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**Icosahedral Reconstruction**

Wen Jiang

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**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

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**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’’

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**Icosahedral Particles**

pyruvate dehydrogenase 200Å P22 phage 700Å Herpes Simplex Virus 1250Å

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**Image Processing Preprocessing Image refinement Particle selection**

CTF fitting Image refinement Orientation determination 3-D reconstruction

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**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

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**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

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**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

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**fitctf.py Examples http://ncmi.bcm.tmc.edu/homes/wen/fitctf Z= -2.11μm**

RDV Z= -3.35μm Z= -2.11μm RyR1

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**Image Refinement Classic method EMAN method common-lines**

Fourier-Bessel reconstruction EMAN method projection matching direction Fourier inversion reconstruction

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**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

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**Cross Common Line Intersection of two planes in Fourier space**

From Z. Hong Zhou’s dissertation, p36

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**Orientation Common Line Locations**

Fourier plane normal in 3D: common line in 3D: common line in 2D: ref raw

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**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

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**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.

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**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

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**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

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**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?

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**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

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**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”

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**Fourier Bessel 3-D Reconstruction**

SX Sy Sz Very efficient Parallel reconstruction

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**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

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**SAVR: Semi-Automated Virus Reconstruction**

CTF fitting Initial model Initial center / orientation Refine center / orientation Model re-projection Reconstruction

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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)

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**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)

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