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Proc Natl Acad Sci U S A. Sep 4, 2007; 104(36): 14237–14242.
Published online Jun 5, 2007. doi:  10.1073/pnas.0700959104
PMCID: PMC1964855
Multidimensional Ultrafast Spectroscopy Special Feature
Research Articles, Chemistry, Biophysics

Transient 2D IR spectroscopy of ubiquitin unfolding dynamics

Abstract

Transient two-dimensional infrared (2D IR) spectroscopy is used as a probe of protein unfolding dynamics in a direct comparison of fast unfolding experiments with molecular dynamics simulations. In the experiments, the unfolding of ubiquitin is initiated by a laser temperature jump, and protein structural evolution from nanoseconds to milliseconds is probed using amide I 2D IR spectroscopy. The temperature jump prepares a subensemble near the unfolding transition state, leading to quasi-barrierless unfolding (the “burst phase”) before the millisecond activated unfolding kinetics. The burst phase unfolding of ubiquitin is characterized by a loss of the coupling between vibrations of the β-sheet, a process that manifests itself in the 2D IR spectrum as a frequency blue-shift and intensity decrease of the diagonal and cross-peaks of the sheet's two IR active modes. As the sheet unfolds, increased fluctuations and solvent exposure of the β-sheet amide groups are also characterized by increases in homogeneous linewidth. Experimental spectra are compared with 2D IR spectra calculated from the time-evolving structures in a molecular dynamics simulation of ubiquitin unfolding. Unfolding is described as a sequential unfolding of strands in ubiquitin's β-sheet, using two collective coordinates of the sheet: (i) the native interstrand contacts between adjacent β-strands I and II and (ii) the remaining β-strand contacts within the sheet. The methods used illustrate the general principles by which 2D IR spectroscopy can be used for detailed dynamical comparisons of experiment and simulation.

Keywords: molecular dynamics, protein folding, temperature jump, time-resolved spectroscopy

From one perspective, protein folding is a chemical dynamics problem concerning description of the interplay of noncovalent interactions that involve the protein and surrounding solvent and exploration of the configurational space that leads to formation of the native structure. Although individually these interactions act on short time and distance scales, collectively they result in nanometer-scale conformational changes observed over time scales from picoseconds to seconds. The vast range of length and time scales, and the collective nature of folding coordinates, ensure that no single technique can time-resolve all relevant structural changes in solution (13). Most experimental methods favor either temporal or structural resolution and are limited to characterizing folding rates (kinetics) rather than mechanism (dynamics). From a computational approach, molecular dynamics (MD) simulations offer detailed dynamical information at atomic resolution for single molecules (4). Yet, simulation of folding is also challenged by the microsecond or longer time scales required, the need for extensive sampling of the ensemble, and only indirect experimental benchmarks. These challenges have spurred an interest in comparison between experiment and simulation that builds on their combined strengths to address mechanistic questions (5, 6).

As an ultrafast vibrational spectroscopy that probes transient molecular structure in solution, two-dimensional infrared (2D IR) spectroscopy provides an avenue to directly reveal protein folding dynamics. 2D IR spectroscopy achieves its time resolution through the use of femtosecond mid-IR pulse sequences and its structural information by probing vibrational couplings (79). It is now being used in several contexts to characterize the structure and dynamics of proteins and peptides (1015), including unfolding (1619). The target in the majority of these studies is amide I spectroscopy of the polypeptide backbone. Despite lacking atomic resolution, amide I IR spectroscopy is appealing because changes in peak positions and spectral lineshape reflect variations in protein secondary structures (20). In addition, models to calculate amide I spectra have advanced to the point where it is feasible to directly connect amide I 2D IR spectra with structure (9, 15, 2123). Thus, it becomes possible to perform transient 2D IR spectroscopy of protein folding in silico, using MD simulation to interpret the underlying mechanism of unfolding within the framework of experimentally constrained time scales and structural changes. Here we present such a method of revealing dynamics in experiments, characterizing how ubiquitin unfolds after a temperature jump (T-jump) and drawing on MD computer simulations to assist in the detailed dynamical interpretation.

Transient folding studies are a common experimental approach to time-dependent studies of protein folding (2, 2426), but most experiments characterize kinetics: the rates of crossing between stable minima on a free-energy surface. What has always been desirable, but difficult to achieve, is to describe dynamics: a direct, time-dependent characterization of molecular structure. Observation of dynamics in experiments is typically hindered by barriers along the reaction coordinate. However, there is now evidence that fast-folding experiments initiated with a T-jump can shift equilibrium conditions in such a way that a nonequilibrium state is prepared at or near the folding transition state (27, 28). These “downhill” unfolding experiments work in a diffusive regime with barriers of ≈kT and show nanosecond-to-microsecond time scale nonexponential relaxation (25).

