リム傑威
Lim Jackwee
THEORY EM
The resolution chart
8 Å Alpha helices
5 Å Alpha helix grooves
4.5 Å Separation of beta-strands
3.8 Å Most sidechains
3.5 Å All side chains, metal ions
< 3.5 Å Useful for Pharma
Equation 1: Determination of λ at different accelerating voltages kV (keVmax)
λ = h/(2meV)^0.5
= 6.62*10^-34Js/(2*9.1*10^-31kg*1.6*10^-19C*V)^0.5
= 12.25* 10^-10 / (V)^0.5
λrelativistic = λ * 70% *speed of light
= λ * 1/(1+eV/(2mc^2))^0.5
Accelerating voltage (kV) λ (relativistic) (nm) λ(relativistic) (pm) λ(relativistic) (Å) 100 0.00370 3.70 0.0370
200 0.00251 2.51 0.0251
300 0.00197 1.97 0.0197
Equation 2: Effect of Objective Aperture (OA) radius on Abbe resolution limit at 300kV (keVmax)
k0: wave vector of fast e- before scattering
k1: wave vector of fast e- after scattering
q: magnitude of scattering 2k0sin(Θ/2) for a full angle of the cone of light
Why half angle of the cone light to determine Abbe resolution limit?
Source: http://www.ou.edu/research/electron/bmz5364/resolutn.html
: http://micro.magnet.fsu.edu/primer/java/imageformation/rayleighdisks/
According to Abbe diffraction theory,
NA = sin(Θ/2) * n, NA is the numerical aperture of the objective
, n is the refractive index separating the specimen and the objective front lens
, Θ/2 is the half cone of light
Since angle (Θ/2) is very small, sin(Θ/2) == Θ/2 (rad)
NA = Θ/2 (rad) * n
By Rayleigh criteria for circular aperture to separate two points by at least the radius of the airy disc.
airy disc radius, Å = 1.22 * λ (Å)/(2 * NA)
= 1.22 * λ (Å)/(2 * Θ/2 (rad) * n)
When two adjacent airy discs reach Rayleigh criteria,
Resolution = airy disc radius, Å = 1.22 * λ (Å)/(2 * Θ/2 (rad) * n)
= 0.612 * λ (Å)/(Θ/2 (rad) * n)
First to determine half the angle of the cone Θ/2 (mrad), note the units um and mm used)
OA diameter: 10um
OA radius: 5um (to determine for half the angle of the cone Θ/2)
Δ(OA-sample plane): 2.5mm
(Θ/2) = 5um/2.5mm = 2mrad of light from specimen plane intercepted by the objective aperture or the OA plane
Second to determine Abbe resolution limit derived from Θ/2 or the OA plane
OA plane = 2mrad (0.002 rad)
Abbe resolution limit (Å) at 300kV = 0.612 * λ300kV (Å)/(sin(OA plane, rad) * n), n =1 in vacuum
= 0.612 * 0.0197/ (0.002*1) = 6.02
Abbe resolution limit (Å) at 200kV = 0.612 * λ200kV (Å)/(sin(OA plane, rad) * n), n =1 in vacuum
= 0.612 * 0.0251/ (0.002*1) = 7.68
OA radius (um) Δ(OA-sample plane) (mm) OA plane (mrad) sin(OA plane) (rad) λ300kV (relativistic) (Å) Abbe resolution
limit (Å)
5 2.5 2 0.002 0.0197 6.02 30 6.98 4.3 0.0043 0.0197 2.80
50 7.10 7.0 0.0070 0.0197 1.72
70 7.22 9.7 0.0097 0.0197 1.24
100 7.35 13.6 0.0136 0.0197 0.89
At a narrow OA plane (Θ/2) window of 2mrad, e- >> the aperture angle mrad scatter above/below the sample plane and not intercepted in the OA plane.
With increasing OA radius, more e- pass and the spatial frequency increases.
