Reconstructing three-dimensional shape envelopes from time-resolved small-angle X-ray scattering data

Abstract

Modern computing power has made it possible to reconstruct low-resolution, three-dimensional shapes from solution small-angle X-ray scattering (SAXS) data on biomolecules without a priori knowledge of the structure. In conjunction with rapid mixing techniques, SAXS has been applied to time resolve conformational changes accompanying important biological processes, such as biomolecular folding. In response to the widespread interest in SAXS reconstructions, their value in conjunction with such time-resolved data has been examined. The group I intron from Tetrahymena thermophila and its P4-P6 subdomain are ideal model systems for investigation owing to extensive previous studies, including crystal structures. The goal of this paper is to assay the quality of reconstructions from time-resolved data given the sacrifice in signal-to-noise required to obtain sharp time resolution.

Figure 1

Radius of gyration () versus time for the P4–P6 subdomain. The points are calculated from fits to the Guinier region of the data (Guinier & Fournet, 1955 ▶), with the errors being determined by the 95% confidence intervals. The black line is the fit of the equation with , and  ms. When measured by SAXS, P4–P6 folding is accurately described by a single exponential; thus the global compaction of P4–P6 is apparently a two-state process.

Figure 2

Averaged reconstructions of the P4–P6 subdomain. Each shape is labeled with the time elapsed since mixing and the MNSD value that reflects the uniqueness of the reconstruction. While the MNSDs of two shapes are larger than 0.7, examination of the individual reconstructions (not shown) confirms that the averages represent the ensembles. All reconstructions are depicted on the same spatial scale.

Figure 3

Comparison of the P4–P6 reconstruction with the crystal structure. The reconstruction of folded P4–P6 (∼150 ms after folding) is docked with the crystal structure of Protein Data Bank code 1gid (Cate et al., 1996 ▶), showing the agreement between the two. Situs (Wriggers & Chacón, 2001 ▶) was employed to find the best match between the two structures.

Figure 4

GNOM and DAMMIN fits to the experimental data. This plot demonstrates the quality of typical fits to the data by both GNOM and DAMMIN. The dots represent 10.6 ms P4–P6 folding data, which have been scaled by a beam intensity monitor to account for small changes in X-ray intensity. The solid line is the GNOM fit to this data, and the dashed line is calculated from a single reconstruction, both of which are scaled to match the data by the programs that produced them. The curve found by GNOM fits the data well within the noise, but the noise is large compared with the precision of the reconstruction, which leaves room for error. DAMMIN and GNOM curves are indistinguishable, demonstrating how precisely the reconstruction fits the GNOM representation of the data. The consequences of these observations are discussed in the text.

Figure 5

Folding time course for the full-length ribozyme. The points are calculated from a fit to the Guinier region of the data (Guinier & Fournet, 1955 ▶), with the errors being determined by the 95% confidence intervals. The solid line is a fit to the expression =  +  + + , where , , , ,  ms,  ms and  ms. Radius of gyration versus time for the Tetrahymena ribozyme shows two long-lived intermediates on the folding pathway. Open circles correspond to data points acquired at the APS with the continuous-flow mixer; filled circles represent data collected with a stopped-flow mixer at CHESS.

Figure 6

Reconstructions for selected time points during folding of the full-length ribozyme. This figure indicates the time elapsed since mixing and shows the MNSD between ten individual reconstructions of scattering states along the folding pathway of the ribozyme. The initial and final states are shown, along with two states that correspond to the measured plateaus in the curve of versus time.

Figure 7

Variations in reconstructions of P4–P6. Above is a plot showing differences that arise in the GNOM fit to P4–P6 data acquired at 125 and 168 ms after folding was initiated. The GNOM fit shows variation in the high- region, despite the underlying data being nearly identical within the noise. Below are three individual reconstructions each for the 125 ms (upper) and 168 ms (lower) data. Although there is variation between the models reconstructed from a single curve, the variation is greater between the top and bottom sets of models. This is also reflected quantitatively in the MNSD, which is 0.58 and 0.63 for the 125 and 168 ms points, respectively, but 0.69 between shapes from the different reconstructions, slightly higher. Thus, in spite of the overall similarity in the data, models at these two time points reconstruct to slightly different shapes.

Figure 8

Variations between reconstructions from the same SAXS data. This figure shows calculated scattering intensities for the most widely varying reconstructions of the scattering data representing unfolded molecules. The black line in both figures indicates the range over which we have acquired data, from approximately  Å to  Å. Top: Although these reconstructed models for the full-length ribozyme are very different, we note that the scattering profiles of both of these models agree well with our measurements (data not shown) and with each other within the data range. Discrepancies that are evident outside of the scattering regime might indicate there is more information to gather at larger . Bottom: For P4–P6 reconstructions the agreement is excellent both within and beyond the data range.