Tomographic series alignment and reconstruction
An example of gold fiducial markers on
holy carbon is provided for training:
The pixel size is about 5 Å/pixel, the fiducial markers are about 100 Å in diameter, the tilt axis is close to the x-axis, and the tilt series started at -60˚ and proceed in 5˚ steps.
The pixel size is about 5 Å/pixel, the fiducial markers are about 100 Å in diameter, the tilt axis is close to the x-axis, and the tilt series started at -60˚ and proceed in 5˚ steps.
1. Preparation
The tomographic tilt series is represented in the parameter files in Bsoft as a single field-of-view with multiple micrographs, one for each image. The image must therefore be in a multi-image format such as PIF or Spider before it is processed. The programs bhead, bimg and bnorm have an option to convert 3D slices into a stack of 2D images for multi-image formats, and the program btomo automatically does the conversion:bimg -v 7 -images gold3.map gold3.pif
In preparation for alignment and reconstruction, the contrast variation in the series due to increased thickness at higher tilt angles must be compensated. To normalize the contrast in the series, the central part of the histogram of each micrograph is fitted to a Gaussian function, and rescaled to a given average and standard deviation:
bnorm -v 7 -rescale 127,10 -data byte -out gold3.star gold3.pif gold3_norm.pif
2. Setting the initial parameters
Some of the initial parameters can be set up with btomo:btomo -v 7 -sampling 5 -axis -5.7 -tilt -60,5 -gold 10 -out gold3_2.star gold3.star
All of the initial parameters can set up in bshow:
bshow gold3.star &
Set the following parameters:
- Enter the correct pixel size in the main window
- Select the menu item "Micrograph/Tomography" and enter the fiducial marker radius in pixels
- Enter the tilt axis angle (which must be known to within about a degree - see below)
- Enter the tilt angles:
- Select the menu item "Tomography/Set tilt angles" and enter the start and incremental angles
- or select the menu item "Tomography/Read rawtlt file" the read the angles from a *.rawtlt file
3. Generating seed fiducial markers
In bshow, change to the zero-degree tilt image and select the menu item “Tomography/Find markers in current image”. This will cross-correlate a synthetic marker based on the marker radius with the image, and present a set of peaks and a dialog box. Adjust the slider in the dialog box until a satisfactory set of markers are selected and click on "Done". Markers can be added or deleted manually. Eliminate markers that are close to edges, because they might not stay within the frames of all the images in the series. Save to a parameter file using the menu item "Micrograph/Write parameters" - in this case the file is called "gold3_seed.star".4. Finding the tilt axis
Often the tilt axis for a particular magnification on a microscope is not known accurately, or there might be a misunderstanding of the definition of the tilt axis. In Bsoft, the tilt axis angle is defined as the counterclockwise rotation angle from the x-axis to the tilt axis. To find the tilt axis angle to within acceptable accuracy, the tomax script can be used:tomax -angles -10,1,10 gold3_seed.star
The output gives the residual for a single iteration attempt at tracking the markers, and the tilt axis angle with the lowest residual should be used subsequently.
Output from the tomax script:
| Tilt axis angle determination: ----------------------------- Tue Mar 27 15:25:05 EDT 2007 File = gold3_seed.star Angles = -10,1,10 Angle Residual -10 8.31441 -9 6.82922 -8 5.49762 -7 3.66594 -6 2.36111 -5 1.94484 -4 2.87278 -3 4.3095 -2 5.4044 -1 6.708 0 8.16417 1 8.89508 2 9.68846 3 10.0579 4 10.4262 5 10.872 6 10.959 7 11.2977 8 11.4032 9 11.4698 10 11.4875 |
The best tilt axis angle is -5˚ and that will be used for tracking.
