Molecular replacement translation search

The model protein is used to search the crystal space until an approximate location is found. This is, in a simplistic way, analogous to the child s game of blocks of differing shapes and matching holes. Classical molecular replacement does this in two steps. The first step is a rotation search. Simplistically, the orientation of a molecule can be described by the vectors between the points in the molecule this is known as a Patterson function or map. The vector lengths and directions will be unique to a given orientation, and will be independent of physical location. The rotation search tries to match the vectors of the search model to the vectors of the unknown protein. Once the proper orientation is determined, the second step, the translational search, can be carried out. The translation search moves the properly oriented model through all the 3-D space until it finds the proper hole to fit in. 

Fokine, A. and Urzhumtsev, A. (2002) On the use of low-resolution data for translation search in molecular replacement. Acta Crystallogr. D 58,72-74. 

Because ALBP is related to several proteins of known structure, molecular replacement is an attractive option for phasing. The choice of a phasing model is simple here just pick the one with the amino-acid sequence most similar to ALBP, which is myelin P2 protein. Solution of rotation and translation functions refers to the search for orientation and position of the phasing model (P2) in the unit cell of ALBP. The subsequent paper provides more details. 

A GA method has been developed [92, 93] for ab initio phasing of low-resolution X-ray diffraction data from highly symmetric structures. The direct-space parameterization used incorporates information on structural symmetry, and has been applied to study the structures of viruses, with resolution as high as 3 A [93]. A GA has also been introduced [94] to speed up molecular replacement searches by allowing simultaneous searching of the rotational and translational parameters of a test model, while maximizing the correlation coefficient between the observed and calculated diffraction data. An alternative GA for sixdimensional molecular replacement searches has been described [95,96] and GA methods have also been used [97] to search for heavy atom sites in difference Patterson functions. 

In these instances, the need for heavy atoms can be frequently side-stepped by performing a reciprocal space search in 6 dimensions - 3 rotational and 3 translational. For each point in this vast 6-dimensional space, the calculated Fourier amplitudes from the suitably rotated and translated model can be compared with the experimental Fourier amplitudes. Such an exhaustive search can in principle give the correct orientation and location of the available approximate model in the new crystal. This allows the calculation of approximate phases for the crystal structure and ultimately leads to an accurate atomic structure. However, such a molecular replacement solution does not always work. This is because in practice, a truly exhaustive 6-dimensional search is not possible given present day computing resource. So this 6-dimensional problem is routinely split into two far smaller and consecutive 3-dimensional problems - 3-dimensional... 

It is possible, as shown by Rossmann and Blow (1962), to search for redundancies in Patterson space that correspond to the multiple copies of molecular transforms. Rossmann and Blow show, however, that the Patterson map does not need to be computed and used in any graphical sense, but that an equivalent search process can be carried out directly in diffraction or reciprocal space. Using such a search procedure, called a rotation function, they showed that noncrystallographic relationships, both proper and improper rotations, could be deduced in many cases directly from the X-ray intensity data alone, and in the complete absence of phase information. Translational relationships (only after rotations have been established) can also be deduced by a similar approach. Rotation functions and translation functions constitute what we call molecular replacement procedures. Ultimately the spatial relationships among multiple molecules in an asymmetric unit can be defined by their application. 

This alternative way of looking at a Patterson map is illustrated by a four atom and a five atom structure in Figures 9.5 and 9.6. This is sometimes a useful way of considering the Patterson map because it provides the basis for various kinds of Patterson search methods where the objective is to find the image of a known part of a molecule in Patterson space. It is also the basis for the rotation and translation functions used in molecular replacement procedures (see Chapter 8). 

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