The determination of the phases of the structure factors of non-centrosymmetric crystals by the method of double isomorphous replacement

Harker, David

doi:10.1107/s0365110x56000012

Cited by 97 publications

(50 citation statements)

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“…However, for non-centrosymmetric crystals there exists the problem of determining the position of one atom relative to another without a fixed symmetry element as origin. The first solution of this problem is due to Harker (1956) who considers trial-and-error techniques based on selected reflections. Bragg (1958) suggested a method of fitting sinusoidal curves to the envelope of the differences plotted as a function of sin 0, which can then be shown to correspond to the structure-factor graph of the heavy-atom content of the unit cell.…”

Section: Introductionmentioning

confidence: 99%

The accurate determination of the position and shape of heavy-atom replacement groups in proteins

Rossmann¹

1960

Acta Cryst

112

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If two isomorphous heavy-atom derivatives of a protein are available with structure factors 2/1 and F2 respectively, then a Patterson synthesis with coefficients (IF1[ -IF2[) 2 will give accurate information about the relative position and shape of the heavy-atom peaks in the two compounds. IntroductionGreen, Ingrain & Perutz (1954) introduced the method of isomorphous replacement with heavy atoms to the X-ray analysis of the centro-symmetric zone of horse haemoglobin. In order to determine the phase angle of general reflections multiple isomorphous replacement has to be used, involving the preparation of a series of isomorphous compounds each bearing one or more heavy atoms placed on different sites . The 'heavy atoms' in proteins may often consist of sizeable organic residues to which one or more heavy atoms are attached, producing irregular 'lumps' on an electron-density map.Patterson coefficients ([FHeavy I --IFl)e can be used to determine the position of the heavy atoms in centrosymmetric projections. However, for non-centrosymmetric crystals there exists the problem of determining the position of one atom relative to another without a fixed symmetry element as origin. The first solution of this problem is due to Harker (1956) who considers trial-and-error techniques based on selected reflections. Bragg (1958) suggested a method of fitting sinusoidal curves to the envelope of the differences plotted as a function of sin 0, which can then be shown to correspond to the structure-factor graph of the heavy-atom content of the unit cell. Perutz (1956) proposed two correlation functions, later modified and improved by Blow (1958), which depend on calculating certain Fourier summations from which the heavyatom positions can be deduced. The great advantage of the Perutz-Blow approach is that an overall picture of the cell is obtained, so that subsidiary sites can be discovered. The present paper deals with another Fourier technique which is believed to possess the advantage of giving less background effect, thus leaving no doubt in placing the atomic centre within about 0.4 A from data with 6A resolution. TheoryLet the vectors F(OP), FI(OQ), Fe(OR) be the representation on the Argand diagram of the structure factors of the plane (hkl) for the unsubstituted compound, and for the isomorphous heavy atom derivatives 1 and 2 respectively ( In AROQ f2 = F~ + F~-2F1F2 cos ~ .The difference in phase, ~, between the phase angles of the heavy-atom derivatives 1 and 2 will be small if the heavy-atom contribution in each of the compounds is only a small fraction of the total scattering 15" 222 POSITION AND SHAPE OF HEAVY-ATOM REPLACEMENT GROUPS IN PROTEINS material, as must inevitably occur in the majority of reflexions in a protein structure. Thus to a first order approximation cos ~ = 1. Hencewhere F1 and F2 are the magnitudes of the measured structure factors.I am indebted to Sir Lawrence Bragg for pointing out that the above approximation is not strictly true because cos ~ tends to unity only as a consequence of f bei...

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Section: Introductionmentioning

confidence: 99%

The accurate determination of the position and shape of heavy-atom replacement groups in proteins

Rossmann¹

1960

Acta Cryst

112

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“…A well illustrated description of the SAS application of Harker phase constructions (Harker, 1956) has been given by Kartha (1976). For an anomalously scattering heavy-atom-containing protein PH with a known heavy-atom substructure H, given the measured Friedel pairs of magnitudes IFpH,÷HI and IFpH,-HI and the calculated phased structure factors FH.+H and FH_ n, the Harker construction provides two alternative phase estimates, ~PPH.+n or ~P~'H.+n, for the -t-H reflection from the PH structure (and two corresponding estimates, ~PH,-H or ~O[,H_ n, for the -H reflection).…”

Section: A Sas Perturbed Tangent Formula and An Applicationmentioning

confidence: 99%

On Integrating the Techniques of Direct Methods with Anomalous Dispersion. IV. A Simplified Perturbation Treatment for SAS Phasing

Guo¹,

Blessing²,

Langs³

et al. 1997

Acta Cryst Sect A

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Results from probabilistic theory for the singlewavelength anomalous-scattering (SAS) Friedel pair, two-phase structure invariants, ~n = ~°H + 9-s, are used to show that the SAS three-phase structure invariants, ~Prm = 9n + 9K + 9-n-~, tend to positive values that are easily estimated. Appropriate averages of the estimates provide SAS perturbation corrections in the form of positive origin shifts for the probability distribution of apHK values and for the tangent formula. The theoretical probabilistic results are verified by empirical statistical analyses of model-calculated phases and experimentally measured structure-factor magnitudes for a small-molecule and a protein crystal structure.

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“…Harker, therefore, decided to develop automatic diffractometers as opposed to the ®lm methods being used in Cambridge. In 1956, he published a procedure for plotting the isomorphous data of each re¯ection in a simple graphical manner that allowed an easy determination of its phase (Harker, 1956). Unfortunately, the error associated with the data tended to create a lot of uncertainty.…”

Section: Globular Proteins In the 1950smentioning

confidence: 99%

From the Structures of Simple Salts to Those of Sophisticated Viruses

Rossmann¹

1998

Acta Cryst Sect A

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An account is given of the development of X-ray crystallography from its beginnings in 1912 to its present successes in the determination of virus structures. Brief mention is made of early inorganic and subsequent organic molecule structure determinations, which eventually laid the foundations for the ®rst protein structures in 1957±1959. Various experimental and computational advances were required for these successes. However, additional technical advances were necessary before the ®rst near atomic resolution structures of spherical viruses became possible in 1978±1979. Current emphasis is in probing the multifunctional biological properties of viral capsids when they infect cells.

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The determination of the phases of the structure factors of non-centrosymmetric crystals by the method of double isomorphous replacement

Cited by 97 publications

References 1 publication

The accurate determination of the position and shape of heavy-atom replacement groups in proteins

The accurate determination of the position and shape of heavy-atom replacement groups in proteins

On Integrating the Techniques of Direct Methods with Anomalous Dispersion. IV. A Simplified Perturbation Treatment for SAS Phasing

From the Structures of Simple Salts to Those of Sophisticated Viruses

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