Electron Tomography

Electron Tomography is one of 3D Reconstruction using electron microscope. It is the method that reconstruct 3D image by electron micrographs which is projected the same photo field for several angle, then it creates Tomogram by using computer.

　In the following, describe its method in order.

take tilt-series images

　When sample is taken by this method, image that is tilted at a regular interval around an axis is made. As tilt angle increases, the photo field become wider, thus objects in image come around to the center gradually.

1 Axis Tilt(Center is untilted image)

When you will take 2 Axis Tilt 's image, rotate the sample 90 degree, and take as well as 1 Axis Tilt.

2 Axis Tilt(Center is untilted image)(as 90° rotation image for 1 Axis Tilt's image)

Image Correction

　Tilt-series image's defocus is larger than normal electron photograph's one, because it is taken as whole field is underfocus. In this case, CTF Correction is not required, because outside data of 1st thon ring don't have almost information if you use electron gun as LaB6. But, in the case of using field-emission electron gun (FEG), note that you might get a incorrect data.

Rough Alignment

　Align roughly each tilt image by using the correlation among images around center.

Input file(tilt at range: ±60°, interval: 2°, around Y-axis)

10° interval

Preprocess(Windowing)

　By Windowing, remove noise of edge of image.

Windowing of this time is x: 80%, y: 90%

Command(In the case of 1st image): mrcImageWindowing -i Set1000.roi -o Set1000.mask -W 0.2 0.2 0.1 0.1

When you use This Makefile, it performs for all roi file.

Setting data

# For Windowing
WIN_X=0.2
WIN_X_MAX=0.2
WIN_Y=0.1
WIN_Y_MAX=0.1
WIN_MODE=18

Command

make Windowing

Output file(.mask)

10° interval

Alignment

　Because objects move parallelly depending on tilt angle, align about it. Now, align among the images whose angle is close to each other so as not to be affected by tilt.

e.g. case of images whose interval is 2 degree
　Align 2° image to 0° image.
　Align 4° image to Aligned 2° image.
　Align 6° image to Aligned 4° image.
　.
　.

　(Align "-" as well as "+")

case of using mrcImageCorrelation

　Perform alignment by using This Makefile. Even if you don't use the Makefile, you perform command sequentially, and you can align. But, Input file list for mrc2Dto3D is required to be created.

Example 1

Input file

10° interval

Command

make CorFit1

Output file(.fit)

10° interval

Fine Alignment

　Align the position and the angle of tilt axis as possible.

Example 1(Alignment of tilt axis)

　Calculate tilt of axis by using mrcImageTiltAxisSearch.

Input file(1 axis tilt data whose axis is tilted by 10 degree)

10° interval

Used Makefile's Setting

# RotMode
ROTMODE=ZOYS
# Rot1
ROT1MIN=10
ROT1MAX=10
ROT1D=10
# Rot2
ROT2MIN=-60
ROT2MAX=60
ROT2D=2
# Rot3
ROT3MIN=0
ROT3MAX=0
ROT3D=30
### For mrcImageMove
SHIFT2MAX=10
SHIFT3MAX=0
### For mrcImageTiltAxisSearch
TILTMIN=0
TILTMAX=20
TILTN=10
TILTITER=1
TILTSCALE=5

Command

make TiltFit

Output of axis tilt(It is stored at .tiltinfofile)

9.895

difference about 3D Reconstruction

Before correction
After correction
xy-plane	yz-plane	zx-plane

Example2(Repeatedly Alignment of tilt axis)

Repeat to use mrcImageTiltAxisSearch, referring tilt of output axis.

Input file(1 axis tilt data whose axis is tilted by 1 degree)

10° interval

Used Makefile's Setting

# For mrcImageTiltAxisSearch
IN_TILT_EXT=roi
# RotMode
ROTMODE=ZEYR
# Rot1
ROT1MIN=1
ROT1MAX=1
ROT1D=1
# Rot2
ROT2MIN=-60
ROT2MAX=60
ROT2D=10
# Rot3
ROT3MIN=0
ROT3MAX=0
ROT3D=10
### For mrcImageTiltAxisSearch
TILTMIN=-10
TILTMAX=10
TILTN=10
TILTITER=100
TILTSCALE=5

Command

make TiltFit

transition of tilt of axis

0.084
0.161
0.230
0.294
0.345

...

