Finding Defocus with Ctfplotter for Three Example Tilt Series

(IMOD 4.10)

University of Colorado, Boulder

This document will guide you through running Ctfplotter to find defocus for three different tilt series, one where the signal of the CTF is very strong, one where it is weak, and one where it is sometimes strong and sometimes weaker.  It will explain some of the most important aspects of the process.  For more details, consult the Guide to Ctfplotter, which fully explains each aspect of the interface and also has screen shots based on these three data sets.  Labels in the Etomo or 3dmod interface are shown in Bold, and entries in fields are shown in italics.

Determining Defocus in a Tilt Series from a K2 Camera:

This tilt series, from Cindi Schwartz, is of a flagellum of a Giardia cell, taken with a K2 camera on a Krios microscope at Janelia Farm.  The total dose was 26 electrons/square Angstrom.  Images were taken in superresolution mode with an exposure time of 0.5 sec to avoid having to save and align subframes, and reduced by a factor of 4 with antialiasing.  With this protocol, they may have somewhat better high-frequency information than a typical tilt series taken in counting mode without binning, so the power spectra may be particularly good here.

• Download the sample data set from our web site.
• Move the data set file "K2-CTF-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "K2-ctf".
• cd to the directory with the file
• Enter the command:
      imoduntar K2-CTF-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf K2-CTF-Data.tar.bz2
• Enter the data set directory with:
      cd K2-ctf
• Start Etomo with the command
      etomo WTI042413_1series4.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
Notice that a spherical aberration of 0 is allowed, and is appropriate if data were collected on an aberration-corrected microscope, as these were.
• The Expected defocus has already been set to 6.0 in this data set.
• The Config file has already been selected to access a configuration file listing noise files in the "Janelia" subdirectory of the data set directory.
• Press Run Ctf Plotter.  Note that the CTF is analyzed in the raw stack, so the aligned stack does not need to exist before running Ctfplottter.
• Three windows open: the plotter window, a dialog for setting parameters controlling which views are analyzed and various aspects of the power spectrum computation, and a dialog for setting parameters for fitting to the power spectra.
• The magenta curve in the plotter window shows the rotationally averaged power spectrum plotted versus spatial frequency.  The green curve is a fitted curve, which in general may not fit well until fitting parameters have been adjusted.
• The units of spatial frequency along the X axis are reciprocal pixels and range from 0 to 0.5/pixel. Below the frequency labels are the corresponding values for periodicity (resolution) in Angstroms.
• Power is always very high at low frequencies, so the first operation is to zoom up the part of the curve that shows the CTF effect. Click the mouse just under the hump in the curve after 0.1/pixel and drag the zoom area out to the right edge, just under the curve, so that the Y axis range is about -0.1 to 0.5.
• Since the fitting looks good already, switch to use the Current defocus estimate in the Angle Range and Tile Selection dialog.
• The frequency of the first zero determined from the fit is shown at the top of the plotter window after Z:, and the corresponding defocus is shown after D:.  It is ~4.6 microns instead of the nominal 6 microns. The fitting range in the Fitting Parameters dialog starts at a low frequency appropriate for the higher nominal defocus but too early for this lower actual defocus.  It is best if the fitting is done to a linearly falling part of the curve and excludes the portion before that curving away from a line.  Press Start to change X1 Starts to 0.17.
• It is not helpful to see the curves much beyond where the fitting starts, so the graph can be zoomed again. Click a bit above and to the left of where the fitting starts (which is at 0.17/pixel and 0.3 in Y) and drag out to just below the right end of the curves to give a Y axis range of about -0.05 to 0.35.
• This average over many views appears to have good signal out to the fourth zero, but the useful range for fitting may be less when fewer views are averaged. For now, change X2 Ends to 0.4, just past the frequency of the third zero.  Press the Enter key or Apply (in either dialog) to fit with a changed value.
• Notice the entry for Error: on the output line in the plotter window, which shows the mean deviation between the power spectrum and the fitted curve over the fitting range, in the log units of the Y axis.
• Turn on Vary exponent of CTF function; the fit looks slightly better and the error drops by more than 10% (e.g., from 0.0039 to 0.0033), so that is an appropriate parameter to include when fitting these data.
• To assess whether fitting to a single image is possible, go back to the Angle Range and Tile Selection dialog and change the Number of views to fit: to a smaller value, like 9. Notice the line below this spin box, summarizing the angular range and view numbers being fit. Click the down arrow of the spinner to reduce the number of views progressively down to 1. The curve does become noisier, but the fitting still appears good out to ~0.43/pixel.
