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Dualfrequency 2DIR spectroscopy heterodyned photon echo of the peptide bond

Contributed by Robin M. Hochstrasser
Abstract
The structure fluctuations of the peptide bond interacting with solvent are examined through the coupling and correlations of the frequency distributions of amide I and amide II transitions. The fluctuations of the two modes are anticorrelated as a result of the solventinduced changes in the mixing of the dominant valencebond structures of the peptide. Significant anharmonic coupling of the two modes is seen. The results are the application of a new approach to twodimensional infrared (2DIR) spectroscopy in which the pulse sequences used to produce the vibrational echoes incorporate two frequencies. This dualfrequency arrangement greatly extends the capabilities of 2DIR spectroscopy by allowing the coupling between widely separated modes to be characterized in analogy with heteronuclear NMR. The experiment exposes the cross peaks, representing the mode coupling, free of the interference of the strong diagonal peaks that typically dominate 2DIR spectroscopy. The alignment and dephasing of coupled transitions, in this example the amide I and amide II transition dipoles, is also determined by these experiments.
Multidimensional IR spectroscopy, in particular 2DIR spectroscopy, is a powerful new method with which to obtain the time dependence of structural features of complex molecular systems, including peptides and proteins, under ambient conditions in solutions (1–7). Furthermore, the methods allow the determination of key parameters of the anharmonic potential surfaces of peptides and hence provide important tests of theoretical calculations of molecular structure and dynamics (8, 9). These coherent nonlinear IR techniques permit experimental determination of the coupling and angular relations of vibrators by using experimental protocols that are analogous to those developed for NMR. The first such experiments concerned the amide I modes of peptides, which are mainly C⩵O vibrators (1–5, 10–12). In such cases all of the relevant frequencies of an interacting ensemble of modes could readily be bracketed by the spectral bandwidth of 120fs IR laser pulses. The response of such a system to sequences of three pulses, each with the same center frequency in the amide I region, gave rise to coherent signals, the 2D and 3D correlation spectra of which yielded the relevant structural and dynamical information. In a recent advance, 2DIR spectroscopy experiments incorporating two pulses with different frequencies, one in the N—H and the other in the amide I region of peptides, were successful in measuring the coupling and angular relations between N—H and C⩵O modes in some simple peptides (13–15).
In this article we report a dualfrequency 2DIR spectroscopy heterodyned photonecho experiment. The 2DIR spectra, which require manipulation of the vibrational coherences by the interaction of short laser pulses with inhomogeneously broadened distributions of transition frequencies, consist of diagonal features and cross peaks. The diagonal peaks are independent properties of each of the anharmonic modes, but they do not readily provide the correlations between modes that relate to 3D structure. On the other hand, the cross peaks are present only when the modes are interacting, and they contain the information essential to determining structure and structure distributions. In 2DIR spectra the diagonal peaks are often much stronger than and interfere with the cross peaks, so it is important to find methods that can eliminate them from the signals. One such approach is to choose polarization conditions for the laser pulses involved in the heterodyne echo experiment that entirely eliminate diagonal contributions (16, 17). However, a new type of experiment is needed that effects this elimination and permits measurements of the correlations of modes that are widely separated in frequency. The dualfrequency IR echo experiment reported in this article has this purpose. It allows, if necessary, the complete elimination of the diagonal peaks from the 2DIR spectra and focuses attention on the coupling, frequency distributions and angular relations between pairs of modes.
Methods
IR Pulse Generation.
