General principles of 3DR method - Fourier-Bessel mathematics - Common lines 500 Å

Transcript

1 Outline - Background - References; examples; etc. - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry ΞΨΖ ϑουρναλ ϖιρυσ χαυσεσοφ µυχη Box Graphics Digitize Micrograph G y x Determine Ιντερπρετ Ρεφινε Ιντερπαρτιχλε ετεχτ Νορµαλιζε θ Ξ Ψ Ζ φ ω Β ξψ Παρτιχλε Χοµπυτε αχκ Πυβλιση et ισπλαψ/ινσπεχτ/αναλψζε Ρανδ Ρεγυλαρ εφινε initial µορε out προϕεχτ παρτιχλε ιµαγε θ,φ and παρτιχλ θ,φ,ω,ξ,ψ στρυχτυρε estimate ορ ιµαγε Ρεφινε ϖαλυεσ αρτιφαχτσ γριδ ρεχονστρυχτιον float περιση οριεντατιον εοριγινσ µεανσ/ϖαριανχεσ στρυχτυρε οφ ιµαγεσ οριγινσ παραµετερσ θ,φ of (αστιγµατισµ, ρεφινεµεντ Ιχοσαηεδραλ 5 ασψµµετριχ υνιτ:?αδδ παιν συφφερινγ ιν µεν, ςιρυσ ωοµεν, ανδστρυχτυρε χηιλδρεν... Ινχρεασε display micrograph individual particle Χορρελατε δριφτ, Ρεµοϖε Ιµποσε (Χροσσ χορρελατε ετχ.) βαχκγρουνδ centers ρεσολυτιον particle ανδ ωιτη στρυχτυρε 5 εστιµατε σψµµετρψ οτηερ (x,y γραδιεντσ (ε.γ. ιµαγεσ ρεσολυτιον βιοχηεµιχαλ, ωιτη ιν ετχ.) δατα οριεντατιον (Χοµπαρε ϖαλυεσ ιν ιµαγεσ ασψµµετριχ ωιτη προϕεχτεδ υνιτ Σηαδεδ τριανγλε βουνδεδ βψ φολδ, images origins) Φουριερ προϕεχτεδ τρανσφορµσ ϖιεωσ οφ ρεχονστρυχτιον) ανγλεσ ϖιεωσ (θ,φ,ω) οφ ρεχονστρυχτιον) φολδ, ανδ τωο αδϕαχεντ 5 φολδ αξεσ - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005) REFERECES Crowther, R. A., Amos, L. A., Finch, J. T., DeRosier, D. J. and Klug, A. (970) Three dimensional reconstructions of spherical viruses by Fourier synthesis from electron micrographs. ature 6:4-45 First D reconstructions of negatively-stained, spherical viruses: Human wart virus Tomato bushy stunt RAMM Workshop, La Jolla, CA (ov -0, 005) REFERECES Crowther, R. A., DeRosier, D. J. and Klug, A. (970) The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. Proc. Roy. Soc. Lond. A 7:9-40 Crowther, R. A. (97) Procedures for three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs. Phil. Trans. R. Soc. Lond. B. 6:-0 General principles of DR method - Fourier-Bessel mathematics - Common lines 500 Å RAMM Workshop, La Jolla, CA (ov -0, 005) RAMM Workshop, La Jolla, CA (ov -0, 005) REFERECES - Reference list available as handout - For die-hards: Reovirus Rotavirus HSV Baker, T. S.,. H. Olson, and S. D. Fuller (999) Adding the third dimension to virus life cycles: Three-Dimensional reconstruction of icosahedral viruses from cryo-electron micrographs. Microbiol. Molec. Biol. Reviews 6:86-9 RAMM Workshop, La Jolla, CA (ov -0, 005) ωv LA- βv SpV-4 Polyoma φx74 CaMV FHV HRV Å HPV Polio Ross River CPMV CCMV B9

2 HSV HSV ωv LA- Polyoma PBCV- ωv LA- Polyoma PBCV- βv SpV-4 φx74 FHV HRV-4 Polio CPMV CCMV B9 βv SpV-4 φx74 FHV HRV-4 Polio CPMV CCMV B9 500 Å 500 Å Outline - Background - References; examples; etc. - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005) Symmetry RAMM Workshop, La Jolla, CA (ov -0, 005) Regular Polyhedra (Platonic Solids) Icosahedral (5) Point Group Symmetry There are just five platonic solids: From equilateral triangles you can make: with faces at each vertex, a tetrahedron with 4 faces at each vertex, an octahedron with 5 faces at each vertex, an icosahedron From squares you can make: with faces at each vertex, a cube vertices (5- fold) From pentagons you can make: with faces at each vertex, a dodecahedron RAMM Workshop, La Jolla, CA (ov -0, 005)