Our interpretation of a downhill unfolding experiment is shown by the free-energy profiles in Fig. 1. At the initial temperature, equilibrium exists between a folded state and an unfolded state. The abrupt T-jump shifts the barrier and free-energy profile along the observed unfolding coordinate by an amount that depends on the degree of disorder in the native state. A fraction of the originally folded population is trapped near the new unfolding transition state. This subensemble unfolds in a quasi-barrierless manner, whereas the majority of the population equilibrates at the new temperature by longer-time activated barrier crossing. The fast response of this transient subensemble appears as the “burst phase” signal in conventional protein-folding kinetics. With sufficient time resolution, a structure-sensitive probe such as 2D IR provides an opportunity to describe unfolding dynamics by watching the downhill process, which is temporally isolated from the slower unfolding kinetics (29).

Fig. 1.
Downhill unfolding dynamics. A T-jump induces a barrier shift toward the folded state. A subensemble is trapped at the shifted transition state and unfolds in a downhill manner on the nanosecond–microsecond time scale (A). The downhill unfolding ...

In the following, we track the unfolding of ubiquitin from nanosecond to millisecond time scales with 2D IR spectroscopy, to structurally characterize the burst phase and the slow unfolding kinetics. The experiments probe two vibrational modes of ubiquitin's β-sheet and the random coil region. Spectral changes can be interpreted as a sequential unfolding of strands within the sheet, ending with the strand I–II hairpin. (The structure of ubiquitin and a 2D representation of the contacts between strands of the sheet are presented in Fig. 2.) The detailed picture emerges from comparison with MD simulation. We demonstrate this by using a spectroscopic model to calculate transient 2D IR spectra from a T-jump unfolding simulation of ubiquitin, which we use to interpret the collective frequency shifts and intensity changes observed in the experimental data. This method provides a general approach to dynamical interpretations of folding experiments and testing of folding simulations.

Fig. 2.
Structure of ubiquitin. (a) Crystal structure of ubiquitin (30) rendered with MOLMOL (31). (b) Projection of the β-sheet of ubiquitin. A square box with a digit n represents a peptide group formed by residues n and n + 1. Red and purple lines ...

Experimental Results and Discussion

Equilibrium Measurements.

The 2D IR spectrum correlates the frequency of initial vibrational excitation (ω1) with a final detection frequency (ω3). The frequencies of diagonal peaks can be assigned to chemically distinct vibrational modes. The presence and splitting of cross-peaks characterizes the anharmonic coupling of the vibrations and helps decompose congested spectra. We concentrate on the diagonal and cross-peaks between two vibrational bands of β-sheets (ν[perpendicular] and ν), whose individual amide oscillators vibrate in-phase perpendicular or parallel to the β-strands, respectively (16, 18, 32, 33). The splitting between these modes and the frequency of ν[perpendicular] in particular are indicators of the size of the folded β-sheet (32) and provide an important signature in transient experiments.

Fig. 3 shows equilibrium 2D IR spectra taken at 63 and 72°C, the initial and final temperatures of the T-jump experiment. Absorptive spectra were acquired with parallel (ZZZZ) and perpendicular (ZZYY) probing polarizations. For ubiquitin, the ν[perpendicular] and ν β-sheet modes are observed on the red (1,642 cm−1) and blue (1,676 cm−1) sides of the amide I spectrum. At 63°C, these two transitions are not clearly resolved because of inhomogeneous broadening but appear as a broad diagonal peak both for the fundamental transition (ν = 0→1, positive) and for the overtone transition (ν = 1→2, negative). The overtone transition lies below the fundamental along the ω3 axis because of the anharmonicity of the vibrational potential. Because the ν[perpendicular] and ν modes have nearly orthogonal transition moments, the cross-peaks are small in the parallel polarization geometry but are enhanced and form a cross-peak ridge in the upper left corner (purple arrow) in the perpendicular polarization geometry. Loss of negative intensity (a positive change) in the lower right corner (green arrow) also indicates the presence of a positive cross-peak in this region. The overall Z-shape of the perpendicular spectrum, which arises from interference effects between ν[perpendicular] and ν diagonal and cross-peaks, is a characteristic signature of the β-sheet structure (11).