The dualfrequency 2DIR spectroscopy experiment uses a Ti:Sapphire laser system (ClarkMXR CPA2001) to provide IR laser pulses at 775 nm with a 130fs pulse duration and 700μJ pulse energy to pump an optical parametric amplifier. The total output of the optical parametric amplifier was 70 μJ per pulse, which was split into two parts to enable pumping of two difference frequency generators, which produced independently tunable, phaselocked midIR pulses. For the given optical parametric amplifier frequency the tuning range in the 6μm region was 150 cm^{−1}. In the Nmethylacetamide (NMA) experiment, one difference frequency generator produced IR pulses of 0.15 μJ per pulse with a central frequency ω_{1} = 1,675 cm^{−1} propagating toward the sample in direction k_{1} (Fig. 1) and local oscillator pulses having 0.01 μJ per pulse, the latter being further attenuated before use. The output of the second difference frequency generator (≈0.3 μJ per pulse) was split into two equal parts to generate two IR beams with central frequency ω_{2} = 1,540 cm^{−1} for the NMA experiment and vector directions k_{2} and k_{3}. A halfwave plate and a wiregrid polarizer controlled the polarization vector of each beam. The intensities of each of the pulses were measured accurately to be used in the spectral simulations. A mercurycadmiumtelluride detector (EG & G, Judson, PA) recorded the sum of the field generated in the k_{1} − k_{2} + k_{3} direction and the local oscillator field (Fig. 1), and the heterodyned signal was processed.
Beam Configurations.
The IR beams were tuned such that one is centered on the amide I band of NMA (k_{1}, ω_{1}), and the other is close to the amide II band (k_{2} and k_{3}, ω_{2}) (Fig. 2). If the spectra of these pulses at ω_{1} and ω_{2} are chosen to have no overlap, then there can be no diagonal peak in the direction k_{1} − k_{2} + k_{3}, because the generated field must be in the frequency range of ω_{I} − ω_{II} + ω_{II} = ω_{I}. However, the intensities of the k_{2} and k_{3} beams centered at the amide I band were chosen to have ≈8% of their peak values at the frequency of the amide II band. Similarly, the intensity of the k_{1} beam centered at the amide II band presented a small fraction (≈4%) of its peak value at the amide I band region. These small contributions of band overlap enabled weak diagonal amide I and amide II reference peaks to be recorded in the 2DIR spectra in addition to the dominant cross peak.
ThreePulse Integrated Photon Echo.
In the integrated threepulse echo experiment all three pulses have the same frequency, either ω_{I} or ω_{II}. The echo signal at each chosen value of τ and T is sent directly to a detector without heterodyning and integrated over the time interval t by the response time of a detector in a manner that has already been described in detail (18–20). The grid of (τ, T) data was globally fitted to obtain the timecorrelation functions of the vibrational frequencies that are required to interpret the crosspeak data obtained by 2DIR spectroscopy. The integrated echo of NMAD was studied previously in ^{2}H_{2}O (4).
DualFrequency Heterodyned Transient Grating.
The interval τ is fixed at zero in this experiment such that a linear combination of amide I and II transitions is prepared (see Fig. 3). This coherence is transferred after an interval T. The signal is obtained as a function of T and t. Fourier transformation along t yields a timedependent transientgrating spectrum in the region of the amide I band that oscillates with the frequency difference of the amide I and II transitions.
Beam Coherence.
When the beams from both difference frequency generators were combined in a Michelson interferometer and sent to a monochromator a strong spectral interferogram was observed when the delay between the two pulses was scanned. These interferograms depended on the choice of the center frequencies of the two pulses, and the measurements served to verify the stability of the phase difference of the two sources persisting over periods of many hours. The frequency dependence of the phase of each pulse was not measured, but it was verified that phase variations expected from the optical materials used did not affect the conclusions. Comparable phase stability was not yet achieved when pulses from two optical parametric amplifiers were combined in the interferometer.
Sample.
The sample was a 150 mM solution of NMA in DMSO contained in a CaF_{2} cell having a path length of 25 μm. The linear IR spectrum is shown in Fig. 2.
Modeling the 2DIR Spectra.
In the 2DIR experiment on NMA we chose the time delay between the second two of the incident sequence of three pulses to be zero. Thus in the limit of largefrequency bandwidth there are only two times in the problem: τ, the delay between the first pulse and the second pair; and t, the period of free evolution between the second pair and the local oscillator pulse. We used two different pulse sequences in the experiment that we refer to as rephasing and nonrephasing sequences. For the rephasing sequence the k_{1} (ω_{1}) and k_{3} (ω_{2}) were at a fixed zero delay, and the k_{2} (ω_{2}) pulse delay was scanned. In the nonrephasing sequence the k_{1} (ω_{1}) and k_{2} (ω_{2}) beams were at a fixed time delay of zero, and the k_{3} (ω_{2}) pulse was scanned. These scans generated the τaxis data. Heterodyned photonecho signals were recorded for every delay τ by scanning the local oscillator pulse over a time interval t of ≈2 ps in steps of 10 fs. The experimental 2D matrix S(τ, t) was double Fourier transformed along t and τ to generate a complex 2DIR spectrum, S̃(ω_{τ}, ω_{t}).
