How to Know You Are in the Wrong Spacegroup When Scaling

HKL2000 Tutorial

Author: Dr. Miroslaw Gilski

Purpose of this practise .
In this practise you lot will learn how to process raw diffraction images and how to become through data reduction to a set of intensities or structure factor modules

The HKL suite is a package of programs intended for the analysis of X-ray diffraction data collected from single crystals. It consists of three parts:

• XdisplayF for visualization of the diffraction pattern
• Denzo for data reduction and integration
• Scalepack for merging and scaling of the intensities obtained by Denzo or other programs.

X-ray diffraction data analysis performed by the HKL package (Otwinowski,1993; Otwinowski & Minor, 1997) or similar programs, is used to obtain the following results

• determination of crystal symmetry (showtime Bravais lattice, then Laue class, the space grouping);
• estimates of unit jail cell parameters;
• estimates of reflection intensities (equivalent to sqare of structure factor amplitudes);
• error estimates of the intensities;
• detector calibration;
• detection of a hardware malfunctions.

Other results, such as indexing of the diffraction pattern, are in nearly cases just intermediate steps to attain the above goals. The HKL system also has tools for validating the results past self-consistency checks.
The fundamental stages of information analysis are:

1. visual inspection of the diffraction images;
2. (auto)-indexing;
3. refinement of diffraction geometry parameters;
4. integration of the diffraction peaks;
5. conversion of the data to a common scale;
6. symmetry determination and merging of symmetry related reflections;
7. statistical summary and estimation of errors.

Recommended Reading

1. International Tables for Crystallography Volume F: Macromolecular Crystallography
2. Z. Otwinowski and W. Modest, " Processing of X-ray Diffraction Data Nerveless in Oscillation Mode ", Methods in Enzymology, Volume 276: Macromolecular Crystallography, office A, p.307-326, 1997,C.West. Carter, Jr. & R. Chiliad. Sweet, Eds., Academic Press (New York).
3. HKL-2000 Online Manual

Your diffraction data

In this practice y'all volition be working with an X-ray diffraction data set collected for a single crystal of trypsin at DESY (Deutches Elektronen Synchrotron) in Hamburg by dr Szymon Krzywda. The data directory contains 113 raw diffraction images recorded to the maximum resolution of 2.15 Å. The wavelength of the Ten-ray radiations used was 0.81600 Å, and the detector was a MAR Research CCD device with 165 mm diameter. The experiments were carried out at beamline X11 belonging to the EMBL (European Molecular Biology Laboratory).

1. How to launch the HKL2000 package ?

   To get-go the HKL2000 programme type:
   # /dwelling/nfs/xtal/hkl2000/hklbin/HKL2000
   In detector type window select the following detector: DESY-X11.
   

2. "HKL Main" window - select the files with images you wish to integrate.

   • in the "Directory Tree" window highlight the directory with the images: /domicile/nfs/xtal/data/TR_tryg
     HKL2000 uses a special naming scheme for files containing diffraction images. Each image file name is constructed accordingto the following template: datasetname_###.ext, where datasetname is the proper noun of our data set (usually project proper name), ### is a 3-digit sequence number of the sequent images and .ext defines detector type (e.thousand. mccd for MAR CCD, img for ADSC Quantum, etc.).
     
   • click on the ">>" button in the "New Raw Information Dir" field.
     
   • in the same way cull the output directory in "New Output Information Dir"
   • select the "Show All Files" button and click the "Load Data Sets" push.
   • Click on any image, the program will fix the whole range of images from this dataset. In our case they range from 1 to 113. Click "Done".
     
   • In the "Experiment Geometry", "Frame Geometry" fields check the crystal-to-detector Distance, for this dataset 200 mm, likewise as "Oscillation range", "Frame Width". This information is retrieved from the headers of the images. Likewise note the wavelength of the X-ray beam.
     

3. Indexing of the information (to effigy out the Laue class, Bravais lattice and cell dimensions)

   • Now you can go to the "Summary" tab page where you can inspect and edit the parameters for each data set.
   
