In the presented time-resolved Laue crystallographic experiment, a chemical reaction in PYP crystals is triggered by a short laser pulse and x-ray pulses are used to probe structural changes at various time delays after reaction initiation. Data used in this study was collected over three synchrotron runs: two at BioCARS at the Advanced Photon Source (APS) and one at beamline ID09 at the European Synchrotron Radiation Facility (ESRF). Data collected at the ESRF covered the time range of 1 ns to 10 ms, while that collected at APS covered the time range of 6 ms to 1.33 s. In total, 47 time points from 1 ns to 1.33 s were used in the subsequent singular value decomposition (SVD) analysis of the data (Fig. 5). The wavelength of the excitation laser was 485 nm and the pulse duration was typically several nanoseconds.

More specifically, APS data were collected by using APS Undulator A at a 25 mm gap (first harmonic at 11.4 keV) in the standard operating mode of the APS storage ring. Laser pump pulses of 7 ns duration (full width half maximum; fwhm) from a Nd:YAG pumped dye laser (Coumarin 480; 485 nm) were used to illuminate the crystal from two sides to significantly increase the extent of photoactivation. Laser light was delivered to the sample via two separate optical fibers, with the total laser pulse energy of 1.3 ~ 1.7 mJ and the laser beam diameter at the sample of 0.6 and 0.9 mm for two fibers. The 6 ms duration of the probe x-ray pulses was determined by the opening time of the fast x-ray chopper running at 301.7 Hz. A single chopper opening at a given time delay following the laser pulse was selected by a ms shutter. Crystal temperature was maintained at 15°C by an FTS crystal cooler. X-ray diffraction images were recorded on a MAR165 CCD detector by repeating the pump-probe sequence 15 times at 0.5 Hz and thus accumulating 15 x-ray exposures before the detector readout.

The ESRF data were collected on beamline ID9B at the ESRF. The x-rays were produced by a 236-pole in-vacuum undulator with a magnetic period of 17 mm. The undulator was operated with a 5.0 mm gap where the fundamental energy is 13.4 keV. The white beam was focused into a 0.10 × 0.06 mm² spot by a toroidal mirror with an energy-cut-off at 27 keV. The synchrotron was operated in four-bunch mode, with four equidistant bunches separated by 705 ns. The bunch current was 10 mA and the pulse length 150 ps (fwhm). Single pulses of x-rays were selected by a chopper rotating at 986.7 Hz, the 360th subharmonic of the orbit frequency. The chopper defined an open window of 500 ns centered on the selected pulse. Finally a pulsed millisecond shutter picked out a single pulse from the 986.7 Hz pulse train from the chopper. The Laue experiment was repeated quite slowly, at 0.5 Hz, due to the relatively long cycling time of PYP and the time it takes to cool the sample with a cold N₂ gas stream (15°C). The sample excitation was done with the "Vibrant" nanosecond laser made by Quantel. This 10 Hz laser was synchronized to the RF clock and it produced 2.3 ns (fwhm) pulses with a jitter of 0.7 ns (rms). An OPO module converted the 1062 nm light from the fundamental to 485 nm with energy per pulse of ~2.5 mJ in the 1 mm² spot. The laser beam was brought to the sample in a 1 mm diameter fiber, which was connected to a focusing telescope. The laser beam was focused to a 0.5-mm diameter spot.

Time-resolved crystallographic data are four-dimensional; three traditional reciprocal space dimensions (hkl) and one additional dimension for the time delay. In previous experiments, an entire angular range was scanned at a fixed time delay and subsequently moved to another time delay. However this mode of data collection suffered from the systematic errors due to the inconsistent photoactivation between time points. To avoid this problem, time delay rather than the angular setting was the fast variable for all data sets collected in this work (1). That is, we collected data at all desired time points at one angular setting; advanced the angular setting to survey a different region of reciprocal space and repeat all time points; and continued in this way until the crystal no longer provides usable data. Normally, multiple crystals were used to obtain complete data in reciprocal space. This method of data collection greatly minimizes systematic errors between time points and facilitates SVD analysis (2). A time series on a typical crystal consisted of a negative time point and four to six positive time points. The negative time point (-20 ns) allowed us to assess whether the protein had fully recovered the dark state after a cool-off time following each laser pulse, typically two seconds. To facilitate the comparison of the ESRF and APS data sets, the 10 ms time point was taken in all data sets.

Statistics for individual dark and light data sets are shown in Table 2. All images from the APS runs were processed in LaueView (3, 4) including deconvolution (resulting in singles and multiples), with the exception of the G07 and G08 data sets. These two data sets and all ESRF data were processed in precognition (Renz Research, http://www.renzresearch.com/precognition), a program for Laue data analysis without deconvolution (resulting in singles only). The loss of multiples had only a small effect (less than 2%) on completeness as the data were collected with an undulator with quasi-monochromatic data. Time-resolved experiments yield structure factor amplitudes of the initial, dark state |F^D(hkl)| and time-dependent structure factor amplitudes |F(hkl,t)|. In our experiment, the structure factor amplitudes at a negative time point served as |F^D(hkl)|. From these amplitudes, time-dependent difference structure factor amplitudes DF(hkl,t) = |F(hkl,t)| - |F^D(hkl)| are obtained for each time point t.