Fig. 3.
Equilibrium thermal unfolding of ubiquitin monitored by 2D IR spectroscopy. Parallel (ZZZZ) (a) and perpendicular (ZZYY) (b) polarization geometries. Spectra are normalized to the maximum of the 63°C spectrum. Twenty-one contours are plotted for ...

As the temperature is raised, the ν[perpendicular] transition blue-shifts along the diagonal, which is observed as a negative/positive doublet in the difference spectrum (marked with red arrows in Fig. 3 a Right and b Right). Concomitantly, in the off-diagonal region (lower right corner), the negative/positive doublet (marked with green arrows) appears, indicating the depletion of the ν[perpendicular] cross-peak intensity. These changes indicate disruption of the β-sheet. This disruption is accompanied by an increase in diagonal intensity in the random coil region of the amide I spectrum, νR, indicating an increase in disordered structures that result from unfolding (blue arrow). Conversely, in the perpendicular difference spectrum (Fig. 3b Right), this region is dominated by depletion of the cross-peak intensity (purple arrow) because cross-peaks are enhanced in this polarization geometry. The spectral features of these two difference spectra help in the interpretation of the transient 2D IR difference spectra.

Transient Thermal Unfolding of Ubiquitin.

Previously (17), we demonstrated that the transient unfolding response of ubiquitin can be divided into three stages. The fastest change is observed coincident with the nanosecond T-jump pulse as a result of increased thermal excitation of the solvent. The second stage is the microsecond downhill unfolding of the subensemble trapped at the unfolding transition state, as illustrated in Fig. 1. The last stage is millisecond unfolding over a barrier. Transient 2D IR spectra capture these changes as described below.

Transient 2D IR difference spectra (ZZZZ) after a T-jump from Ti = 63°C to Tf = 72°C are shown in Fig. 4 for delays between τ = 100 ns and 7 ms. The maximum spectral changes observed are 2.7%. For the fastest response observed, the τ = 100 ns spectrum, the protein conformational change is small and the spectrum is similar to those observed for a T-jump performed at low initial temperature (Ti = 25°C) for which the protein does not unfold [see supporting information (SI) Text and SI Fig. 8]. The difference spectrum shows an increase in the amplitude of the broad positive and negative diagonal peaks as a result of the small transmission increase at 6 μm on temperature elevation. The depletion on the red side of the diagonal region (red ellipse) is attributed to the blue shift of the sheet vibrations caused by a weakening or partial disruption of hydrogen bonds within the sheet. This loss feature is more intense for Ti = 63°C than for Ti = 25°C, indicating that it is not just a result of the sample density decrease. Time-dependent spectral changes observed in the subsequent spectra are different from those observed at Ti = 25°C and originate in unfolding of the protein. This is apparent from the similarity between the transient difference spectrum at 7 ms and the equilibrium difference spectrum shown in Fig. 3a.

Fig. 4.
Transient 2D IR difference spectra (ZZZZ) after a T-jump from 63 to 72°C. Transient difference spectra are plotted as a function of delay τ. Twenty-one contours are plotted at ±1.5% of the maximum of the reference spectrum at ...

In Fig. 4, distinct transient spectral changes are observed in three different spectral regions: (i) the low-frequency diagonal region, (ii) the off-diagonal region for ω1 > ω3, and (iii) the high-frequency detection region (upper half of each spectrum). In the low-frequency diagonal region (lower left), the amplitude of the negative/positive doublet of the β-sheet ν[perpendicular] mode rises over microsecond-to-millisecond time scales and shifts to the blue along the diagonal axis as a result of β-sheet unfolding. The disruption of the β-sheet can also be monitored by the cross-peak intensity in the lower right. Although initially dominated by a negative peak originating from the D2O thermal transmission increase, with increased delay the negative/positive cross-peak doublet is formed and pushes the negative diagonal peak to the blue. For the upper half of the transient spectrum, the changes are less dramatic. The transmission increase induces a positive change in this region, and the increase of the random coil component by thermal unfolding also appears as a positive change, both of which lead primarily to lineshape variations. The global time-dependent changes in the transient spectra characterized through singular value decomposition (SVD) are shown in Fig. 5a. The relaxation curve obtained from the first SVD component shows a gradual nonexponential decay from 100 ns to 100 μs, an abrupt decay on the 2-ms time scale, and finally a return to baseline for τ > 5 ms. The final stage represents the refolding of the protein after the temperature of the sample reequilibrates.