   
   
   • After that navigate to the "Alphabetize" tab
   • Striking the "Display" button to see the first image and evaluate its quality.
   • An image appears in a new pop-up window. How does the image look? Are the spots distinct or smudged. Are they very close to each other or overlapped ? Tin can yous come across the shadow of the x-ray axle terminate? The program for visualization of the diffraction pattern (XdisplayF) has a number of useful options
     You can effort some of them, for example "Dim" and "Bright" modify the paradigm brightness. "Floor Up" and "Floor Down" change the displayed background level. Tin can you run into the h2o band ? Can yous explain it?
   • Click on the "Height Search" push to select the peaks/reflections yous want the program to index. Red selections circles should appear. Is the number of selected peaks sufficient for indexing?
   • At present striking the "Index" button. The program volition endeavor to fit the reciprocal lattice divers by these reflections to a corresponding direct lattice ("Bravais Lattice Tabular array" window). The result is a table of all possible Bravais lattices with a deformation (or embarrassment) indicator (in %) showing how much the theoretically required constraints on the lattice would exist violated. For instance, if all the angles of the cryatal alttice were unlike from ninety deg, then information technology would be very difficult to fit it to an orthogonal arrangement of coordinates (high % of baloney). Optimally, you should cull the highest symmetry lattice with a low distortion parameter. HKL2000 volition propose the unit cells that can alphabetize the diffraction pattern in the best way (green color) - the lowest per centum indicate the all-time fit of your data and lattice.
   • The HKL2000 program will always select the lowest symmetry space group for a particular system during "Bravais Lattice" selection process (P2 for monoclinic, P222 for orthorhombic, P3 for hexagonal system, etc.) - the correct space group can be selected during the Scaling process.
   • Select your lattice and click "Apply & Close".
   • Now you demand to refine your indexing parameters to adapt the detector and unit of measurement cell parameters to the information.
     Expect at the "Refinement Options" field on the right. The basic subset of the parameters (selected by default) is a good style to outset refinement.
   • Inspect the reflection predictions on the image window (in yellow).
   • Click on the "Refine" button.
     The refined parameters are visible in the upper correct portion of the screen. In the xdisp window all reflections should be present in the yellow prediction circles. Click on the "Refine" button and check again.
   • Click on "Fit All" and and then "Refine" - expect at the "Refinement Information" field.
   • Click on the "Refine" push several times till the resulting numbers converge (no change in the last bike).
   • Click on the "Zoom air current" button. Press the middle mouse push button on the primary window in the desired expanse to meet a magnified view of the detector in the Zoom window. You can "Zoom in" and display the Integration box ("Int. Box"). This is the area within which the program volition analyze the pixels in order to make up one's mind the size and intensity of each reflection. In the Zoom window you should be able to see the individual pixels of the detector, each with its own degree of blackness, proportional to the number of 10-ray quanta accumulated during the exposure. At very high magnification, y'all can even read the numerical intensity values of each pixel. Zoom in a different expanse of the image and inspect the integration boxes. Now you lot are ready to integrate the data.

4. Integration
   

   • In this procedure each reflection intensity is evaluated and integrated according to a spot profile and pixel density. In this procedure, the plan analyzes each image to locate the reflections and make up one's mind their intensities. The reflection position (in second space), the intensity, and background volition exist stored in a working directory every bit a series of files with the extension .x
   • From the Index window, click on the "Integrate" button. During the integration calculations you should closely monitor the &chi² statistics of the 10 and y positions of the reflections, the cell parameters, the crystal orientation, and the distance parameter. The mosaicity of crystal is monitored in the lower-left histogram. This plots indicates the partiality of the reflections on an image, and (indicated by an arrow) the expected rotation (in degrees) required to tape a full reflection.
     
   • The &chi² values are mistake estimate. The college the &chi² number, the poorer the fit of the predictions to the real data on the image, and thus the worse the information quality.
   • In the display window (lower right window) you lot tin can see how the different parameters change as the crystal rotates from image to image during the exposure (large fluctuations may indicate experimental problems).
     Integrating the total dataset will require a couple of minutes.