At this stage of the data reduction we have multiple, incomplete data sets of difference structure factor amplitudes from different crystals for each time point. These data sets have to be combined to obtain one highly redundant and complete data set per time point. For this purpose, weighted averaging was carried out on individual values for DF(hkl,t) that correspond to the same time point. An averaged data set of DF(hkl,t) with a significantly enhanced signal to noise ratio (5) was obtained to 1.6-Å resolution for each time point (Table S1). Experimental, weighted difference electron density maps &#916;r(t) were then generated by using weighted difference structure factor amplitudes, wDF(hkl,t), where w is a weighting factor to weight down observations with high experimental errors (6): w = 1 / ( 1 + s²/<s²> ). Phases were obtained from the dark (7, 8) PYP structure. This procedure is referred to as the difference Fourier approximation (9). Data statistics for averaged time-resolved Laue data sets are provided in Table 3.

Basically, SVD separates time- and real space-dependent data into only a few main spatial components and their time variations. The general steps involved in SVD are as follows. First, an M × N data matrix A is formed by arranging M grid points of &#916;r(t) at N time points. SVD decomposes this time- and real space-dependent data matrix A into three matrices (13): left singular vectors (lSVs) in matrix U, each of which consists of an entire time-independent difference map; right singular vectors (rSVs) in matrix V^T, each of which contains the time dependence of the corresponding lSV; and the diagonal matrix S, whose diagonal elements, the singular values (SV), represent the degree to which their respective lSVs and rSVs contribute to the data matrix. In a mathematical form, A = USV^T, where V^T denotes the transpose of matrix V. Although N singular vectors result from the SVD, only a few of them contain signal. Selection of lSVs containing significant structural signal allows reconstitution of the data matrix U‘S’V’^T = A’ ~ A. In this reconstitution, vectors containing noises are excluded, thereby increasing the signal to noise ratio of the resulting matrix A’ compared with the original matrix A. This procedure has been called SVD-flattening (2, 11, 12). Here, SVD-flattening was performed at the 3s level with both the early and late data sets. Note that here the selection of significant singular vectors and values is greatly facilitated because the lSVs can be examined for features that chemically and structurally make sense (see below), a property unique to time-resolved crystallography (10).

After the SVD was reapplied to matrix A’, the procedure of rotation (13) was used to repartition signal that has spread to less significant singular vectors into significant ones. The significant rSVs are globally fit with a sum of exponentials. From this, relaxation times common to all rSVs can be determined. In later stages, the rSVs can be fit with different candidate mechanisms which reproduce the relaxation times according to V’ = CP, where C is a matrix containing the concentrations of the intermediates based on a candidate mechanism and P is a set of linear parameters to bring the concentration to the scale of rSVs (13). The time-independent difference electron densities of the intermediates for this candidate mechanism, denoted by the matrix F, can then be extracted as follows:

Since FC^T = A’ = U‘S’V’^T

= U‘S’P^TC^T

then F = U‘S’P^T. (1)

Eq. 1 can also be referred to as the projection of the lSVs onto the intermediate states.

When we attempted to perform SVD on the ESRF and APS data together, a discontinuity in rSV 2 was observed (Fig. 6), likely because of a significant increase in signal-to-noise in the APS data sets arising from increased photoactivation due to laser illumination from two sides of the crystal (14). Therefore, we proceeded to analyze the ESRF and APS data separately.

In the analysis of the ESRF data, SVD was individually performed on each time series (Table 2). From each of these analyses, rSV 1 was scaled to the others by a multiplicative factor to minimize deviation at the 10-ms time point, common to all crystals and time series. A clear trend was observable (Fig. 7A). After performing SVD on all of these early data sets together, quality factors (QFs) for the lSVs, a measure of their signal-to-noise level, were calculated (12). The QFs for the chromophore binding pocket are shown in black in Fig. 7B. Based on these QFs, singular vectors 2-6 were rotated, resulting in those shown in red in Fig. 7B. After rotation, only two significant singular vectors were identified, 1 and 2, as judged by the significant drop-off in QF between lSVs 2 and 3. Their corresponding rSVs were quite smooth and both were fit well by the same single exponential with a relaxation time of ~20 ns (Fig. 7C).