Fig. 5.
Semilog plot of transient changes in 2D IR spectra. (a) Temporal profile of unfolding and refolding of ubiquitin constructed from the first SVD component of the transient difference spectra shown in Fig. 4. (b) Transient changes of slices at ω ...

The short time response corresponds to a downhill unfolding path in which interstrand contacts within the β-sheets of a small fraction of the total population are gradually reduced. This can be shown by using slices through the transient spectra for ω1 = 1,620 and 1,642 cm−1. The slice at ω1 = 1,642 cm−1 (Fig. 5b) shows a clear blue shift in the diagonal peak. The difference signal of the ν[perpendicular] mode, (ω1, ω3) = (1,642, 1,639), is positive initially but becomes negative with a time-dependence that contains both the fast downhill and slower millisecond components (Fig. 5c). In that slice, the off-diagonal region (ω1, ω3) = (1,642, 1,663), which is dominated by the random coil region of the spectrum, is observed to rise gradually over the entire unfolding period. For the slice at ω1 = 1,620 cm−1, the positions of the diagonal peaks do not change but the amplitude increases slightly. However, the positive peak initially formed in the ν[perpendicular] region at ω3 ≈ 1,640 cm−1 blue-shifts with delay time on microsecond and millisecond time scales (Fig. 5e). Although the shift may be the partial result of temperature-dependent solvent transmission changes, the similarity in the relaxation profiles (Fig. 5 c and e) indicates that the decrease in intensity of the ν[perpendicular] diagonal region is correlated with the blue shift of the ν[perpendicular] assigned peak along the shown ω1 = 1,620 cm−1 slice as unfolding of the β-sheet proceeds. The change in intensity indicates a decrease of amide vibrations contributing to the β-sheet mode, whereas its blue shift may indicate a decrease in delocalization of the β-sheet excitation and, therefore, a decrease in its folded size.

Line-Broadening During Unfolding.

Variation of the homogeneous vibrational linewidth observed in the T-jump from Ti = 63°C can be used to characterize changes in amide group fluctuations during the unfolding of the protein. In addition to vibrational population relaxation, homogeneous line-broadening of amide I vibrations of proteins depends on solvent perturbations and structural fluctuations of the protein. The correlation time of solvent fluctuations, characterized through the amide I frequency correlation function for N-methylacetamide, has been shown to be ≈1 ps (or 10 cm−1 of linewidth) (34). In a protein, this contribution changes based on the solvent accessibility of the amide groups. Backbone fluctuations in the protein's local minimum on a ≈1-ps time scale also contribute to the homogeneous linewidth by modulating the coupling and hydrogen bonding between amide I oscillators.

For proteins consisting of many amide I oscillators, the lineshape and linewidth of an IR absorption spectrum strongly depend on the distribution of amide I frequencies. Because of this broad, inhomogeneous character, the homogeneous line-broadening cannot be independently observed in the FTIR spectrum. However, the inhomogeneous and homogeneous parts can be separated in the 2D lineshape through diagonal and antidiagonal slices, respectively (35). Thus, any changes to amide I frequency fluctuations as a result of solvent exposure of those peptide units should be observed as antidiagonal broadening.

The relative change of the homogeneous linewidth (ΔΓr) induced by a T-jump is defined as

equation image

where Γ(τ, ωAD) is the antidiagonal linewidth (FWHM) along the slice ωAD = (ω1 + ω3)/2 for the transient 2D IR spectrum at delay τ. In Fig. 5f, time-dependent changes of the homogeneous width are plotted for two frequency components: the ν[perpendicular] mode (ωAD = ω[perpendicular] = 1,642 cm−1) and the random coil region (ωAD = ωR = 1,668 cm−1). The changes in ΔΓR in the random coil region (ωAD = ωR) track the temperature relaxation. Conversely, for the ν[perpendicular] mode, the initial change of 0.8% at 100 ns increases to ≈1.1% at 6 ms before reequilibrating with the refolding of the protein.

The variation of homogeneous linewidth in the random coil region follows the transient temperature profile because the coil regions are flexible and solvent-exposed, even in the folded state. This conclusion is supported by the broader linewidth of this region in the equilibrium spectrum. The antidiagonal widths for the ν[perpendicular] and random coil features in Fig. 3a are 10.6 and 12.7 cm−1, respectively, and they increase by 17% and 7%, respectively, between the initial and final temperatures. The increase of the random coil region is smaller, as in the transient case. The changes in the homogeneous linewidth for the T-jump from 25 to 35°C, where structural change is small, track the temperature profile, regardless of the frequency (SI Text and SI Fig. 10).