The pathways that produce the cross peak for the rephasing (R_{1} and R_{2}) and nonrephasing (R_{3} and R_{4}) sequence experiments are illustrated in Fig. 3. These diagrams represent time lines for the interaction of successive pulses with a molecule in the sample for the particular set of vector directions of the incident pulses (21). In Fig. 3 the symbols I and II refer to the amide I or amide II excitations, and the combination of left and right indices at any vertical position along the time line represents the coherence existing at that time. For example, the system begins in an amide II transition coherence. After the interaction with the pulse in direction k_{1} in diagram R_{2} of Fig. 3 the system is in a coherent superposition of I and II vibrational states. Pulse k_{3} completes the coherence transfer to the amide I transition. The index I + II in diagrams R_{1} and R_{3} corresponds to the combination state of the amide I and amide II modes. As indicated above, in the 2DIR spectroscopy experiments the value of T, shown in Fig. 3 as the delay between k_{1} and k_{3} in the rephasing experiment or between k_{1} and k_{2} in the nonrephasing experiment, was set equal to zero.
An analysis of the integrated threepulse echo signal yielded the vibrational frequency correlation functions for the vibrators (data not shown). The fast component of the correlation function is the correlation time of a motionally narrowed contribution to the line width. After the fast decay the correlation function and peak shifts (18) showed the decay on the fewpicosecond time scale, whereas a plateau indicates a static distribution of structures. Up to ≈500 fs, during which the 2DIR signals are strongest, the decay is slow enough for us to interpret the data in terms of a Bloch dynamics theory (5), which permits a simplification of the expressions for the 2DIR spectrum. Inclusion of the evident spectral diffusion in the modeling did not change the results significantly.
According to the theory of 2DIR spectroscopy (5, 22, 23) the crosspeak signal in the Bloch approximation obtained by adding results from the rephasing S_{R}(τ,t) and nonrephasing S_{NR}(τ, t) pulse sequences is predicted to be 1 where the conventional Bloch relaxation function is G_{0}(t, τ) given by The parameters ω_{I} and ω_{II} are the angular frequencies (i.e., ω/2πc is the frequency in cm^{−1}) and σ_{I} and σ_{II} the inhomogeneous widths of the amide I and amide II transitions, the T_{1} values are the population relaxation times of the indicated states, D is the rotational diffusion coefficient, and the γ values are the total homogeneous dephasing rates of the amide I and amide II fundamental transitions. The correlation coefficient between the static distributions of amide I and amide II frequencies is given by f = 〈x_{I}x_{II}〉/σ_{I}σ_{II}, where x is the frequency deviation from the mean of the indicated frequency distribution. The timeindependent polarization anisotropy (16) is given by the product of direction cosines 〈a_{α}b_{β}c_{γ}d_{δ}〉, where the first through fourth pulses, polarized a, b, c, and d in the laboratory frame, excite the transition dipoles α to γ in the molecular frame. The offdiagonal anharmonicity is Δ_{I,II}, chosen such that the frequency of the transition between II and I + II is ω_{I} − Δ_{I,II}. By inspection of Eq. 1 the real part of the 2DIR spectrum, obtained from the double Fourier transform of S(τ, t), displays peaks (ω_{II}, ω_{I}) and (ω_{II}, ω_{I} − Δ_{I,II}). In practice, a state to which the amide II population relaxes was also included in the pathways in the manner of figure 2 in ref. 13.
