Isomorphous replacement methods

The method of isomorphous replacement is the primary method used to determine the relative phases of protein crystal structures. The phenomenon of isomorphism was first described by Mitscherlich in 1819. and is described in Chapter 2. Isomorphous crystals have, by definition, almost identical structures, but with one or more atoms replaced by chemically similar ones (with different X-ray scattering power). The method by which relative phases are determined for a pair of isomorphous crystals depends on a knowledge of the intensity differences between the data sets for the two isomorphous crystals and the location of the varied atom, a quantity that is available from an analysis of the Patterson map or difference map. 

The method of isomorphous replacement is rarely used for small molecules, in part because small unit cells are seldom exactly isomorphous, the change in the identity of one atom causing a significant change in unit-cell dimensions. The use of this method from small molecules, however, illustrates the steps in the procedure. 

If two centrosymmetric crystal structures are isomorphous, the arrangement of atoms is the same in both and only one atom (sometimes more than one) has a different atomic number in the two structures. The differences in the intensities for the Bragg reflections, therefore, result only from the differences in the scattering powers of the two atoms, M, and M2, that can replace each other. The contribution to the structure factors made by the rest of the structure, F/j, is the same for both crystal structures. If the structure amplitudes are F and F2 for a given Bragg reflection in the two structures, then the calculated difference is illustrated by the use of vectors as  

An excellent example of a series of isomorphous compounds is that of the alums, described in Chapter 2. The space group of the alums, which are cubic, is Pa3 with four 7 i/ 3(S04)2T2H20 per unit cell. The potas- 

FIGURE 8.23. Calculation of phase angles for a centrosymmetric crystal by the method of isomorphous replacement. Two isomorphous crystals have structure amplitudes I El I and T2. The replaceable atom M hcis calculated structure factors M = Ml -M2. From these it is possible to deduce relative phases (signs) for Fi and F2- In each ca.se the vector from Fi to F2 must be the same as the vector Fmi—Fm2- 

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The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are... 

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. 

Green, D. W., Ingram, V. M. and Perutz, M. F. (1954). The structure determination of heamoglobin IV. Sign determination by the isomorphous replacement method. Proc. R. Soc. London A225, 287-307. 

Ramakrishnan, V. and Biou, V. (1997). Treatment of multiwavelength anomalous diffraction data as a special case of multiple isomorphous replacement. Method Enzymol. 276, 538-557. 

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... 

These two compounds were solved together, using an isomorphous replacement method [6]. Fig. 6 shows the c-axis projection of theophylline. Caffeine has the hydrogen in the intermolecular hydrogen... 

In 1954, Perutz introduced the isomorphous replacement method for determining phases. In this procedure a heavy metal, such as mercury or platinum, is introduced at one or more locations in the protein molecule. A favorite procedure is to use mercury derivatives that combine with SH groups. The resulting heavy metal-containing crystals must be isomorphous with the native, i.e., the molecules must be packed the same and the dimensions of the crystal lattice must be the same. However, the presence of the heavy metal alters the intensities of the spots in the diffraction pattern and from these changes in intensity the phases can be determined. Besides the solution to the phase problem, another development that was absolutely essential was the construction of large and fast computers. It would have been impossible for Perutz to determine the structure of hemoglobin in 1937, even if he had already known how to use heavy metals to determine phases. 

The isomorphous replacement method becomes ineffective for protein crystals beyond a resolution of 2 to 2.5 A, because the addition of a heavy atom may cause some alteration in structure and it is difficult to observe small changes in intensities that are already very weak. But, structures may be refined to high resolution, as in the molecular replacement procedure, by using the measured intensities at higher resolution and the model structure that has been determined at resolutions of 2 to 2.5 A. 

In order to find a possible disordering of the guest, the isomorphous replacement method was used. 1-methylnaphthalene was replaced with 1-bromonaphthalene, and the resulted inclusion compound was isostructural with the methylnaphthalene one. 

Early crystallographic studies of TMADH provided data from two derivatives at 6 resolution that revealed the domain structure and certain elements of secondary structure (Lim et al., 1982 Lim et al., 1984). Higher resolution data at 2.4 resolution have been collected and the structure solved by the multiple isomorphous replacement method with anomolous scattering (Lim et al., 1986). Analysis of the diffraction pattern lead to the identification of ADP as the third cofactor in TMADH. At the time the 2.4 data set was analysed, there was no sequence information available for TMADH (Lim et al., 1986), except for a 12 residue peptide which contained the covalently bound flavin (Kenney et al., 1978). Gas-phase sequencing of isolated peptides initially provided 80% of the primary sequence of... 

GOase from D. dendroides has been crystallised from acetate buffer at pH 4.5 using ammonium sulphate as precipitant. The structure has been solved by the multiple isomorphous replacement method using three heavy atom derivatives and the model refined to 1.7 resolution to allow detailed structural analysis (Ito et al., 1991 Ito et ah, 1994). 

Comparison of isostructural crystals. Phases can be estimated by comparing intensities of isomorphous (isostructural) crystals that differ only in the identity of one atom. This isomorphous replacement method is the method of choice for macromolecular (protein and nucleic acid) phase determination. In this case the isomorphism is generally between the crystalline macromolecule and its heavy-atom derivative obtained by replacing some of the solvent in the crystal by a compound containing a heavy atom. 

Isomorphous replacement method A method for deriving relative phases by comparing the intensities of corresponding Bragg reflections from two or more isomorphous crystals. If the locations in the unit cell of atoms that vary between each isomorph have been located, for instance from a Patterson map, then the relatiw phase of each Bragg reflection can be assessed if a sufficient number of isomorphs is studied (at least 1 for a centrosymmetric crystal, at least 2 for a noncentrosymmetrir crystal). 

When small crystal structures are studied, all Bragg reflection data are used, and relative phase angles are derived by one of the methods described in Chapter 8, and electron-density maps are calculated to the maximum possible resolution that the wavelength of the X rays permit. On the other hand, because isomorphous replacement methods are used to obtain relative phase angles for macromolecular structures, it is usual to calculate electron-density maps at low resolution initially, and to increase the resolution as more phases from isomorphous replacement data become available. Traditionally the structure determination is divided into three resolution shells that correspond to the minima of the radial distribution of intensities. ... 

Determine relative phases by isomorphous replacement methods and calculate an electron-density map. Alternatively use molecular replacement methods to determine the structure and calculate an electron-density map. 

We have crystallized the enzyme and determined the X-ray structure of PEPC by a multiple isomorphous replacement method. Our current structural model suggests that PEPC forms a dimer of dimers and provides the mechanism for allosteric regulation. 

PEPC from E. coli was crystallized as described previously [1] with minor modifications. X-ray diffraction data were collected at station BL-6B of the Photon Factory, Japan. Intensity data were obtained using a Weisssenberg camera for macromolecule crystallography and imaging plates as a detector [5]. The data were processed using DENZO and scaled by the program SCALEPACK [6]. The crystal structure was determined by multiple isomorphous replacement method. 

As with the isomorphous replacement method, the locations x, y, z in the unit cell of the anomalous scatterers must first be determined by Patterson techniques or by direct methods. Patterson maps are computed in this case using the anomalous differences Fi,u — F-h-k-i-Constructions similar to the Harker diagram can again be utilized, though probability-based mathematical equivalents are generally used in their stead. 

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. 

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