Chapter 2: Autoindexing and Cell Refinement

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Step 11: Resolution Limits, Fitting Radius, and Spot Size

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Step 11: Resolution Limits, Fitting Radius and Spot Size

While referring to the indexed image, carefully set the correct Resolution limits, Profile Fitting Radius, and Spot Size. Click the refine button to update the display after changing any of these parameters. If the crystal roty value displayed in the Refinement Information panel is colored red (i.e. for 45o < roty < 135o) click on the reference zone button in the Controls panel and choose a new zone with a better value for roty.

What is the Profile Fitting Radius and how do I determine what it should be?

The Profile Fitting Radius is the radius of the area around each particular spot, in mm, containing neighboring spots, used to calculate the average spot profile (Figure 35). The spot in question is fitted to the average profile of all the spots within the specified radius. Generally, the radius is set so those spots on roughly 3-5% of the area of the detector are included in the averaging.

           

Figure 35. The Integration Box and Zoom windows with Profile Fitting Radius and Spot Size boxes

The particular size of the area chosen depends on how much the profiles vary across the film and the density of the spots on the film. For example, if the spot profiles vary a lot across the film, then you would choose a smaller radius. If you have a small lattice and the spots are widely separated, you might want to choose a larger radius.

The calculation of the average profile is a time consuming task and it is proportional to the number of spots in the profile fitting radius circle, but too small a radius will not capture enough spots and lead to a noisy average profile. Too large a radius will average out significant profile variations.  

To see the Profile Fitting Radius in the Image Display window click prof fit r button (Figure 36). A thin circle corresponding to the profile fitting radius will appear and will move around with the cursor. The pred display changes now too. Instead of seeing all of the predicted reflections, you see only those preds that correspond to the reflections that are stronger than the weak level (usually set at 5 σ). Only this subset is shown because these are the only reflections used in the calculation of the average spot profile within the radius. (Note: to return to the normal mode, click prof fit r button again).

Figure 36. Profile fitting radius button

A good rule of thumb is that the Profile Fitting Radius should enclose about 10 to 50 spots whose intensities are above the weak level. Useful increments of the profile fitting radius are 2.5% of the detector size (e.g. 5 mm for a 200 mm wide IP).

The radius can be set in the Index window under the Integration Box panel in the lower left quadrant of the window (Figure 35). The value is given in millimeters, and you can adjust it iteratively, hitting the refine button in between your guesses. In general it is preferable to enlarge the radius so as to make sure that there are no orphan reflections (reflections that, when placed in the center of the circle, have no other non-weak reflections within the circle); however, keep in mind that if you are using a 3D Window greater than 1, that the Profile Fitting Radius is actually the “Profile Fitting Sausage”, (since it encompasses the stack of frames in the 3D Window, and more spots may be used than it first seems from examining a single frame.

How do I set the spot size? Is it all that important? Why do larger spots make my χ2 ‘s worse?

The final parameter to set is the Spot Size. This is generally a function of the size of your crystal and the quality of the X-ray beam (collimation, crossfire, parallelism, etc.) but it must be set for proper integration.

If you choose too small a Spot Size significant data is lost because it is cut off. Choosing too large a Spot Size runs the risk of 1) rejecting reflections due to overlaps, 2) including portions of the neighboring reflection in the measured intensity, and 3) including too much of the background in your intensity measurement.  

Setting the Spot Size is somewhat of a tradeoff, since not all the spots on an image are of the same size, and unfortunately, one spot size and shape must suffice for the entire set of images (with the exception of correcting for the elongation caused by the intersection of reflections at high angle to the detector face, which is corrected by the parameter Elongation Limit). However, it is unlikely that your data will suffer too much because profile fitting limits the damage caused by including the background in the spot. As a general rule of thumb, then, it is best to try to adjust the spot shape to fit some of the medium to strong spots on the image.

The spot can be either circular or elliptical. Clicking on the more options button allows you to specify elliptical spots if your spot shapes are sufficiently elongated (Figure 37).

*  However that there is only so much that can be done to compensate for problems with crystal order, split crystals, CuKα1, CuKα2 splitting, etc. Bad crystals are still going to give bad data.

After making the changes to your spot shape, or turning on the Elongation Limit option, you can verify that the spot shape has changed by examining the image and the predicted spots in the Zoom window of the Image Display window.

    

Figure 37. The Integration Box and Zoom windows with more option for spot size and shape

What is the Elongation Limit?

Note that Denzo now has an option to take into account the radial elongation to the spots that arises from the intersection of the diffracted X-rays at high angle with the detector. This is activated by checking the Elongation Limit button in the Integration Box panel. The default value for Elongation Limit (expressed as the fraction of the box size the spot is allowed to elongate) is 0.7. The range is from 0 to 1.

Resolution Limits: should I set this here or not worry about it?

