Page 134 - Macromolecular Crystallography

MAD PHASING 123

type inhibitor (MbBBI) will be used as an example phase calculation and refinement, phase improve-
(Murthy, 2000). The asymmetric unit of the crys- ment through density modification algorithms, and
tals, space group P2 1 2 1 2 1 , consists of two molecules interpretation of resulting maps in terms of a molec-
of the enzyme, in complex with one molecule of ular model (Terwilliger, 1997a, 2003, 2004). The
the inhibitor. The asymmetric unit, overall has a approach implemented in this program system to
two-fold non-crystallographic symmetry which is the determination of anomalous scatterer positions
very approximate for the inhibitor and somewhat is based on Bayesian statistics that takes into account
better for the two protease molecules. The MbBBI correlated errors between measurements at different
sequenceshowsevidenceofhavingevolvedthrough wavelengths. The theoretical basis of the approach
gene duplication, leading to inexact, but discernible, is described in Terwilliger (1994a, 1997b, 1997c). The
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sequence symmetry (Chen et al., 1992). One heavy | F A (h)| and a quantity α, which is closely related
atomderivative, bysoakinginHoC1 3 , wasobtained, to φ, are computed through a Bayesian probabil-
and turned out to be non-isomorphous with the ity estimate from the input MAD data (Terwilliger,
native. MAD data were measured at three wave- 1994b). The anomalous scatterer positions implied
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lengths at APS on the IMCA beam line at three by the | F A (h)| and α are verified by correlation of
wavelengths bracketing the LIII edge of Ho +++ the calculated Patterson function and the observed
to a resolution of 2.1 Å (Terwilliger, 2002). Four functions, that are computed from the Bijvoet and
Ho +++ sites in the asymmetric unit were deter- Dispersive differences. Additional verification of the
mined through Patterson functions, using SOLVE correctness of the solution is done through cross-
(Terwilliger, 2003), although the automated struc- validation difference Fourier maps. The quality of
ture solution capabilities of the program were not the obtained solutions is expressed as Z-scores,

used. The estimated f values at the three wave- which compare the figures of merit for a particular
lengths were −18.4 (inflection point), −12.0 (Peak), solution with those for random values of estimated
and −9.0 (Remote). The positions, occupancies, and parameters. The score thus provides an estimate of
B factors of the sites determined were refined in the probability of having obtained the solution by
MLPHARE (Project, 1994). The data at the inflection chance. In the final calculation of phases, an error
point were treated as the native data, because they formulation, broadly based on the Blow and Crick
had the most negative estimated f , which would error model (Blundell and Johnson, 1976), explic-

give positive real occupancies for the heavy atom itly considers errors that are propagated to structure
sites in the MIR formulation factor calculation at each wavelength due to inaccu-
racies in the anomalous scatterer model, and leads
0

Q ∝ f (F PHi ) − f(F P ) = f inflection − f Peak/Remote to maximum likelihood estimates for the | F T (h)|
0
and φ T (h). Native maps computed using these
of the problem. The anomalous occupancies are quantities are improved through density modifica-
determined by the f values that are estimated at tion procedures. The SOLVE/RESOLVE system was
the different lengths. The heavy atom refinement used for the solution of the VCP structure, although
produced an improvement from the initial figure of solvent flattening, symmetry averaging, and build-
merit of 0.47 to a final one of 0.53. It was further ing of the atomic model was done outside of it.
improved using density modification and averag- The MAD data for the Eu +++ derivative, statis-
ing, by exploiting the two-fold symmetry within the tics for which are listed in Table 8.1, were used.
asymmetric unit, to 0.66. An electron density map SOLVE suggested the presence of four Eu +++ sites
using these phases could be readily interpreted in in the asymmetric unit, which is in substantial agree-
terms of the complete structure (Murthy et al., 2000). ment with the estimate derived from comparison
SOLVE/RESOLVE is a program system that of expected signals with measured diffraction ratios
permits automation of all the steps between pro- detailed above (Table 8.1). The solution obtained had
cessed data and interpretation of phased maps. an overall Z-score of 29.3, with a figure of merit
These include scaling of data measured at multi- of 0.65 to a resolution of 2.2 Å. This improved to
ple wavelengths, location of anomalous scatterers, 0.78 on solvent flattening and non-crystallographic