3 Icosahedral (5) Point Group Symmetry Icosahedral (5) Point Group Symmetry vertices (5-0 fold) faces (- fold) RAMM Workshop, La Jolla, CA (ov -0, 005) vertices (5-0 fold) faces (- 0fold) edges (- fold) RAMM Workshop, La Jolla, CA (ov -0, 005) Icosahedron 55 Dodecahedron 55 Icosahedral (5) Point Group Symmetry Different shapes, but both have 5 symmetry vertices, 0 faces, 0 edges 0 vertices, faces, 0 edges (6 5-folds, 0 -folds, 5 -folds) (0 -folds, 6 5-folds, 5 -folds) Asymmetric unit is /60 th of whole object Object consists of 60 identical subunits arranged with icosahedral symmetry RAMM Workshop, La Jolla, CA (ov -0, 005) 0 dimers 0 trimers pentamers From Eisenberg & Crothers, Table 6-, p.767 Symmetry T=6 T=laevo T=l HSV Rotavirus Reovirus Purely mathematical concept (concerns lattices) Real objects (e.g. viruses) with 5 symmetry often consist of multiples of 60 subunits T=4 ωv T= LA- T=7d Polyoma T=7 CaMV T=7dextro HPV T=4 Ross River Subunits arranged such that additional, local or pseudosymmetries exist RAMM Workshop, La Jolla, CA (ov -0, 005) T=4 T= T= T= T= T= T= T= βv SpV-4 φx74 FHV HRV-4 Polio CPMV CCMV 500 Å T= B9

4 Triangulation umber! " T=6 T=69d T symmetry is OT incorporated into or enforced by the D reconstruction algorithms HSV T=4 T= T=7d ωv LA- Polyoma # $ PBCV- T=4 T= T= T= T= T= T= T= T= βv SpV-4 φx74 FHV HRV-4 Polio CPMV CCMV B9 RAMM Workshop, La Jolla, CA (ov -0, 005) 500 Å Triangulation umber! " T symmetry is OT incorporated into or enforced by the D reconstruction algorithms % " & '( % ) * " - Specimen consists of stable particles with identical structures (else averaging is invalid) - Programs test for and assume presence of icosahedral (5) symmetry RAMM Workshop, La Jolla, CA (ov -0, 005) Outline - Background - References; examples; etc. RAMM Workshop, La Jolla, CA (ov -0, 005) Protocol Electron Cryo-Microscopy Sample : ~- µl at -5 mg/ml - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry Specimen support: holey carbon film (- µm) ΞΨΖ ϑουρναλ ϖιρυσ χαυσεσοφ µυχη Digitize Micrograph Graphics Box G y x Determine Ιντερπρετ Ρεφινε Ιντερπαρτιχλε ετεχτ Νορµαλιζε θ Ξ Ψ Ζ φ ω Β ξψ Παρτιχλε Χοµπυτε αχκ Πυβλιση et ισπλαψ/ινσπεχτ/αναλψζε Ρανδ εφινε Ρεγυλαρ initial µορε out προϕεχτ παρτιχλε ιµαγε θ,φ and παρτιχλ θ,φ,ω,ξ,ψ στρυχτυρε estimate ορ ιµαγε Ρεφινε ϖαλυεσ αρτιφαχτσ γριδ ρεχονστρυχτιον float περιση οριεντατιον εοριγινσ µεανσ/ϖαριανχεσ στρυχτυρε οφ ιµαγεσ οριγινσ παραµετερσ θ,φ of (αστιγµατισµ, ρεφινεµεντ Ιχοσαηεδραλ 5 ασψµµετριχ υνιτ: παιν συφφερινγ ιν µεν,?αδδ ςιρυσ ωοµεν, ανδστρυχτυρε χηιλδρεν... Ινχρεασε micrograph display individual particle Χορρελατε δριφτ, Ρεµοϖε Ιµποσε (Χροσσ χορρελατε ετχ.) βαχκγρουνδ centers ρεσολυτιον particle ανδ ωιτη στρυχτυρε 5 εστιµατε σψµµετρψ οτηερ (x,y γραδιεντσ (ε.γ. ιµαγεσ ρεσολυτιον βιοχηεµιχαλ, ωιτη ιν ετχ.) δατα οριεντατιον (Χοµπαρε ϖαλυεσ ιν ιµαγεσ ασψµµετριχ ωιτη προϕεχτεδ υνιτ Σηαδεδ τριανγλε βουνδεδ βψ φολδ, images origins) Φουριερ προϕεχτεδ τρανσφορµσ ϖιεωσ οφ ρεχονστρυχτιον) ανγλεσ ϖιεωσ (θ,φ,ω) οφ ρεχονστρυχτιον) φολδ, ανδ τωο αδϕαχεντ 5 φολδ αξεσ - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005) µm

