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)