• To see whether this is still the case throughout the tilt range, leave the number of views at 1 and press Step Up to go to the positive end of the tilt range then Step Down to go back down to the negative end of the range. The power spectrum looks good and the fitting appears reliable at each tilt angle.
• If the first zero appears elevated when first stepping to an angle (such as 61 degrees), press Apply one or more times to see if the fitting to the baseline improves. In general, repeatedly computing the spectrum and fit in this way with each new defocus is a good way to assess the stability of fitting.
• This assessment only took a few steps because the Step view range spin box was left at its initial value of 11. You can make this value smaller to see more angles, or 1 to step through every angle.
• Most of the single view spectra show signal out close to the fourth zero, so change the entry for X2 Ends in the Fitting Params dialog to 0.44.
• Turn on Fit each view separately and press Autofit All Views. The fitting goes in two directions from the current angle, unless that angle is at one end of the range. The table is filled in as the fitting proceeds.
• Press Graph values. A graph of defocus versus tilt angle pops up, showing variations of over 1 micron above 40 degrees. You can left-click at a point in this window and a popup will appear with its coordinates (you have to left-click again to dismiss the popup).
• Scroll the table in the Angle Range dialog to get to these angles with the big   Double-click a series of lines in the table to check the curve-fitting in this region, or set the Step view range to 1 and use Step Up and Step Down to look at successive views.  The curve-fitting is clearly correct; the defocus changes from image to image have been measured accurately.
• Now that you have gone through the basics of determining defocus, the next step is to assess whether astigmatism can be determined as well. When there is astigmatism, the defocus varies with direction. In a 2-D power spectrum, the Thon rings (which correspond to the dips at CTF zeros in the rotationally averaged 1-D power spectra here) are approximately elliptical instead of circular. Astigmatism thus has two parameters, the difference between the maximum and minimum defocus and the angle of the axis of maximum defocus. Ctfplotter finds astigmatism by measuring the defocus in 1-D power spectra rotationally averaged over a restricted angular ranges of the 2-D power spectrum, referred to as wedges.
• Return to low tilt by entering 0 in the Middle tilt angle text box. (The program will adjust the entry to the nearest actual angle.)
• Press the + button to the left of Find astigmatism in the Fitting Params dialog to open the controls for finding astigmatism.
• Notice that Min views for astigmatism has the default value of 5. This means that wedge spectra will be combined from 5 views when defocus is being found for single views. It is generally advisable to find astigmatism from more views than those used for finding defocus, because the wedge spectra have less data in them than full 1-D spectra, and combining more views will keep the signal-to-noise ratio up and make the CTF fitting comparably reliable. See the Guide to Ctfplotter for more details on this point.
• Turn on Find astigmatism and watch the wedge spectra as the angle of the wedge changes. It is important to see these wedge spectra initially to make sure that the fitting looks good and that the spectrum does not take on a strange shape in some part of the angular range. The whole process is iterated because the astigmatism is rather high for this data set.
• After the analysis, the program computes a spectrum for the single selected view that is fully adjusted for the astigmatism and measures defocus from that. Note that the CTF signal now appears clearly all the way out to 0.5/pixel.
• Check the fitting to the wedges at a few other angles by typing them into the Middle tilt angle text box, for example 30, 60, -30, and -60
• Return to zero tilt by entering 0 for the Middle tilt angle. It is generally advisable to start autofitting at zero tilt because fitting is likely to be more challenging at high tilt.
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• Press Autofit All Views to fit to all views. The programs asks if you want to remove all existing entries from the table. Press Yes.
• You can turn off Show wedge fits in the Fitting Params dialog to save time if you are confident that the wedge fitting is reliable. It can be turned on and off during autofitting, so one approach is to turn it off for lower angles and turn it back on as it approaches high tilt.
• Press Graph values; this time there are graphs for the astigmatism amount and axis angle as well as the defocus. It is not clear how much of the view-to-view variablity in the latter two parameters is real. There would be considerably more variability with Min views for astigmatism set to only 1.
• Press Save to File and exit Ctfplotter and Etomo.

