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102 MACROMOLECULAR CRYS TALLOGRAPHY

article by Urzhumtseva and Urzhumtsev (1997) and that can be evaluated using FFT (Harada et al.,
Protocol 7.2. 1981; Stubbs and Huber, 1991) and this is avail-
In Protocol 7.3 we show a typical command file able in several MR packages, such as AMoRe
for the AMoRe package (Navaza, 2001), one of the (Navaza, 2001).
most widely used packages for MR.

7.5 The need to find a better score for
7.4 How does one know the solution the rotation function: the Phaser
has been found? euphoria
Sometimes, it is not so easy to convince oneself that Many people have recognized that the rotation
the solution of the molecular replacement problem function suffers from some drawbacks and have
has, in fact, been found, even after rigid-body refine- tried to improve the score by using origin-removed
ment; indeed, the first solution is not always well Patterson functions, normalized structure factors
detached and different scores may produce different E-values, etc. (Brünger, 1997).
rankings. The most commonly used scores are corre- Brünger and colleagues developed a ‘direct
lation coefficients on either intensities or structure- rotation function’, which is just a correlation coef-
factor amplitudes, and R-factors. Even though these ficient between E obs and E mod (Omega), the normal-
criteria are formally related (Jamrog et al., 2004), ized structure factors of the crystal and of the rotated
they can produce different rankings, especially if no model, respectively. However, in this case the model
solution is clearly detached. Some other criterion is is placed in a P1 cell of dimensions and angles iden-
then needed to discriminate between the potential tical to the ones of the crystal being studied. This
solutions. works well but requires quite a lot of cpu as it is not
One possibility is to run simulated annealing amenable to FFT (DeLano and Brünger, 1995).
refinement in torsion angle space as implemented in Another idea is to use different runs of the same
CNS (Brünger et al., 1998). As this is one of the most program with slightly different models; it is most
powerful programs in terms of radius of conver- aptly described as an application of a ‘consistency
gence, it is especially useful to look for the decrease principle’, namely it is required that the solution
of the free-R-factor (Adams et al., 1999), but this is a should appear consistently in all runs, even with
rathercpu-intensivetaskifseveralpossiblesolutions a rather low score. Special algorithms have been
are to be tested. developed to cluster similar solutions in eulerian
In difficult cases, there is actually a way to angles space and convincing results have shown
bring the R-work and R-free down by means other that it is indeed possible to increase the signal-
than just rigid-body or dihedral angle molecular to-noise ratio of the rotation function in this way
dynamics, while still exploring just a few degrees (Urzhumtsev and Urzhumtseva, 2002).
of freedom, using the Normal Mode Analysis pro- Recently, Read extended the maximum likelihood
tocol (Delarue and Dumas, 2004). This is imple- formalism to the molecular replacement problem.
mented in http://lorentz.immstr.pasteur.fr and will Maximum likelihood puts on analytical grounds the
be described in the paragraph on ‘exploring struc- notion that the best model is the one which maxi-
tural diversity’ below (Lindahl et al., 2006). mizes the probability of having measured the actual
Another possibility is to look at the packing experimental data at hand (structure factors). In
of the top 10 solutions, because this can prove his first implementation (BEAST), Read could show
a very discriminating criterion. Even if the solu- that he would get a much clearer signal in difficult
tion is well detached, it is still mandatory (and cases, but the program was pretty slow (Read, 2001).
reassuring) to examine carefully the corresponding Recently, he and his team developed a much more
packing arrangement. This necessary (but not suf- rapid version of his algorithm (PHASER), based on
ficient) condition can actually be implemented in an approximation which can be evaluated by FFT,
the translation function using analytical expression and this was incorporated in a single package that