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

Abstract

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...

Improving radiation-damage substructures for RIP

“…For weak derivatives, an accurate knowledge of the scale factor might not be required (Rossmann, 1960); however, it has been shown that adjustment of the scale factor to compensate for the additional scattering power of heavy atoms for strong derivatives can lead to significant improvements (Nikonov, 1983). Although individual structure-factor amplitudes might grow stronger with X-ray dose, the total scattering power will normally decrease during an RIP experiment.…”

“…1) is similar to that corresponding to an MIR experiment (Kendrew et al, 1958), where F const can be thought of as the structure factor belonging to the native structure, whereas F before and F after can be seen as equivalent to two different heavy-atom derivatives. Rossmann (1960) Harker section of a calculated data series for turkey egg-white lysozyme (TEL) in space group P2 1 , based on PDB code 1ljn. TEL has four disulfide bonds, three of which were subsequently altered.…”

The beginnings of structural biology

“…One of these related to determining the relative positions of heavy atoms. By writing a Fourier summation program in machine code for the recently homebuilt EDSAC2 computer (situated across the quadrangle in the Mathematical Laboratory), and by virtue of the 3-dimensional data Max and Ann Cullis had collected, I was able to develop a simple and unambiguous solution of the relative heavy atom sites (Rossmann, 1960) within my first 3 months in Cambridge. Max was delighted and brought in all the old hands like Bernal, Sir Lawrence, and Dorothy Hodgkin to show them the new results.…”

“…Over the next few months, and later in collaboration with David Blow, it was possible to develop many of the techniques that are now standard fare in protein structure determinations. These included heavy atom refinement procedures (Rossmann, 1960), the use of anomalous dispersion for heavy atom site determination (Rossmann, 1961) and phase improvement, single isomorphous replacement (Blow & Rossmann, 1961), and phase combination (Rossmann & Blow, 1961). The other things that stand out in my recollections of my first year in Cambridge are punting parties along the Cam, scones at the "Orchard" in Granchester (while wasps were busy competing for the jam), unlocking large iron gates to the Old Cavendish Site with illegal copies of an enormous key possessed by everybody, and 2-way traffic in Petty Cury, a very narrow street leading to Cambridge's market place.…”

Isomorphous binding of mercury-substituted thiosaccharides to pertussis toxin crystals yields crystallographic phases

“…Isomorphous replacement requires the preparation of a crystal in which very few heavy atoms are bound at identical points in each unit cell without introducing significant conformational changes (Blundell & Johnson, 1976). Heavy-atom sites in the unit cell may then be located with difference Patterson methods (Rossmann, 1960). When crystals contain more than a few bound heavy atoms, difference Patterson maps are not readily interpretable (Dodson & Vijayan, 1971).…”