5 Protocol Electron Cryo-Microscopy Protocol Electron Cryo-Microscopy Sample : ~- µl at -5 mg/ml Sample : ~- µl at -5 mg/ml Specimen support: holey carbon film (- µm) Specimen support: holey carbon film (- µm) 00 nm µm Protocol Electron Cryo-Microscopy Protocol Electron Cryo-Microscopy Sample : ~- µl at -5 mg/ml Sample : ~- µl at -5 mg/ml Specimen support: holey carbon film (- µm) Specimen support: holey carbon film (- µm) Microscope: kev with FEG Microscope: kev with FEG Defocus range: - µm underfocus Dose: 0-0 e-/å Film: SO-6 ( min, full strength) Micrographs: >000s(?) Particles: > > 06 (?) Target resolution: 0-6 Å --> 4Å (?) +, -./ FEI Tecnai F0 Polara Outline - Background - References; examples; etc. - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry ΞΨΖ ϑουρναλ ϖιρυσ χαυσεσοφ µυχη Digitize Micrograph Graphics Box G y x Determine Ιντερπρετ Ρεφινε Ιντερπαρτιχλε ετεχτ Νορµαλιζε θ Ξ Ψ Ζ φ ω Β ξψ Παρτιχλε Χοµπυτε αχκ Πυβλιση et ισπλαψ/ινσπεχτ/αναλψζε Ρανδ εφινε Ρεγυλαρ initial µορε out προϕεχτ παρτιχλε ιµαγε θ,φ and παρτιχλ θ,φ,ω,ξ,ψ στρυχτυρε estimate ορ ιµαγε Ρεφινε ϖαλυεσ αρτιφαχτσ γριδ ρεχονστρυχτιον float περιση οριεντατιον εοριγινσ µεανσ/ϖαριανχεσ στρυχτυρε οφ ιµαγεσ οριγινσ παραµετερσ θ,φ of (αστιγµατισµ, ρεφινεµεντ Ιχοσαηεδραλ 5 ασψµµετριχ υνιτ: παιν συφφερινγ ιν µεν,?αδδ ςιρυσ ωοµεν, ανδστρυχτυρε χηιλδρεν... Ινχρεασε micrograph display individual particle Χορρελατε δριφτ, Ρεµοϖε Ιµποσε (Χροσσ χορρελατε ετχ.) βαχκγρουνδ centers ρεσολυτιον particle ανδ ωιτη στρυχτυρε 5 εστιµατε σψµµετρψ οτηερ (x,y γραδιεντσ (ε.γ. ιµαγεσ ρεσολυτιον βιοχηεµιχαλ, ωιτη ιν ετχ.) δατα οριεντατιον (Χοµπαρε ϖαλυεσ ιν ιµαγεσ ασψµµετριχ ωιτη προϕεχτεδ υνιτ Σηαδεδ τριανγλε βουνδεδ βψ φολδ, images origins) Φουριερ προϕεχτεδ τρανσφορµσ ϖιεωσ οφ ρεχονστρυχτιον) ανγλεσ ϖιεωσ (θ,φ,ω) οφ ρεχονστρυχτιον) φολδ, ανδ τωο αδϕαχεντ 5 φολδ αξεσ - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005)