In the analysis of the APS data, without using any scale factors, the time series overlap well and show a clear trend in rSV 1 (Fig. 7D). After scaling the data together and calculating QFs for the chromophore binding pocket (black squares in Fig. 7E), it is clear that there are at least two significant singular vectors. However, it is difficult to assess whether there are any other significant ones because there is no sharp cutoff in QF. Based on the QFs, singular vectors 2-10 were rotated, with the results shown in red squares in Fig. 3E. This reveals clearly that there are three significant singular vectors and values. This is due to the rotation partitioning signal into singular vectors 2 and 3 at the expense of the singular vectors 4-10. lSVs 4-30 all have very low QFs and do not show significant signal and difference maps calculated from the insignificant singular vectors 4-30 show little-to-no signal (Fig. 8B). The three significant rSVs can be fit well by a sum of three exponentials with relaxation times of 180 ms, 5 ms and 52 ms (Fig. 7F).

The simplest mechanism which generates the single relaxation time (Fig. 7B) observed in the ESRF data are a two state system with an irreversible transition: a ® b. The mechanism could be more complicated if the a or b states are heterogeneous or if there is reversibility. Reversibility is highly unlikely in the early stages of a photocycle, in which an initially highly strained chromophore thermally relaxes from high energy structures to low energy ones.

In the APS data, the data could be fully described by three singular vectors and values whose rSVs could readily be fit with three exponentials whose exponents are well separated in time (Fig. 7E). This suggests that the data could be fit with a simple sequential mechanism: b ® g ® d ® dark state, where the b state must be consistent between the ESRF and APS data since they overlap in time in the 10-ms range. From these two mechanisms, we extracted the time-independent, species-associated difference electron densities (2).

Difference refinement was performed in shelx-97 and the R-factors (R-free) for the refined structures were 35.6 (38.3) for I_CP, 37.0 (39.1) for pR_CW + pR_E46Q, 11.7 (11.6) for pB₁ and 18.1 (18.6) for pB₂. These R-factors are high compared to those seen in conventional static crystallographic refinement, which is likely due to the relatively lower signal-to-noise ratio of our difference data. Extrapolated maps (15) for these intermediates (Fig. 9 A-D) show good qualitative agreement and residual maps (D F_calc - D F_obs) (Fig. 9 E-H) show little difference density in the chromophore binding pocket. Chromophore binding pocket views of refined intermediate structures are shown in Fig. 10. The best measure of the quality of the intermediate structures and the candidate chemical kinetic models is in the posterior analysis (2), which show a good fit between our model and the data (see below).

To assess the quality of difference refinement, we compared the refined intermediate structures to the associated electron density extrapolated to 100% photoactivation (F^epol = F^calc + e * D F, where e was adjusted to estimate for occupancy) (15). This comparison is shown for the chromophore in Fig. 9 A-D, which shows good correlation between features in the electron density map with the refined intermediate structures. We also calculated residual maps after the refinement of the four states, which are shown in Fig. 9 E-H. For the a and b states, there are few features; features in the c and d states are likely due to the occupancy refinement, as the positive features are primarily on atoms which are already present in the refined model. However, the best way to assess the quality of these structures and candidate chemical kinetic mechanisms is posterior analysis, in which global analysis is used to fit the calculated to the experimental difference density.

Difference electron density calculated from the structures of the refined intermediates (I_CP, pR_CW, and pR_E46Q from the early analysis and pB₁ and pB₂ from the late analysis; see below) was used in posterior analysis, a process in which the experimental maps are fit with intermediate difference electron density using different candidate mechanisms (2). We chose the model shown in Fig. 4A (see paper) based on the initial constraints of the model, i.e., the number of intermediates and the number of relaxations, and simple kinetic reasoning. Because the ESRF data could be fit well with an a ® b mechanism (where a corresponds to I_CP and b corresponds to pR_CW and pR_E46Q), the initial part of the mechanism allowed for parallel decays of I_CP to pR_CW and pR_E46Q. Similarly, we obtained a very good fit of the g state with the single intermediate pB₁, so pR_CW and pR_E46Q were allowed to decay to it in parallel. Based on the decline in total signal starting at ~ 10 ms (Fig. 7F), it was likely that there was a significant pB₁ to dark state pathway along with the pB₁ to pB₂ transition, consistent with what has previously been observed in E46Q PYP (12). Fitting with this mechanism resulted in the rate coefficients shown in Fig. 4 legend (see paper).

To assess the quality of the model shown in Fig. 4A (see paper), we systematically set rate coefficients to 0 and then calculated the magnitude of the total squared deviation over all forty-seven time delays of features above +3s or below -3s level in the experimental or calculated maps. The result of this analysis is shown in Fig. 11. Setting rate coefficients to 0 results in an increased deviation between the calculated and observed difference maps during the time range when the interconversion takes place. From this, we can conclude that our model indeed fits the data very well. However, we need to emphasize that this mechanisms is the simplest one that fits our data. Other mechanisms containing back reactions (16) cannot be ruled out because they would fit equally well and extract structures identical to the ones observed here.

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