Page 126 - Macromolecular Crystallography

CHAPTER 8

MAD phasing

H. M. Krishna Murthy

8.1 Introduction Krishna Murthy (1996). Briefly, assuming that the
wavelength dependent structure factor expression
From a relatively small beginning, nearly two
may be written as:
decades ago (Guss et al., 1988; Murthy et al., 1988;
Hendrickson et al., 1988, 1989), phase calculation f if
λ 0 k k 0
using Multiple-wavelength Anomalous Diffraction F T (h) = F T (h) + f 0 + f 0 F Ak (h)
(MAD) data has become more widespread and gen- k k k
erally used. There are many reviews that cover Where
diverse aspects of the process (Hendrickson, 1991;
λ
Smith, 1991; Ogata, 1998; Ealick, 2000). This F T (h) is the structure factor at wavelength λ
0
review will concentrate on the most recent develop- F T (h) is the structure factor contribution from all
ments and experimental details, and is essentially normal scatterers
0 F (h) is the structure factor contribution from the
an update to the author’s earlier review (Krishna Ak
th
Murthy, 1996). k kind of anomalous scatterer

f and f = dispersive and Bijvoet components
k k
for the k th kind respectively, of the anomalous
8.2 Theoretical background
diffractor at wavelength λ, and
0
Phasing in macromolecular structure determination f = normal scattering factor,
k
entails the independent determination of the sine
then, the experimentally measurable quantity,
and cosine functions of the phase angle. Tradition-
namely, wavelength dependent intensity, assuming
ally, this has been accomplished through measure-
for simplicity a single kind of anomalous diffractor
ment of diffraction data on one or more heavy atom
(k = 1), may be written as:
derivatives of the macromolecule, and using the
2
λ
0
2
0
Multiple Isomorphous Replacement (MIR) method- | F T (h)| =| F T (h)| + a(λ)| F A (h)| 2
ology. In favourable cases, a single derivative that 0 0 0 0
A
T
has measurable anomalous diffraction can also be + b(λ)| F T (h)|| F A (h)| cos[ φ (h) − φ (h)]
used, in a variation of MIR termed single iso- 0 0 0 0
+ c(λ)| F T (h)|| F A (h)| sin[ φ (h) − φ (h)]
T
A
morphous replacement supplemented with anoma-
lous scattering (SIRAS). MAD phasing exploits where
the signals generated from atoms in crystals that 2
f f
have absorption frequencies close to that of the a(λ) = , b(λ) = 2 ,
wavelength of incident X-rays. The theoretical f 0 f 0
underpinnings of anomalous diffraction are cov- f
c(λ) = 2 and f = (f 2 + f 2 1/2 .
)
ered in detail in several standard works (Blundell 0
f
and Johnson, 1976; James, 1982). A more elabo-
0
0
0
rate outline of the derivation of the formulae is Also φ (h) is the phase of F T (h) and φ (h) is the
A
T
0
given in references Hendrickson (1985, 1991) and phase of F A (h).
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