6 Icosahedral Particle Image Reconstruction Scheme Icosahedral Particle Image Reconstruction Scheme Micrograph Digitize Graphics Box xyget Determine Ιντερπρετ Ρεφινε Ιντερπαρτιχλε ετεχτ Νορµαλιζε Ιχοσαηεδραλ Χοµπυτε ισπλαψ/ινσπεχτ/αναλψζε Ρ εφινε initial out ιµαγε and θ,φ,ω,ξ,ψ στρυχτυρε estimate ιµαγε Ρεφινε αρτιφαχτσ ρεχονστρυχτιον float οριεντατιον ασψµµετριχ οριγινσ µεανσ/ϖαριανχεσ παραµετερσ of (αστιγµατισµ, ρεφινεµεντ υνιτ: micrograph display individual particle οριεντατιον Χορρελατε δριφτ, Ρεµοϖε ΖΨΞφθ Πυβλιση ΞΨΖ ϖιρυσ ϑουρναλ χαυσεσ (Χοµπαρε Σηαδεδ Ιµποσε (Χροσσ χορρελατε ετχ.) βαχκγρουνδ centers ορ οφ µυχη τριανγλε ιµαγεσ particle ανδ στρυχτυρε ωιτη 5 περιση παιν ωφθ55ξψβαχκ προϕεχτ Αδδ? Παρτιχλεθ,φ ανδ Ρεγυλαρ µορε συφφερινγ παρτιχλε ιν ϖαλυεσ µεν, γριδ στρυχτυρε οφ ιµαγεσ θ,φ ωοµεν, Ινχρεασε ςιρυσ ανδ Στρυχτυρε χηιλδρεν... ϖαλυεσ ιν ρεσολυτιον ασψµµετριχ σψµµετρψ εστιµατε οτηερ (x,y ωιτη βουνδεδ γραδιεντσ (ε.γ. προϕεχτεδ ιµαγεσ υνιτ ρεσολυτιον βιοχηεµιχαλ, βψ φολδ, ωιτη ιν ετχ.) δατα images origins) ανγλεσ φολδ, Φουριερ προϕεχτεδ ϖιεωσ (θ,φ,ω) ανδ τρανσφορµσ οφ ϖιεωσ τωο ρεχονστρυχτιον) αδϕαχεντ οφ ρεχονστρυχτιον) 5 φολδ αξεσ? Black Box Icosahedral Particle Image Reconstruction Scheme Expand Data Set PROGRAM(S) PSC, PhotoScan Uniconv RobEM More Data? Resample Rebox RobEM RobEM AutoPP Refinement PFTSEARCH, OOR, PO R Refine CTF Select Black Box EMDR, PDR RobEM, PCUT, PSF CUTSHELL MAPFFT, EMRES Refine? Done? Visualize & Interpret D Structure Archive Data RobEM, O, Chimera, Explorer, EMfit, Situs, PIFASC, Uniconv MAPMA Etc. Expand Data Set Expand Data Set More Data? Resample Rebox More Data? Resample Rebox Refinement PFTSEARCH, OOR, PO R Refinement Refine CTF Select Refine CTF AUTODEM EMDR, PDR RobEM, PCUT, PSF CUTSHELL MAPFFT, EMRES Refine? Done? Refine? Done? Visualize & Interpret D Structure Visualize & Interpret D Structure Archive Data Archive Data

7 Expand Data Set More Data? Resample Rebox Refinement Refine CTF Refine? Done? Visualize & Interpret D Structure Archive Data Extracted Masked Floated

8 Apodized Square mask; unfloated Circular mask; unfloated Circular mask; floated Circular mask; floated & apodized

9 ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files Gradient removed ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files Gradient not removed

10 ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files Extracted Masked Floated Apodized ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files

11 ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files ormalize means/variances, Apodize Create Parameter Files

12 Goal: determine phase origin and view orientation for each boxed particle MOST IMPORTAT STEP? 0 ' ' People who don t know which end is up Specifying Direction of View: (θ,φ,ω) Orientation BPV Projections: Icosahedral ASU Z (0,0) Z Standard Setting 5 θ θ φ X 5 θ 5 ω φ (80,-5) 5 X (90,0) (90,90) 5 φ 5

13 BPV Projections: / Icosahedral ASU How do we determine the (θ, φ, ω, x, y) parameters? Two methods: θ. Common lines ew or unknown structure. Model-based (template) matching φ General features of structure are known or a crude model can be generated How do we determine the (θ, φ, ω, x, y) parameters? Two methods:. Ab initio (e.g. Common lines) ew or unknown structure. By guess and by golly How do we determine the (θ, φ, ω, x, y) parameters? Two methods:. Ab initio (e.g. Common lines) ew or unknown structure. Model-based (template) matching General features of structure are known or a crude model can be generated Common Lines The gospel according to Tony Crowther (Phil. Trans. R. Soc. Lond. B.(97) 6:-0) [Common lines] arise as follows: An observed section of the transform intersects an identical symmetry-related section in a line, along which the transform must have the same value in both sections The common line lies in the original section. However, regarded as lying in the symmetry-related section it must have been generated by the symmetry operation from some other line in the original section. The gospel continued: Common Lines We therefore have a pair of lines in the original transform plane along which the transform must have identical values A similar pair of lines will be generated by each possible choice of pairs of symmetry operations The angular positions of these lines are dependent on the orientation of the particle.

14 Simple example: object with single three-fold axis of symmetry X C B A ABCD = D transform of image from particle not viewed along an axis of symmetry D Object D Projection (θ,φ,ω) D Fourier Transform A D C Z B D Let Z-direction coincide with -fold axis of symmetry -fold operation generates two additional FT sections (only A B C D is shown) Both planes have common values along the line (,,) of their intersection Adapted from Moody (990) Fig. 7.68, p.45 C X B A A B A B A Z D C AA D C D BB D C B Original Transform Plane CC DD Adapted from Moody (990) Fig. 7.68, p.45 Adapted from Moody (990) Fig. 7.69, p.46 For a general view, icosahedral symmetry generates: Symmetry-Related Transform Plane 5-folds: -folds: -folds: 0 0 x = pairs x = 0 pairs x = 5 real lines 7 common lines

15 (80,) (69,0) (89,-) (80,) ω (80,) (80,,0) What is (θ,φ,ω) for this particle? ω ω (80,,5) (80,,0)

16 ω ω (80,,0) (80,,90) ω (80,,80) (80,,ω) Metric: Identify ω that gives lowest phase residual Repeat process for all possible (θ,φ,ω) combinations > 50,000 combinations for angular search intervals

17 Common Lines The (θ, φ, ω) that results in the lowest phase residual is selected as the best estimate for the particle view orientation The common lines procedure is similarly used to determine the particle phase origin (x, y) Recall: two methods to determine (θ, φ, ω, x, y):. Common lines. Model-based (template) matching Bulk of structures now solved this way Details discussed in practical session Project Model (m views) m Projections Interpolate Projections Polar PRJs m -D FFT (θ, φ ) j m Polar FTs ID θ φ ω x y Select best images Projection (θ,φ,0) j Rotate by ω j (θ,φ) j ω j Polar PRJ (θ, φ,0) j Invert γ Sum average all projections Projection (θ,φ,ω) j Polar PRJ (θ, φ,0) j (θ,φ,ω,,) j=,n Cross-correlate --> (x,y) j (θ,φ,ω) j Rotationally correlate --> (φ,ω) j (θ, φ ) j Correlate --> (θ, φ ) j (,) j Circular Average Cross-correlate --> (x o,y o ) j j j n Images (j=,n) Interpolat e Image j Polar image j -D FFT Polar FT j ( 0, 0 ) j

18 ID θ φ ω x y Goal: weed out bad particle images before computing D reconstruction PRJ CC PFT CC CMP CC ?? PFT Coefficient ± 0.075

19 Goal: combine only good particle images to compute a D density map In theory In practice From Lake (97), p.74 Steps:. Compute D FFT of each particle image. Combine all D FFTs to build up D Fourier-Bessel transform Φ Z R Overall scheme: ρ g G F Central section F(R,Φ,Z) Crowther, DeRosier and Klug, 970, p.9 Adapted from Crowther (97) Fig. 4, p. ρ g G F Steps:. Compute D FFT of each particle image. Combine all D FFTs to build up D Fourier-Bessel transform. Compute G n s on each annulus G = B B ( ) - B F 4. Compute g n s from G n s (Fourier-Bessel transform) 5. Compute polar density map (ρ(r,φ,z)) from g n s 6. Convert from polar to Cartesian map ( ρ(r,φ,z) --> ρ(x,y,z) ) Option: correct for CTF effects in particle FFTs before FFTs are merged to form the D FFT

20 Goal: assess resolution of D density map to determine what to do next Even Images Odd Images Compute Even DR Compute Odd DR Mask Even DR (r -r ) Mask Odd DR (r -r ) Unmasked Reovirus Even Images Odd Images Even Images Odd Images Compute Even DR Compute Odd DR Compute Even DR Compute Odd DR Mask Even DR (r -r ) Mask Odd DR (r -r ) Mask Even DR (r -r ) Mask Odd DR (r -r ) FT Even SFs FT Odd SFs Masked Reovirus

21 Even Images Odd Images Compute Even DR Compute Odd DR Mask Even DR (r -r ) Mask Odd DR (r -r ) FT Even SFs FT Odd SFs Correlation Coefficient Unmasked Reovirus Compute and plot phase differences and correlation coefficients as function of spatial frequency Spatial Frequency (/Å) 8.7Å 6.9Å Masked Reovirus ote: quality of D density map is not identical everywhere in the map Resolution 7Å Reovirus Radius r = 45 r = 6 Resolution 8Å Resolution 9Å Reovirus Reovirus Radius r = 5 r = 80 Radius r = r = 405

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23 Done? Refine? Done? More Data? Refinement Refinement Refine CTF Refine CTF Refine? Done? Refine? Done?