0.701
0.700
0.685
0.706
0.701

The tilt of axis approaches gradually 1.

3D Reconstruction

　Reconstruct 3D image from 2D image set.

Original 3D data's image

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

0 (0, 0, 0) 4 (31, 26, 26) 0.0116844 0.147033 0.000287174

mrc2Dto3D

Example1 (Reconstruction of 1 axis tilt)

　If the tilt axis don't deviate, set the angle information directly to input file list.

Input file

10° interval

Command: mrc2Dto3D -i Input.3dlst -o Input.3d -m 1

By using This Makefile, perform the following command for reconstruction.

Setting data

# For Reconstruction
IN_3D_EXT=fit
# RotMode
ROTMODE=YOYS
# Rot1
ROT1MIN=-60
ROT1MAX=60
ROT1D=2
# Rot2
ROT2MIN=0
ROT2MAX=0
# Rot3
ROT3MIN=0
ROT3MAX=0

Command

make 3DList
make Input.3d

Output file(Input.3d)

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00437076 (39, 34, 36) 0.00799233 (37, 34, 36) 3.45089e-06 0.000342836 6.69601e-07

Example2 (Reconstruction of 2 axis tilt)

Perform 3D Reconstruction for images of 2 axis tilt.

Input file(tilt at range: each ±60°, interval: each 10°, around X, Y-axis))

1st line is X-axis tilt, 2nd line is Y-axis tilt

By using This Makefile, perform 3D Reconstruction.

Command

make all

Halfway, X runs for determine essential part of image. This time, select whole field and save to ROI information.
Output Information file

DataA_006.mrcsmth-0000.roi Rect        0.000000       0.000000       63.000000       0.000000       63.000000       63.000000        0.000000       63.000000

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-9.32199 (29, 37, 34) 21.995 (40, 35, 32) 0.0280746 1.38771 0.00271036

Example3 (Reconstruction of 2 axis tilt with Double)

By using mrc2Dto3D's Option -Double, perform 3D Reconstruction.

Changed part

.roilst.mrc3d:
#	mrc2Dto3D -I $*.roilst -o $*.mrc3d -single 0 -InterpolationMode 2 -m 1 
	mrc2Dto3D -I $*.roilst -o $*.mrc3d -Double -InterpolationMode 2 -m 1 

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-10360.9 (41, 24, 0) 8132.05 (40, 35, 31) 86.0574 673.594 1.31561

3D Reconstruction with Radon Transform)

　Radon Transform can perform 3D reconstruction without using mrc2Dto3D. Perform as the Following.

Aligned 2D image list
↓mrcImageSinogramCreate
Sinogram list
↓mrcRadon2Dto3D
3D Radon file
↓mrcImageInverseRadonTransform

3D file (Finished)

Example 1

Use This Makefile and Input is .roilstfile by Example2.

Command

make Radon3D

Output file

xy-plane	yz-plane	zx-plane

Min Max Mean SD SE

1.84923e+06 (0, 59, 28) 1.17991e+07 (34, 31, 30) 3.63631e+06 1.64358e+06 3536.42

Example2

　Use This Makefile changing option of Inverse Radon Transform.

Changed part

### RadonTransform
RBP_MODE=4
RBP_OPTION=-Rmin 0.05 -Rmax 0.1

Command

make Radon3D

Output file

xy-plane	yz-plane	zx-plane

Min Max Mean SD SE

-344789 (25, 25, 0) 631546 (37, 34, 28) 4381.1 76358.4 164.297

Problems of Electron Tomography image

Missing Area

　Reconstructed image don't have enough angle data, so it have the region that doesn't have information called "Missing Area" (1-Axis: Wedge, 2-Axis: Pyramid). Thus, it has a Blur depending on angle.

Used MakeFile.

