Transient 2D IR spectroscopy of ubiquitin unfolding dynamics

Chung et al. 10.1073/pnas.0700959104.

Supporting Information

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SI Text
SI Figure 7
SI Figure 8
SI Figure 9
SI Figure 10




Fig. 7. Beam alignment and data processing for transient 2D IR spectroscopy. Alignment of beams in the sample region (a). The LO is vertically displaced by 100 mm from the other three beams (a, b, and c) that generate the third-order signal.





Fig. 8. Transient 2D IR spectra of ubiquitin (25®35°C). (Left) Reference 2D IR spectrum of ubiquitin at Ti = 25°C in the ZZZZ polarization geometry. Twenty-one contours are plotted in ±60% of the maximum. (Right) Transient 2D IR difference spectra [DS(t)]. Twenty-one contours are plotted from ±1.5% of the maximum of the reference spectra. Depletion of the signal on the red side of the diagonal regions at 200 ns is marked with a red ellipse. The guidelines parallel to the two frequency axes (w1 and w3) mark the two resonances of the b-sheet in ubiquitin.





Fig. 9. Comparison of DVE spectra measured and reconstructed from 2D IR spectra. (a) DVE difference spectra obtained from the T-jump at Ti = 63°C. Each spectrum is divided by the maximum of the reference DVE spectrum. (b) DVE difference spectra constructed from the absolute value square of the projection of complex 2D IR spectra onto the w3 axis. (c) Comparison of relaxation profiles constructed from the first singular value decomposition component of the n^ region (1,577-1,651 cm-1).





Fig. 10. Relative changes in the antidiagonal width for a T-jump from Ti = 25°C, plotted with a temperature relaxation profile normalized to the initial change (dashed line).





SI Text

2D IR Spectroscopy. For equilibrium and transient measurements, we used Fourier transform 2D IR spectroscopy employing 90-fs mid-IR pulses resonant with the amide I vibrational band (l= 6 mm; FWHM, 160 cm-1). Details of how we perform equilibrium Fourier transform 2D IR spectroscopy are given elsewhere (1). Briefly, the third-order nonlinear signal from which the 2D IR spectrum is derived is obtained from three sequential pulses (a, b, and c in SI Fig. 7), which are crossed in and focused to a 100-mm-diameter spot at the sample and delayed with respect to each other by time intervals t1, t2, and t3. The nonlinear polarization generated by these pulses emits a signal into the wave-vector matched direction (ks = -ka + kb + kc). The third-order signal is combined with the LO on either side of a 50:50 beam splitter, yielding two matched pairs of combined fields with a p phase shift between them. Each pair of fields is dispersed by a monochromator and imaged onto one stripe of a dual-stripe mercury-cadmium-telluride (MCT) array detector (2 ´ 64). Balanced detection is performed by subtracting signals on the lower stripe from those on the upper stripe to obtain heterodyned components and to minimize the baseline fluctuation by removing the LO intensity and the homodyne echo signal (2, 3).

The array disperses the heterodyned signal into the w3 dimension of the spectrum. The heterodyned signal is collected as a function of t1, the delay between the first and second 6-mm pulses. Numerical Fourier transformation with respect to t1 results in the w1 dimension. We obtain the complex 2D IR correlation spectrum by summing the rephasing (kR = -k1 + k2 + k3) and nonrephasing (kNR = k1 - k2 + k3) spectra (4). Here we present the absorptive or real part of the correlation spectrum

, as described previously (1). Both the equilibrium and transient 2D IR spectra were obtained by undersampling in the t1 dimension with a step of 14 fs from 0 to 2.1 ps and 0 to 1.2 ps for rephasing and nonrephasing spectra, respectively. The actual frequency w1 is obtained by reflecting the transformed frequency (w1u) to the Nyquist frequency (wN) as w1 = 2wN - w1u. The combination of balanced detection and undersampling provides the needed improvement in data acquisition time for T-jump measurements. All beams have polarizations controlled with wire-grid polarizers, allowing parallel (ZZZZ) and perpendicular (ZZYY) spectra to be acquired.

Transient 2D IR spectroscopy. Here we provide a summary of the methods necessary to surmount three technical challenges to obtain the transient data: (i) synchronization of the high-energy 20-Hz nanosecond T-jump laser with the 1-kHz 2D IR femtosecond laser system, (ii) acquisition of interferometric measurements through a T-jumped sample region, and (iii) signal-to-noise improvements to overcome the reduced repetition rate for data acquisition (described above). Full experimental details and technical challenges of the T-jump 2D IR spectrometer required for these measurements will be published elsewhere (5).

T-jump synchronization. For transient 2D IR spectroscopy, changes in the 2D IR spectrum are monitored after the preparation of a nonequilibrium state by an abrupt T-jump. A 7-ns T-jump laser pulse (l= 2 mm, 4.2 mJ) is obtained from a beta barium borate (BBO)-based optical parametric oscillator (OPO) pumped by the second harmonic of a 20-Hz, Q-switched Nd:YAG laser and focused to 500 mm in the sample. Weak absorption of the T-jump pulse by O-D overtone stretching vibrations of water raises the temperature by 9° from Ti to Tf on the same timescale of the T-jump pulse duration. The transient temperature profile is characterized by the small change of solvent transmission at 6 mm. The temperature remains constant at Tf from 10 ns to ≈100 ms and then re-equilibrates to Ti by 10 ms (see Fig. 5f).

