Page 121 - Macromolecular Crystallography

110 MACROMOLECULAR CRYS TALLOGRAPHY

(Delarue and Dumas, 2004). It is intended to be derivatives does not allow for a straightforward
used as a generalization of Rigid Body refinement, interpretation of the map, it is still possible to use the
as the six degrees of freedom of global rotation and experimental phases in conjunction with the model
translation are also included as Normal Modes of at hand. Indeed, MR in even a poor experimental
null frequency. Convincing test cases, as well as real map will in general give a much stronger signal-to-
cases, have shown that it works well and, although noise ratio than regular MR based on structure factor
it was originally described to work with C-alpha- moduli only. This can be done in reciprocal space
only models, it has now been modified to include all usingananalogofthetranslationfunction, calledthe
atoms in the refinement and has also been put on line phased translation function (Bentley, 1997). This is
as a web-server at http://lorentz.immstr.pasteur.fr simply a correlation coefficient between maps of the
(Lindahl et al., 2006). model placed at different origins and the experimen-
tal one. This can be carried out in reciprocal space,
where all the products of type (|F |.|F |) have
7.11 How to get the best (least-biased) ∗ obs model ∗
starting phases been replaced by Re(F obs .F model ), where F model is
the complex conjugate of F model . Once the model
Once the best possible molecular replacement solu- has been placed correctly in the unit cell of the
tion has been found and refined by, for example, crystal, experimental phases can be combined with
the CNS simulated annealing protocol in internal phases from the model, followed by solvent flat-
coordinates space, there is a need to use the least tening using a molecular envelope derived directly
possible biased phases, as recently emphasized in from the model. This usually results in a much
Rupp et al. (2002). This is usually done by using better map. However, the rotation function is still,
SIGMAA-weighted maps, originally due to Read in general, no easier to solve than without the exper-
(Read, 1986, 1990) and implemented in most crys- imental phases, so one might think that all of this
tallographic packages (Refmac5 (Murshudov et al., is of little use. There is, however, a way out of it,
1997), CNS (Brünger et al., 1998), etc.). Then, one which is to scan the entire rotation function space
can go on and try to use directly automatic con- with the phased translation search as a score (see
struction methods such as ARP/wARP (Perrakis Protocol 7.6). The present author has used it in a
et al., 2001) or Resolve (Terwilliger, 2003). How- number of cases with success: it is, in general, com-
ever, we wish to point out here that there exists putationally doable and leads to a very clear signal
a very general formalism based on mean-field the- (Li de la Sierra et al., 2001; Delarue et al., 2002).
ory and statistical mechanics (Delarue and Orland, Another special case where the signal of the rota-
2000) which, in principle, should allow most of tion function could be enhanced concerns crystals
the errors contained in the model phases to be where the self-rotation function can be interpreted
eliminated and which points to the use of other without ambiguity; in this case, the so-called locked
kinds of weighted coefficients, calculated in a self- cross-rotation function (Tong and Rossmann, 1997)
consistent manner, as inputs to the Fourier trans- allows to search for cross rotations which are com-
forms to calculate the map. Even though the method patible with the self rotation function. This usually
still remains to be implemented in a space-group results in a much better signal-to-noise ratio.
general program, preliminary results in the space
group P2(1)2(1)2(1) show great promise (Delarue,
7.13 Concluding remarks
unpublished work).
It seems pretty clear that easy-to-use and web-
interfaced, automated protocols will be more and
7.12 Special cases: phased TF and
locked RF more useful in the near future. The possibility of
combining different tools at different steps of the
If, for some reason, MR failed, leaving no option integrated process makes it inevitable that more of
but to look for heavy atom derivatives and if, for them will be developed and open to the public.
lack of isomorphism, the phasing power of these What is good about this kind of approach is that