Original 3D image(rename to Target.ini3d)

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

0 (0, 0, 0) 2 (29, 29, 14) 0.108302 0.364429 0.000711774

3D Reconstruction of Projection image of 1 Axis Tilt(Y-axis: -60° ~ 60°: 10° interval)

Changed part

TILTAXISNUMBER=1	# Single: 1 Double: 2 

Command

make Target.ini2d
make TestData2DSet
make all

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00330818 (52, 36, 32) 0.00425516 (13, 37, 32) 2.08481e-05 0.000467848 9.13766e-07

3D Reconstruction of Projection image of 2 Axis Tilt(X, Y-axis: -60° ~ 60°: 10° interval)

Changed part

TILTAXISNUMBER=2	# Single: 1 Double: 2 

Command

make Target.ini2d1
make TestData2DSetDouble
make all

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00248567 (12, 38, 32) 0.00344027 (13, 37, 32) 2.07529e-05 0.000401237 7.83666e-07

Problem of position and focus of image

　Because sample is taken being gradually tilted, the distance between it and lens is change as well. Thus, how to correct is one of the point.

Correction of parallel transform

　As tilt angle is large, the photo field is wide, and the sample approaches tilt axis. For this correction, calculate the distance of parallel shift by using mrcImageCorrelation. In addition, compare between near images, because these shape change depending on tilt of sample

Determine axis

　Tomogram does not always tilt around set axis. Because it has a little error depending on several factors as performance of electron microscopy or situation of sample. Speaking about error of tilt axis, mrcImageTiltAxisSearch can calculate it.

Image Process for Tomograph

　Perform the following preprocesses for analysis of reconstructed 3D image.

Smoothing

　Perform the smoothing for noise removing of reconstructed 3D image.

Example1

Input file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00268221 (76, 92, 66) 0.00642324 (89, 42, 71) 2.0386e-06 0.000254286 1.63933e-07

Command: mrcImageSmoothing -i Input-Tomogram3D.mrc -o Input-TomogramSmth.mrc -m 1

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00136636 (75, 42, 133) 0.00292404 (94, 65, 68) -9.48921e-07 0.00013513 8.71152e-08

Segmentation

　Because tomogram contains a variety of structures, it requires tasks such as cutting out a segment of interest from the 3D image. Support software is required for it. There is cutting out from 2D image in some cases.

Cut out 3D image

　Cut out parts that is determined as particle from reconstructed 3D image. Cut out data is used by 3D image analysis or average.

Example1

If the width and the coordinates of the part to be cut has been found, you can use mrcImageCenterGet.

Input file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.00136636 (75, 42, 133) 0.00292404 (94, 65, 68) -9.48921e-07 0.00013513 8.71152e-08

Command: mrcImageCenterGet -i Input-TomogramSmth.mrc -o Input-TomogramSub.mrc -Cx 67 -Cy 67 -Cz 67 -Nx 27 -Ny 27 -Nz 27

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.0012017 (5, 9, 13) 0.00263957 (13, 6, 15) 2.22923e-05 0.000388094 2.76625e-06

Cut out 2D image

　If a target of reconstruction is not whole photo field but a part of field, there is a case to cut out partially 2D image from tilt image. It is low cost than reconstruction of whole. Therefore this method is used in case of not needing whole data. Because samples are taken being tilted gradually, coordinates and angles need to be changed for each image. Cut out by using mrcImageCenterGet, mrcImageROI, mrcImageROIs and so on. It takes significant time that all parts are cut out. Thus, it takes how to calculate and cut out automatically other tilted image by deciding manually cut out of range in the reference(untilted) image.

Operation movie: (.mov) (.mp4)

Perform 3D Reconstruction as the following.

Tilted Image(Multiple 2D images)(Prepared)

↓	Set range of cutting out.(Display2: untilted image only)

Information file for cutting out untilted image(ROIInformation)

↓	Calculate the range of cutting out tilted images.(Currently, Makefile performs this process.)

