Efficient methods for the linearization and solution of phase-invariant equations

Langs, D. A.; Han, Fusen

doi:10.1107/s0108767395001000

Cited by 4 publications

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“…Furey et al (1985) were among the first to attempt to use these SAS triples co estimates to determine macromolecular phases by using multisolution tangent formula methods. Alternative methods to determine these phases employing the SAS triples co estimates have been proposed (Han et al, 1991;Langs & Han, 1995;Langs et aL, 1998) and other strategies may be developed in the future. However, the published formulae to evaluate the co estimates are sufficiently complex and cumbersome as to discourage most investigators from writing computer codes to obtain these phase-invariant estimates for their own research applications.…”

Section: Introductionmentioning

confidence: 99%

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

Langs¹

1998

J Appl Cryst

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Section: Introductionmentioning

confidence: 99%

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

Langs¹

1998

J Appl Cryst

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Improvement of SAS triple invariant estimates for macromolecular direct-methods phasing

2001

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Single-wavelength anomalous dispersion (SAS) data can in principle be phased by direct methods since a priori estimates of the three-phase structure invariants can be computed from these data. The mean phase error of the most reliable triple estimates for a small protein, however, is typically no better than 60, and does not bode well for applications to larger structures. A procedure is described that can substantially lower the error in these estimates and introduce a larger number of useful triple invariants into the phasing process. The mean phase error of the most reliable triples for a 2.5 A Ê resolution data set from a Pt derivative of a 115-residue protein was reduced from 55 to 25 by this method. It was also possible to identify a signi®cant number of the poorest triple estimates, those with mean phase errors approaching 90, such that they could be reliably down-weighted or excluded from the phasing process.

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Progress on the direct-methods solution of macromolecular structures using single-wavelength anomalous-dispersion (SAS) data

1999

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In the past few years, a number of strategies have been outlined to resolve the SAS phase ambiguity given that unique estimates 3(h, k) of the triple invariants are available. A new least-squares method is described that can in principle resolve the phase ambiguity to determine macromolecular phases provided that 3(h, k) estimates are unbiased. Limitations of the method in practical applications are discussed. An example is given where the correct solution can be identi®ed by use of the SAS tangent formula in the instance that traditional SAS phasing methods have lead to an incorrect heavy-atom substructure.

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Efficient methods for the linearization and solution of phase-invariant equations

Cited by 4 publications

References 2 publications

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

Improvement of SAS triple invariant estimates for macromolecular direct-methods phasing

Progress on the direct-methods solution of macromolecular structures using single-wavelength anomalous-dispersion (SAS) data

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