Synchronization between the mid-IR probe pulses and the T-jump pulse relies on subsequent division of the 82-MHz photodiode signal from the Ti:sapphire oscillator pulse train to 1 kHz and 20 Hz, respectively. For each T-jump pulse, 50 mid-IR pulses probe the sample at 1-ms intervals. The delay t between the T-jump pulse and the first probe pulse is controlled electronically between 10 ns and 1 ms. The 49 following probe pulses detect millisecond structural changes, leading to the ability to probe time delays between 100 ns and 50 ms. In this paper, we display the transient difference correlation spectrum,

, between the transient response and a reference spectrum at the initial temperature Ti, which, in practice, is obtained from the mid-IR pulse preceding the T-jump. To maximize signal strength, transient spectra were acquired in the parallel (ZZZZ) polarization geometry.

For T-jump measurements, to keep the relative phase between the LO and the third-order signal constant at the T-jump point in the sample, the LO is sent through the same region as the other beams. However, to avoid pump-probe signals from the LO, it is vertically displaced by 100 mm from the focal spot of the other three beams (see SI Fig. 7). Because the focal spot size of the T-jump laser (500 mm in diameter) is much bigger than that of the 6-mm beams (100 mm in diameter), the temperature at the two spots is similar and the relative phase between the LO and the third order signal does not change.

Sample Preparation. Ubiquitin was purchased from Sigma Aldrich (U6253; St. Louis, MO). The concentration of the ubiquitin sample was 30 mg/ml in 0.35% (wt/wt) DCl/D2O solution (pH* ≈ 1). The solution was placed between two CaF2 windows separated by a 50-mm-thick Teflon spacer. The windows are mounted in a brass sample cell, whose temperature was controlled at Ti to ±0.1°C with a circulating water bath. IR spectroscopy of the sample reveals a sigmoidal unfolding curve with a melting temperature of 64.0°C.

T-Jump 2D IR Spectrum of Ubiquitin at Ti = 25°C: Ultrafast Response. In our previous observations in the transient DVE experiment (6), ultrafast responses were seen to arise from solvated regions of the protein on the nanosecond timescale. The ultrafast responses induced by a T-jump in the DVE spectra are characterized by two features: increase of the signal due to increased solvent transmission at 6 mm and depletion of the intensity on the red side of the spectrum (≈1,600 cm-1) due to decreased hydrogen bonding with the solvent. 2D IR versions of these responses during the T-jump (25 ® 35°C) are shown in SI Fig. 8.

To separate the possible temperature-dependent effects of density and transmission changes from protein unfolding signals, we compare the unfolding response to a low-temperature transient response at Ti = 25°C, in which the protein does not unfold. In the transient 2D IR difference spectrum at 100 ns, both the positive and negative diagonal peaks become stronger as a result of the increased transmission of the probe beams and the LO. Also, the weakening of solvent hydrogen bonds induces the blue shift of peaks and the loss of intensity of the diagonal region on the red side (marked with a red ellipse in SI Fig. 8). However, very little spectral change is found at 1 ms except for the decrease in the magnitude of the signal. This lack of spectral change is expected because there are no significant structural changes in this low temperature range. The spectral change is mostly due to the modulation of the transmission of the solvent by a temperature re-equilibration. However, there is a slight difference between the reference spectrum and transient difference spectra. The antidiagonal width of the positive peak in the transient spectra is broader than that in the reference spectrum. Because the antidiagonal width of a 2D IR spectrum represents the homogeneous linewidth (7), this change indicates the increase in homogeneous broadening with temperature. Quantitative analysis of this effect is found in the main text.

Comparison with DVE Results. A DVE spectrum is mathematically identical to the squared absolute value of the projection of a complex 2D IR spectrum onto the w3 axis as

. [1]

Therefore, the result of the T-jump DVE experiment can be reproduced from 2D IR spectra by integrating them over the w1 axis. SI Fig. 9 a and b show the differences in the measured and reconstructed DVE spectra. Although the spectral shape and the amplitude of changes are somewhat different because of the different spectral shape of the femtosecond IR pulses between the two measurements, their time-evolutions describe the same dynamics. At 100 ns, both spectra show depletion of the intensity at ≈1,600 cm-1. Also, a decrease and blue shift in the n^ region due to the unfolding of the protein occurs on the microsecond-to-millisecond time scale.

For better comparison, we applied singular value decomposition (SVD) to the n^ region. The relaxation profiles are obtained from the coefficients of the first SVD component and are compared in SI Fig. 9c. As expected, the two relaxation curves match each other well. The two unfolding phases on the microsecond and millisecond timescales and the refolding phase after 7 ms observed in the DVE spectra are successfully reproduced from 2D IR spectra, which confirms that the two different measurements are probing the same dynamics. This consistency provides a very important basis for the comparisons made in further analyses shown in the main text.