When f = 0, the case of uncorrelated distributions, the signal with cosh = 1 and sinh = 0 reduces to the difference between two components having opposite signs that are slightly displaced (by Δ_{I,II}) along the ω_{t} axis. The node separating the positive and negative parts of the 2D spectrum is then parallel to the ω_{τ} axis in the region of ω_{τ} = ω_{II}, and thus we refer to this as an “untilted” spectrum. The effect of finite f is to tilt or twist this spectrum one way or the other depending on the sign of f. The node adopts a positive slope when f > 0 and a negative slope when f < 0. Because the 2DIR spectra contain both absorptive and dispersive contributions, this tilting is present in S̃_{R}(ω_{τ}, ω_{t}) and S̃_{NR}(ω_{τ}, ω_{t}) even for uncorrelated modes. Therefore an accurate determination of the frequency correlation requires fitting the data to theoretical simulations of the purely absorptive spectrum, S̃(ω_{τ}, ω_{t}), isolated by adding the complex rephasing and nonrephasing spectra after the procedure from NMR (24), which was applied recently to 2DIR spectroscopy (5, 25, 26).
Results
Dualfrequency 2DIR absolute magnitude spectra S̃_{R}(ω_{τ}, ω_{t}) and S̃_{NR}(ω_{τ}, ω_{t}) corresponding to the rephasing and nonrephasing sequences are shown in Fig. 4. The cross peak caused by coupling of the amide I and amide II modes is much stronger than the diagonal peaks and is tilted slightly toward the antidiagonal direction. The amide I diagonal peak at 1,662 cm^{−1} is stronger in the rephasing spectrum, which implies that the amide I band consists of an inhomogeneous distribution of frequencies that persists over the experimental time scale (5, 23, 27), again justifying the use of Bloch dynamics. Three separate measurements showed that the cross peak is 1.23 ± 0.05 times stronger in the nonrephasing spectrum. This ratio is sensitive to the correlation coefficient. For example, when the two vibrators are uncorrelated it is 1.0, whereas for negative f the ratio is always greater than unity. Therefore a negative correlation between the amide I and amide II frequency distributions is indicated.
As expected, the real parts of the 2DIR spectroscopy cross spectra in the nonrephasing and rephasing sequences exhibit tilted resonances (see Fig. 5). The absorptive spectra Re{S̃(ω_{τ}, ω_{t})} modeled with different correlation factors are shown in Fig. 6. The tilt of both negative and positive peaks is very sensitive to the correlation factor and exists only when the frequencies of the vibrators are correlated (Fig. 6 a and c). It is the negative correlation that causes the tilt toward the antidiagonal direction of the absorptive spectra similar to the observations (Fig. 7a). The tilt angle is also affected by the width of the frequency distributions in each of the interacting modes. These inhomogeneous contributions to the line widths for both amide I and amide II transitions were acquired from the analysis of the diagonal peaks.
Diagonal Spectra.
The 2DIR spectroscopy amide II diagonal spectrum is shown in Fig. 8 as the sum of rephasing and nonrephasing sequences. In this case the tilt angle of 0.26 ± 0.04 radians, defined as the angle between the ω_{τ} axis and the line parallel to the node in the real part of the 2DIR spectrum in the region of ω_{τ} = ω_{II}, determines the inhomogeneous contribution to the line width. Simultaneous fitting of the absorptive 2DIR spectroscopy, which yields the ratio σ_{II}/γ_{II}, and the linear spectra, which give a combination of the two parameters, allowed both σ_{II} and γ_{II} to be determined accurately. The modeling establishes σ_{II}/2πc = 11.2 cm^{−1} and γ_{II}/2πc = 12.3 cm^{−1}, corresponding to a ratio of σ_{II}/γ_{II} = 0.91. The population relaxation time T_{1} was determined experimentally to be 0.3 ps for the amide II mode, and thus the only adjustable parameters in this fitting procedure were the pure dephasing of amide II, determined to be 1.5 ps, and σ_{II}. A similar analysis for the amide I diagonal peak results in σ_{I}/2πc = 7.3 cm^{−1} and γ_{I}/2πc = 4.0 cm^{−1} giving a ratio of σ_{I}/γ_{I} = 1.8. These parameters are needed to interpret the crosspeak signals.
