Heavy atom method, diffraction

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. 

The relative stereochemistry of stephadiamine (16) was clarified by X-ray diffraction analysis, using the direct method, and the absolute configuration was solved by the heavy-atom method, using the N-p-bromobenzoyl derivative (6). Stephadiamine (16), a C-norhasubanan alkaloid, is not regarded as a hasubanan congener in the strict sense, but as a new member of oe-amino acid derivatives (6). 

The method, also called heavy atom method, consists in introducing a heavy atom in the molecule. Then X-rays with a wave length close to the X-ray absorption of the heavy atom is introduced. As a result a phase shift is superimposed on the ordinary diffraction pattern and configuration is then deduced. The method was first employed in 1951 by Bijvoet et al. to examine sodium rubidium tartrate who concluded that it is possible to differentiate between the two optically active forms. In other words it was possible to determine the absolute configuration of the enantiomers. Since then the absolute configurations of about two hundred optically active compounds have been elucidated by their correlation with other substances of known configuration. 

As discussed in section 2.3, the electron diffraction intensities need to be corrected before being employed for structure analysis. An empirical method has been set up to correct simultaneously all kinds of distortions in the diffraction data by referring to the heavy atom method and the Wilson statistic technique in X-ray crystallography. After correction, the intensity of each diffraction beam can approximately lead to the modulus of the corresponding structure factor [26]. 

The application of the Patterson technique to locate strongly scattering atoms is often called the heavy atom method (which comes from the fact that heavy atoms scatter x-rays better and the Patterson technique is most often applied to analyze x-ray diffraction data). This allows constructing of a partial structure model ( heavy atoms only), which for the most part define phase angles of all reflections (see Eq. 2.107). The heavy atoms-only model can be relatively easily completed using sequential Fourier syntheses (either or both standard, Eq. 2.133, and difference, Eq. 2.135), sometimes enhanced by a least squares refinement of all found atoms. 

In order to exploit the heavy atom method with crystals of conventional molecules, or to utilize the isomorphous replacement method or anomalous dispersion technique for macro-molecular structure determination, it is necessary to identify the positions, the x, y, z coordinates of the heavy atoms, or anomalously scattering substituents in the crystallographic unit cell. Only in this way can their contribution to the diffraction pattern of the crystal be calculated and employed to generate phase information. Heavy atom coordinates cannot be obtained by biochemical or physical means, but they can be deduced by a rather enigmatic procedure from the observed structure amplitudes, from differences between native and derivative structure amplitudes, or in the case of anomalous scattering, from differences between Friedel mates. 

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are attached to the protein, and the coordinates of these heavy atoms in the unit cell are determined. The X-ray diffraction pattern of both the native protein and its heavy atom derivative(s) are determined. Application of the so-called Patterson function determines the heavy atom coordinates. Following the refinement of heavy atom parameters, the calculation of protein phase angles proceeds. In the final step the electron density of the protein is calculated. 

La Fortelle, E. D. and Bricogne, G. (1997). Maximum-likelihood heavy-atom parameter refinement for multiple isomorphous replacement and multiwavelength anomalous diffraction methods. Method Enzymol. 276, 472 94. 

In order to understand the interactions between these bis-intercalating drugs and IMA more fully, we have crystallized several complexes of them and undertaken the structure determination by x-ray diffraction technique. One of the crystal forms diffracts to 1.6 A resolution with a space group of F222. The crystal structure was determined by the multiple isomorphous replacement method using three different heavy atom derivatives. The structure was refined to an R-factor of 19% and there were moderate number of solvent molecules clearly visible. The crystal... 

The following discussion relates chiefly to complex crystals in w hich all the atoms have much the same diffracting powers—crystals such as those of many organic compounds for it is in these circumstances chat the indirect method of trial and error must often be used. For crystals containing a minority of heavy atoms together with a larger number of lighter atoms in the unit cell, the direct or semi-direct methods described in Chapter X are more appropriate. 

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