Unfolding Mechanism of Ubiquitin.

Ubiquitin has a five-stranded mixed parallel/antiparallel β-sheet and an α-helix (see Fig. 2a), and it is one of the most actively studied folding systems. Several experimental and simulation studies have reported sequential folding after the formation of a stable core that includes the strand I–II hairpin and the α-helix (3640). The stability of this N-terminal 1–37 fragment has been investigated by fragmentation studies, multidimensional NMR experiments, and MD simulation (4145). MD simulations suggested a transition state with β-strands I, II, and V intact and an unfolding pathway involving strands III–V before unfolding of the hydrophobic core (45, 46).

Our previous T-jump experiments on this system (17) lent further support to the two-state model for ubiquitin unfolding. Those experiments used dispersed vibrational echo (DVE) spectroscopy, a nonlinear spectroscopy that can be related to a power spectrum of the 2D IR signal projected onto the ω3 axis. We interpreted the DVE transients as sequential unfolding of the less stable strands III–V (≈3 μs) before unfolding of the protein's hydrophobic core (≈80 μs). A physical picture to describe the multiphase unfolding process was proposed in terms of a free-energy surface consisting of two coordinates to which the IR experiments are most sensitive: (i) the native contacts between strands I and II and (ii) the remaining native contacts between adjacent strands I, V, III, and IV. These contacts are depicted in Fig. 2b. Fluorescence-probed downhill folding induced by a barrier shift at 8°C has been reported for a cold denatured ubiquitin mutant, F45W (28), with a time scale of ≈100 μs. The difference in time scale likely originates from the temperature-dependent difference between the folding and unfolding free-energy surfaces.

The results from transient 2D IR spectroscopy capture the previous DVE results and expand on them by disentangling spectral changes along the ω1 frequency dimension. The separation of the diagonal and cross-peak region dynamics, and the ability to monitor the frequency-dependent homogeneous linewidth, have yielded a unique description of the solvent-exposed random coil regions. The observation that diagonal and off-diagonal ν[perpendicular] features relax in a correlated fashion also shows that the original interpretation of the DVE experiments was valid. However, because of the delocalized nature of amide I vibrational eigenstates, a complete picture including the order of strands unfolding has relied on qualitative comparisons with other experiments and with MD simulation. By calculating 2D IR spectra from protein structures sampled along an unfolding pathway consistent with our hypothesis, we seek to make a comparison by identifying similarities in intensity changes and frequency shifts.

Comparison with Simulation.

Amide I eigenstates are sensitive to subangstrom changes in the distance between β strands and in hydrogen bond lengths (21, 47, 48), but spectral congestion masks these changes in FTIR spectra. The cross-peaks observed with 2D IR help to recover sensitivity and allow for rigorous comparisons of amplitude changes and peak shifts. To provide an atomistic test of the qualitative picture presented, we analyze the ubiquitin-unfolding MD simulation of Alonso and Daggett (46) by calculating 2D IR spectra, using structures sampled along an experimentally relevant set of reaction coordinates.

We choose structures by projecting the T-jump simulation along two coordinates that are closely related to the β-sheet contacts to which 2D IR is sensitive: summed Cα distances between native contacts. These are defined by

equation image

where RN−M describes a sum of pairwise Cα distances (i, j) between hydrogen-bonded strands N and M. By using the strand diagram in Fig. 2b, R1 and R2 are the sum of contact distances illustrated in purple and red, respectively. The simulation trajectory is plotted along these coordinates in Fig. 6 to visualize the steps (A–E) in the progressive unfolding of the protein. Beginning from the crystal structure, the initial reaction to the T-jump is global expansion and increased disorder of the protein (A). The unfolding proceeds through transitions (A→B→C→D), during which contacts between strands III and IV, V and III, and I and V are broken sequentially, yielding a persistent configuration in which the α-helix has rotated to align with strands II and I (D). The final transition breaks these contacts, and only the helix is structured by the end of the simulation (E). This pathway is consistent with the studies guiding our hypothesis, including our T-jump DVE results indicating that β-sheet unfolding occurs on two distinct time scales.

Fig. 6.
Thermal unfolding simulation and calculation of 2D IR spectra. (Upper Left) The unfolding simulation (46) is plotted along the coordinates R1 and R2 defined in the text. Protein snapshots correspond to five persistent structural regions (shown in green, ...