5. Scaling
   

   • Subsequently the integration step you volition have in the working directory a series of .x files which define the intensities of the reflections constitute on each image. You lot now need to scale the data so that all the equivalent reflection can exist merged together. Reflections volition be merged not just from the same image (when they are symmetry-equivalent) but also between dissimilar images. When a reflection is non complete on a single image is it called a partial, and continues on a the following image. Sometimes, during the experiment the crystal tin can motility slightly in the beam and may diffract more or less strongly as it rotates. Also, the X-ray beam intensity fluctuates with fourth dimension. In addition, the diffraction power may decay over time due to radiation harm, or due to poor cryo-protection as ice rings develop. The scaling attempts to normalize these furnishings.
     Finally, the scaling averages all equivalent reflections to provide a unique gear up of information.
     
   • To start scaling go to the "Scale" tab (on the pinnacle "HKL2000" window) and click the "Scale Ready" push. Next scroll up the window with scale results and expect at the "Crystal - Global Refinement" and "Global Statistics". Note the percentage of reflections marked for rejection and the full linear R-factor - they will exist very importanf during space grouping conclusion.
   • Select "Utilize rejections on next run" and striking the "Calibration Prepare" push button once again.
   • Click on "Evidence Log File" (if yous see a crimson warning window, y'all should go to the "Options" menu, choose "Editor" and select the "vi" editor). In a new editor window scroll to the end of the log file and locate the "Summary of reflection intensities and R-factors by shells" table. Look at the "Chi**2" column - all values in each resolution shell should ideally be equal to 1.0 (in practice from 0.9 to one.1). If they are very different information technology is neccesary to "Arrange Error Model". In the pop-up window "Errors" adjust the Error Model for each zone (increase or decrease errors). Each fourth dimension when you alter the Error Model, close the log file window and hit the "Calibration Fix" push to run the Scalepack program again.
   • Infinite Group Determination: How to do this with Scalepack?

     Scalepack can be used to determine the space group of your crystal. What follows is a clarification of how y'all would continue from the lattice type given by Denzo to determine your space group. This whole analysis assumes that y'all accept a crystal of an enantiomorphic compound, such as protein, where but proper symmetry (proper rotation) is possible. Since the controlling process is based on comparison (merging) of potentially equivalen reflections, it will only work if you have enough data, i.due east. if the redundancy of the data set is sufficiently high. You lot also need enough information for the analysis of systematic absences.

     To determine your space group, follow these steps:
     • Scale by the principal space group in Scalepack. The primary infinite groups are the first space groups in each Bravais lattice type in the table below. Note the χ2 statistics. Now try a higher symmetry space grouping (next down the list) and echo the scaling, keeping everything else the same (remember to "Delete Reject File" and run Scalepack - "Calibration Set up" push - twice, every fourth dimension you alter the "Space Grouping")
       If the χ2 is about the aforementioned, then you lot know that this is OK, and you can keep. If the χ2 are much worse, then you know that this is the wrong space group, and the previous choice represented the correct Laue class.
       The exception is primitive hexagonal, where you should try P61 after failing P3121 and P3112.
     • Examine the bottom of the log file or simulated reciprocal lattice flick for the systematic absences. If this was the correct space group, all of these reflections should be absent and their values should be very small-scale. Compare this list with the listing of reflection atmospheric condition by each of the candidate space groups. The fix of absences seen in your data which corresponds to the absences characteristic of the listed space groups identifies your space group or a pair of enantiomorphic space groups (differing in screw axis handedness). Notation that you cannot do whatever better than this (i.e. become the handedness of screw axes) without phase information.
     • If it turns out that your space grouping is orthorhombic and contains one or ii screw axes, you lot may demand to reindex the data to align the spiral axes with the standard definition. If you have one screw centrality, your infinite grouping should exist P2221, with the screw centrality along c. If yous have two spiral axes, then your space group is P21212, with the spiral axes along a and b. If the Denzo indexing is not the aforementioned every bit these, and so you should reindex the reflections using the Reindex push button.

