Correcting the Image N. Grigorieff What is Wrong with the Image? - PowerPoint PPT Presentation

Correcting the Image N. Grigorieff

What is “Wrong” with the Image? Xing Zhang 2007

Electron Diffraction 4 Å 3.4 Å Baldwin & Henderson 1984

Image Contrast [ ] ( ) ( ( ) ( ) ) ( ) ( ) ( ) 2 MTF = + 2 k k k k k k P S B ENV CTF i i ( ) ( ) S = signal + + 2 2 2 k k B MTF B B i = imaged background s e ENV i = CTF envelope MTF = Detector MTF B s = shot noise B e = detector noise Zeng et al. 2007

Things to Worry About • Quality – Resolution, contrast • Contrast transfer function – Defocus, astigmatism, beam tilt, envelope • Magnification – Variations from image to image/within images • Ewald sphere (for large objects) • Contrast normalization • Inelastic and multiple scattering – Energy filter, diffraction theory

Rotavirus Double-Layer Particles 1000 Å

Side Chains Rotavirus double-layer particles 8400 particles Xing Zhang Ethan Settembre 2007

Image Quality - Grids

Image Quality – Location on Grid

Image Quality - Defocus

3.8 Å 6.5 Å Thin Rings

Determining the CTF CTFFIND3 Image power spectrum Model Experiment E = 120 kV, ∆ f = 21000 Å, C s = 2 mm, A = 0.15 Mindell & Grigorieff 2003

Defocus Gradient Defocus [Å] y x CTFTILT [ μ m] van Heel et al. 2000 Mindell & Grigorieff 2003

Displaced Information Δ f Θ Δ r = Δ f Θ

Margins Δ = Δ Θ r f = × 25000 Å 5.3mrad = 130 Å 160 Å

Ewald Sphere k L k R A B F L F R k 0 A' O B' B* A * Phase error = 60° for 700 Å particle at 300 kV

Normalization ( ) ( ) − , avg ( ) I x y I ˆ = , I x y ( ) var I [ ] ( ) ( ) − , avg bg ( ) I x y I ˆ = , I x y [ ] ( ) var bg I Sorzano et al. 2004

Maximum Likelihood ( ) ( ) ∫ φ φ Θ φ ( ) , n d X p 1 N ∑ + = Structure for i i ( 1 ) n ( ) A ∫ φ Θ φ ( ) n +1 iteration , n d N p = 1 i i ( ) ⎡ ⎤ 2 φ − ⎛ ⎞ M 1 ( ) ( ) X A Probability φ Θ = − φ Θ ⎜ ⎟ ⎢ ⎥ , exp i | p f σ π σ 2 i function ⎝ ⎠ ⎢ 2 ⎥ 2 ⎣ ⎦ φ : alignment parameters X i : i th image N : # of images Θ : model parameters σ : noise in images : positional probab. f Sigworth 1998

Noise Model Zeng et al. 2007

ML processing of 2D crystals Crystallography Alignment of individual unit cells using ML approach

Systematic Error 70 60 Model phase error [deg] 50 40 Refined 3D structure 30 of bacteriorhodopsin 20 10 10 20 30 40 50 60 70 Data phase error [deg] Grigorieff et al. 1996

Inelastic Image Unfiltered 0 eV 25 eV 300 kV, 6 μ m underfocus, 15 eV energy window Chen Xu 2007

Things to Worry About ? • Quality – Resolution, contrast • Contrast transfer function – Defocus, astigmatism, beam tilt, envelope • Magnification – Variations from image to image/within images • Ewald sphere (for large objects) • Contrast normalization • Inelastic and multiple scattering – Energy filter, diffraction theory

Acknowledgements • Rotavirus DLP Xing Zhang, Ethan Settembre (Harrison lab) • Purple membrane Fritz Zemlin, Erich Beckmann • ML of 2D crystals Xiangyan Zeng (Stahlberg lab) • CTFFIND3/TILT Joe Mindell • Ewald sphere Matthias Wolf, David DeRosier • Inelastic scattering Chen Xu • Financial Support: HHMI, NIH, NSF Humboldt Foundation