13 C in natural abundance. The main helix exciton band (the 23 or 24 unlabeled residues) of [0,11], [11,13] and [11,14] peaks at about 1631.7 0.5 cm1 (1633 cm1 for [12,13]) and it has a FWHM of 28.3 cm1 that incorporates both the A (z polarized) and E (x; y polarized) helix bands. The 13 C@16 O isotopomer fit peaks at 1594 0:3 cm1 and the 13 C@18 O at 1570:7 0:8 cm1 . The separations between the two isotopic labels are 24.7, 22.4 and 28 cm1 in [11,13], [11,14] and [12,13], respectively. The gaussian fit FWHM for the 13 C@18 O label is 15.2 cm1 . The amide-I mode of a 13 C@18 O labeled peptide with molecular formula H3 CCH(NH2 HCl) 13 C@18 ONHCH2 CH(CH3 )2 had a peak (1597.6 cm1 ) extinction coefficient of 314 M1 cm1 compared with 310 M1 cm1 for the 12 C@16 O salt amide peak (1657.2 cm1 ) indicating that the transition moment magnitudes, (proportional to pffiffi e), are equal and the isotope shift is 59.6 cm1 . 2.3. Pump–probe experiments
2.1. Materials The isotopically labeled 25-residue alanine rich helical polypeptides based on Ac-(A)4 K(A)4 K(A)4 K(A)4 K(A)4 Y-NH2 containing the isotopic amide carbonyl labels 13 C@16 O and 13 C@18 O were obtained by standard peptide synthesis, purified by reverse- phase HPLC and characterized by electrospray mass spectrometry [27]. The 18 O amino acids were synthesized by 18 OH2 exchange. These syntheses will be described in detail elsewhere. The isotopomers contain none, one or one each of the isotopic amide carbonyl labels 13 C@16 O and 13 C@18 O which are referred to as [alanine residue with 13 C@16 O, alanine residue with 13 C@18 O]. We examined: [noneB0 , noneB0] (data not shown), [0,11], [12,13], [11,13] and [11,14]. The central residues are nearly completely helical in phosphate buffer at 0 °C [28], the conditions of all experiments here.
The anharmonicity of the amide 13 C@18 O group of 14.2 cm1 was obtained from the broad-bandpump/broad-band-probe [1] of the 13 C@18 O model compound, whose 1 ! 2 transition intensity is ca. double that of 0 ! 1. The pump–probe spectra of [12,13], [11,13] and [11,14] provided the anharmonicities for both isotopically substituted amides. The decay of the pump–probe signal gave 545 fs for the T1 relaxation time of the 13 C@18 O vibrator. The population relaxation times of the overtone states of the isotopically replaced amide modes of [11,13] and [11,14] were deduced to be about 360 fs by attributing the increased width of the 1 ! 2 transition to a T1 process. 2.4. 2D IR spectroscopy The nonlinear spectra were obtained precisely as in previous heterodyned echo experiments at
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Fig. 1. The linear FTIR spectra of the isotopomers [0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d). The thin lines are fits. The stick heights represent the relative intensities.
6 lm [2,3,7,18]. Three infrared pulses arrived with interval s, between the first and second pulse, and a waiting time T ¼ 0. The signal at wavevector k1 þ k2 þ k3 was detected as a function of s and t
(the interval between the heterodyning and signal fields). A double Fourier transform in s and t yielded the 2D IR spectrum along the frequency axes xs and xt . The center frequency of the 120 fs
Fig. 2. Absolute value 2D IR rephasing spectra. ([0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d)). Sixty contour lines were drawn from zero to the maximum intensity.
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mid-IR pulses was at the mean of the 13 C@18 O and 13 C@16 O peaks. For [0,11], the exciton band states and the 13 C@18 O labeled amide band clearly appear in the 2D IR spectrum (see Fig. 2), along with the cross peaks between them. The signal from 13 C@16 O modes in natural abundance was seen but is not evident in Fig. 2. The other isotopomers exhibit the spectral features of the labeled amides as shown in Figs. 2b–d. After adjustment with a constant phase factor found from comparisons with pump–probe spectra and some normalization, the absorptive spectra were obtained by adding the rephasing ðk1 arrives first, R) and non-rephasing ðk2 or k3 arrives first, NR) spectra [7,18,29]. Each of the absorptive 2D IR spectra of Fig. 3 in the region of the 13 C@16 O and 13 C@18 O amide transitions display eight resonant peaks: two pairs of diagonal peaks corresponding to the v ¼ 0 to v ¼ 1 and v ¼ 1 to v ¼ 2 transitions, a cross peak pair appeared above and below the diagonal. The narrow-band-pump/ broad-band-probe spectra were computed from the 2D IR data set by using a 10 cm1 FWHM gaussian distribution centered at either the 13 C@16 O or 13 C@18 O amide-I resonance and projecting its real part onto the xt axis to obtain the off-diagonal anharmonicity values for [12,13], [11,13] and [11,14] of
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D12;13 ¼ 9:0 1:0, D11;13 ¼ 3:2 0:8 and D11;14 ¼ 4:5 0:6 cm1 , respectively.
