Isomorphous derivatives

The addition of one or more heavy atoms to a macromolecule introduces differences in the diffraction pattern of the derivative relative to that of the native. If this addition is truly isomorphous, these differences will represent the contribution from the heavy atoms only thus the problem of determining atomic positions is initially reduced to locating the position of a few heavy atoms. Once the positions of these atoms are accurately determined, they are used to calculate a set of phases for data measured from the native crystal. Although, theoretically, one needs only two isomorphous derivatives to determine the three-dimensional structure of a biological macromolecule, in practice more than two are needed. This is due to errors in data measurement and scaling and in heavy-atom positions, as well as lack of isomorphism. 

There was some hope that the successes with cryotempeiature methods would make progress less dependent on a high intensity synchrotron beam and that at least preliminary experiments such as the search for isomorphous derivatives would become feasible in our own laboratory. However, experience in the past year has taught us that neither a weaker synchrotron beam nor a rotating anode ever yields a diffraction pattern comparable in Bragg resolution to Figure 8c. 

If two isomorphous derivatives in which the replaceable atoms have considerably different diffracting powers are available, an improved form of this method can be used. Strychnine sulphate pentahydrate and the corresponding selenate form isomorphous monoclinic crystals of space group C2 Bokhoven, Schoone, and Bijvoet (1951) solved the centrosymmetric b projection by the straightforward method first used... 

Fig. 2X3. Determination of phase angles in non-centrosymmctric crystals, a. Amplitudes and phases for corresponding reflections in isomorphous sulphate and selenate of strychnine. b. Knowledge of -Fguiphi aeb and ifse fs) gives magnitude but not sign of a c. Amplitudes and phases for a protein and two isomorphous derivatives with heavy atoms at different sites, d. Knowledge of Fp, Fp x p+Y fx> fy and gives unique...

Bradshaw, J. P., Miller, A., and Wess, T. J. (1989). Phasing the meridional diffraction pattern of type I collagen using isomorphous derivatives. J. Mol. Biol. 205,... 

Crystals of the material are grown, and isomorphous derivatives are prepared. (The derivatives differ from the parent structure by the addition of a small number of heavy atoms at fixed positions in each — or at least most — unit cells. The size and shape of the unit cells of the parent crystal and the derivatives must be the same, and the derivatization must not appreciably disturb the structure of the protein.) The relationship between the X-ray diffraction patterns of the native crystal and its derivatives provides information used to solve the phase problem. 

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. 

Another problem that frequently arises with multiple isomorphous derivatives is that of handedness. In space group P2i2i2i, Patterson maps for two independent derivatives may be interpreted to yield a set of symmetry related sites for one derivative and, independently, a second set for the other. Because handedness is completely absent in a Patterson map (because it contains a center of symmetry), there is an equal chance that the heavy atom constellation for the first will be right handed, and the constellation for the other will be left handed, and vice versa. This won t do. The two heavy atom sets will not cooperate when used to obtain phase information. There are ways of unraveling this problem too, and once again, it involves difference Patterson maps between the two derivative data sets and cross vectors. This case can also be resolved by calculating phases based on only one derivative and then computing a difference Fourier map (see Chapter 10) for the other. 

For example, if we have another heavy atom isomorphous derivative available with heavy atom sites different from those found in the first derivative, when the preceding process is repeated, we will get two solutions, one true and one false for each reflection from the second derivative as well. The true solutions should be consistent between the two derivatives while the false solution should show a random variation. Thus, by comparing the solutions obtained from these two calculations, one (the computer) can establish which solution represents the true phase angle. This is the principle of the MIR method. One can also utilize the anomalous scattering (AS) data of the first derivative to resolve the phase ambiguity. In this case, the technique is called the SIRAS approach. If two derivatives and anomalous data are used, then it is called the MIRAS approach. 

In the analysis of the topology of such nets we can look for a classification scheme that will allow one to uniquely assign equal nets (up to isomorphism) derived from totally different crystal structures. Remember that the topology is not influenced by the metrical properties of the structure (angles, distances), so that a 4-connected diamondoid net is such, even if highly distorted (the geometry around the nodes could be far from tetrahedral), and also, obviously, is not dependent on the chemical nature of each node/vertex. 

The chemical preparation step in which the protein is isolated, purified, and crystallized is critical in that the protein preparation must be chemically homogeneous otherwise, the resulting disorder will muddle the electron-density map. The preparation of isomorphous derivatives by soaking native protein crystals in various mercury, platinum, lead, uranium, etc., solutions also is critical since several crystals of each derivative are required for x-ray data collection (because of irradiation damage) and all the crystals should have the same heavy-atom distribution and concentration. The protein structure documentation should provide evidence that the preparative protein chemistry is sound. 

The use of native labels avoids the difficult task of finding isomorphous derivatives. Sulfur is present in the amino acids methionin and cystein. The latter very often form disulfide bridges between adjacent protein chains. It is an important constituent of rubber and it is also found in fossile fuels and many minerals. Phosphorus is present in ribonucleic acids and in polar head groups of membranes. 

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. 

For proteins, the structures selected are the native protein and, in the most favorable cases, several isomorphous derivatives with different heavy atoms, every one bound at a certain site in the protein. 

FIGURE 5.22 The phase relations between the stmcture factor of the sample (parent) crystal (P) and the stmcture factor of its isomorphic derivatives, with heavy (H) atoms ... 

As an example, by reacting copper fumarate and copper 2-methyl ftimarate with pyrazole in solvothermal conditions, two isomorphous derivatives based on the [Cu3(/u-3-OH)(/u,-pz)3] moiety (see Fig. 30.13) were isolated. Moreover, both compounds self-assemble forming ID waved CPs that further interconnect, generating almost identical 2D sheets [20]. 

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