ISSN:1399-0047    

DOI:10.1107/S090744499201028X

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

ISSN:1399-0047    

DOI:10.1107/S0907444992009739

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Owing to the breakdown of Friedel's law when anomalous scatterers are present, unique values of the three‐phase structure invariants in the whole range from 0 to 2π are determined by measured values of diffraction intensities alone. Two methods are described for going from presumed known values of these invariants to the values of the individual phases. The first, dependent on a scheme for resolving the 2π ambiguity in the estimate ωHKof the triplet ϕH+ ϕK+ ϕ−H−K, solves by least squares the resulting redundant system of linear equations ϕH+ ϕK+ ϕ−H−K= ωHK. The second attempts to minimize the weighted sum of squares of differences between the true values of the cosine and sine invariants and their estimates. The latter method is closely related to one based on the `minimal principle' which determines the values of a large set of phases as the constrained global minimum of a function of all the phases in the set. Both methods work in the sense that they yield values of the individual phases substantially better than the values of the initial estimates of the triplets. However, the second method proves to be superior to the first but requires, in addition to estimates of the triplets, initial estimates of the values of th

ISSN:1399-0047    

DOI:10.1107/S0907444992008564

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

The direct‐methods programSA YTANis applied to data at various restricted resolutions for a small protein. It is shown that useful sets of phases can be obtained even down to 3 Å resolution. Conventional figures of merit are not very discriminating for the phase sets developed, but modified figures of merit seem capable of selecting the better phase sets, at least for those generated from 2 Å or higher resoluti

ISSN:1399-0047    

DOI:10.1107/S0907444992009636

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A conventional direct method, using the Sayre equation as a basis, has been shown to be capable of solving a small protein with data of 3.0 Å resolution or better. An analysis of the Sayre equation, with data of various resolutions and with different lower limits of |E| for the contributors in the summation, shows that its effectiveness for phasing is independent of structural complexity but does decline as the resolution becomes worse. It is suggested that a practicable lower limit for the application of conventional direct methods is about 3.5 Å. For large macromolecular structures the number of contributors to the summation in the Sayre equation becomes too large to handle and it is suggested that real‐space methods should be used

ISSN:1399-0047    

DOI:10.1107/S0907444992009624

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Conventional small‐molecule methods of solving the phase problem from native data alone, without the use of heavy‐atom derivatives, known fragment geometries or anomalous dispersion, have been tested on 0.9 Å resolution data for two small proteins: rubredoxin, fromDesulfovibrio vulgaris, and crambin. The presence of three disulfide bridges in crambin and an FeS4unit in rubredoxin enabled automated Patterson interpretation as well as direct methods to be tried. Although both structures were already well established, the known structures were not used in the phasing attempts, except for identifying successful solutions. Direct methods were not successful for crambin, although the correct phases were stable to phase refinement and gave figures of merit clearly superior to any obtained in theca500 000 random starting phase sets that were refined. It appears that the presence of an iron atom in rubredoxin reduces the scale of the search problem by many orders of magnitude, but at the cost of producing `over‐consistent' phase sets that overemphasize the iron atom and involve partial loss of enantiomorph information. However, about 1% of direct‐methods trials were successful for rubredoxin, giving mean phase errors of about 56° (for allE>1.2) that could be reduced to about 20° by standardE‐Fourier recycling methods. Limiting the resolution of the data degraded the quality of the solutions and suggested that the limiting resolution for routine direct‐methods solution of rubredoxin is about 1.2 Å. With the 0.9 Å data, automated Patterson interpretation convincingly finds the three disulfide bridges in crambin and the FeS4unit in rubredoxin, and in both casesE‐Fourier recycling starting from these `heavier' atoms yields almost the complete structure. Whereas crambin could only be solved in this way at very high resolution, rubredoxin could be solved by Patterson interpretation down to 1.6 Å. These results emphasize the benefits of collecting protein data to the highest possible resolution, and indicate that when a few `heavier' atoms are present, it may prove possible in favorable cases to solve the phase problem from a single native data set col

