摘要:

The entropy‐dynamics method seeks maxima for the entropy of the electron density forNatoms in a crystal cell, when the Fourier amplitudes are fixed, but their phases are unknown. By analogy with molecular dynamics, the effective potential energy is the negative entropyV= −NS. The kinetic energy is proportional to the squared velocities of the electron densities at grid points in the map. It reduces to a sum of Fourier‐mode rotor energies. Each rotor angle experiences a couple equal to the phase gradient ofS, and local dynamical equilibrium yields a Boltzmann distribution ofS. Discrete phase angles (e.g.signs) are treated as quantized rotor modes. The distributions depend on apopularityfunction of the entropy histogram. Trial calculations have been made of phase averages and correlations in a centrosymmetric projection of the membrane protein bacteriorhodopsin. The maximum‐entropy solution and the correct solution do not always c

ISSN:1399-0047    

DOI:10.1107/S0907444992008102

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Entropy maximization has proven effective in treating certain aspects of the phase problem of X‐ray diffraction. Much of its development has been expressed in probabilistic language, although image enhancement has been somewhat more physical or geometric in description. Here phasing and entropy maximization are embedded in the quantum mechanical problem of reconstructing an electronic one‐matrix under experimental constraints. Entropy on anN‐representable one‐particle density matrix is well defined. The entropy is the expected form, and it is a simple function of the one‐matrix eigenvalues which all must be non‐negative. Certain other properties are pertinent to phasing which is implicit in one‐matrix reconstruction governed by entropy maximization. Throughout this work reference is made to informational entropy, not the entropy of t

ISSN:1399-0047    

DOI:10.1107/S0907444992009429

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

The specific properties of the range of possible electron‐density values may serve as useful additional information for the determination and refinement of structure‐factor phases. Fourier synthesis histograms (showing the spectra of frequencies of different possible values) produce the most adequate representation of these properties. The mathematical background and practical uses of these histograms are discussed. The investigation provides new information on some traditional methods of phase refinement, including density‐modification procedures, maximization of Cochran's integral value and other techn

ISSN:1399-0047    

DOI:10.1107/S0907444992009247

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Xtal3.2, a crystallographic software package, is an international development project involving about 40 researchers over a full spectrum of crystallographic interests. This development has been supported by many national and international agencies and commercial institutions since the first version in 1983. The 1992 release,Xtal3.2, contains software for 95 different calculations. These range from the processing of raw diffraction data to interactive molecular graphics, atomic charge estimation, electronic publication preparation, and the structure solution and refinement of small and large molecules. Tests of theXtalprograms for phase determination and phase refinement by the application of `maximum entropy' are presented.

ISSN:1399-0047    

DOI:10.1107/S0907444992008898

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

ISSN:1399-0047    

DOI:10.1107/S0907444992009235

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

The condensing‐protocol strategy for obtaining low‐resolution real‐space envelopes of macromolecules from native Fourier intensities alone was recently reported [Subbiah (1991).Science,252, 128–133]. The present work introduces three improvements to the original methodology. In terms of thejindex, which was defined as the crude ratio of correctly placed scatterers to those incorrectly placed, these changes collectively contribute tojvalues that range from 8 to 28 and in one case even infinity. This compares with the previously reported values of 1.9 and 2.6. Nevertheless, under different conditions, both the original and the current improved condensing protocol can preferentially converge on the solvent or the matter region. Since such control is not absolute there still remains a certain amount of ambiguity in deciding whether the congealed gas represents bulk solvent or bulk matter. To overcome this ambiguity, a simple method based on the systematic placement of point scatterers on a grid lattice within and without the envelope is presented. This `sign‐fixing' method is shown to work with both perfect envelopes as well as the cruder envelopes produced by the improved condensing protocol. The new methodology is illustrated using four macromolecular

ISSN:1399-0047    

DOI:10.1107/S0907444992009697

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Synchrotron radiation has been used extensively to overcome a variety of technical challenges involved in data collection from macromolecular crystals. The next generation of such sources offer a higher brilliance at much shorter wavelengths than hitherto available. Hence, the quality of X‐ray diffraction data from crystals of biological macromolecules will be further improved in terms of reduced systematic and random errors, in conjunction with a very high degree of completeness of, and multiple measurements within, the data set. Real data sets should be able to approach closely the quality of ideal data sets. Tests at CHESS are described of the feasibility of recording protein crystal diffraction patterns at ultra‐short wavelengths (λ = 0.3 Å) and very‐short wavelengths (λ = 0.5 Å), in monochromatic rotating cry

ISSN:1399-0047    

DOI:10.1107/S0907444992006747

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

An automated refinement procedure (ARP) for protein models is proposed, and its convergence properties discussed. It is comparable to the iterative least‐squares minimization/difference Fourier synthesis approach for small molecules. ARP has been successfully applied to three proteins, and for two of them resulted in models very similar to those obtained by conventional least‐squares refinement and rebuilding withFRODO. In real time ARP is about ten times faster than conventional refinement. In its present form ARP requires high (2.0 Å or better) resolution data, which should be of high quality and a starting protein model having about 75% of the atoms in roughly the correct position. For the third protein at 2.4 Å resolution, ARP was significantly less powerful but nevertheless gave definite improvement, in the density map

ISSN:1399-0047    

DOI:10.1107/S0907444992008886

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

A general scheme for the improvement of electron‐density maps is described which combines information from real and reciprocal space. The use of Sayre's equation, solvent flattening and histogram matching within this scheme has been described previously [Main (1990).Acta Cryst. A46, 372377]. Non‐crystallographic symmetry averaging, the use of a partial structure and constraints on individual structure factors have now been added. A computer program,SQUASH, is described which applies all these constraints simultaneously. Its application to the maps of several structures has been successful, particularly so when non‐crystallographic symmetry is present. Uninterpretable maps have been improved to the point where a significant amount of the structure can be recognized. Applying the constraints simultaneously is more powerful than applying them all in s

ISSN:1399-0047    

DOI:10.1107/S0907444992007698

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY

摘要:

Not all crystallographic structural investigations are amenable to a phasing solution by direct methods alone. Guideline procedures are outlined which are intended to help the evaluation of whether direct‐methods procedures may be expected to phase diffraction data for large molecular structures. This analysis is directed at three separate levels of inquiry: (1) How good are the primary data and canEvalues be derived to represent a point‐atom structure. (2) How well do the data interact through phase relationships and may they be expected to produce a stable phasing solution. (3) What is the prognosis for finding recognizable solutions. Data are presented from the post‐mortem analyses of a number of large, difficult‐to‐solve, structures to illustrate each of these points. Direct‐methods practitioners are to be encouraged that crystal structures having more than 300 atoms per asymmetric unit may occasionally be determined utilizing present methodologies provided that ana prioriprognosis for obtaining a solution is favorably high, adequate computational resources are available, and sufficient persistent effort

ISSN:1399-0047    

DOI:10.1107/S0907444992006231

出版商:International Union of Crystallography    

年代:1993

数据来源: WILEY