3. Discussion The shaded regions in Fig. 4 represent the oneand two-exciton bands of the tagged helix with isotopomer levels located below these bands. In a typical Liouville path represented by the dashed (ket side) and solid (bra side) arrows, the second two pulses transfer the vibrational coherence from one isotope to the other by means of transitions involving the two quantum levels. The three upper levels are the two overtones and the combination band whose energies are again determined by their couplings to each other and to the band states. The dynamical parameters of each of the isotopomers are equal within 20% of the dephasing times. The plots of the absolute value of the T ¼ 0 response along s for different xt gave comparable peak shift signals for all isotopic components. The isotopomer transitions are sharper than the band transitions and the spectra of the helix excitons are narrowed in the direction perpendicular to the diagonal, resulting from the echo-like response of the 2D IR signals. The isotopomer
Fig. 3. Absorptive spectra of samples a–d defined in Fig. 2. The relative signal strengths were chosen for each spectrum to show the proper contrast between the negative (dark) and positive (bright) features (contour lines drawn in 2% intervals).
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zero order energy 2ε
ε (k1)+ε (k2)
two-quantum states
2ε-∆b-2δb 2ε-δa-δb 2ε-∆a-2δa
Energy
ε ε-δb ε-δa
ε (k)
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0 Fig. 4. Relevant energy levels of the isotopically tagged helix. The isotope shifts are da (13 C@18 O) and db (13 C@16 O), while Da and Db are diagonal anharmonicities. The shaded areas represent the helix one- and two-exciton bands.
transitions are more symmetric and their inhomogeneous widths are representative of fluctuations having standard deviation of ca. 4 cm1 at single amide-I sites. The cross peaks show that the isotopomer residues are coupled in all cases: the state containing one excitation in each isotopomer is never at the same energy as the sum of the two isotopomer energies. In order to estimate the coupling constants from these measured off-diagonal and diagonal anharmonicities, a model is needed for both linear and nonlinear spectra. As a first simple approach, we considered the energies of a separated pair of tagged residues, 13 C@16 O with observed frequency m16 and 13 C@18 O with frequency m18 , having v ¼ 1 ! v ¼ 2 transitions at m16 D16 and m18 D18 and a combination band frequency of m16 þ m18 D16;18 where D16;18 is the off-diagonal anharmonicity. We estimated D16 , D18 and D16;18 assuming that only two modes were involved [5]. Robust values of the unperturbed diagonal anharmonicities are obtained from model compounds and confirmed from the 2D IR spectra of the isotopomeric helices. The Hamiltonians Hs and
Hd of the single (2 2) and double (3 3) excitations are written in the basis of the uncoupled isotopomers where D16;18 ¼ 0; the harmonic approximation sets the part of the bilinear transfer matrix element between pffiffiffi v ¼ 1 and v ¼ 2 states of different groups at 2 times those for v ¼ 0 to v ¼ 1. The observed energies are the eigenvalues of Hs and the differences between those of Hs and Hd . It is a simple calculation to find the coupling constants, bij , needed to generate the observed set of two fundamentals, two overtones and one and we find values: combination band, b12;13 ¼ 9:5; b11;13 ¼ 5:0; and b11;14 ¼ 5:5 cm1 . However, the known diagonal and off-diagonal anharmonic shifts could not be simultaneously fit by this approach. For a 13 C@16 O residue, a more correct approach should incorporate the coupling of it to the helix one- and two-exciton states. While the foregoing Ôseparated pairÕ model is conceptually simple it cannot be entirely correct, because the isotopomers do not only interact with each other but also with the remaining 12 C@16 O amides of the helix. We recently reported an empirical computational method [30] for predicting the linear and 2D IR spectra of amide-I modes for a-helices of finite length. It incorporates transition charge interactions between all except nearest neighbor amides. The nearest neighbor couplings are obtained from density functional theory calculations. The inhomogeneous broadening is incorporated by averaging over Hamiltonians that contain gaussian random fluctuations of their diagonal frequencies. The input includes atomic coordinates for the helix. The pulse frequency and spectral width were chosen to match those used in the experiment. The homogeneous broadening is chosen to match observations on peptides. We also showed explicitly that a Hamiltonian matrix having equal diagonal energies and with couplings obtained by this recipe gave results that were very close to the density functional results for peptides having up to four amide units, confirming the earlier idea that the spectra of nearly degenerate sets of amide-I modes can be considered without regard to their interactions with other types of modes. For Ramachandran angles / ¼ 58°, w ¼ 47° and x ¼ 180° corresponding to a typical a-helix, we obtained a complete set of model