Information file for cutting out each tilted image

↓	Cut out images(mrcImageROIs)

Multiple cut out image files(Number of cutting out × Number of tilted image)

↓	Alignment(mrcImageCorrelarion + Makefile's process)

Aligned information file for cutting out (Number of tilted image)

↓	Cut out images again.(mrcImageROIs) (* It resets the position and cut out them.)

Aligned image(ROI)file(Number of cutting out × Number of tilted image)

↓	Create Angle Information file.(Makefile performs this process.)

Angle Information file(Number of cutting out)

↓	3D Reconstruction(mrc2Dto3D)

3D image(Number of cutting out)

Example1(Subtomogram of 1 axis tilt)

Input file's image(parts)(y-axis tilt: -60° ~ 60°: 2° interval)

-60°(p1_001.mrc)

0°(p1_031.mrc)

60°(p1_061.mrc)

Use This Makefile.

Command

make all

After input the command, Display2(2D viewer) is opened, then select ranges of cutting out, and create the Information file(.roiinfo).

Select ranges of cutting out, and determine by Edit->OK.	If you wish to cut out multiple images, select ROI->MultiROI.

This time, Extracting "Information" only is enough for automatically cutting out. Push the save button that is right side of "InfoFileName" on "ROI Information" window, then the file is created. (Or set "Information" for "ExtractMode", and push the "Extract" button.)

Output Information file in this time.

p1_031-0000.roi	Rect	20	30	60	30	60	70	20	70
p1_031-0001.roi	Rect	15	75	55	75	55	115	15	115
p1_031-0002.roi	Rect	25	110	65	110	65	150	25	150
p1_031-0003.roi	Rect	45	0	85	0	85	40	45	40
p1_031-0004.roi	Rect	60	50	100	50	100	90	60	90
p1_031-0005.roi	Rect	55	80	95	80	95	120	55	120
p1_031-0006.roi	Rect	55	120	95	120	95	160	55	160
p1_031-0007.roi	Rect	85	15	125	15	125	55	85	55
p1_031-0008.roi	Rect	85	51	125	51	125	91	85	91
p1_031-0009.roi	Rect	85	91	125	91	125	131	85	131
p1_031-0010.roi	Rect	93	130	133	130	133	170	93	170
p1_031-0011.roi	Rect	115	25	155	25	155	65	115	65
p1_031-0012.roi	Rect	120	60	160	60	160	100	120	100
p1_031-0013.roi	Rect	123	100	163	100	163	140	123	140
p1_031-0014.roi	Rect	115	140	155	140	155	180	115	180
p1_031-0015.roi	Rect	152	152	192	152	192	192	152	192

When you create Information file(.roiinfo) for one image by Display2, it calculates automatically other image's range, and cuts out them.

cut out automatically images(columns: each selected range, rows: each file(angle))(.pad)

-60°	0°	60°

After cutting out, it performs 3D Reconstruction for each image.

Reconstructed 3D images(.mrc3d)

xy-plane
yz-plane
zx-plane

Example2(Subtomogram of 2 axis tilt)

　Perform cutting out and reconstruction from 2 axis tilted images.

Input file's images(parts)(x-axis, y-axis tilt: -60° ~ 60°: 10° interval)

x-axis tilt	-60°	0°	60°
y-axis tilt	-60°	0°	60°

Use This Makefile.

Command

make all

This time, cut out ROI files about these regions.