Determining Defocus in a Tilt Series from a CCD camera:

This tilt series is of a preparation of bovine papilloma virus (BPV), taken by Mary Morphew on an F20 with a US4000 CCD camera at a nominal defocus of -3 microns.  It is the series used in the Ctfplotter Guide to illustrate program operations.  Here, it illustrates some of the challenges in doing CTF correction on relatively low-defocus tilt series take with a CCD, which provides poorer information at high frequencies than a direct detector.

• If you already unpacked the data set for the SIRT tutorial, skip to "Enter the data set directory".
• Download the sample data set from our web site.
• Move the data set file "CTF-SIRT-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "ctf-sirt".
• cd to the directory with the downloaded file
• Enter the command:
      imoduntar CTF-SIRT-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf CTF-SIRT-Data.tar.bz2
• Enter the data set directory with:
      cd ctf-sirt
• Start Etomo with the command
      etomo bpv_-3_3a.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
• As for the K2 data set, the Config file has already been selected to access a configuration file listing noise files in the "F20" subdirectory of the data set directory.
• Set the Expected defocus to 3.0.
• Press Run Ctf Plotter.
• If you press the help icon in the upper right of the Ctfplotter window, it will bring up the Ctfplotter Guide; the Examples section there shows screen shots from this data set.
• The power spectrum has two dips in the falling part of the curve, neither of which correspond to zeros.  The dip at the first zero is not evident until the curve is zoomed.  Zoom it up by selecting the top of the second hump in the magenta curve and dragging the selection region to a point before a frequency of 0.4/pixel and just below the baseline.
• Double-click the left mouse button at the first zero (frequency 0.25/pixel).  The defocus readout on the top line changes to show the defocus corresponding to this point, 3.6 microns. 
• The fitting range set from the nominal defocus is particularly inappropriate in this case.  Set X1 Starts to 0.185 to fit the falling phase of the power spectrum back to where its slope changes.  Set X2 Ends to 0.29 because the signal falls off there, well before the location of the second zero.  Press the Enter key or Apply to fit with the changes.
• You can now zoom up another step to make it easier to see the CTF signal.  Select a point just above where the two curves diverge on the left and drag the selection box out to the right edge under the baseline.
• Select Current defocus estimate in the Angle Range dialog now that the fitting is being done to an appropriate range.
• Press Step Up twice to reach the positive end of the tilt range, and then Step Down four times to get to the negative end of the range. The spectra look adequate, although at the positive end of the range, the dip is less well-defined.
• The dip at the positive end can be made deeper by skipping the last few tilts. One way to do this is to enter 1-3 in the Views to skip text box, which makes the tilt range being analyzed be the same as on the negative side. This is more convenient than adjusting the Middle tilt angle entry, and when you use the Step buttons or autofitting, the program will continue to leave these views out of the fit.
• You can now press Autofit All Steps to fit to 40-degree ranges at 20-degree intervals.
• Double-click each line in the table to check the result.  In general, if you think that the zero is not correctly found by a fit, you can double-click where you think the bottom of the dip is located, and press Store Defocus in Table to replace the value from the fit.
• It is possible to find astigmatism in this data set. Set Min views for astigmatism to 40 first, then turn on Find astigmatism and step through the tilt ranges. However, you may find that the fitting is unstable if you press Apply repeatedly at one high tilt end of the range. It is easy for the fitting to become unreliable with this data set; for example, a Baseline fitting order of 0 or 2 does not work throughout the tilt range.
• Press Save to File and exit Ctfplotter and Etomo.
• If you are going to do the practice SIRT reconstruction with this dataset, or if you want a corrected stack for any other reason, then select up to 12 CPUs in the parallel processing table, and press Correct CTF then Use CTF Correction when it is done.