C. Fang et al. / Chemical Physics Letters 382 (2003) 586–592
coupling constants, of which some of the largest ones are: b12 ¼ 7:5; b13 ¼ 4:7; b14 ¼ 6:1; b15 ¼ 0:5; and b16 ¼ 0:7 cm1 , where b12 means nearest neighbor, b13 is next to nearest neighbor and so on. The simulated 2D IR spectra are shown in Fig. 5 using zero order isotope shifts of da ¼ 65 and db ¼ 44 cm1 and a diagonal anharmonicity of 14 cm1 . The simulation generates the essential features of the results as a comparison of Figs. 2 and 5 illustrates. The magnitudes of the couplings calculated in this manner are similar to those deduced from the separated pair modeling of the data, and their signs are consistent with expectations for the intensities in the linear spectra calculated from the separated pair wave functions using perturbation theory. The relative intensities of the transitions in the linear and 2D IR spectra depend on the spatial separations of the modes, the angles between the transition dipoles and the signs of the couplings. The intensities of the linear spectra from the full simulation are similar to the observed values suggesting that the signs and magnitudes of the computed couplings given above are appropriate. However, the signs of the coupling constants are
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most confidently determined from the 2D IR because these signals are freer from the background and baseline subtraction ambiguities present in the linear spectra. It is evident from the results shown in Figs. 2 and 3 that the 13 C@18 O peak is definitely stronger than that of 13 C@16 O in [11,13] and [11,14] but considerably weaker than that of 13 C@16 O in [12,13]. By comparing expectations for these ratios with the simulations and with simple perturbation models, we can conclude that b12 > 0, b13 < 0 and b14 < 0. These signs are those expected from transition charge or transition dipole coupling. The simulated off-diagonal anharmonicities are in the correct order and within better than a factor of two of experiment: we find D12;13 ¼ 5:2, D11;13 ¼ 2:5 and D11;14 ¼ 3:1 cm1 . The shifts of the isotopomer peaks can be estimated from perturbation theory of isotopic trap spectra [31] that incorporate the coupling to the exciton band of the helix. The result depends on the factor B2 ¼ ðb212 þ b213 þ b214 þ ), and B2 ¼ 117 (cm1 )2 for our parameters, which causes a )1.80 cm1 shift of all the 13 C@18 O peaks and )2.66 cm1 for all the 13 C@16 O peaks computed from B2 =da and B2 =db , respectively. The remaining shifts are from the interaction between the
Fig. 5. The simulated 2D IR spectra of [0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d). These are absolute value spectra with da ¼ 65 and db ¼ 44 cm1 , polarization hzzzzi and gaussian frequency fluctuation of 4 cm1 . The diagonal peak at xt 1645 cm1 is due to the failure of the energy fluctuations to properly capture the broadening of the exciton transitions.
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13
C@18 O and 13 C@16 O levels. These shifts are da Þ ¼ 1:81; 0:71 and )1.20 cm1 for the C@18 O level of [12,13], [11,13] and [11,14], respectively. The corresponding shifts for the 13 C@16 O level are b2ij da =db ðda db Þ ¼ 3:96; 1:55 and 2.62 cm1 . The perturbation theory results agree reasonably with experiment although they are inadequate for computation of the off-diagonal anharmonicities of tagged helices. b2ij db =da ðdb 13
4. Conclusions Insertion of 13 C@16 O and 13 C@18 O labels at known residues on the helix enabled the coupling and the delocalized character of the amide-I modes to be measured. The off-diagonal anharmonicities agree reasonably with couplings that derive from transition charge interactions for all but the nearest neighbors, which need through bond interaction. An essential point about our procedure is that its goal is to find 2D IR signatures of anharmonicities and hence of conformations in complex structures. This Ôtop downÕ approach to peptide structure determination is already very useful and hopefully will make contact with and be given a much firmer basis by Ôbottom upÕ approaches involving detailed theory of anharmonicity and high resolution experiments on peptides of ever increasing size. The signals shown in Fig. 2 indicate that one in 35 residues could have been detected, meeting the requirements for applications of the 2D IR method to single residue substituted small proteins. Acknowledgements This research was supported by grants: NIH (GM 12592 and RR01348) and NSF to RMH; and NSF (CHE9984844) and NIH (R15GM54334) to SMD.
References [1] P. Hamm, M. Lim, R.M. Hochstrasser, J. Phys. Chem. B 102 (31) (1998) 6123. [2] M.C. Asplund, M.T. Zanni, R.M. Hochstrasser, Proc. Natl. Acad. Sci. USA 97 (15) (2000) 8219.
[3] M.T. Zanni, S. Gnanakaran, J. Stenger, R.M. Hochstrasser, J. Phys. Chem. B 105 (28) (2001) 6520. [4] O. Golonzka, M. Khalil, N. Demirdoven, A. Tokmakoff, Phys. Rev. Lett. 86 (10) (2001) 2154. [5] P. Hamm, R.M. Hochstrasser, in: M.D. Fayer (Ed.), Ultrafast Infrared and Raman Spectroscopy, Dekker, New York, 2001, p. 273. [6] S. Woutersen, P. Hamm, J. Chem. Phys. 115 (16) (2001) 7737. [7] N.-H. Ge, M.T. Zanni, R.M. Hochstrasser, J. Phys. Chem. A 106 (6) (2002) 962. [8] I.V. Rubtsov, J. Wang, R.M. Hochstrasser, Proc. Natl. Acad. Sci. USA 100 (10) (2003) 5601. [9] Y. Tanimura, S. Mukamel, J. Chem. Phys. 99 (12) (1993) 9496. [10] J.P. Gordon, C.H. Wang, C.K.N. Patel, R.E. Slusher, W.J. Tomlinson, Phys. Rev. 179 (2) (1969) 294. [11] T.J. Aartsma, D.A. Wiersma, Phys. Rev. Lett. 36 (23) (1976) 1360. [12] J.Y. Bigot, M.T. Portella, R.W. Schoenlein, C.J. Bardeen, A. Migus, C.V. Shank, Phys. Rev. Lett. 66 (9) (1991) 1138. [13] S. Mukamel, Principles of Nonlinear Spectroscopy, Oxford University Press, New York, 1995. [14] D. Zimdars, A. Tokmakoff, S. Chen, S.R. Greenfield, M.D. Fayer, T.L. Smith, H.A. Schwettman, Phys. Rev. Lett. 70 (1993) 2718. [15] P.A. Anfinrud, C. Han, R.M. Hochstrasser, Proc. Natl. Acad. Sci. USA 86 (1989) 8387. [16] P. Hamm, M. Lim, R.M. Hochstrasser, Phys. Rev. Lett. 81 (24) (1998) 5326. [17] P. Hamm, M. Lim, W.F. DeGrado, R.M. Hochstrasser, J. Phys. Chem. A 103 (1999) 10049. [18] N.-H. Ge, R.M. Hochstrasser, Phys. Chem. Commun. 5 (2002) 17. [19] M. Khalil, N. Demirdoven, A. Tokmakoff, J. Phys. Chem. A 107 (27) (2003) 5258. [20] N.-H. Ge, R.M. Hochstrasser, Trends in Optics and Photonics 72 (2002) 255. [21] J.B. Asbury, T. Steinel, C. Stromberg, K.J. Gaffney, I.R. Piletic, A. Goun, M.D. Fayer, Chem. Phys. Lett. 374 (3,4) (2003) 362. [22] J. Bredenbeck, J. Helbing, R. Behrendt, C. Renner, L. Moroder, J. Wachtveitl, P. Hamm, J. Phys. Chem. B 107 (33) (2003) 8654. [23] H. Torii, M. Tasumi, J. Raman Spectrosc. 29 (1998) 81. [24] S. Cha, S. Ham, M. Cho, J. Chem. Phys. 117 (2002) 740. [25] A. Warshel, S.T. Russell, Q. Rev. Biol. 17 (1984) 283. [26] S. Krimm, J. Bandekar, Adv. Protein Chem. 38 (1986) 181. [27] S.M. Decatur, J. Antonic, J. Am. Chem. Soc. 121 (1999) 11914. [28] R.A.G.D. Silva, J.Y. Nguyen, S.M. Decatur, Biochemistry 41 (2002) 15296. [29] M. Khalil, N. Demirdoven, A. Tokmakoff, Phys. Rev. Lett. 90 (4) (2003) 047401. [30] J. Wang, R.M. Hochstrasser, Chem. Phys. (2003) (in press). [31] M.R. Phillpot, D.P. Craig, Proc. Roy. Soc. (London) A 291 (1965) 583.
Two-dimensional infrared measurements of the coupling between amide modes of an a-helix C. Fang a, J. Wang a, A.K. Charnley a, W. Barber-Armstrong b, A.B. Smith III a, S.M. Decatur b, R.M. Hochstrasser a,* a
Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, PA 19104-6323, USA b Department of Chemistry, Mount Holyoke College, South Hadley, MA 01075, USA Received 8 September 2003; in final form 14 October 2003
Published online:
Abstract The 2D IR spectra of doubly isotopically substituted a-helices with 13 C@16 O and 13 C@18 O labels enabled the couplings between amide-I modes separated by one, two and three residues to be measured. The magnitudes and signs of couplings between the isotopomers and between them and the helix exciton band states confirm that the states of the helix and isotopomers are delocalized. The results are compared with simulations. The off-diagonal anharmonicities agree reasonably with a set of couplings that derive from transition charge interactions except for nearest neighbors for which the coupling is modified by through bond interactions. Ó 2003 Published by Elsevier B.V.
1. Introduction The IR spectra of proteins are intimately connected with their complete three dimensional structures on the length scale of chemical bonds. However, their vibrational transitions are not spectrally resolved. Our strategy is to insert both 13 C@16 O and 13 C@18 O labels into secondary structures. Since their isotope shifts are different, a pair of isotopic peaks are created and 2D IR spectroscopic methods can then be used to analyze
*
Corresponding author. Fax: +1-215-8980590. E-mail address: [email protected] (R.M. Hochstrasser). 0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.cplett.2003.10.111
the coupling between those specific pairs of molecular transitions. The development of methods to obtain structural changes in proteins is an important experimental challenge to which 2D IR [1–8] can contribute significantly. The photon echo is an essential component of 2D IR [9]. The earliest echoes on molecules were in the infrared [10], soon followed by nanosecond two pulse echoes in the visible [11]. As optical lasers improved, measurements were extended to faster responding liquids and glasses [12], to heterodyning, gating and three pulse methods (see e.g., [13]) and meanwhile the IR echo was extended to the picosecond regime [14]. Femtosecond infrared experiments on proteins and aqueous systems [15] evolved to femtosecond three pulse echoes of
C. Fang et al. / Chemical Physics Letters 382 (2003) 586–592
ions in water [16], peptides and proteins [17], and finally to heterodyning of phase locked IR echoes which enabled the assembly of complex multidimensional vibrational spectra [2]. Earlier, pump– probe 2D IR spectra on peptides and proteins [1], which relate to the real part of the heterodyned 2D IR experiment [18], had been reported. Recently, dual frequency 2D IR was accomplished [8] and 2D IR spectroscopy of vibrators [18,19] is currently expanding in the study of liquids [20,21], glasses and biological systems [22]. In this work, the labels are inserted into residues of an a-helix and the 2D IR is used to determine the couplings. Also the population times, the inhomogeneous distributions and the correlations of the fluctuations of the vibrational frequencies at the various sites can be measured. We also simulate the complete 2D IR spectra neglecting through bond [23,24] and polarizability [25] effects and calibrate the method from known helix properties [6,26–28].
