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Icosahedral Reconstruction

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. Y. Z. X. Conventions. Y. Z. X. EMAN Z along 5 fold sym axis Y along 2 fold sym axis

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Icosahedral Reconstruction

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  1. Icosahedral Reconstruction Wen Jiang

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

  3. Y Z X Conventions Y Z X • 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’’ • MRC • X, Y, Z axes along 2 fold sym axes for orientation (0,0,0) • Euler: Z  Y’  Z’’

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

  5. Image Processing • Preprocessing • 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, 10-15 seconds / micrograph • Tend to over-select

  7. Ethan Example Herpes 2.1 Å/pxiel6662x8457 pixels15 seconds in total $ time ethan.py jj0444-8bit.mrc 298 600 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 14.578 total

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

  9. Z= -2.11μm Z= -3.35μm RyR1 Z= -0.41μm Z= -1.14μm RDV fitctf.py Examples http://ncmi.bcm.tmc.edu/homes/wen/fitctf

  10. Image Refinement • Classic 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. common line in 3D: common line in 2D: Orientation  Common Line Locations Fourier plane normal in 3D: 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

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

  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. Sz Sy SX Fourier Bessel 3-D Reconstruction • Very efficient • Parallel reconstruction

  22. SAVR: Semi-Automated Virus Reconstruction V: New Python scriptsClass Module: EM.pyProgram: virus.py, crossCommonLineSearch.py I: IMIRSortAll, eliminateOrt, buildTemplate, globalRefine, ctfForAll, refineAll, reconstructParallel II: EMANC++/Python programming library, runpar, proc2d, proc3d, volume, iminfo, ctfit, boxer IV: New C++ glue programsfftimagic, Imagic2OrtCen, OrtCen2Imagic III: New C++ algorithmic programsWaveOrt, cenalign, symmetrize, icosmask, projecticos

  23. SAVR: Semi-Automated Virus Reconstruction CTF fitting Initial model Initial center / orientation Model re-projection Refine center / orientation 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 (http://ncmi.bcm.tmc.edu)

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

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