Temperature Dependence of Homogeneous Broadening. When the structural change due to a T-jump is small, the line-broadening is dominated by increased solvent fluctuations induced by the rapid temperature change, and the deviation from the thermal profile can be used to separate this effect from conformational changes due to protein unfolding. In SI Fig. 10, time-dependent changes of the homogeneous width for three frequency components (the n^ mode, the random coil region, and the n|| mode) during a low-temperature T-jump (25 ® 35°C) are plotted. Changes of all three frequency components track the temperature relaxation profile. Because the magnitude of the change is very small (<2%), width changes can be assumed to be linear with temperature within the relatively small T-jump range of 10°C. Therefore, we can conclude that the increase in linewidth at low temperature is fast and solely a result of the increased thermal fluctuations (primarily solvent perturbations), without significant structural change in the protein.

Simulating 2D IR Spectra. Our calculations of 2D IR spectra require two elements: (i) an atomistic molecular dynamics simulation with explicit water and (ii) a structure-based spectroscopic model that draws on the simulation trajectory to model 2D IR spectra. We use a MD simulation of ubiquitin unfolding following an instantaneous T-jump from the crystal structure to 498 K, which was originally presented as trajectory D2 in ref. 8. The 1.6-ns trajectory was provided by Valerie Daggett (Department of Medicinal Chemistry, University of Washington, Seattle, WA), with snapshots of the protein structure sampled at 1 ps. Although the trajectory was supplied without water molecules, structures were resolvated for spectral calculations because the solvent is important for reproducing the spectra.

Simulation details. The ubiquitin unfolding trajectory was obtained with atomic coordinates for the protein. Protein snapshots were resolvated by inserting them into cubic boxes of equilibrated SPC/E D2O encasing the protein at least 10 Å in each direction and removing solvent molecules closer than 2.2 Å. This resulted in 5,000-7,000 water molecules. Although the denaturation simulation was performed at low pH, resolvation was done at neutral protein charge to eliminate the slow counterion diffusion degrees of freedom. By using the CHARMM 30b1 package and the CHARMM22 force field, the system was energy-minimized with steepest descents and cubic periodic boundaries for 500 steps, during which the protein was constrained in space with a 24-kcal/mol·Å2 harmonic restoring force. Particle mesh Ewald sums with k = 0.32 were used for the electrostatic energies. Van der Waals interactions were shifted to truncation at 14 Å. With all bond lengths fixed using the SHAKE algorithm, the water was then allowed to equilibrate around the fixed protein structure during 10 ps of dynamics with a 2-fs time step in the NPT ensemble at 300 K and 1 atm. A 20-ps sampling dynamics were run in which structures were saved each 50 fs and used to calculate spectra.

Modeling details. Because IR spectroscopy characterizes vibrational eigenstates, a model is required in order to translate the atomistic structure into 2D IR spectra. We use a local amide Hamiltonian (LAH) model that is widely used to describe amide I spectroscopy of proteins and peptides (9-11). The model assigns a local-mode Hamiltonian on the basis of the protein's peptide units, which contains local-mode frequencies (site energies) and vibrational couplings (through-bond and through-space). The LAH is diagonalized and used to obtain transition dipole eigenvectors and energy eigenvalues for the system, which can then be used to calculate experimental observables from a response function (12).

Considering only the vibrational subspace of amide I vibrations, each structure from the simulation was used to generate a local amide Hamiltonian. Amide I site energies are sensitive to CO and NH hydrogen bonding and are parameterized through linear correlation coefficients between the amide I energy and the electrostatic potential originating in the surrounding protein and solvent. We used the four-site model of Bour and Keiderling (13) (sampled at Ca, C, O, and N atomic sites), which we have referred to as "Bour4" (12). Coupling elements between these sites depend on their distance and relative orientation (14). Through-bond coupling is assigned from an ab initio calculated (f,y) map that builds in through-bond coupling. Through-space couplings use the electrostatic, transition charge model. A local transition dipole is also set for each site and, after diagonalization, mix to form the eigenstate transition dipole for each corresponding energy. The Hamiltonian is also scaled and anharmonically shifted to provide two-quantum energies and generate two-quantum transition dipoles. With these parameters, a 2D IR spectrum is calculated for each structure snapshot, assuming Lorentzian lineshapes (G = 10 cm-1) for perpendicular (ZZYY) polarization. Realistic, inhomogeneous lineshapes are generated by assuming the static limit and summing 100 2D IR spectra with different solvent configurations for each protein structure. Protein conformational variation in each region is accounted for by summing spectra from different snapshots, as follows: A (0, 70, 114 ps), B (150, 160, 168, 169, 170 ps), C (179, 186, 190, 200, 286 ps), D (315, 400, 424, 510, 511, 512 ps), E (523, 524, 525 ps).

A significant distinction from the experimental difference spectra is that the simulated transient spectra only reflect the unfolding dynamics and do not include the signal changes resulting from the transmission change of the D2O solvent.

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This Article

  1. Published online before print June 5, 2007, doi: 10.1073/pnas.0700959104 PNAS September 4, 2007 vol. 104 no. 36 14237-14242
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