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. 2016 Apr;72(Pt 4):477-87.
doi: 10.1107/S2059798316001224. Epub 2016 Mar 24.

Direct-methods structure determination of a trypanosome RNA-editing substrate fragment with translational pseudosymmetry

Blaine H M Mooers  1
Affiliations

Direct-methods structure determination of a trypanosome RNA-editing substrate fragment with translational pseudosymmetry

Blaine H M Mooers. Acta Crystallogr D Struct Biol. 2016 Apr.

Abstract

Using direct methods starting from random phases, the crystal structure of a 32-base-pair RNA (675 non-H RNA atoms in the asymmetric unit) was determined using only the native diffraction data (resolution limit 1.05 Å) and the computer program SIR2014. The almost three helical turns of the RNA in the asymmetric unit introduced partial or imperfect translational pseudosymmetry (TPS) that modulated the intensities when averaged by the l Miller indices but still escaped automated detection. Almost six times as many random phase sets had to be tested on average to reach a correct structure compared with a similar-sized RNA hairpin (27 nucleotides, 580 non-H RNA atoms) without TPS. More sensitive methods are needed for the automated detection of partial TPS.

Keywords: Patterson analysis; RNA structure determination; ab initio phasing; helical symmetry; noncrystallographic symmetry.

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Figures

Figure 1
Figure 1
Initial ab initio structure determination of the 32-nucleotide dsRNA by direct methods using SIR2014 (PDB entry 5da6). (a) Data quality as indicated by R meas and the 〈I/σ(I)〉 signal-to-noise ratio. (b) The distribution of the final figure of merit (fFOM2) for the 194 phasing trials in the first experiment. (c) The weighted mean phase error (wMPE) versus resolution and the map correlation coefficient (mapCC) versus resolution for the winning phase set in (b) (Lunin & Woolfson, 1993 ▸). The final refined model served as the source of the ‘true’ phases. (d) F oexp(SIR2014 phases) electron-density map for dsRNA with the model from automated peak picking without knowledge of the RNA stereochemistry. The atom types are colored as follows: carbon, green; nitrogen, blue; oxygen, red; phosphorus, orange. The map was rendered with PyMOL.
Figure 2
Figure 2
Native Patterson map of the dsRNA obtained with 1.05 Å resolution diffraction data (PDB entry 5da6). (a) Map at the w = 0 level contoured at the 12σ level. (b) Map at the u = 0 level contoured at the 12σ level. A stick model of the biological unit without the solvent is overlaid on the unit-cell origin. The single-colored strand was generated by crystallographic symmetry. The off-origin peak at 29 Å corresponds to the length of one helical turn and the peak at 58 Å corresponds to the length of two helical turns.
Figure 3
Figure 3
Comparison of the final structures of (a) the dsRNA (PDB entry 5da6) and (b) the hairpin RNA (PDB entry 3wd4). The single-colored strand in (a) was generated by crystallographic symmetry.
Figure 4
Figure 4
Native Patterson map generated from the 0.97 Å resolution diffraction data of the hairpin RNA (PDB entry 3wd4). (a) Map generated with all of the data contoured at the w = 0 level and contoured at the 3σ level. (b) The same map contoured at the 12σ level. A stick model of the RNA (solvent is hidden) is shown at its position in the unit cell.
Figure 5
Figure 5
Initial structure determination of the known 27-nucleotide hairpin from random phases by direct methods using SIR2014. (a) Distribution of the fFOM2. (b) F oexp(SIR2014 phases) map.
Figure 6
Figure 6
(a, c) The distribution of the number of failed trials tested (i.e. the number of random phase sets tested) to reach a correct structure in (a) 64 independent phasing experiments with the dsRNA data and (c) 364 phasing experiments with the hairpin data. The curves are the fitted geometric distributions. The geometric distribution has a single parameter, the probability of success in a trial. This probability the associated standard error: probability = 0.004142 ± 0.000491 for the dsRNA data and probability = 0.0321 ± 0.0012 for the hairpin data. (b, d) Geometric probability plots of the theoretical values versus observed data for (b) the dsRNA and (d) the hairpin RNA. The correlation coefficient was 0.95 for the dsRNA and 0.99 for the hairpin RNA. Probability computations were performed with the MASS package in R (Venables & Ripley, 2002 ▸).
Figure 7
Figure 7
Intensity and structure-factor statistics. The cumulative distribution function (cdf) of the normalized intensities (Z = E 2) for the observed data (solid lines) and the Wilson acentric distribution (dashed lines) for (a) the dsRNA data and (b) the hairpin data. (c, d) Each structure factor was divided by its corrected sigma and then averaged by its l Miller index. (c) The diffraction data for the dsRNA; (d) the diffraction data for the hairpin RNA.
Figure 8
Figure 8
Distribution of the z components of the SIR2014 RELAX shift vectors for moving misplaced trial structures to the correct origin in phasing experiments with the dsRNA data in the presence of TPS.
Figure 9
Figure 9
Cumulative scattering power of the diffraction data from the dsRNA (solid line) and hairpin RNA (dashed line). The quotient of the structure factor squared and the sum of the squared structure factors gave the relative contribution of a particular reflection to the total scattering power. The contribution of F 000 was ignored. The points indicate the numbers of strong reflections removed in deletion data sets that tested the importance of the strongest reflections in phasing experiments.
Figure 10
Figure 10
Comparison of the phasing experiments with all of the data and three deletion data sets. Each data set was used in 30 phasing experiments. (a) With the dsRNA (PDB entry 5da6), there were 30, 20, seven and four successes from top to bottom. (b) With the hairpin (PDB entry 5d99), there were 30, 30, 20 and five successes from top to bottom.
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