1. Icosahedral Reconstruction
Wen Jiang

2. Icosahedral Symmetry 5, 3, 2 fold axes 60 fold symmetry in total
6 five fold axes
10 three fold axes
15 two fold axes
60 fold symmetry in total

3. Conventions Z Y Y Z X X MRC EMAN
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’’

4. Icosahedral Particles
pyruvate dehydrogenase
200Å
P22 phage
700Å
Herpes Simplex Virus
1250Å

5. Image Processing Preprocessing Image refinement Particle selection
CTF fitting
Image refinement
Orientation determination
3-D reconstruction

6. Particle Selection Manual selection boxer Automated selection
batchboxer
ethan (for spherical particles)
By Kivioja and Bamford et al.
“Ring Filter”
Only ONE parameter (R)
Fast, seconds / micrograph
Tend to over-select
Kivioja T, Ravantti J, Verkhovsky A, Ukkonen E, Bamford D.
Local Average Intensity-Based Method for Identifying Spherical Particles in Electron Micrographs.
Journal of Structural Biology Vol. 131, No. 2, pp , August 1, 2000

7. Ethan Example Herpes 2.1 Å/pxiel 6662x8457 pixels 15 seconds in total
$ time ethan.py jj0444-8bit.mrc jj0444.box jj0444.img
Opening file jj0444-8bit.mrc
Width: 6662
Height: 8457
Averaging 121 pixels
Filtering jj0444-8bit.mrc: **********
Total number of squares is 567
Number of peaks after sector test is 163
Number of peaks after first distance check is 81
Number of peaks after discarding too small ones is 80
Refining centers
74 particles found from jj0444-8bit.mrc
10.31s user 2.08s system 84% cpu total

8. CTF Fitting Manual fitting ctfit Automated fitting fitctf fitctf.py
subject to:
Algorithm: constrained nonlinear optimization using a sequential quadratic programming (SQP) method)
Automated fitting
fitctf
fitctf.py
8 unknown parameters: Z, B, A, Q, n1, n2, n3, n4

9. fitctf.py Examples http://ncmi.bcm.tmc.edu/homes/wen/fitctf Z= -2.11μm
RDV
Z= -3.35μm
Z= -2.11μm
RyR1

10. Image Refinement Classic method EMAN method common-lines
Fourier-Bessel reconstruction
EMAN method
projection matching
direction Fourier inversion reconstruction

11. 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

12. Cross Common Line Intersection of two planes in Fourier space
From Z. Hong Zhou’s dissertation, p36

13. Orientation  Common Line Locations
Fourier plane normal in 3D:
common line in 3D:
common line in 2D:
ref
raw

14. Orientation Determination By Common Line Search
search for the orientation and center parameters that minimize the mean phase differences among all the pairs of common lines

15. 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.

16. 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
784*360*10*10 =2.82X107 trials/particle

17. 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

18. 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?

19. Is The Best Solution Correct?
Z score cutoff
better, less sensitive to defocus
unstable for very small defocus (<1μm) 
3.5
0.0
0.5
residual μ
safe range x

20. 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”

21. Fourier Bessel 3-D ReconstructionSX Sy Sz
Very efficient
Parallel reconstruction

22. SAVR: Semi-Automated Virus Reconstruction
V: New Python scripts Class Module: EM.py Program: virus.py, crossCommonLineSearch.py
IV: New C++ glue programs fftimagic, Imagic2OrtCen, OrtCen2Imagic
I: IMIRS ortAll, eliminateOrt, buildTemplate, globalRefine, ctfForAll, refineAll, reconstructParallel
II: EMAN C++/Python programming library, runpar, proc2d, proc3d, volume, iminfo, ctfit, boxer
III: New C++ algorithmic programs WaveOrt, cenalign, symmetrize, icosmask, projecticos

23. SAVR: Semi-Automated Virus Reconstruction
CTF fitting
Initial model
Initial center / orientation
Refine center / orientation
Model re-projection
Reconstruction

24. Features of SAVR
Minimal user inputs to start processing and user intervention free once started
Fast crash recovery
All computation intensive steps parallelized
Cross platform compatible (shared memory and distributed memory systems)
Free from NCMI Web server (

25. Virus Structures At Sub-nanometer Resolutions Using SAVR
Herpes (8.5Å)
Rotavirus (9Å)
Rice Dwarf (6.8Å)
P22 Procapsid (8.5Å)
P22 Phage (9.5Å)
CPV (9Å, 6Å)
ε15 Phage (9Å)