Cross Peaks in DualFrequency 2DIR Spectra.
By using spectrally shaped laser pulses the crosspeak profile can be measured accurately, and the coupling and the correlations of the frequencies of the two vibrators can be determined. The correlations help to establish mechanisms for the coupling of modes, thus they add to the structural constraints. The correlations between the frequencies of one of the vibrators and the offdiagonal anharmonicity can readily be incorporated into the modeling (13), but no indication of such correlations was observed for the amide I/II modes of NMA.
The crosspeak features in the absorptive spectrum (Fig. 7a) are tilted in the antidiagonal direction by an angle of −0.045 ± 0.006 radians. A simulation of the dualfrequency 2DIR spectroscopy cross peak (Fig. 7b) with the parameters for amide I and amide II transitions given above for the diagonal peaks gave a frequency correlation factor of f = −0.28 ± 0.06. The crosspeak tilt angle is more sensitive to the inhomogeneous contribution σ_{II} than that of σ_{I}. This is because the amide II band has a much smaller value of σ/γ, which results in a blurring of the frequency distribution by the larger homogeneous broadening.
Polarization Effects.
The ratio of the 2DIR spectral amplitude at the isolated cross peak for parallel to that for perpendicular polarized fields at ω_{1} and ω_{2} was found to be 1.35 ± 0.1.
Discussion
The importance of 2DIR spectroscopy as a structural and dynamical probe of peptides and other complex systems lies in its ability to simplify spectra and yield properties that are not available from linear spectra. However, the spectra are often diffuse and dominated by diagonal signals that obscure the interesting new information carried by the cross peaks, which may arise because of very small coupling constants. The present results show that by using dual frequencies the cross peaks can be isolated and studied independently of the diagonal peaks. Furthermore the method permits the measurements of coupling between modes that are separated in frequency by more than the bandwidth currently achievable by single laser pulses in the IR. For example measurement of the coupling of the N—H and C⩵O modes of peptides would require singlefrequency pulses having a width of 9 fs centered between the two modes. However, the vibrational dynamics of the coupled modes is sufficiently slow that it can be measured with 250fs pulses. Therefore the method of choice will be dualfrequency 2DIR spectroscopy either by means of IR echoes, exemplified by the experiments described here, or the pumpprobe 2DIR spectroscopy methods described in our earlier work on N—H/C⩵O coupling (14).
Coupling Strength.
The coupling strength was determined from comparisons of the diagonal amide I mode signal and the dualfrequency cross peak. An offdiagonal anharmonicity of Δ_{I,II}/2πc = 3.5 ± 0.5 cm^{−1} was obtained, clearly indicating a significant coupling between the two modes. This may seem to be a small effect, but it should be remembered that the observed signal, Eq. 1, is the difference between two large quantities that disappears if the modes are uncoupled when t < T. The existence of the coupling is confirmed by the observation of cross peaks and of the oscillations seen in the heterodyned transientgrating signal (data not shown). The experimental result stands in contrast to recent computations that have predicted the anharmonic coupling between the amide I and amide II modes in the same peptide unit to be zero (28). The coupling, β, between the I and II modes that is implied by the measured anharmonicity can be estimated in lowest order from a threelevel model in which the I + II combination band couples to both the I and II overtones through a bilinear interaction β(ω_{I}ω_{II}/ℏ^{2})^{1/2}Q_{I}Q_{II}, where the Q values are the normal (harmonic) modes. This threelevel model, the predictions of which are obtained by diagonalization of a threebythree matrix in the basis of 2 × I, 2 × II, and I + II, predicts a value of 27 cm^{−1} for β, which does not seem unreasonable for the interaction of two transition charge distributions spread over the same set of four peptide atoms.
Frequency Correlations.
