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.
RL Point A : fulfills all 3 conditions. Will
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.
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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