Page 104 - Macromolecular Crystallography

ISOMORPHOUS REPLACEMENT 93

spectrometry, gel electrophoresis, and microPIXE degree of substitution for each heavy atom. An ideal
(particle-induced X-ray emission). However, it is case is one in which: (a) the native and derivative
important to note that most of these techniques are data are of very good quality, (b) the derivative
just a guide that can help in evaluating derivative shows a high degree of isomorphism, (c) only one
formation, but the ultimate method is to identify highly substituted heavy atom is present per macro-
intensity changes between native and derivative molecule, and (d) the heavy atom is of sufficiently
crystals and to be able to confirm the significance of high atomic number to give significant differences.
these changes by calculating the position of ordered A simple example of how to interpret a Patterson
heavy-atomsites. Thiscanbeachievedbycomparing map is described by Abdel-Meguid (1996).
the different statistics calculated from the native and
putative derivative data or between Friedel mates 6.7.2 Difference Fourier
within the derivative data; significant differences
should indicate successful derivative formation. As can be seen from Eq. 4, a Fourier synthesis
requires phase angles as input, thus it cannot be
used to locate heavy-atom positions in a derivative
6.7 Determination of heavy-atom
positions if no phase information exists. However, it can be
used to determine such positions in a derivative, if
By far, the most common procedure for the deter- phases are already available from one or more other
mination of heavy-atom positions is the difference derivatives. As in the case of a difference Patterson,
Patterson method; it is often used in combination the Fourier synthesis here also employs difference
with the difference Fourier technique to locate sites coefficients. They are of the form:
in second and third derivatives.
m(F PH − F P )e iα P (7)
where F PH and F P are the structure factor amplitude
6.7.1 Difference Patterson
of the derivative and the native, respectively; α P the
The Patterson function (Patterson, 1934) is a phase- protein phase angle calculated from other deriva-
less Fourier summation similar to that in Eq. 4 but tives; and m (figure of merit; whose value is between
2
employingF ascoefficients, thusitcanbecalculated zero and one) is a weighting factor related to the
directly from the experimentally measured ampli- reliability of the phase angle.
tudes (F P ) without the need to determine the phase The success of this technique is highly depen-
2
angle. In the case of macromolecules, (F PH −F P ) are dent on the correctness of α P , since it has been
used as coefficients in Eq. 4 to produce a Patterson clearly demonstrated that Fourier summations with
map (hence the name difference Patterson). Such a correct phases but wrong amplitudes can result in
map contains peaks of vectors between atoms (inter- the correct structure, while having incorrect phases
atomic vectors). Thus in the case of a difference even with correct amplitudes results in the wrong
Patterson of macromolecules, it is a heavy-atom vec- structure.
tor map. For example if a structure has an atom Difference Fourier techniques are most useful
at position (0.25, 0.11, 0.32) and another atom at in locating sites in a multisite derivative, when a
position (0.10, 0.35, 0.15), there will be a peak in Patterson map is too complicated to be interpretable.
the Paterson map at position (0.25–0.10, 0.11–0.35, The phases for such a Fourier must be calculated
0.32–0.15), meaning a peak at (0.15, −0.24, 0.17). from the heavy-atom model of other derivatives
The interpretation of Patterson maps requires in which a difference Patterson map was success-
knowledge of crystallographic symmetry and space fully interpreted, and should not be obtained from
groups. Chapter 4 of Blundell and Johnson (1976) the derivative being tested, in order not to bias
offers a concise review of these topics. The ease of the phases. Also, difference Fourier techniques can
interpretation of these maps depends on the quality be used to test the correctness of an already identi-
of the data, the degree of isomorphism, the num- fied heavy-atom site by removing that site from the
ber of heavy-atom sites per macromolecule and the phasing model and seeing whether it will appear in