A negative correlation between amide I and amide II frequencies must be related to the bondorder changes induced by solvent and structural fluctuations. The two dominant valencebond structures for the ground state of NMA are shown in Fig. 9. The N—C doublebond character of ≈40% (29) is responsible for the planarity of the peptide group. The interactions of NMA with DMSO in the different solvent configurations cause it to adopt a range of structures. Each structure is considered to correspond to a slightly different admixture of the dominant valencebond functions. Those structures with more doublebond character of the carbonyl group will have less N—C doublebond character. The amide I band is mainly the C⩵O stretch motion, thus its frequency is reduced in structures with more N—C doublebond character. The amide II mode is significantly an N—C stretching motion, and thus its frequency would be increased accordingly. This provides an explanation as to why the frequencies in the distributions of the two modes are anticorrelated. The analysis provides an example of the power of 2DIR spectroscopy in exposing the detailed content of structural distributions and has obvious applications in experiments with more complex peptides where structural distributions are functionally important.
Angular Properties.
The 2DIR spectral amplitudes were measured for the fields at ω_{1} and ω_{2} having parallel and perpendicular polarizations. The ratio, P, of these two measurements according to Eq. 1 is 〈Z_{II}Z_{I}Z_{II}Z_{I}〉/〈Z_{II}X_{I}Z_{II}X_{I}〉, which is directly related to the alignment of the amide I and II transition dipoles (16, 23) through the relationship where θ_{I,II} is the angle between the transition moments and the average, 〈 〉, is over the distribution of alignments found in the structure distribution. The two possible alignments obtained from the experimental ratio at the peaks of the distributions are 45 ± 5° and 135 ± 5°. Assuming the amide I transition dipole to be 20° from the C⩵O bond (13, 30) and the OCN angle to be ≈123° (29), the preferred direction of the amide II mode is 8 ± 5° to the N—C bond and 65 ± 5° to the C⩵O bond. The former value compares well with 12°, obtained recently for the amide II dipole alignment to the N—C bond in AcProNHMe (13), and the latter is close to the value of 73° reported earlier for this alignment (30).
DualFrequency Echoes.
Traditional pictures of photon or spin echoes often imply that the creation of the macroscopic signal requires rephasing to occur within the same inhomogeneous distribution that was involved in the coherence evolution after the first pulse (27, 31). We see here that what is important in obtaining an echo are the correlations between the distributions that are present during τ and t, which possibly may have quite different origins and may lose and regain macroscopic polarization on different time scales. Socalled twocolor echoes have been reported for electronic transitions by using visible laser pulses (32, 33).
Conclusions
Dualfrequency heterodyned 2DIR spectra are obtained for NMA in DMSO. Tunable suppression of the diagonal peak contribution to 2DIR spectroscopy is demonstrated up to complete elimination. Construction of 2DIR spectra of the isolated cross peaks is shown to be a useful and convenient way to visualize and measure frequency correlations in 2DIR spectroscopy. The amide I/amide II frequency correlation factor in NMA is determined to be −0.28 ± 0.06, consistent with solventinduced structure fluctuations of the admixtures of principal valencebond structures of the peptide bond. The coupling between amide I and II modes is estimated as 27 cm^{−1} from a measured mixedmode anharmonicity of 3.5 cm^{−1}.
Implementation of dualfrequency spectrally shaped coherent IR pulses to 2DIR spectroscopy opens up new and exciting possible applications to biological macromolecules. Current laser technology can provide very large bandwidth IR pulses (200–300 cm^{−1}) having widely tunable center frequencies. These could be used in pairs in the manner described herein to access a broad range of the vibrational spectrum. A detailed picture of the evolution of the anharmonic nature of the potential surfaces of macromolecules will be obtainable while structural changes are taking place. The two frequencies could be chosen to access different modes of a peptide structure or two modes belonging to different types of molecules such as a protein and a nucleic acid, a protein mode and solvent, or a protein tertiary interaction. Sequences of five IR pulses can also be envisaged (21) that will be able to expose even more complex spatial relationships.
Acknowledgments
We thank Dr. M. T. Zanni for helpful comments. This research was supported by grants from the National Institutes of Health and National Science Foundation with instrumentation from the National Institutes of Health Research Resource Grant PHS 41 RR03148.
Abbreviation
 NMA,
 Nmethylacetamide
 Accepted March 5, 2003.
 Copyright © 2003, The National Academy of Sciences
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