Single isomorphous replacement

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.

Karle, J. Triplet phase invariants from single isomorphous replacement or one-wavelength anomalous dispersion data, given heavy-atom information. Acta Cryst. A42, 246-253 (1986). 

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. 

Blow, D. M., and Rossmann, M. G. 1961. The single isomorphous replacement method. Acta Cryst. 14 1195. 

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. 

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. 

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...

The value of heavy atom derivative is made, so that now FH1, FH2, FHpi, FHp2 and FP are to be determined. This is called multiple isomorphous replacement (MIR) and is generally used rather than the single isomorphous replacement technique. The values for FHi and Fh2 can be determined using Patterson techniques. Two equations similar to equation 6.6 now exist ... 

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

Figure 2.13 (a) The Harker plot. For acentric reflections the use of a single isomorphous derivative (SIR - single isomorphous replacement) leaves a phase ambiguity at A and B. The use of a second derivative at a different binding site, in the absence of errors would decide uniquely between A and B for the protein phase, ap. 

These authors describe the use of SIROAS applied to protein crystallography in general, and to glutamate dehydrogenase in particular involving a mercury derivative. The acronym, SIROAS, is an adaptation of the standard Cu Ka acronym SIRAS, single isomorphous replacement... 

SIROAS Single isomorphous replacement with optimised anomalous... 

X-ray crystallography is currently the most powerful analytical method by which three-dimensional structure information on biological macromolecules may be obtained at high resolution. Its application is however limited first by the preparation of single crystals suitable for X-ray diffraction and second by the so-called phase problem , that is the calculation of phases of difBaction data. Several approaches are available in order to circumvent this latter problem. The most commonly used methods are the multiple and single isomorphous replacement (MIR, SIR). These methods, as well as multiple anomalous difBaction (MAD), require the preparation of heavy atom derivatives, usually by the introduction of electron-dense atoms at distinct locations of the crystal lattice. This is usually done by crystal soaking experiments. 

The preparation of isomorphous heavy-atom derivatives. If only one iso-morphous derivative is prepared, the method is known as a single isomorphous replacement if more than one derivative is prepared the method is known as multiple isomorphous replacement. 

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). 

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