ISSN:1399-0047    

DOI:10.1107/S0907444992007364

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Analogies between the freeRstatistic [Brünger (1992).Nature(London),355, 472–474] and the statistical methods of cross validation and bootstrap are discussed. Several new applications which make use of the previously observed correlation between the freeRvalue and the phase accuracy of crystal structures are presented. One application concerns the relative weighting of individual restraint classes in macromolecular refinement. The freeRvalue provides an objective statistical basis for the optimal choice of the weights. The results for the refinement of a penicillopepsin crystal structure at 1.8 Å resolution indicate that overall bond length and bond angle weights, derived from uncertainties observed in small‐molecule crystal structures, appear to be transferable to macromolecules. In another application, the landscape of theRvalue around the crystal structure was investigated for unrestrained modeling of diffraction data with equal atomic scatterers. Others have suggested applications toab initiophasing because of the simplicity of the liquid‐like system of equal atomic scatterers. However, there are a large number of incorrect configurations of the scatterers whoseRvalues at 1.8 Å resolution are close to that of the correct configuration given by the positions of the non‐hydrogen atoms in the penicillopepsin crystal structure. A substantial number of the incorrect configurations have higher freeRvalues than the correct one. It is therefore conceivable that the freeRvalue could be used as a selection criterion to distinguish between certain incorrect configurations and configurations close to t

ISSN:1399-0047    

DOI:10.1107/S0907444992007352

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A new multisolution phasing method based on entropy maximization and likelihood ranking, proposed for the specific purpose of extending probabilistic direct methods to the field of macromolecules, has been implemented in two different computer programs and applied to a wide variety of problems. The latter comprise the determination of small crystal structures from X‐ray diffraction data obtained from single crystals or from powders, and from electron diffraction data partially phased by image processing of electron micrographs, theab initiogeneration and ranking of phase sets for small proteins; and the improvement of poor quality phases for a larger protein at medium resolution under constraint of solvent flatness. These applications show that the primary goal of this new method – namely increasing the accuracy and sensitivity of probabilistic phase indications compared with conventional direct methods – has been achieved. The main components of the method are (1) a tree‐directed search through a space of trial phase sets; (2) the saddle‐point method for calculating joint probabilities of structure factors, using entropy maximization; (3) likelihood‐based scores to rank trial phase sets and prune the search tree; (4) efficient schemes, based on error‐correcting codes, for sampling trial phase sets; (5) a statistical analysis of the scores for automatically selecting reliable phase indications. They have been implemented to varying degrees of completeness in a computer program (BUSTER) and tested on two small structures as well as on the small protein crambin. The main obstructions to successfulab initiophasing in the latter case seem to reside in the accumulation of phase sampling errors and in the lack of a properly defined molecular envelope, both of which can be remedied within the methods proposed. A review of the Bayesian statistical theory encompassing all phasing procedures, proposed earlier as an extension of the initial theory, shows that the techniques now available inBUSTERbring closer a number of major enhancements of standard macromolecular phasing techniques, namely isomorphous replacement, molecular replacement, solvent flattening and non‐crystallographic symmetry averaging. The gradual implementation of the successive stages of this `Bayesian programme' should lead to an increasingly integrated, effective and dependable phasing procedure for macromolecular structur

ISSN:1399-0047    

DOI:10.1107/S0907444992010400

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Methods for constructing everywhere‐positive electron‐density maps with Fourier amplitudes matching those for arbitrarily large sets of observed data, utilizing dual‐function methods for maximization of entropy, are described. Possible strategies for utilizing these maps for the determination and extension of phases in macromolecular structure determination are suggested, and problems are disc

ISSN:1399-0047    

DOI:10.1107/S0907444992009740

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Three procedures, or `tools', have been developed and tested for applying maximum‐entropy methods to phase extension and toab initiophase determination. The phase expander tool has been used in connection with the solution of two previously unknown macromolecular structures. An efficient algorithm for the determination of an electron‐density distribution that is everywhere positive and that agrees with observed structure amplitudes (tools II and III) has been used to determine the phases of X‐ray diffraction data from recombinant bovine chymosin, a protein with 323 amino‐acid residues in the molecular chain, the structure of which was recently determined using replacement methods. By use of the same maximum‐entropy methods, the structure amplitudes from the unknown structure of bovine heart creatine kinase, a protein with 381 amino‐acid residues, have been phasedab initioto 2.7 Å resolution. The phases of the centric reflections have also been confirmed by a satisfactory solution of the Patterson map of a mercury derivative. The current status of the structure interpretation is presented. This technique has also been applied to a test case where 48 centric reflections from bovine prothrombin fragment 1 data were phasedab initioand subsequently used in the determination of Patterson solutions for a heavy‐atom der

ISSN:1399-0047    

DOI:10.1107/S0907444992009752

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY