icosahedral reconstruction wen jiang. icosahedral symmetry 5, 3, 2 fold axes –6 five fold axes...
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Icosahedral Reconstruction
Wen Jiang
Icosahedral Symmetry
• 5, 3, 2 fold axes– 6 five fold axes– 10 three fold axes– 15 two fold axes
• 60 fold symmetry in total
X
Z Y
X
YZ
Conventions
MRC• X, Y, Z axes along 2 fold sym
axes for orientation (0,0,0)• Euler: Z Y’ Z’’
EMAN• Z along 5 fold sym axis• Y along 2 fold sym axis• X near 3 fold sym axes for
orientation (0,0,0)• Euler: Z X’ Z’’
pyruvate dehydrogenase
200Å P22 phage 700Å
Herpes Simplex Virus1250Å
Icosahedral Particles
Image Processing
• Preprocessing Particle selection CTF fitting
• Image refinement Orientation determination 3-D reconstruction
Particle Selection
• By Kivioja and Bamford et al.
• “Ring Filter”
• Only ONE parameter (R)
• Fast, 10-15 seconds / micrograph
• Tend to over-select
• Manual selection boxer
• Automated selection batchboxer ethan (for spherical
particles)
Herpes 2.1 Å/pxiel6662x8457 pixels15 seconds in total
$ time ethan.py jj0444-8bit.mrc 298 600 jj0444.box jj0444.imgOpening file jj0444-8bit.mrcWidth: 6662Height: 8457Averaging 121 pixelsFiltering jj0444-8bit.mrc: **********Total number of squares is 567Number of peaks after sector test is 163Number of peaks after first distance check is 81Number of peaks after discarding too small ones is 80Refining centers74 particles found from jj0444-8bit.mrc
10.31s user 2.08s system 84% cpu 14.578 total
Ethan Example
CTF Fitting
• Manual fitting ctfit
• Automated fitting fitctf fitctf.py
222 )()()()(min
2
sNesCTFsIsI Bssimage
subject to:
Iimage (s) N(s)
A 0
B 0
1Q0
Z 0 (under focus)
Algorithm: constrained nonlinear optimization using a sequential quadratic programming (SQP) method)
Iimage (s) Is(s)CTF 2(s)e 2Bs2
N(s)
)))(cos())(sin(1()( 2 sQsQAsctf
)2/(2)( 243 sZsCs S
N(s) n3e n1 s n2s (n4 s)2 / 4
8 unknown parameters: Z, B, A, Q, n1, n2, n3, n4
Z= -1.14μm
Z= -0.41μm
RDV
Z= -3.35μm
Z= -2.11μm
RyR1
fitctf.py Examples
http://ncmi.bcm.tmc.edu/homes/wen/fitctf
Image Refinement
• Classic method common-lines Fourier-Bessel reconstruction
• EMAN method projection matching direction Fourier inversion
reconstruction
Icosahedral Reconstruction Using EMAN
• EMAN now supports icosahedral reconstruction
• User interface is essentially the same as for other symmetries
• A few points special for large virus aimed at high resolution:
projections at <1° step can use > 1GB memory, add “projbatches=<n>” with n>1 to refine
half 3-D map can be used for large 3-D map (>5003)
3-D reconstruction use only single CPU. can take several hours to reconstruction a large 3-D map. working on parallel version
support mixed platform processing
Cross Common Line
From Z. Hong Zhou’s dissertation, p36
Intersection of two planes in Fourier space
ref
raw
Orientation Common Line Locations
1
0
0
refref Rn
1
0
0
rawraw Rn
refn
rawncommon line in 3D: refraw nnC
C
Fourier plane normal in 3D:
)
0
0
1
(cos 1
1
refref
refref
C
CRC
)
0
0
1
(cos 1
1
rawraw
rawraw
C
CRC
common line in 2D:
Orientation Determination By Common Line Search
N
j
N
j
jk
k
s
sskijkjikijjjjkjiiii
i
jkRR
RwyxRyxR
yxR
1maxminmax
1
)(
1,,,,,,,,
)()(
),,(),,,(),,,(
),,,,(
max max
min
search for the orientation and center parameters that minimize the mean phase differences among all the pairs of common lines
Search Strategy
• Original Fortran implementation (Crowther et al)
• center the particle by cross-correlation
• self common line to get a starting orientation by exhaustive searching orientation in 1° step
• cross common line to do local refinement of orientation and center by Gradient or Simplex.
Search Strategy
• Exhaustive cross common line search
• enumerate all centers and orientations in an asymmetric unit
• simple but really slow
• for 1 degree, 1 pixel step: 3X107
trials/particle
Search Strategy
• A new global optimization algorithm
• hybrid Monte Carlo and Simplex
• global search for both orientation and center
• complicated, but accurate and fast
• ~4x103 trials/particle.
• >104 times faster than exhaustive search
Is The Best Solution Correct?
• Absolute score (residual) cutoff
dominant criterion
needs different cutoff values for images at different defocuses
how to pick a single number that suits all imaging conditions?
• Z score cutoff
Is The Best Solution Correct?
x
Z
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-600 -400 -200 0 200 400
3.5
0.0 0.5residual
μ
safe range
x
better, less sensitive to defocus
unstable for very small defocus (<1μm)
Is The Best Solution Correct?
• Consensus cutoff
agreement among different methods (projection matching vs. common line)
agreement among multiple runs of the global common line search
more reliable than absolute value and Z-score cutoff
bias toward “safer side”
Fourier Bessel 3-D Reconstruction
0
2)2(),(),( RdRRrJZRGZrg nnn
n
izZinn dZeeZrgzr 2),(),,(
n
inΦnn eiZRGZΦRF ),(),,(
SX
Sy
Sz
• Very efficient
• Parallel reconstruction
I: IMIRSortAll, eliminateOrt,
buildTemplate, globalRefine,
ctfForAll, refineAll, reconstructParallel
II: EMANC++/Python
programming library, runpar, proc2d, proc3d, volume,
iminfo, ctfit, boxer
III: New C++ algorithmic programs
WaveOrt, cenalign, symmetrize, icosmask,
projecticos
IV: New C++ glue programs
fftimagic, Imagic2OrtCen, OrtCen2Imagic
V: New Python scripts Class Module: EM.py
Program: virus.py, crossCommonLineSearch.py
SAVR: Semi-Automated Virus Reconstruction
SAVR: Semi-Automated Virus Reconstruction
CTF fitting
Refine center / orientation
Initial model
ReconstructionModel re-projection
Initial center / orientation
Features of SAVR
• Minimal user inputs to start processing and user intervention free once started
• Cross platform compatible (shared memory and distributed memory systems)
• All computation intensive steps parallelized
• Free from NCMI Web server (http://ncmi.bcm.tmc.edu)
• Fast crash recovery
P22 Procapsid (8.5Å) P22 Phage (9.5Å)
Herpes (8.5Å) Rotavirus (9Å) Rice Dwarf (6.8Å)
Virus Structures At Sub-nanometer Resolutions Using SAVR
CPV (9Å, 6Å) ε15 Phage (9Å)