       Bravais Lattice	Primary assigned Space Groups	Candidates	Reflection Conditions along screw axes
       Primitive Cubic	P213	195   P23
       		198   P213	(2n,0,0)
       	P4132	207   P432
       		208   P4232	(2n,0,0)
       		212   P4332	(4n,0,0)*
       		213   P4132	(4n,0,0)*
       I Centered Cubic	I213	197   I23	*
       		199   I213	*
       	I4132	211   I432
       		214   I4132	(4n,0,0)
       F Centered Cubic	F23	196   F23
       	F4132	209   F432
       		210   F4132	(2n,0,0)
       Primitive Rhombohedral	R3	146   R3
       	R32	155   R32
       Primitive Hexagonal	P31	143   P3
       		144   P31	(0,0,3n)*
       		145   P32	(0,0,3n)*
       	P3112	149   P312
       		151   P3112	(0,0,3n)*
       		153   P3212	(0,0,3n)*
       	P3121	150   P321
       		152   P3121	(0,0,3n)*
       		154   P3221	(0,0,3n)*
       	P61	168   P6
       		169   P61	(0,0,6n)*
       		170   P65	(0,0,6n)*
       		171   P62	(0,0,3n)**
       		172   P64	(0,0,3n)**
       		173   P63	(0,0,2n)
       	P6122	177   P622
       		178   P6122	(0,0,6n)*
       		179   P6522	(0,0,6n)*
       		180   P6222	(0,0,3n)**
       		181   P6422	(0,0,3n)**
       		182   P6322	(0,0,2n)
       Primitive Tetragonal	P41	75   P4
       		76   P41	(0,0,4n)*
       		77   P42	(0,0,2n)
       		78   P43	(0,0,4n)*
       	P41212	89   P422
       		90   P4212	(0,2n,0)
       		91   P4122	(0,0,4n)*
       		95   P4322	(0,0,4n)*
       		93   P4222	(0,0,2n)
       		94   P42212	(0,0,2n),(0,2n,0)
       		92   P41212	(0,0,4n),(0,2n,0)**
       		96   P43212	(0,0,4n),(0,2n,0)**
       I Centered Tetragonal	I41	79   I4
       		eighty   I41	(0,0,4n)
       	I4122	97   I422
       		98   I4122	(0,0,4n)
       Primitive Orthorhombic	P212121	16   P222
       		17   P2221	(0,0,2n)
       		18   P21212	(2n,0,0),(0,2n,0)
       		xix   P212121	(2n,0,0),(0,2n,0), (0,0,2n)
       C Centered Orthorhombic	C2221	20   C2221	(0,0,2n)
       		21   C222
       I Centered Orthorhombic	I212121	23   I222	*
       		24   I212121	*
       F Centered Orthorhombic	F222	22   F222
       Primitive Monoclinic	P21	3   P2
       		4   P21	(0,2n,0)
       C Centered Monoclinic	C2	five   C2
       Primitive Triclinic	P1	1   P1

       
       
   • The mathematical fit betwixt symmetry-related reflections is indicated by the Rmerge residual of the data. A well behaved dataset will take a low Rmerge (below ten%).
   • When you roll the scalepack output window from tiptop to lesser, you volition have the following graphs:
     • Calibration and B vs Frame:
       The scale factor was immune to vary during this run and you can encounter how the calibration factor changed during of data collection.
     • Completeness vs Resolution:
       The completeness is plotted versus intensity of the reflections. Potent reflections in yellow and all reflections in blueish.
     • χ2 vs Frame or vs Resolution:
       We are watching the χ2 values to determine the quality of the error estimate in the information. Nosotros would like our average χ2 value to equal 1.00 and the Rfactor to be every bit small as possible (lower than 8-ten%).
     • I/sigma vs resolution:
       Due to the handful of an atom nosotros tin can run across how the reflection intensity decreases in college resolutions.
     • Low resolution vs completeness:
       Information technology is of import to have both high and low resolution data consummate.
     
     The "Scaling window" likewise allows admission to various parameters (number of zones, Error calibration factor, etc.) and various scaling options (B restrain, Dissonant, etc.
     These options are fully documented in the HKL2000 manual.

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