Molecular replacement orientation 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. 

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. 

Each refined orientation of the probe received a correlation coefficient that shows how well it fits the Patterson map of ALBP. The orientation receiving the highest correlation coefficient was taken as the best orientation of the probe, and then used to refine the position of the probe in the ALBP unit cell. The orientation and position of the model obtained from the molecular replacement search was so good that refinement of the model as a rigid body produced only slight improvement in R. The authors attribute this to the effectiveness of the Patterson correlation refinement of model orientation, stage two of the search. 

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... 

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