2. Methods and experimental results More details of the methods and results will be given in a future publication.
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2.2. Linear spectroscopy Fig. 1 presents the linear IR data for each of the compounds studied with the main helix peak fitted to two gaussian contributions, one from helical and the other from more random structures. Another gaussian centered at 1596 cm1 accounted for the 13 C in natural abundance. The main helix exciton band (the 23 or 24 unlabeled residues) of [0,11], [11,13] and [11,14] peaks at about 1631.7 0.5 cm1 (1633 cm1 for [12,13]) and it has a FWHM of 28.3 cm1 that incorporates both the A (z polarized) and E (x; y polarized) helix bands. The 13 C@16 O isotopomer fit peaks at 1594 0:3 cm1 and the 13 C@18 O at 1570:7 0:8 cm1 . The separations between the two isotopic labels are 24.7, 22.4 and 28 cm1 in [11,13], [11,14] and [12,13], respectively. The gaussian fit FWHM for the 13 C@18 O label is 15.2 cm1 . The amide-I mode of a 13 C@18 O labeled peptide with molecular formula H3 CCH(NH2 HCl) 13 C@18 ONHCH2 CH(CH3 )2 had a peak (1597.6 cm1 ) extinction coefficient of 314 M1 cm1 compared with 310 M1 cm1 for the 12 C@16 O salt amide peak (1657.2 cm1 ) indicating that the transition moment magnitudes, (proportional to pffiffi e), are equal and the isotope shift is 59.6 cm1 . 2.3. Pump–probe experiments
2.1. Materials The isotopically labeled 25-residue alanine rich helical polypeptides based on Ac-(A)4 K(A)4 K(A)4 K(A)4 K(A)4 Y-NH2 containing the isotopic amide carbonyl labels 13 C@16 O and 13 C@18 O were obtained by standard peptide synthesis, purified by reverse- phase HPLC and characterized by electrospray mass spectrometry [27]. The 18 O amino acids were synthesized by 18 OH2 exchange. These syntheses will be described in detail elsewhere. The isotopomers contain none, one or one each of the isotopic amide carbonyl labels 13 C@16 O and 13 C@18 O which are referred to as [alanine residue with 13 C@16 O, alanine residue with 13 C@18 O]. We examined: [noneB0 , noneB0] (data not shown), [0,11], [12,13], [11,13] and [11,14]. The central residues are nearly completely helical in phosphate buffer at 0 °C [28], the conditions of all experiments here.
The anharmonicity of the amide 13 C@18 O group of 14.2 cm1 was obtained from the broad-bandpump/broad-band-probe [1] of the 13 C@18 O model compound, whose 1 ! 2 transition intensity is ca. double that of 0 ! 1. The pump–probe spectra of [12,13], [11,13] and [11,14] provided the anharmonicities for both isotopically substituted amides. The decay of the pump–probe signal gave 545 fs for the T1 relaxation time of the 13 C@18 O vibrator. The population relaxation times of the overtone states of the isotopically replaced amide modes of [11,13] and [11,14] were deduced to be about 360 fs by attributing the increased width of the 1 ! 2 transition to a T1 process. 2.4. 2D IR spectroscopy The nonlinear spectra were obtained precisely as in previous heterodyned echo experiments at
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Fig. 1. The linear FTIR spectra of the isotopomers [0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d). The thin lines are fits. The stick heights represent the relative intensities.
6 lm [2,3,7,18]. Three infrared pulses arrived with interval s, between the first and second pulse, and a waiting time T ¼ 0. The signal at wavevector k1 þ k2 þ k3 was detected as a function of s and t
(the interval between the heterodyning and signal fields). A double Fourier transform in s and t yielded the 2D IR spectrum along the frequency axes xs and xt . The center frequency of the 120 fs
Fig. 2. Absolute value 2D IR rephasing spectra. ([0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d)). Sixty contour lines were drawn from zero to the maximum intensity.
C. Fang et al. / Chemical Physics Letters 382 (2003) 586–592
mid-IR pulses was at the mean of the 13 C@18 O and 13 C@16 O peaks. For [0,11], the exciton band states and the 13 C@18 O labeled amide band clearly appear in the 2D IR spectrum (see Fig. 2), along with the cross peaks between them. The signal from 13 C@16 O modes in natural abundance was seen but is not evident in Fig. 2. The other isotopomers exhibit the spectral features of the labeled amides as shown in Figs. 2b–d. After adjustment with a constant phase factor found from comparisons with pump–probe spectra and some normalization, the absorptive spectra were obtained by adding the rephasing ðk1 arrives first, R) and non-rephasing ðk2 or k3 arrives first, NR) spectra [7,18,29]. Each of the absorptive 2D IR spectra of Fig. 3 in the region of the 13 C@16 O and 13 C@18 O amide transitions display eight resonant peaks: two pairs of diagonal peaks corresponding to the v ¼ 0 to v ¼ 1 and v ¼ 1 to v ¼ 2 transitions, a cross peak pair appeared above and below the diagonal. The narrow-band-pump/ broad-band-probe spectra were computed from the 2D IR data set by using a 10 cm1 FWHM gaussian distribution centered at either the 13 C@16 O or 13 C@18 O amide-I resonance and projecting its real part onto the xt axis to obtain the off-diagonal anharmonicity values for [12,13], [11,13] and [11,14] of
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D12;13 ¼ 9:0 1:0, D11;13 ¼ 3:2 0:8 and D11;14 ¼ 4:5 0:6 cm1 , respectively.