Although the large T-jump (ΔT = +200°C) and the lack of extensive sampling in the simulation prohibit a thermodynamic and kinetic comparison, we can still search for spectral features that correlate with structural changes by calculating 2D IR spectra from solvated snapshots in each persistent structural region. Sample spectra are plotted in Fig. 6. The equilibrium spectrum, reproduced from our previous work (21), shows the Z-shape typical of β-sheets, with an intense ν[perpendicular] transition at 1,640 cm−1 melding into the random coil region at 1,660 cm−1, a high-frequency ν peak at 1,677 cm−1, and cross-peak ridges extending along ω1 between ν and ν[perpendicular]. As the protein unfolds, the spectral features gradually transition to produce an unstructured, blue-shifted, diagonally elongated spectrum.

For better comparison with the experiment, Fig. 6 also shows the simulated transient difference spectra and quantifies changes in peak intensity and frequency from configurations A to E. The difference spectra show derivative features indicating a correlated drop in ν[perpendicular] at 1,640 cm−1 with an increase in the random coil region at 1,670 cm−1. This is accompanied by loss of negative ν[perpendicular], ν cross-peak intensity in the lower-right region of the spectrum and appears as a positive change. The cross-peak ridge loses >50% of its intensity and blue-shifts by 2 cm−1 in transition from A to C, where III–V strand contacts are broken. The blue shift is also apparent in the ν[perpendicular] diagonal region but is less clear because of interference with the broad random coil peak. Blue-shifting of the ν[perpendicular] peak has been predicted to appear with localization of a vibrational exciton upon loss of vibrational coupling (32). The dynamics are complete by the final spectrum which, like the 7-ms experimental transient, can be compared with the equilibrium difference.

There is a large disparity of time scales between the ≈1-ns simulation and the 100-ns to ≈1-ms experimental responses that cannot be accounted for with the thermal change in diffusion. The difference is due to the different nature of the free-energy surface at 227°C (simulation) vs. 72°C (experiment) and to differences in comparing single-molecule and ensemble representations. The downhill unfolding subensemble prepared in the experiment moves along a corrugated free-energy surface while surmounting and accumulating behind barriers of ≈kT. This friction and exploration along orthogonal coordinates delays and disperses the ensemble from a high-temperature limit that would behave similarly to the single protein in this single unfolding trajectory.

Conclusions

We have presented an approach for characterizing protein folding dynamics that uses 2D IR spectroscopy of burst-phase unfolding interpreted through comparison with MD simulation. The interpretation of transient 2D IR spectra is consistent with calculated spectra from a simulation that shows a progressive unfolding of the β-sheet. The ability to quantitatively model amide I IR spectroscopy on the basis of proposed structures allows for a detailed connection between unfolding dynamics in experiments and simulations. In the future, one can imagine using 2D IR to discriminate between different simulated unfolding pathways, which will enable experimentally verified simulations to report on variables that cannot be probed by experiment.

Materials and Methods

Details of our experimental methods, materials, and controls are provided in SI Text and in refs. 7 and 49. Briefly, heterodyne-detected 2D IR correlation spectra are obtained by using 90-fs, 1-kHz mid-IR pulses resonant with the amide I vibrational band. Changes are monitored from 10 ns to 50 ms after a 9°C T-jump generated by a synchronized 20-Hz, 7-ns laser pulse resonant with an OAn external file that holds a picture, illustration, etc.
Object name is cjs0807.jpgD overtone of the water. The ubiquitin sample (30 mg/ml in pH* 1 DCl/D2O solution) is sandwiched between two CaF2 windows with a 50-μm-thick Teflon spacer and mounted in a brass sample cell kept at temperature Ti to ±0.1°C with a circulating water bath. Modeling details are available in SI Text.

Supplementary Material

Supporting Information:

Acknowledgments

We thank Valerie Daggett (Department of Medicinal Chemistry, University of Washington, Seattle, WA) for providing the trajectories of ubiquitin unfolding described in ref. 46. This work was supported by National Science Foundation Grants CHE-0316736 and CHE-0616575 and by The David and Lucile Packard Foundation. Additional support came from Department of Energy Grant DE-FG02-9ER14988.

Abbreviations

DVE
dispersed vibrational echo
MD
molecular dynamics
T-jump
temperature jump.

Footnotes

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0700959104/DC1.

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