Determining Defocus in a Tilt Series from a DE-12 Camera:

This tilt series, from Cindi Schwartz, is of a preparation of microtubules decorated with the motor protein Eg5, taken with a DE-12 camera during a demo on the F20 microscope in Boulder.  The tilt series had a 2 degree increment and the total dose was 79 electrons/square Angstrom.  Parts of the series have good signal for determining CTF, but not all of it.

• Download the sample data set from our web site.
• Move the data set file "DE-CTF-Data.tar.bz2" to the directory where you want to work on it.  Its contents will unpack into a subdirectory named "DE-ctf".
• cd to the directory with the file
• Enter the command:
      imoduntar DE-CTF-Data.tar.bz2
  or, anywhere except on Windows without Cygwin, you can use
      tar -xjf DE-CTF-Data.tar.bz2
• Enter the data set directory with:
      cd DE-ctf
• Start Etomo with the command
      etomo MTEg5series5D.edf
• Open the Final Aligned Stack page and switch to the Correct CTF tab.
• The Expected defocus has already been set to 6.0 in this data set.
• The Config file has already been selected to access a configuration file listing noise files in the "DE12-Div2" subdirectory of the data set directory.
• Press Run Ctf Plotter.
• Zoom the power spectrum by clicking on the magenta curve to the left of 0.1/pixel and dragging the selection region to a point before a frequency of 0.4/pixel and just below the baseline.
• The power spectrum shows a clear signal out to the third zero and the green fitted curve matches the location of the zeros fairly well, so the defocus estimate is good.  Select Current defocus estimate.
• In the Fitting Params dialog, set X1 Starts to 0.11, since it is not helpful to fit any farther to the left of the first zero.   Set X2 Ends to 0.25 to fit out to the third zero, and press the Enter key or Apply.
• Turn on Vary exponent of CTF function; the fit does not look significantly better so there is no reason to leave this option on.  When the signal is weak, adding this fifth parameter to the fit can reduce the reliability and stability of the fits.  Turn it off.
• To see if single images can be fit, set the Number of views to fit to 1 .  This curve is noisier but the fitting still seems reasonable.
• To see if fitting is good at other tilt angles, sample some angles by pressing Step Up and Step Down. You can lower the Step view range by entry to sample more finely. Most of the negative angles give plausible fits, but many positive angles have much less signal and cannot be fit reliably, particularly around 20-30 degrees. Since inaccurate defocus values can do more harm than good, we need to fit to multiple views instead, with the reduced goal of estimating the trend in defocus through the series.
• Now switch Number of views to fit to 4 to fit to 8 degree ranges, and set Step view range by to 2. Step through some angles in the troublesome range. The signal is still quite weak in some spectra but the fit appears to work.
• Now assess whether and how to find astigmatism by pressing the + button next to Find astigmatism. Set Min views for astigmatism to 8 to start with, to maintain the same signal-to-noise ratio in the wedge spectra as in the full spectra. Set Middle tilt angle to 0 and turn on Find astigmatism. The wedge spectra all look good and the astigmatism is about 0.6 microns.
• Set Middle tilt angle to 21; notice that the spectrum changes shape dramatically and that the signal after the first zero essentially vanishes in some parts of the angular range. The astigmatism estimate is over 1.0, which is too big a change from zero degrees to be plausible. These data must be averaged over many more views to give reliable estimates of astigmatism.
• Set Min views for astigmatism to 20. The fits may appear better, but then set Middle tilt angle to 45. The spectrum still flattens out for some wedges, and you will probably see jumps up and down and failures of the baseline fitting.
• Given this result, we need to fall back to finding one astigmatism estimate for the whole tilt series. Set Min views for astigmatism to 100 (or any value as big as the number of views). The wedge spectra all look good.
• Set the Middle tilt angle of 0 and press Autofit All Steps.  Notice that it does not repeat the wedge fitting at each angle.
• Press Graph Values to see the graph of defocus versus tilt angle. There are still some sizable variations at positive tilt angles. Double-click the lines in the table at some of these angles to see how reliable these fits look.  The signal gets rather low at some tilts, but the noise is low enough to allow you to see that the defocus is being found adequately.