Multiple isomorphous replacement phasing

In the crystallographic case, the limited radius of convergence of refinement arises not only from the high dimensionality of the parameter space, but also from what is known as the crystallographic phase problem . With monochromatic diffraction experiments on single crystals, one measures the amplitudes of the reflections, not the phases. The phases, however, are required to compute electron density maps, which are obtained 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. However, electron density maps computed from a combination of native crystal amplitudes and multiple isomorphous replacement phases are sometimes insufficiently accurate to allow a complete and unambiguous tracing of the macromolecule. Furthermore, electron density maps for macromolecules are... 

In small-molecule crystallography the phase problem was solved by so-called direct methods (recognized by the award of a Nobel Prize in chemistry to Jerome Karle, US Naval Research Laboratory, Washington, DC, and Herbert Hauptman, the Medical Foundation, Buffalo). For larger molecules, protein aystallographers have stayed at the laboratory bench using a method pioneered by Max Perutz and John Kendrew and their co-workers to circumvent the phase problem. This method, called multiple isomorphous replacement... 

The intensity differences obtained in the diffraction pattern by illuminating such a crystal by x-rays of different wavelengths can be used in a way similar to the method of multiple isomorphous replacement to obtain the phases of the diffracted beams. This method of phase determination which is called Multiwavelength Anomalous Diffraction, MAD, and which was pioneered by Wayne Hendrickson at Columbia University, US, is now increasingly used by protein cystallographers. 

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... 

The problem of phase determination is the fundamental one in any crystal structure analysis. Classically protein crystallography has depended on the method of multiple isomorphous replacement (MIR) in structure determination. However lack of strict isomorphism between the native and derivative crystals and the existence of multiple or disordered sites limit the resolution to which useful phases may be calculated. 

In order to resolve the phase ambiguity from the first heavy-atom derivative, the second heavy atom must bind at a different site from the first. If two heavy atoms bind at the same site, the phases of will be the same in both cases, and both phase determinations will provide the same information. This is true because the phase of an atomic structure factor depends only on the location of the atom in the unit cell, and not on its identity (Chapter 5, Section III.A). In practice, it sometimes takes three or more heavy-atom derivatives to produce enough phase estimates to make the needed initial dent in the phase problem. Obtaining phases with two or more derivatives is called the method of multiple isomorphous replacement (MIR). This is the method by which most protein structures have been determined. 

A preliminary x-ray structure of T. thermophilus manganese catalase (oxidized state) at 3 A resolution has been reported [80], The original solution was obtained by multiple isomorphous replacement followed by phase improvement [80], Recently both the reduced (MnnMnn) (Figure 10) and the oxidized... 

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... 

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. 

The most general method of solving the phase problem for protein crystals is that of multiple isomorphous replacement in which two or more isomorphous heavy-atom derivatives are used.1 The principle of the method is shown in Figure 3. In Figure 3a a circle with radius Fp, the amplitude of a reflection from the native protein, is shown with center at the origin, O. It is assumed that the heavy atoms in at least two derivatives have been located and referred to the same unit cell origin. This can be a difficult problem and mistakes can be made, but... 

Figure 6.28 Representation in the Gaussian plane of the phase relationships derived by multiple isomorphous replacement, MIR, 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 derivatives, FPHi and FPH2, lie on circles of radii FPHi and Fph2 with centres at the tips of the vectors -FHi and -Fje. The intersection of the three circles represents a unique solution to the position of FP, corresponding to a single phase angle...

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