Examine the indexed diffraction pattern carefully. The cursor can be used to determine the resolution of a particular spot. In general, you want to be a on the generous side (say 0.2 Ĺ) with setting the resolution limits, since they can always be lowered in Scaling if you were too optimistic. Conversely, if you are too stingy with the resolution limits in Denzo you will have to go back and re-integrate all your frames again, since Scalepack cannot increase the resolution limits beyond what you have set in Denzo. You may have to darken the image - by clicking on the bright button several times - in order to see the high resolution reflections clearly. Using the Zoom window also helps. Once you have determined the proper resolution limits, go back to the Index window and input the new resolution limits into the proper little box. Then hit the refine button again and the new predicted reflections will appear in the diffraction pattern window. You may have to do this a couple of times until you get it right. Look in all quadrants of the diffraction image - often crystals diffract anisotropically.

What are all these parameters Rotx, Roty, Rotz, X-beam, Y-beam, crossfire, mosaicity?

These are parameters that define crystal and the geometry of the diffraction experiment.

The crystal Rotx, Roty, and Rotz angles define the orientation of the crystal lattice in space for the calculation of the predicted reflections.

It is inconvenient and non-intuitive to work with images in the data conventions, because we are used to thinking about diffraction geometry in terms of the X-ray beam, the spindle axis, and the laboratory frame of reference (horizontal, vertical). There are two possible conventions within this "intuitive" set:

Gravity/beam system (not used in Denzo)

In this system, the X-ray beam is defined as being perpendicular to the direction of the force vector due to gravity ("down"). The beam is the z axis, gravity is parallel to the y axis, and the x axis is perpendicular to both of these. In terms of crystal orientation rotations

This convention has the advantage that it does not change with different camera spindle geometry. In addition, it corresponds directly to the common orthogonal detector directions, in that the detector directions x and y on the film or IP are perpendicular to the X-ray beam. A disadvantage of this system is that the x axis may or may not correspond to the spindle axis, depending upon the χ (chi) and Ω (omega) setting angles of the 3-axis goniostat. For the purposes of aligning your crystal, this makes life more complicated, as we are used to thinking about aligning crystals by moving the arcs on a goniometer head. For χ equal 90 or 270 degrees and W equal to zero, however, the spindle axis is parallel to the x axis and thus rotx corresponds to rotations about the spindle axis.

Although this system will not (formally) work in Outer Space (where the gravity vector is essentially zero), nor in the event that the X-ray beam is vertical, the fact remains that (so far) all macromolecular crystallography is done with horizontal X-ray beams on the surface of good old planet Earth, and thus it is a viable option. While Denzo does not use this convention, XdisplayF does.

Spindle/beam system (used in Denzo)

The spindle/beam system is the Denzo crystal and cassette orientation convention. In this system,

In terms of crystal orientation rotations:

The advantage of this system is that it is very intuitive to the crystallographer. In addition, with Eulerian χ values of 0, 90, 180 or 270 degrees the spindle and vertical axes are parallel to the x or y axes of the detector. The main disadvantage of this system is that it is dependent on knowing the geometry of the camera.

While the crystal and cassette orientations follow the spindle/beam convention for Denzo, the beam, box printout, spot, margin, film width and length in the Denzo log file follow the data convention

The X-beam and Y-beam values are the distance from the edge of the data to the beam spot, in mm.

Crossfire is a measure of the X-ray beam divergence and focusing as it leaves the collimator and illuminates the crystal. Crossfire, being a symmetric tensor, has x, y, and xy components. It affects the prediction of partial reflections and their positions, not their angular width. It is expressed as angular divergence of the beam. The default value is zero crossfire, i.e. a perfectly parallel beam or a beam focused on the detector.

Mosaicity is defined in Denzo as the rocking angle, in degrees, in both the vertical and the horizontal directions, which would generate all the spots seen on a still diffraction photograph. It includes contributions due to X-ray bandwidth, beam crossfire, etc. Mosaicity is refineable when integrating your frames if the 3D Window is set to be at least twice as large as the refined mosaicity. For example, if your crystal has a mosaicity of about 1 degree, then a 3D Window encompassing 2 degrees or more of data should allow for proper refinement. If mosaicity is growing beyond reasonable limit during refinement it indicates mis-indexing or wrong definition of the goniostat. Most common is the movement of the crystal in opposite direction than assumed.

All of these parameters are subject to refinement by the integration program.

What is the Reference Zone? How is this useful?

The Reference Zone shows the current zone and other zones which are crystallographically equivalent to the current zone. Keep in mind that upon indexing the crystal for the first time (which is just another way of stating that the crystal orientation parameters are being determined) Denzo makes an arbitrary choice of reference zone (Figure 38). Being able to choose an equivalent zone is useful in a number of ways.

  1. If the crystal roty happens to fall between 45 and 135 degrees, this has a higher correlation than other zones and makes the refinement of the crystal orientation more difficult (although it will still work). Choosing an equivalent zone from the list is an easy way to overcome this.

  2. If for some reason, two or more data sets are collected from the same crystal, without removing the crystal or changing its orientation relative to the goniostat, and the data sets are indexed independently of one another, then it is possible that Denzo will arbitrarily assign a different reference zone to the two data sets. Unfortunately, this will result in a different original index for reflections which otherwise should be equivalent, and so merging reflections between data sets will not work. However, by choosing the same reference zone for both data sets, scaling and merging reflections can be done correctly and accurately.

38. The Reference Zone window

 

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