**15. Location of Heavy Atoms from
Protein F Data**

In principle both the Patterson interpretation and
direct methods are suitable for the location of heavy atoms from protein
or oligonucleotide isomorphous or anomalous *F*
data-sets.

For both the anomalous and isomorphous cases the
user must prepare a file name.hkl containing
*h*,
*k*,
*l*, *F* and
(*F*) [or (*F*)^{2}
and ((*F*)^{2})]
in the usual format (3I4,2F8.2), terminated by the dummy reflection with
*h* = *k* = *l* = 0. The sign of *F*
is ignored. The auxiliary program SHELXPRO provides some facilities for
the generation of this file, as does for example the CCP4 system.

Careful scaling of the derivative and native data,
pruning of statistically unreasonable *F*-values,
and good estimated standard deviations are essential to the success of
this approach. It should be emphasised that treating *F*
as if it were *F* involves an approximation which, at best, will add
appreciable 'noise'.

SHELXS-96 will usually recognize that it has been
given macromolecular *F*
data (from the cell volume and contents) and will then set appropriate
defaults, so as with small molecules the .*ins* file will often simply
consist of TITL..UNIT, then TREF (for direct methods) or PATT (Patterson
interpretation) and finally HKLF 3 (because the .*hkl* file contains *F*
(HKLF 3) or (*F*)^{2}
(HKLF 4). The UNIT instruction should contain the correct number of heavy
atoms and the ** square root** of the number of light atoms in
the cell; they may conveniently be assumed to be nitrogen. The mean atomic
volume and density printed by the program should of course be ignored.
It is strongly recommended that these standard TREF and PATT jobs are tried
first before any parameters are varied.

Unfortunately there are two fundamental difficulties
with the application of direct methods to *F*
data. The first is that the negative quartets are meaningless, because
the *F*-values represent
lower bounds on their true values, and so are unsuitable for identifying
the very small *E*-values which are required for the cross-terms of
the negative quartets. On the other hand the *F*
values do correctly identify the *largest**E*-values,
and so the old triplet formula works well. The second problem is that the
estimation of probabilities for the triplet formula for the use in figures
of merit: what should replace the 1/*N* term (where *N* is the
number of atoms per cell) when *F*-data
are used?

Most of the recent advances in direct methods exploit
either the weak reflections or more sophisticated formulas for probability
distributions, so are wasted on *F*
data. Nevertheless, direct methods will tend to perform better in space
groups with (a) translation symmetry (not counting lattice centering),
(b) a fixed rather than a floating origin and (c) no special positions;
thus P2_{1}2_{1}2_{1} (the only space group to
fulfill all three criteria) is good but P1, C2, R3 and I4 are unsuitable.

If the standard direct methods run fails to find
convincing heavy-atom sites, it should first be checked that the program
has put out a comment that it has set the defaults for macromolecular data.
The number of phase permutations may have to be increased (the first TREF
parameter) or the number of large *E*-values for phase refinement
may have to be changed (one should aim for at least 20 triplets per refined
phase), but if too many phases are refined the performance is degraded
because the *F*-values
only identify the strongest *E*-values reliably. The probability estimates
may be changed by modifying the UNIT instruction, or more simply by changing
the third TREF parameter, which multiplies the products of the three *E*-values
in the triplet probability formula; for small molecules a value in the
range 0.75 to
0.95 gives the best probability estimates, but it may be necessary to go
outside this range for *F*-data.

For location of the heavy-atom site by Patterson
interpretation of *F*-data
it may well be necessary to increase the number of superposition vectors
to be tried (the first parameter on the PATT instruction), since the heavy-atom
to heavy-atom vectors may be well down thePatterson peak-list. This number
can be made negative to increase the 'depth of search' at the cost of a
significant increase in computer time. The second number (the minimum vector
length for the superposition vector) should be set to at least 8 Å
(and to a larger value if the cell is large), and it can usually be made
negative to indicate that special positions are not to be considered as
possible heavy atom sites. An advantage of Patterson as opposed to direct
methods is that such false solutions can be eliminated at a much earlier
stage.

The third PATT parameter is also fairly critical
for macromolecular *F*-data;
it is the apparent resolution, and is used to set the tolerances for deconvoluting
the superposition map. If - as can easily happen with area detector data
- a few *F*-values are
at appreciably higher resolution than the rest of the data, this may fool
the program into setting too high an effective resolution. In such cases
it is worth experimenting with several different values, e.g. 3.5 Å
instead of 3.0 etc. The only other parameter which may need to be altered
is maxat, if more than 8 sites are expected.

A typical *F*
PATT run (e.g. PATT 10 -12 2.5) will produce a relatively large number
of possible solutions, some of which may be equivalent. The 'correlation
coefficient' (which is defined in the same way as in most molecular replacement
programs) is the only useful figure of merit for comparison purposes. Hand
interpretation of the 'crossword table' is not as easy as for small molecules,
because the minimum interatomic distances are not so useful; it is however
still necessary to find a set of atoms for which the Patterson minimum
function values are consistently high for at least most of the pairs of
sites involved. This information tends to be more decisive for the higher
symmetry space groups, because when there are more vectors between symmetry
equivalents, it is unlikely that all will be associated with large Patterson
values simultaneously by accident.

Chapter 14. Patterson Interpretation and Partial Structure Expansion