The P4–P6 domain folds in isolation, independent of the remaining structural elements of the Tetrahymena
ribozyme. Cate et al.
) reported the crystal structure and Lipfert et al.
) presented static reconstructions of this ~160 nucleotide domain. Time-resolved SAXS studies have shown that global folding is accurately described by a two-state model, in which linear combinations of the folded and unfolded scattering curves can accurately reproduce the scattering of the intermediate time points (Schlatterer et al.
). A plot of
time after mixing with Mg
fits a single exponential equation, consistent with a single-phase collapse of the molecule (Fig. 1). Crystal structures reveal that the major feature of the folded state is a 150° bend near the middle of the RNA helix. Electrostatic repulsion in the initial, low-salt state restricts the shape of the RNA molecule to extended conformations (Das et al.
). Thus P4–P6 folding as observed by SAXS can be treated as a two-state process where, upon the addition of Mg
, P4–P6 folds nearly in half. This bent structure is stabilized by native tertiary contacts (Schlatterer et al.
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 (more ...)
We reconstructed shapes reported by each time-resolved SAXS profile acquired during P4–P6 folding. The initial SAXS data for these reconstructions are presented in the supplementary material of Schlatterer et al.
). These structures, pictured in Fig. 2, indicate a progression from a thin, elongated structure to a more compact state, consistent with the folding model described above. Additionally, the final state can be docked into the crystal structure (Cate et al.
) as shown in Fig. 3. The agreement between the ten individual reconstructions for each curve, indicated quantitatively by the MNSD, is good. The large-scale features of the reconstructions reproduce well over the set; however, smaller features vary from one reconstruction to the next. A typical comparison of the theoretical scattering curves of the reconstructions to the GNOM
fit and the data, shown in Fig. 4, demonstrates the fit of both GNOM
and the reconstructions to the data. To quantify the agreement we computed the signal-to-noise ratio (S/N) as
where the output from GNOM
was used as the fit. While the overall S/N was 27, quite good, the same analysis carried out on subsections of the data makes clear the lower S/N in the high-
range, as demonstrated in Table 1. The noise in the data manifests itself as minor features in the curves output by GNOM
. These features are unlikely to represent physical structure, but DAMMIN
fits every feature in the GNOM
curve precisely (Fig. 4). To compare calculated scatter from DAMMIN
to the GNOM
curve and the data, we define the mean discrepancy (MD) between two curves, as
are two curves and N
is the total number of data points in each curve. The MD between the data and the GNOM
, but the MD between the GNOM
fit and the DAMMIN
, over an order of magnitude smaller. This difference demonstrates the strong dependence of the reconstructions on the GNOM
interpretation of the data.
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 (more ...)
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 (more ...)
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 (more ...)
Calculated S/N for different regions of the 158 ms P4–P6 scattering curve
Of particular note is the reconstruction of the scattering curve taken 27 ms after the initiation of folding. This data point was acquired near the mid-point of the compaction illustrated in Fig. 1 and, according to a two-state fit, is approximately 63% unfolded (Schlatterer et al.
). The structure is not as elongated as that of unfolded P4–P6 but longer and thinner than the fully folded construct. A single half-folded P4–P6 molecule would probably have the ends of the helix separated by a 90° bend. In contrast, this structure is consistent with a roughly equal mixture of initial and final states present in the solution. Thus the reconstruction represents a spatial mean of the ensemble rather than an actual physical state of the molecule. In summary, this series of time-resolved reconstructions depicts with large-scale accuracy the averaged process of P4–P6 folding.
While the P4–P6 domain is a smaller molecule with a relatively simple structure, the full-length Tetrahymena
ribozyme contains many helices to locate. Owing to its complex secondary structure, the unfolded state is harder to predict without detailed modeling, and likely corresponds to an ensemble of states. The
time curve, shown in Fig. 5, is likewise more complex. In this case folding takes several minutes. Three distinct collapse phases are observed under the experimental conditions employed, indicating the existence of two long-lived intermediates in addition to the initial and final states. In an effort to capture and characterize a true time-resolved intermediate state, we reconstructed only points where the
of the molecule was not rapidly changing.
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 (more ...)
The resulting averaged shape envelopes, as well as the associated MNSD values, are displayed in Fig. 6. According to Volkov & Svergun (2003
) an MNSD of less than 0.7 indicates ideal agreement between individual reconstructions. In general, we have found this to be true, though when the MNSD is less than 1 strong similarities between different constructs are observed. For this data set, we found the MNSD decreased as folding progressed. Only the final state had an MNSD of less than 0.7.
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. (more ...)