3. Discussion The shaded regions in Fig. 4 represent the oneand two-exciton bands of the tagged helix with isotopomer levels located below these bands. In a typical Liouville path represented by the dashed (ket side) and solid (bra side) arrows, the second two pulses transfer the vibrational coherence from one isotope to the other by means of transitions involving the two quantum levels. The three upper levels are the two overtones and the combination band whose energies are again determined by their couplings to each other and to the band states. The dynamical parameters of each of the isotopomers are equal within 20% of the dephasing times. The plots of the absolute value of the T ¼ 0 response along s for different xt gave comparable peak shift signals for all isotopic components. The isotopomer transitions are sharper than the band transitions and the spectra of the helix excitons are narrowed in the direction perpendicular to the diagonal, resulting from the echo-like response of the 2D IR signals. The isotopomer
Fig. 3. Absorptive spectra of samples a–d defined in Fig. 2. The relative signal strengths were chosen for each spectrum to show the proper contrast between the negative (dark) and positive (bright) features (contour lines drawn in 2% intervals).
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zero order energy 2ε
ε (k1)+ε (k2)
two-quantum states
2ε-∆b-2δb 2ε-δa-δb 2ε-∆a-2δa
Energy
ε ε-δb ε-δa
ε (k)
one-quantum states
0 Fig. 4. Relevant energy levels of the isotopically tagged helix. The isotope shifts are da (13 C@18 O) and db (13 C@16 O), while Da and Db are diagonal anharmonicities. The shaded areas represent the helix one- and two-exciton bands.
transitions are more symmetric and their inhomogeneous widths are representative of fluctuations having standard deviation of ca. 4 cm1 at single amide-I sites. The cross peaks show that the isotopomer residues are coupled in all cases: the state containing one excitation in each isotopomer is never at the same energy as the sum of the two isotopomer energies. In order to estimate the coupling constants from these measured off-diagonal and diagonal anharmonicities, a model is needed for both linear and nonlinear spectra. As a first simple approach, we considered the energies of a separated pair of tagged residues, 13 C@16 O with observed frequency m16 and 13 C@18 O with frequency m18 , having v ¼ 1 ! v ¼ 2 transitions at m16 D16 and m18 D18 and a combination band frequency of m16 þ m18 D16;18 where D16;18 is the off-diagonal anharmonicity. We estimated D16 , D18 and D16;18 assuming that only two modes were involved [5]. Robust values of the unperturbed diagonal anharmonicities are obtained from model compounds and confirmed from the 2D IR spectra of the isotopomeric helices. The Hamiltonians Hs and
Hd of the single (2 2) and double (3 3) excitations are written in the basis of the uncoupled isotopomers where D16;18 ¼ 0; the harmonic approximation sets the part of the bilinear transfer matrix element between pffiffiffi v ¼ 1 and v ¼ 2 states of different groups at 2 times those for v ¼ 0 to v ¼ 1. The observed energies are the eigenvalues of Hs and the differences between those of Hs and Hd . It is a simple calculation to find the coupling constants, bij , needed to generate the observed set of two fundamentals, two overtones and one and we find values: combination band, b12;13 ¼ 9:5; b11;13 ¼ 5:0; and b11;14 ¼ 5:5 cm1 . However, the known diagonal and off-diagonal anharmonic shifts could not be simultaneously fit by this approach. For a 13 C@16 O residue, a more correct approach should incorporate the coupling of it to the helix one- and two-exciton states. While the foregoing Ôseparated pairÕ model is conceptually simple it cannot be entirely correct, because the isotopomers do not only interact with each other but also with the remaining 12 C@16 O amides of the helix. We recently reported an empirical computational method [30] for predicting the linear and 2D IR spectra of amide-I modes for a-helices of finite length. It incorporates transition charge interactions between all except nearest neighbor amides. The nearest neighbor couplings are obtained from density functional theory calculations. The inhomogeneous broadening is incorporated by averaging over Hamiltonians that contain gaussian random fluctuations of their diagonal frequencies. The input includes atomic coordinates for the helix. The pulse frequency and spectral width were chosen to match those used in the experiment. The homogeneous broadening is chosen to match observations on peptides. We also showed explicitly that a Hamiltonian matrix having equal diagonal energies and with couplings obtained by this recipe gave results that were very close to the density functional results for peptides having up to four amide units, confirming the earlier idea that the spectra of nearly degenerate sets of amide-I modes can be considered without regard to their interactions with other types of modes. For Ramachandran angles / ¼ 58°, w ¼ 47° and x ¼ 180° corresponding to a typical a-helix, we obtained a complete set of model