5. Alignment using fiducial markers
From the fiducial marker seed in the zero-degree tilt image, the z coordinates of the markers as well as the image shift for each micrograph is determined (btrack). The basic algorithm first attempts to find the z-coordinate for each marker in an image by doing real space correlations along a line determined by the tilt direction. It then generates a projection image from the whole marker set at the nominal tilt angle and cross-correlates it with the image to find the shift. The process proceeds from the low-angle tilts to higher tilts in both directions, using the lower dependence of the low-tilt images on correct marker z-coordinates. This process is iterated (typically 2-5 times) until the change in z-coordinates drop below one pixel on average or up to the maximum number of iterations. The exact positions of the markers in each micrograph are then refined (-refine markers).btrack -v 1 -axis -5 -exclude none -update -track 5 -refine markers -out gold3_trk.star gold3_seed.star >& gold3_trk.log &
After every iteration a parameter file is written to allow for user inspection (file names gold3_trk_01.star, gold3_trk_02.star, ... ). To follow the progress in tracking, the log file can be queried:
grep Cycle gold3_trk.log
Cycle 1: Average change in positions = 35.8846
Cycle 2: Average change in positions = 0.440963
This gives the change in marker positions for every iteration, with the first always a high number because the z-coordinates are zero at the start. When the change in positions drop below 1, a reasonable alignment has been reached and the program finishes. The overall residual is given at the end of the log file:
tail -2 gold3_trk.log
Average residual = 1.98881 pixels
The new parameter file can read with bshow to examine the marker positions:
bshow gold3_trk.star &
The markers are indicated with orange lines, where each line indicates the difference between the current marker position and the position predicted from the 3D marker model. Markers with big deviations or those that are obviously incorrect, can be adjusted manually and the results saved into a new parameter file (gold3_trk2.star).
Next, several rounds of refinement of the z-coordinates, the view and origin of each image are done to improve the alignment. A general rigid-body target function is used with no restrictions on the view (such as assuming a tilt axis perpendicular to the electron beam), so that the final alignment can be used directly in reconstruction.
btrack -v 1 -reset -refine 10,z,o,v -out gold3_ref.star gold3_trk2.star >& gold3_ref.log &
tail -2 gold3_ref.log
Average residual = 1.13986 pixels
In bshow, single iterations of these refinements can also be done. Select the "Tomography/Refine alignment" menu item. One of three types can be selected:
- Markers, which refines the marker positions on the micrographs
- Z-coordinates, which refines the 3D model z-coordinates
- Micrographs, which refines the geometry associated with each micrograph
- Views
- Origins
- Scales (be careful here, scale refinement may compensate for
tilts and should only be done once and as the last refinement)
6. Tomogram reconstruction
The reconstruction is done in Fourier space with the same algorithm as for single particle analysis, with the modification that separate slabs in Fourier space can be calculated, assembled and backtransformed later (bmgft, btomrec, bzfft). The use of the programs is rather involved, and to handle all the different issues and dependencies, the reconstruction can be done using the tomrec script:tomrec -rec gold3_rec.pif -resol 30 -size 1024,1024,120 -thick 20 -scale 1 -out gold3_rec.star gold3_ref.star >& gold3_rec.log &
7. Denoising
The reconstruction can be denoised using the non-linear anisotropic
diffusion algorithm Frangakis et al. (2001) (bnad). To allow
piecewise and distributed denoising, the tomogram is divided into
overlapping tiles
(btile), each tile denoised (bnad), and the tiles reassembled (bpatch).
The key parameter is the tile overlap, which must be at least as many
pixels as the number of cycles used for denoising. The memory
requirement is high, so the tiles should not be too large (1 Gb of
memory would allow a block of maximum 400x400x200 to be denoised).
The tomogram is first tiled:
btile -v 7 -size 400,400,240 -overlap 100,100,0 gold3_rec.pif tile.mrc
Each tile is then denoised, using the script tomnad.
The tiles are finally reassembled into the full tomogram as floating
point:
bpatch -v 7 -tiles tile.tiles -out patch.mrc tile_0??_nad.mrc
The tomogram is then truncated to the average +- 5*standard deviation
and converted to byte data type:
bimg -v 7 -dat byte -trunc 74,179 patch.mrc gold3_den.pif
8. Resolution determination
The resolution for each micrograph with respect to the reconstruction can be determined using the scripts mgft and tomres, based on the method of Cardone et al. (2005) and described (btomres) in Heymann et al. (2007).
The mgft script prepares the Fourier transforms of all the micrographs:
mgft -size 2048,2048,240 -pad 0 -output ft.star ccv_060118_1_ref.star
The tomres script subsequently calculates the resolution for each micrograph:
tomres -size 2048,2048,240 -resolution 30 -postscript ccv_res.ps ft.star >& ccv_res.log &