24 ΞΨΖ ϖιρυσ Micrograph Digitize Graphics Box xyget Determine Ιντερπρετ Ρεφινε Ιντερπαρτιχλε ετεχτ Νορµαλιζε ΖΨΞφθ Πυβλιση Ιχοσαηεδραλ Χοµπυτε ισπλαψ/ινσπεχτ/αναλψζε Ρϑουρναλ χαυσεσ εφινε initial out ιµαγε and θ,φ,ω,ξ,ψ στρυχτυρε estimate ορ οφ µυχη παιν ωφθ55ξψβαχκ προϕεχτ Αδδ? Παρτιχλεθ,φ ανδ Ρεγυλαρ µορε συφφερινγ παρτιχλε ιν ιµαγε Ρεφινε ϖαλυεσ µεν, αρτιφαχτσ γριδ ρεχονστρυχτιον float περιση οριεντατιον οριγινσ ασψµµετριχ µεανσ/ϖαριανχεσ στρυχτυρε οφ ιµαγεσ παραµετερσ θ,φ of (αστιγµατισµ, ρεφινεµεντ υνιτ: micrograph display individual particle οριεντατιον Χορρελατε δριφτ, Ρεµοϖε ωοµεν, Ινχρεασε (Χοµπαρε ςιρυσ Σηαδεδ Ιµποσε ανδ (Χροσσ χορρελατε Στρυχτυρε ετχ.) χηιλδρεν... ϖαλυεσ βαχκγρουνδ centers ιν ρεσολυτιον τριανγλε ιµαγεσ particle ανδ ωιτη στρυχτυρε ασψµµετριχ 5 εστιµατε σψµµετρψ οτηερ (x,y ωιτη βουνδεδ γραδιεντσ (ε.γ. προϕεχτεδ ιµαγεσ υνιτ ρεσολυτιον βιοχηεµιχαλ, βψ φολδ, ωιτη ιν ετχ.) δατα images origins) ανγλεσ φολδ, Φουριερ προϕεχτεδ ϖιεωσ (θ,φ,ω) ανδ τρανσφορµσ οφ ϖιεωσ τωο ρεχονστρυχτιον) αδϕαχεντ οφ ρεχονστρυχτιον) 5 φολδ αξεσ Expand Data Set Expand Data Set More Data? Resample Rebox More Data? Resample Rebox Refinement Refinement Refine CTF Refine CTF Refine? Done? Refine? Done? Visualize & Interpret D Structure Expand Data Set More Data? Resample Rebox Refinement Refine CTF Refine? Done? Visualize & Interpret D Structure Archive Data Outline - Background - References; examples; etc. - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005) Outline - Background - References; examples; etc. - Symmetry - Icosahedral (5) point group symmetry - Triangulation symmetry - Typical procedure (flow chart) - Digitization and boxing - Image preprocessing / CTF estimation - particle orientation/origin search - Orientation/origin refinement - D reconstruction with CTF corrections - Validation (resolution assessment) - Current and future strategies RAMM Workshop, La Jolla, CA (ov -0, 005) Current and Future Strategies - Parallelization and new algorithms - Parallel versions of EMDR, PFTSEARCH, OOR - EMDR ---> PDR - OOR > PO R - Automation - Semi-auto boxing (RobEM) - Automated origin/orientation refinement (AUTODEM) - Split data set processing - Divide image data at very beginning and refine even and odd data independently. - Minimizes (eliminates?) bias in resolution assessment - Combine independent reconstructions to obtain final DR with highest S/ RAMM Workshop, La Jolla, CA (ov -0, 005)

25 θφω θφω θφω θφω RAMM Workshop, La Jolla, CA (ov -0, 005) θφω RAMM Workshop, La Jolla, CA (ov -0, 005) Current and Future Strategies - Data selection Trying to improve resolution by substantially increasing the number of images averaged ad infinitum may prove less beneficial than simply applying more rigorous quality control measures to weed out bad data. α RAMM Workshop, La Jolla, CA (ov -0, 005)