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Single isomorphous replacement with

As an aside, let us return for a moment to SIR. How can anomalous scattering be used to break the phase ambiguity of SIR if both methods have similar Harker constructions Fortunately, the information from the isomorphous differences and the anomalous differences is not the same, but complementary. If, as is usually the case, the heavy atom is the only anomalous scatterer, the substructure is the same, that is, we can use the same AH for a reflection h, k, l. When the anomalous difference/" and its inverse are added to Fh, we can draw two circles of radii FPh + and FPh centered at the ends of each vector (Figure 24). With the FP -circle centered at the origin, these three circles only intersect at one point, which defines the phase of FP. This method is Single Isomorphous Replacement with Anomalous Scattering - or SIRAS. [Pg.71]

This approach is known as single isomorphous replacement with anomalous scattering (SIRAS). Trigonometric equations can be derived... [Pg.41]

SIROAS Single isomorphous replacement with optimised anomalous... [Pg.585]

The uranyl heavy atom parameters were then used to calculate Fj and Fj two sets of phases for the protein were calculated - one for each possible heavy atom enantiomorph - by the method of single isomorphous replacement with the inclusion of anomalous scattering data. The value of E" was initially calculated from the r.m.s. error in the least squares refinement for the centric zone, and E" was made equal to E/3. The phases, were used to compute difference Fouriers with coefficients (Fp - Fp exp.iap for the other derivatives. The phases calculated from uranyl positions gave a clear indication of the heavy atom positions of other derivatives which agreed well with those positions determined from the Patterson functions. The enantiomorphic set of uranyl positions gave no clear indication of the heavy atom positions. Thus, the correct enantio-morphs and relative origins for derivatives were established. We then carried out a series of phase refinement cycles (16,17). [Pg.46]

Figure 6.3 Isomorphous replacement phase determination (Marker construction), (a) Single isomorphous replacement. The circle with radius Fpp represents the heavy-atom derivative, while that with radius Fp represents the native protein. Note that the circles intersect at two points causing an ambiguity in the phase angle apg and apt, represent the two possible values, (b) Double isomorphous replacement. The same construction as that in single isomorphous replacement except that an additional circle with radius Fpn2 (vector not shown for simplicity) has been added to represent a second heavy-atom derivative. Note that all three circles (in the absence of errors) intersect at one point thus eliminating the ambiguity in the protein phase angle ap. Fm and Ppy represent the heavy-atom vectors for their respective derivatives. Figure 6.3 Isomorphous replacement phase determination (Marker construction), (a) Single isomorphous replacement. The circle with radius Fpp represents the heavy-atom derivative, while that with radius Fp represents the native protein. Note that the circles intersect at two points causing an ambiguity in the phase angle apg and apt, represent the two possible values, (b) Double isomorphous replacement. The same construction as that in single isomorphous replacement except that an additional circle with radius Fpn2 (vector not shown for simplicity) has been added to represent a second heavy-atom derivative. Note that all three circles (in the absence of errors) intersect at one point thus eliminating the ambiguity in the protein phase angle ap. Fm and Ppy represent the heavy-atom vectors for their respective derivatives.
For more than 50 years it has been known that the barely measurable differences between Fhki and F-n-k-t contained useful phase information. For macromolecular crystals lacking anomalous scattering atoms, this phase information was impossible to extract and use because it was below the measurement error of reflections. Anomalous dispersion was, however, sometimes useful in conjunction with isomorphous replacement where the heavy atom substitutent provided a significant anomalous signal. The difference between F ki and F-h-k-i was, for example, employed to resolve the phase ambiguity when only a single isomorphous derivative could be obtained (known as single isomorphous replacement, or SIR) or used to improve phases in MIR analyses. [Pg.189]

Figure 6a. A vector diagram illustrating the native protein (Fp) and heavy atom (F ) contributions to the structure factor (Fp,d for the heavy atom derivative of the protein. Sp, and are the phases for the native protein, the heavy atom, and the heavy atom derivative of the protein, respectively, b. The Marker construction for the phase calculation by the method of single isomorphous replacement corresponding to the situation shown in Figure 6a. The scale has been reduced slightly. The vector AB represents the amplitude (Fh) and phase (an) of the heavy atom. With centre A a circle radius Fp is drawn. Similarly, with centre B a circle radius Fp is drawn. The intersections of the circles at O and O represent the two possibilities for ap. Only one (O) is the correct solution. Figure 6a. A vector diagram illustrating the native protein (Fp) and heavy atom (F ) contributions to the structure factor (Fp,d for the heavy atom derivative of the protein. Sp, and are the phases for the native protein, the heavy atom, and the heavy atom derivative of the protein, respectively, b. The Marker construction for the phase calculation by the method of single isomorphous replacement corresponding to the situation shown in Figure 6a. The scale has been reduced slightly. The vector AB represents the amplitude (Fh) and phase (an) of the heavy atom. With centre A a circle radius Fp is drawn. Similarly, with centre B a circle radius Fp is drawn. The intersections of the circles at O and O represent the two possibilities for ap. Only one (O) is the correct solution.
In addition to the MAD and SAD methods, there are the traditional isomorphous replacement methods that include multiple isomorphous replacement (MIR), which uses several heavy atom derivatives, and single isomorphous replacement (SIR), which uses only one heavy atom derivative. The underlying principle to all these methods is the phase-triangle relationship. To understand this relationship we shall begin our discussions with the isomorphous replacement method. [Pg.21]