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coupling constants, of which some of the largest ones are: b12 ¼ 7:5; b13 ¼ 4:7; b14 ¼ 6:1; b15 ¼ 0:5; and b16 ¼ 0:7 cm1 , where b12 means nearest neighbor, b13 is next to nearest neighbor and so on. The simulated 2D IR spectra are shown in Fig. 5 using zero order isotope shifts of da ¼ 65 and db ¼ 44 cm1 and a diagonal anharmonicity of 14 cm1 . The simulation generates the essential features of the results as a comparison of Figs. 2 and 5 illustrates. The magnitudes of the couplings calculated in this manner are similar to those deduced from the separated pair modeling of the data, and their signs are consistent with expectations for the intensities in the linear spectra calculated from the separated pair wave functions using perturbation theory. The relative intensities of the transitions in the linear and 2D IR spectra depend on the spatial separations of the modes, the angles between the transition dipoles and the signs of the couplings. The intensities of the linear spectra from the full simulation are similar to the observed values suggesting that the signs and magnitudes of the computed couplings given above are appropriate. However, the signs of the coupling constants are
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most confidently determined from the 2D IR because these signals are freer from the background and baseline subtraction ambiguities present in the linear spectra. It is evident from the results shown in Figs. 2 and 3 that the 13 C@18 O peak is definitely stronger than that of 13 C@16 O in [11,13] and [11,14] but considerably weaker than that of 13 C@16 O in [12,13]. By comparing expectations for these ratios with the simulations and with simple perturbation models, we can conclude that b12 > 0, b13 < 0 and b14 < 0. These signs are those expected from transition charge or transition dipole coupling. The simulated off-diagonal anharmonicities are in the correct order and within better than a factor of two of experiment: we find D12;13 ¼ 5:2, D11;13 ¼ 2:5 and D11;14 ¼ 3:1 cm1 . The shifts of the isotopomer peaks can be estimated from perturbation theory of isotopic trap spectra [31] that incorporate the coupling to the exciton band of the helix. The result depends on the factor B2 ¼ ðb212 þ b213 þ b214 þ ), and B2 ¼ 117 (cm1 )2 for our parameters, which causes a )1.80 cm1 shift of all the 13 C@18 O peaks and )2.66 cm1 for all the 13 C@16 O peaks computed from B2 =da and B2 =db , respectively. The remaining shifts are from the interaction between the
Fig. 5. The simulated 2D IR spectra of [0,11] (a), [12,13] (b), [11,13] (c) and [11,14] (d). These are absolute value spectra with da ¼ 65 and db ¼ 44 cm1 , polarization hzzzzi and gaussian frequency fluctuation of 4 cm1 . The diagonal peak at xt 1645 cm1 is due to the failure of the energy fluctuations to properly capture the broadening of the exciton transitions.
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13
C@18 O and 13 C@16 O levels. These shifts are da Þ ¼ 1:81; 0:71 and )1.20 cm1 for the C@18 O level of [12,13], [11,13] and [11,14], respectively. The corresponding shifts for the 13 C@16 O level are b2ij da =db ðda db Þ ¼ 3:96; 1:55 and 2.62 cm1 . The perturbation theory results agree reasonably with experiment although they are inadequate for computation of the off-diagonal anharmonicities of tagged helices. b2ij db =da ðdb 13
4. Conclusions Insertion of 13 C@16 O and 13 C@18 O labels at known residues on the helix enabled the coupling and the delocalized character of the amide-I modes to be measured. The off-diagonal anharmonicities agree reasonably with couplings that derive from transition charge interactions for all but the nearest neighbors, which need through bond interaction. An essential point about our procedure is that its goal is to find 2D IR signatures of anharmonicities and hence of conformations in complex structures. This Ôtop downÕ approach to peptide structure determination is already very useful and hopefully will make contact with and be given a much firmer basis by Ôbottom upÕ approaches involving detailed theory of anharmonicity and high resolution experiments on peptides of ever increasing size. The signals shown in Fig. 2 indicate that one in 35 residues could have been detected, meeting the requirements for applications of the 2D IR method to single residue substituted small proteins. Acknowledgements This research was supported by grants: NIH (GM 12592 and RR01348) and NSF to RMH; and NSF (CHE9984844) and NIH (R15GM54334) to SMD.
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