Comparison of direct electron detectors
Source: Ultramicroscopy. (2014)147:156-63
Falcon 3EC: https://www.fei.com/documents/falcon-3EC-datasheet/
Falcon-II: https://www.fei.com/documents/falcon-II-datasheet/
K2 Summit: http://www.gatan.com/products/tem-imaging-spectroscopy/k2-direct-detection-cameras
DE-20: http://www.directelectron.com/documents/Specs-DE20.pdf
Detector Falcon 3EC Falcon-II K2 Summit DE-20
Operation voltage 200 and 300kV 300kV 300kV 300kV
Sensor size 4096x4096 4096x4096 3838x3710 5120x3840
Physical Pixel size 14um 14um 5.0um 6.4um
Camera architecture DED DED DED DED
Frame rate per second 40fps 18fps 400fps 25-32.5fps
DQE @ 0.5 Ny @
fast mode: 10e/pixel/s (0.45-0.7) > 0.4 >0.52 >0.35
Normal EC mode: 1e/pixel/s
Slow EC mode: 0.7e/pixel/s
DQE score (low spatial frequency) 2 2 Highest (1) 4
DQE score (high spatial frequency) Highest (1) 2 3 4
*High DQE (low spatial frequency) improves particle alignment, thus K2 Summit is preferred for MW < 500kD.
*The K2 sensor pixel is slightly smaller than the area that the electron interacts with, resulting in a 2x2 sub-pixel improvement, beyond the physical Nyquist limit e.g. 3.8k x 3.7k to 7.6k x 7.4k. This 2x2 enhancement is the super-resolution mode, which also minimizes noise due to aliasing (click) of signal whose spatial frequency is higher than Nyquist.
* A total dose of 40-50e/Å^2 is typically collected. Higher total dose 70e/Å^2 may be useful for smaller stable proteins.
Determining the actual pixel size (Å/pixel) of image
(1) Scanning step = 4000 dpi (dots per inch) = 4000 pixel/in
(2) 1 in = 25400 um hence (25400 um/in) / (4000 pixel/in) = 6.35 um/pixel
(3) Magnification = 40000 X
(4) 6.35 um/pixel = 63500 Å/pixel at 40000 X
(5) The actual Å/pixel = 63500/40000 = 1.59 Å/pixel at 1X Magnification (binning = 1)
(6) The Å/pixel at bin 2 = 1.59 Å/pixel * 2 = 3.18 Å/pixel (binning is NOT allowed for actual model refinement)
Detector Falcon-II
Operation voltage 200 and 300kV
Pixel size (um/pixel) 14um
Pixel size (Å/pixel) 140000
Nominal Magnification 75000X
Calibrated Magnification 134600X
Sampling at 1X (Å/pixel) 140000/134600 = 1.04
Effect of structure factor and imperfect particles on the resolution limit
Effect of beam-induced Brownian motion on the resolution limit
Water (18D) CprK (25kD) Hexokinase (100kD) Ribosome (2.5MD)
Dose frame exposure (e/Å^2) 25 25 25 25
Stokes-Einstein Diffusion Coefficient 1/18^0.33 - - -
(D ∝1/MW^0.33) = 0.382 0.0342 0.0216 0.007372
Normalized D (Å^2/s) 1 0.382/0.0342 = 11.2 17.7 51.8 (slowest)
Slowing factor, Normalized D^0.5 (Å) 1 11.2^0.5 = 3.35 4.2 7.2
RMS displacement (Å) 5 5/3.35 = 1.5 1.2 0.7
The RMS displacement of water is ~1Å^2 for each e/Å^2. Thus at 25e/Å^2, the RMS displacement of water is 25Å^2 or 5Å.
Hence random Brownian type of beam-induced motion of biological structure only affects very small particles at resolution of 2 Å or beyond.
Micrographs and power spectra
The pattern of the visible Thon rings in the power spectra describes the quality of the micrograph. At close to focus (e.g. -0.65 µm), the Thon rings are broadly separated by dark minima compared to defocus (e.g. -2.0 µm) with clear rings pattern. The number of dark minima corresponds to loss of phase contrast (information) at different sinusoidal periodicities. The outermost visible Thon ring indicates the achievable resolution in an ideal sample e.g 2/3 of the power spectra ~3-4 Å. The lack of clear circular pattern of Thon rings marks the micrograph for discard due to reasons e.g. drift, severe ice contamination and striped background due to beam or camera gain.
Reference: Signal-to-noise ratio of electron micrographs obtained by cross correlation. Nature. 1975 256: pp376
Defocus range (µm) Defocus steps (µm) Total Dose (e/Å^2)
Larger complexes -0.6 to -2.0 0.3 to 0.5 40 to 50
Smaller complexes ~250 kD -1.8 to -3.8 0.3 to 0.5 > 40
* Overfocus: white outer ring (ringe), Underfocus: black fringe. Thin white fringe indicates slight underfocus which is optimal for TEM, minimises spherical aberration and improves contrast
Counting K2 Falcon II
Dose rate (e-/pix/sec) 5 -
Dose rate (e-/Å^2/sec) 4.2 2.5
Pixel size (Å/pix) 1.1 1.4
For the same total dose, a longer exposure time ~x2 is needed for the integrated Falcon II than the counting K2.
