We can derive a
Patterson map for the intensities, which is an interatomic vector map created by squaring the structure factor amplitudes and setting all phases to zero. This vector map contains a peak for each atom related to every other atom, with a large peak at 0,0,0, where vectors relating atoms to themselves "pile up". Such a map is far too noisy to derive any high resolution structural information—however if we generate Patterson maps for the data derived from our unknown structure, and from the structure of a previously solved homologue, in the correct orientation and position within the
unit cell, the two Patterson maps should be closely correlated. This principle lies at the heart of MR, and can allow us to infer information about the orientation and location of an unknown molecule with its unit cell. Due to historic limitations in computing power, an MR search is typically divided into two steps:
rotation and
translation.
Rotation function In the rotation function, our unknown Patterson map is compared to Patterson maps derived from our known homologue structure in different orientations. Historically
r-factors and/or
correlation coefficients were used to score the rotation function, however, modern programs use
maximum likelihood-based algorithms. The highest correlation (and therefore scores) are obtained when the two structures (known and unknown) are in similar orientation(s)—these can then be output in
Euler angles or
spherical polar angles.
Translation function In the translation function, the now correctly oriented known model can be correctly positioned by translating it to the correct co-ordinates within the asymmetric unit. This is accomplished by moving the model, calculating a new Patterson map, and comparing it to the unknown-derived Patterson map. This brute-force search is computationally expensive and fast translation functions are now more commonly used. Positions with high correlations are output in
Cartesian coordinates. ==Using
de novo predicted structures in molecular replacement==