Introduction to Data Collection

Recording reflections

Let us revisit the Ewald construction and put a detector in front
of the crystal. Maximize your browser to view the text below the sketch.

For a Reciprocal Lattice Point (RLP) to be recorded as a
reflection or diffraction spot, a number of non-trivial conditions need to be
fulfilled :
The RLP needs to
move through the Ewald sphere (ES) at least once, which is usually accomplished
by turning the crystal around the vertical goniostat axis (omega), referred to
as omega-scan.
The RLP must lie
within the resolution sphere (RS) of the crystal. Most protein crystals diffract
to ~2.5 to 1.5 A, a few better, some worse.
The diffracted
x-ray beam must hit the detector.

Examples :

RL Point A : fulfills all 3 conditions.
Will be recorded.
RL Point B : Still
within/on ES and RS, although borderline. Weak reflection exists, but
will not be recorded (does NOT hit detector). More below.
RL Point
C : Although within RS, can never transverse ES and
cannot be recorded in this experiment. More below.
RL Point
D : Still on ES, but outside crystal's diffraction limit.
No reflection exists.

Large area detectors (circular or square image plates or
CCD detectors) often cover the whole resolution range in theta while
centered on theta. in this case, you are essentially done with the data
collection in 2 omega sweeps.We talk about reductions in RL space that needs to
be swept to obtain due to space group symmetry later in the following section.
Restrictions due to goniostat limits may require some tinkering. The case is
different for smaller detectors, which need to be moved off-centre to cover more
theta space, or high resolution data sets, which require to offset the detectors
in theta even more. The following picture will clarify this :

It is obvious that the reflection B, although at (practically) the
same diffraction angle as A, will never be recorded using a single omega sweep.
A reorientation of the crystal will be necessary and multiple omega scans may be
necessary to record all reflections. Detector software usually provides strategy
generators to optimize the coverage within the geometric limitations of the
specific equipment.

Reciprocal space symmetry, completeness, and
'unique' reflections

The aim of a data collection strategy is to collect a complete
dataset, i.e. one covering most of the theoretically possible data points.
Multiple observations of the same reflection are merged and give rise to the
internal R-value, R(int) or R(merge). I use the term 'same reflection' loosely
here on purpose, not 'unique' or 'equivalent'. I will detail this important
point later. The question arises, what actually is a complete data set? What
consequences has 'incompleteness' and how does the internal symmetry of the
crystal affect the symmetry of the diffraction pattern?

Just as you need only the contents of the asymmetric unit (or
motif) to construct the real space cell by applying the space group symmetry
operations, you actually need only to collect the contents of the asymmetric
unit of the reciprocal space to reconstruct the e-density of the asymmetric
unit. The reciprocal space asymmetric unit is defined by space group
point symmetry plus inversion centre, the so called Laue symmetry. The
completeness of a data set is usually reported in % of observed data (not using
any intensity based cutoff) compared to possible data in the asymmetric unit of
the reciprocal space. The lack of actually observed data due to low intensity
statistics or small random coverage holes is most noticable in higher resolution
shells and not a real concern. There are however, distinct problems (i.e.,
streaking in the F-map perpendicular to the affected zone) with large coverage
holes over an entire area. Employ K.C.'s Duck
to explore the effects of incomplete data coverage. It is important to realize
that a complete asymmetric unit of the reciprocal space is necessary to properly
create the asymmetric unit electron density. This is the standard 'completeness'
reported by data reduction programs (e.g., XPREP) etc.

What are unique reflections? Multiple observations of the same and
symmetry related reflections are merged into one unique reflection. A 2-fold
axis, for example, would create similar symmetry in the diffraction pattern, and
only one set of the two related 'sides' of the pattern need to be collected to
create a complete data set. In the absence of anomalous scattering, the RL is
centrosymmetric and so will be our diffraction pattern. When macromolecular
crystallographers refer to 'unique' data they usually consider only one of the
two centrosymmetric sets of the unique diffraction space. This is not exactly
correct, and whenever you plan to use anomalous data (and there is nearly always
a good reason to collect Friedel pairs - you can merge them later if there is
really no anomalous signal), you need to include the centrosymmetrically related
half of the diffraction pattern. Keep this in mind when you look at tables
listing the Laue group
(point symmetry of the RL) vs. the range of indices to be scanned to obtain a
'unique' data set. At the same token, if not sure about the space group, collect
in a lower symmetry laue group. This is of course less of a problem with large
area detectors covering the whole 2-theta range (collect everything - worry
later about SG) then with high resolution data or detectors covering a smaller
solid angle. It is also noteworthy that for data collection purposes Laue
symmetry -3m actually splits into Laue groups -31m and -3m1, depending on the
orientation of the 2 fold axis/mirror in some trigonal space groups. You can use
the SEXIE program to find the Laue group and the extent of the asymmetric unit
of the reciprocal space.

Enter a space group
symbol or space group number and hit enter

You should also be aware that there are different definitions for
the measures of reliability (Rmerge, Rint) around, and you need to check the
documentation of your scaling and merging package to see what it's actually
doing with the data. For a recent article on this issue check Nature Structural
Biology 4 (4), 269, 1997. The statistic aspects of the paper
are well conceived, but please be aware that based on our experience we
do not agree with the authors' conclusions about the
benefit of merging data from different crystals compared to data sets from a
single (unique) crystal. There are physical (i.e., more that statistical)
reasons why you don't want to do this. For example, crystals are often slightly
different in conformational details.

Notes on Data Collection Strategies

From the failure of RLP C in the above experiment
to ever hit the Ewald sphere we conclude that regardless how much we turn the
crystal around omega, a certain segment of RLPs ("Apple Core", "Bow Tie") will
be excluded from data collection. This type of  loss of data is quite small
at low resolution (no more than a few %) and increases with resolution. In
cases, where the crystal axis is not aligned with the rotation axis, this
problem may not even exist if the Laue symmetry is high (symmetry equivalents of
the missing reflections may enter the Ewald sphere). The data collection
strategy software should be able to tell you the achieveble coverage once the
cell is indexed. To ensure 100% collection of the data, we need to tilt the
crystal axis enough to give RLPs in the excluded region a chance to travel
through the ES. The tilt required depends on resolution, my rule of thumb is to
tilt Chi or Kappa by theta(dmax), i.e., for 2 theta of 45deg, a 22 deg tilt
suffices. A second sweep around omega then satisfied diffraction conditions for
the remaining reflections.

NOTE : you always need to watch cases where a
unique axis is parallel to the rotation axis. For example, in P4122
you need to cover only 1/16 of the reciprocal space, but if you sweep only 45
degrees with the c axis aligned with the rotation axis, you get 50% of the data,
although with double redundanc:  The part of the pattern in one half of the
detector is in this case equivalent to the other half, and you have collected 2
times the same 1/32nd of the RL. Smart people do this only once.

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conceived and maintained by Bernhard Rupp. Last revised January 16, 2007
14:51