Output Information files

DataA_006-0000.roi Rect        0.722314      137.147614       33.000000      106.000000       49.053597      122.636041       16.775911      153.783654
DataA_006-0001.roi Rect       15.000000       79.000000       42.000000       79.000000       42.000000      107.000000       15.000000      107.000000
DataA_006-0002.roi Rect       13.000000       39.000000       58.000000       39.000000       58.000000       64.000000       13.000000       64.000000
DataA_006-0003.roi Rect       41.000000      129.000000       84.000000      129.000000       84.000000      154.000000       41.000000      154.000000
DataA_006-0004.roi Rect       51.000000       85.000000       82.000000       85.000000       82.000000      119.000000       51.000000      119.000000
DataA_006-0005.roi Rect       47.269722       69.494676       78.455043       40.316766       95.000000       58.000000       63.814679       87.177909
DataA_006-0006.roi Rect       66.000000        4.000000       92.000000        4.000000       92.000000       44.000000       66.000000       44.000000
DataA_006-0007.roi Rect       77.597890      150.922358       95.484138      132.052220      120.886248      156.129861      103.000000      175.000000
DataA_006-0008.roi Rect       93.000000       92.000000      115.000000       92.000000      115.000000      132.000000       93.000000      132.000000
DataA_006-0009.roi Rect      100.000000       51.000000      121.000000       51.000000      121.000000       93.000000      100.000000       93.000000
DataA_006-0010.roi Rect       98.589377       19.087800      119.760822       10.100593      135.000000       46.000000      113.828555       54.987208
DataA_006-0011.roi Rect      122.000000      141.000000      146.000000      141.000000      146.000000      184.000000      122.000000      184.000000
DataA_006-0012.roi Rect      136.883039       95.213292      160.000000      104.000000      144.116961      145.786708      121.000000      137.000000
DataA_006-0013.roi Rect      127.000000       73.000000      146.061183       60.635990      169.000000       96.000000      149.938817      108.364010
DataA_006-0014.roi Rect      140.000000       22.000000      177.361289       43.286947      166.470292       62.402025      129.109004       41.115078
DataA_006-0015.roi Rect      163.000000      152.000000      183.000000      152.000000      183.000000      190.000000      163.000000      190.000000

cut out automatically images(columns: each selected range, rows: each file(angle))(.pad)

DataA(x-axis tilt)

DataB(y-axis tilt)

ROI files have been cut out automatically for each tilt axis. (It is not easy that each of parts is found, because each size are different...)

Reconstructed 3D images(.mrc3d)

xy-plane
yz-plane
zx-plane

Interpretation of 3D Reconstruction

Averaging of Subtomograms

　If each 3D data that is divided by segmentation is same particle and have different angle, these average image interpolates these "Missing Area", and makes more correct 3D image.

Divided data1

Divided data2(90° rotation)

Average data

xy-plane	yz-plane	zx-plane

Example1

Input file

xy-plane
yz-plane
zx-plane

align by using mrcImageAutoRotationCorrelation3D before averaging 3D image.

Reference file(Center data of Input file)

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.0012017 (5, 9, 13) 0.00263957 (13, 6, 15) 2.22923e-05 0.000388094 2.76625e-06

Command: mrcImageAutoRotationCorrelation3D -i c1-1.mrc -r c2-2.mrc -fit f1-1.mrc -EA YOYS -Rot1 0 0 30 -Rot2 0 330 30 -Rot3 0 330 30 -Xrange 0 0 -Yrange 0 0 -Zrange 0 0

corrected data(-fit 's Output file)

xy-plane
yz-plane
zx-plane

Perform Averaging of corrected files by mrcImageAverage.

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-0.000536652 (6, 13, 12) 0.00177258 (13, 17, 13) 3.22171e-05 0.000228739 1.6304e-06

3D image's quality has been improved by averaging. (Particular, xy-plane)

Example2

Input file

xy-plane
yz-plane
zx-plane

Reference file(Use top data of Input file)

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-5.47817 (34, 19, 20) 16.0715 (31, 22, 19) 0.142234 1.22547 0.0048441

First, perform alignment as well.

Command: mrcImageAutoRotationCorrelation3D -i p1-0001.mrc3d -r Target.mrc3dref -fit p1-0001.3dfit -EA XEYR -Rot1 0 355 5 -Rot2 0 355 5 -Rot3 0 0 30 -M 18

Corrected data(-fit 's Output file)

xy-plane
yz-plane
zx-plane

Some fits the reference file, and some are otherwise.
Because each 3D subtomogram image has different "Missing Area". Thus the correlation value of the orientation that is included in not both of them is Considerably lower.

Perform averaging of Corrected files by using mrcImageAverage.

Output file

xy-plane

yz-plane

zx-plane

Min Max Mean SD SE

-2.32263 (22, 29, 20) 5.20816 (19, 24, 22) 0.0844992 0.49404 0.00195286