Figure 6.27 Representation in the Gaussian plane of the phase relationships derived by single isomorphous replacement, SIR, in a protein. The structure factor of the protein vector, FP, lies on a circle of radius FP centred at O. The structure factor of the heavy metal derivative, FPH, lies on a circle of radius Fph, with centre at the tip of the vector -Fh- The intersection of the two circles represents the two solutions to equation (6.6). The resulting vector FP can be drawn in two positions, corresponding to two different phase angles... Figure 6.27 Representation in the Gaussian plane of the phase relationships derived by single isomorphous replacement, SIR, in a protein. The structure factor of the protein vector, FP, lies on a circle of radius FP centred at O. The structure factor of the heavy metal derivative, FPH, lies on a circle of radius Fph, with centre at the tip of the vector -Fh- The intersection of the two circles represents the two solutions to equation (6.6). The resulting vector FP can be drawn in two positions, corresponding to two different phase angles...
Single (or multiple) isomorphous replacement with optimised anomalous scattering (Helliwell 1977a Helliwell et al 1984a) can be... [Pg.356]

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. [Pg.312]

This limited radius of convergence arises from the high dimensionality of the parameter space, but also from what is known as the crystallographic phase problem [2]. With monochromatic diffraction experiments on single crystals one can measure the amplitudes, but not the phases, of the reflections. The phases, however, are required to compute electron density maps by Fourier transformation of the structure factor described by a complex number for each reflection. Phases for new crystal structures are usually obtained from experimental methods such as multiple isomorphous replacement [3]. Electron density maps computed by a combination of native crystal amplitudes and multiple isomorphous... [Pg.259]

In the discussion of single and multiple isomorphous replacement (called SIR and MIR respectively), we have to this point tacitly assumed all things to be ideal. In reality this is never the case, certainly not in X-ray crystallography. In terms of Harker diagrams this means that for virtually all Fhki, the circles for the first heavy atom derivative and the second heavy atom derivative never really intersect the native circle at a common point. In the best of circumstances they come close, but for many hkl they don t. Figure 8.5c represents a more typical case, and Figure 8.5dhow we have traditionally dealt with it (for details, see Dickerson, 1968 Blundell and Johnson, 1976 Blow and Crick, 1959 Drenth, 1999). [Pg.181]

Excellent and detailed treatments of the use of anomalous dispersion data in the deduction of phase information can be found elsewhere (Smith et al., 2001), and no attempt will be made to duplicate them here. The methodology and underlying principles are not unlike those for conventional isomorphous replacement based on heavy atom substitution. Here, however, the anomalous scatterers may be an integral part of the macromolecule sulfurs (or selenium atoms incorporated in place of sulfurs), the iron in heme groups, Ca++, Zn++, and so on. Anomalous scatterers can also be incorporated by diffusion into the crystals or by chemical means. With anomalous dispersion techniques, however, all data necessary for phase determination are collected from a single crystal (but at different wavelengths) hence non-isomorphism is less of a problem. [Pg.188]

For these reasons the Mossbauer scattering technique in principle is a suitable alternative to the isomorphous replacement method. Several experimental difficulties, however, as for example the preparation of strong Co57 sources (up to 500 mCi/mm2), the enrichment of heme-protein single crystals with Fe57 (49), and the experimentation at low temperatures (77 °K) (115), have prevented the nuclear resonance... [Pg.163]

Fig. 4. Accordion HMQC pulse sequence developed by Zangger and Armitage. - This experiment was developed to facilitate the study of metallothioneins in which cadmium has been inserted as an isomorphic replacement for the zinc atoms normally bound to metallothioneins. By using the accordion HMQC experiment, Zangger and Armitage were able to observe correlation responses to the seven cadmium atoms in a single experiment rather than having to perform several conventional experiments with varied optimization. Fig. 4. Accordion HMQC pulse sequence developed by Zangger and Armitage. - This experiment was developed to facilitate the study of metallothioneins in which cadmium has been inserted as an isomorphic replacement for the zinc atoms normally bound to metallothioneins. By using the accordion HMQC experiment, Zangger and Armitage were able to observe correlation responses to the seven cadmium atoms in a single experiment rather than having to perform several conventional experiments with varied optimization.

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Isomorphs

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