Dose Setup for Frames in Falcon II-EPU
EPU frame Begin End
1 1 2
2 3 4
3 5 6
4 7 8
5 9 14
6 15 20
7 21 26 (hacked to increase the 18fps limit in Falcon II)
*Image shift delay: 10s
Stage shift delay: 12s
Maximum image shift: 10µm
Integration time: 1.5s
Total frames: 26
Subframe accumulation time: 1.5/26 = 58ms (200ms was used in Nature Methods (2013) 10:pp58)
High Resolution Frames up to 20e-/Å^2: Begin1 to End 8
(1) The first frame begin 0 is automatically not collected by EPU due to beam-induced motion and shutter delay ~100ms
(2) For a total dose of 67.5e-/Å^2, the total dose 67.5e-/Å^2 from EPU frame 1to7 (or 26 frames or 2.596e-/Å^2 per frame) is used for initial model building with optional binning to a specific resolution of pixel size 3.5Å/pix. The initial model resolution should not be better than 3.5*3 Å.
(3) For a collected dose of 20e-/Å^2, EPU frame 1to4 (or 8 frames), unbinned and CTF corrected images will be used together with good 2D class averages derived from all-frames (step 2) for high resolution model reconstruction thus discarding EPU frame 5to7 or the last 47.5e-/Å^2 due to radiation damage (begins > 30 e-/Å^2)
(4) The volume * 1.21 = ~ kDa
Reference: Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM. Nature Methods (2013) 10:pp584
The Objective Aperture
(1) At low to medium magnification at LM mode, turn the Objective Aperture towards (to the right) the Holder Entry Port to remove aperture
(2) At high magnification SA mode 62000X, turn the Objective Aperture away (to the left) from the Holder Entry Port to insert aperture to increase contrast
(3) After operation, turn the Objective Aperture back to the right to remove aperture
Troubleshooting
EMAN2 on Macintosh
(1) Changed my terminal to /bin/csh
(2) In terminal: touch ~/.cshrc; open -e ~/.cshrc
(3) In ~/.cshrc: test -r /Applications/EMAN2/eman2.cshrc && source /Applications/EMAN2/eman2.cshrc
(4) In Terminal, type e2display.py
awk options:
http://linux.about.com/library/cmd/blcmdl1_awk.htm
http://www.hcs.harvard.edu/~dholland/computers/awk.html
Low-pass filter (removes high frequency noise) to faciliate particle picking in micrographs ONLY. Low-pass filtered micrographs should NOT be used for actual reconstruction since applying a low-pass filter (Gaussian blurring, B-factor) favors low-resolution information for subframe alignment.
bandpass filter:
http://xmipp.cnb.csic.es/twiki/bin/view/Xmipp/FourierFilter
http://lsbr.niams.nih.gov/bsoft/programs/bfilter.html
#-bandpass 25.3,200,0.02Bandpass filter: resolution limits (angstrom) and band edge width (1/angstrom).
#-sampling 1.5,1.5,1.5Sampling (A/pixel; default from input file; a single value can be given).
cp $FILE $NEWNAME
bfilter -bandpass 25,200,0.02 -sampling 1.35,1.35 $NEWNAME $filter_file
XMIPP to Relion
(1) XMIPP tool volume/resize may be used to even the box size as readable for Relion model reconstruction.
Additional Reading Materials
(1) Avoiding the pitfalls of single particle cryo EM : Einstein from noise. PNAS (2013) 110: pp18037
(2) Prevention of overfitting in cryo-EM structure determination. Nat Methods (2012) 9: pp853
(3) Image Restoration in cryo-Electron Microscopy. Methods Enzymol (2010) 482: pp35 ***
(4) Tilt-Pair Analysis of Images from a Range of Different Specimens in Single-Particle Electron Cryomicroscopy. J Mol Biol (2011) 413: pp1028 ***
(5) SIMPLE: software for ab initio reconstruction of heterogeneous single particles. J Struct Biol (2012) 180: pp420
(6) Methods to account for movement and flexibility in cryo-EM data processing. Methods (2016) 100: pp35 ***
(7) Sampling the conformational space of the catalytic subunit of human γ-secretas. Elife (2015) 4. pii: e11182***
(8) Image Processing for Electron Microscopy Single-Particle Analysis Using XMIPP. Nature Protocols (2008) 3: pp977****
(9) https://biocomp.cnb.csic.es/3DEM-Methods/index.php/Main_Page