Single Isomorphous Replacement Data Research Articles

Combining direct methods with isomorphous replacement or anomalous scattering data. VIII. Phasing experimental SIR data with the replacing atoms in a centrosymmetric arrangement.

A multisolution direct method has been proposed to resolve the phase ambiguity intrinsic in single isomorphous replacement data of proteins with the replacing atoms in a centrosymmetric arrangement. The phase ambiguity of each reflection is in fact a 'sign ambiguity' of the phase difference between the phase of the native protein and that of the replacing atoms, i.e. +/- |Deltatheta| = theta - theta'. The P+ probability formula can be used to derive the signs. The multisolution phasing procedure is initiated using random starting values of P+. A cluster analysis is used instead of figures of merit to find the correct solution. The direct-method phases can be further improved by density-modification techniques. The method was tested with the experimental SIR data at 2 A resolution from a known protein aPP; satisfactory results were obtained.

Use of single isomorphous replacement data of proteins - resolving the phase ambiguity and a new procedure for phase extension.

A procedure combining direct methods and solvent flattening to break the phase ambiguity intrinsic to the single isomorphous replacement (SIR) technique has been tested with the experimental SIR data of the known protein RNase Sa at 2.5 A resolution. The use of direct methods provided better initial phases for the solvent-flattening procedure, while the solvent-flattening procedure greatly improved direct-method phases leading to a traceable Fourier map. A small subset of known phases at low resolution makes direct phasing of SIR data much easier. Accordingly a method for extending low-resolution phases to high-resolution ones is proposed making use of additional SIR information. This reduces the problem of finding a value in the range of 0-2pi for each unknown phase to that of just making a choice between two possible values. Tests with the known protein RNase Sa showed that the method is able to extend phases from a resolution of 6 to 2.5 A leading to an easily traceable Fourier map. The solvent-flattening technique and the combination of which with direct methods were used for the phase extension. Either procedure yielded reasonably good results, but on the whole, the result from the combination of direct methods with solvent flattening is better. Results of the latter procedure were further compared with that from direct phasing of the 2.5 A SIR data and with that from phase extension by solvent flattening without SIR information. An improvement gained by the use of SIR information is evident.

Use of 'random-atom" phasing models to determine macromolecular heavy-atom replacement positions

A procedure is described by which the phase-invariant translation function may be used to provide starting set phases for the minimal function that are significantly better than those generated from random-atom coordinates. Applications to determine the heavy-atom positions for single isomorphous replacement data from macromolecular structures are very encouraging. In the case of chiral space groups, e.g. P4(1)2(1)2 versus P4(3)2(1)2, unlike Patterson functions, these methods provide the correct enantiomorph coordinates for the heavy-atom sites for whichever space group is chosen.

Direct methods with single isomorphous replacement data. I. Reduction of systematic errors

The direct-methods procedure for single isomorphous replacement (SIR) data [Hauptman (1982). Acta Cryst. A38, 289-294], as modified by Fortier, Moore & Fraser [Acta Cryst. (1985), A41, 571-577] has been implemented and tested with a large number of known structures. It was found that the modified procedure greatly reduces the bias toward 'unresolved' SIR invariant values associated with estimates of 0 or pi, but does not remove it entirely. If the heavy atoms are not in a centrosymmetric array the centroid of the distribution of invariant estimates is not centered on true protein values, but is biased toward conventional SIR values by up to 15 degrees, thus errors in the estimates are not random but systematic. When the heavy atoms are in a centrosymmetric array (or single heavy-atom site in space group P21), the distribution of estimates is often sharply bimodal, with peaks centered at both true invariant values and pure 'unresolved' SIR values. Simple procedures are given which can be applied in both situations to reduce significantly the bias with no overall loss of accuracy. An additional correction factor is then described which can be used to remove nearly all of the bias, and improve the accuracy as well. The result is that errors in the corrected invariant estimates are small in magnitude, but are now also random instead of systematic. Since the number of estimates greatly exceeds the number of phases, the remaining random errors should have little impact in phasing processes.

Phasing single isomorphous replacement data with direct methods

Phasing single isomorphous replacement data with direct methods

Maximum entropy calculation of electron density with native and single isomorphous replacement data

Maximum entropy is applied to the calculation of electron density maps from native and single isomorphous replacement (SIR) intensity data. Native intensity data alone at around 3 Å, resolution are shown to be an insufficient constraint to give an interpretable map. When the method is applied to SIR data at the same resolution, either by direct selection between the 'most probable' phases, or by using both intensity data sets directly as constraints, the result is a significant improvement over a conventional 'best' map, as demonstrated by a calculation on data synthesized from a protein fragment. The robustness of the method is demonstrated by a series of calculations using increasingly noisy data.

Pf1 Inovirus: Electron density distribution calculated by a maximum entropy algorithm from native fibre diffraction data to 3 Å resolution and single isomorphous replacement data to 5 Å resolution

We have calculated the electron density distribution of the Pf1 strain of filamentous bacteriophage by a maximum entropy method. In the calculation we included native X-ray fibre diffraction data extending to 3 Å resolution in the meridional direction on 60 layerlines that are resolved to 4 Å in the equatorial direction, and lower resolution data from a single isomorphous derivative iodinated on the Tyr25 residue. The electron density map indicates that the 46-residue protein subunit is a single, gently curved stretch of α-helix with its axis at an angle of about 20° to the axis of the virion. The α-helix subunit curves around the virion axis by about 1 6 turn, and decreases from about 27 Å radius to about 13 Å radius in the virion as the amino acid sequence of the subunit runs from the N terminus to the C terminus. Nearest-neighbour α-helical subunits are about 10 Å apart along their length, and the axis of each subunit makes an unexpected negative angle with its nearest neighbours in the virion. To confirm the validity of the maximum entropy calculation, we have varied the constraints on the calculation. All variations result in either a map that is close to the original map or a map that cannot be interpreted in terms of secondary structure: we find only one map that makes structural sense.