Electron microscopy in molecular cell biology II
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1 Electron microscopy in molecular cell biology II Cryo-EM and image processing Werner Kühlbrandt Max Planck Institute of Biophysics
2 Sample preparation for cryo-em
3 Preparation laboratory
4 Specimen preparation Carbon coated copper grid
5 Rapid freezing in liquid ethane
6 Rapid freezing in liquid ethane
7 Mounting under liquid nitrogen
8 Grid in EM column
9 Grid in EM column EM grid
10 EM grid in a light microscope 0.2 mm
11 Holey carbon film 3 mm 2 µm 60x 660x 6660x
12 Ice thickness holey C film z = 100 nm
13 Ice thickness holey C film z = 100 nm
14 Ice thickness holey C film z = 2 nm Thin ice squeezes out particles
15 Ice thickness holey C film z = 30 nm
16 Ice thickness holey C film z = 30 nm f = 22.5 nm
17 Ice thickness holey C film z = 30 nm f = 22.5 nm Amphipols may help to achieve optimal ice thickness with membrane proteins
18 A cryo-specimen imaged in the EM electrons camera
19 Cryo-EM film image of Frh complex Janet Vonck, Deryck Mills
20 Fourier transforms for image processing
21 Any physical object can be thought of as the sum of a Fourier series of cosine waves
22 Any physical object can be thought of as the sum of a Fourier series of cosine waves in one dimension spectra, sounds, signals of any kind
23 Any physical object can be thought of as the sum of a Fourier series of cosine waves in one dimension spectra, sounds, signals of any kind in two dimensions electron micrographs, any image
24 Any physical object can be thought of as the sum of a Fourier series of cosine waves in one dimension spectra, sounds, signals of any kind in two dimensions electron micrographs, any image in three dimensions! crystal structures, any 3D object
25 The 3D volume of any object can be reconstructed from its 2D projections
26 The 3D volume of any object can be reconstructed from its 2D projections in Fourier space! 2D crystals, single particles
27 The 3D volume of any object can be reconstructed from its 2D projections in Fourier space! 2D crystals, single particles in real space e.g. electron tomography
28 Why Fourier transforms?
29 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions
30 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa
31 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa FTs are perfect tools for crystallography and image processing (diffraction, resolution, signal/noise analysis, alignment etc.)
32 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa FTs are perfect tools for crystallography and image processing (diffraction, resolution, signal/noise analysis, alignment etc.) The FT of a crystal is its diffraction pattern
33 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa FTs are perfect tools for crystallography and image processing (diffraction, resolution, signal/noise analysis, alignment etc.) The FT of a crystal is its diffraction pattern The focal plane of a lens contains the FT of the imaged object
34 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa FTs are perfect tools for crystallography and image processing (diffraction, resolution, signal/noise analysis, alignment etc.) The FT of a crystal is its diffraction pattern The focal plane of a lens contains the FT of the imaged object Computers are very good at calculating FTs
35 Why Fourier transforms? Developed by French mathematician Joseph Fourier ( ) as a method for transforming mathematical functions The FT transforms real space into reciprocal space and vice versa FTs are perfect tools for crystallography and image processing (diffraction, resolution, signal/noise analysis, alignment etc.) The FT of a crystal is its diffraction pattern The focal plane of a lens contains the FT of the imaged object Computers are very good at calculating FTs The calculated FT of an object contains all amplitudes and phases of its structure factors
36 Simple one-dimensional Fourier transform periodic structure unit cell x Fourier transform h
37 Simple one-dimensional Fourier transform periodic structure unit cell x Fourier transform h
38 Simple one-dimensional Fourier transform periodic structure unit cell x Fourier transform h
39 Simple one-dimensional Fourier transform periodic structure unit cell x Fourier transform h
40 Simple one-dimensional Fourier transform periodic structure unit cell F 1 α 1 = 0 h = 1 x Fourier transform h
41 Simple one-dimensional Fourier transform periodic structure unit cell F 2 α 2 h = 2 F 1 α 1 = 0 h = 1 x Fourier transform h
42 Simple one-dimensional Fourier transform periodic structure unit cell F 6 α 6 h = 6 F 2 α 2 h = 2 F 1 α 1 = 0 h = 1 x Fourier transform h
43 Simple one-dimensional Fourier transform periodic structure unit cell F 6 α 6 h = 6 F 2 α 2 h = 2 F 1 α 1 = 0 h = 1 x Fourier transform h
44 Simple one-dimensional Fourier transform periodic structure unit cell F 6 α 6 h = 6 F 2 α 2 h = 2 F 1 α 1 = 0 h = 1 x Fourier transform h
45 Simple one-dimensional Fourier transform periodic structure unit cell F 6 α 6 h = 6 F 2 α 2 h = 2 F 1 α 1 = 0 h = 1 x Fourier transform h
46 2D lattice transforms The Fourier transform of a lattice is another lattice with reciprocal dimensions FFT real lattice reciprocal lattice
47 Fourier transforms of lattices and molecules lattice molecule molecular crystal real space convolution reciprocal space FFT lattice transform x FFT molecular transform multiplication FFT molecular transform seen through holes of lattice transform
48 Fourier transforms of lattices and molecules (convolution of two objects is equivalent to multiplication of their Fourier transform) lattice molecule molecular crystal real space convolution reciprocal space FFT lattice transform x FFT molecular transform multiplication FFT molecular transform seen through holes of lattice transform
49 Same molecule on different lattices no lattice real lattice FFT FFT FFT FFT FFT molecular transform reciprocal lattice
50 Same molecule on different lattices no lattice real lattice FFT FFT FFT FFT FFT molecular transform reciprocal lattice
51 Resolution I: crystals real space FFT FFT -1 FFT -1 reciprocal space cutoff cutoff
52 Resolution II: single particles real space FFT FFT -1 FFT -1 reciprocal space cutoff cutoff molecular transform
53 Amplitudes and phases I Helen Saibil, Birkbeck College London
54 real space Amplitudes and phases II
55 Amplitudes and phases II real space FFT
56 Amplitudes and phases II real space FFT reciprocal space (amplitudes and phases)
57 Amplitudes and phases II real space FFT reciprocal space (amplitudes and phases)
58 Amplitudes and phases II real space FFT FFT reciprocal space (amplitudes and phases)
59 cat phases duck amplitudes Amplitudes and phases III
60 Amplitudes and phases III cat phases duck amplitudes duck phases cat amplitudes
61 Amplitudes and phases III cat phases duck amplitudes FFT -1 duck phases cat amplitudes
62 Amplitudes and phases III cat phases duck amplitudes FFT -1 duck phases cat amplitudes FFT -1
63 Amplitudes and phases III cat phases duck amplitudes FFT -1 duck phases cat amplitudes FFT -1 Phases are more important than amplitudes!
64 Single-particle image processing
65 Noise-free field of single particles Helen Saibil, Birkbeck College London
66 1:1 signal to noise Helen Saibil, Birkbeck College London
67 1:1 signal to noise Helen Saibil, Birkbeck College London
68 3D maps from images Helen Saibil, Birkbeck College London
69 3D maps from images next round Helen Saibil, Birkbeck College London
70 Starting model from conical tilt reconstruction
71 3D reconstruction from 2D projections Helen Saibil, Birkbeck College London
72 Particle selection
73 Particle selection
74 Alignment, classification, class averages raw images aligned images class averages
75 3D reconstruction from class averages
76 3D reconstruction from class averages
77 Reference bias 10,000 images of random noise Janet Vonck
78 Reference bias 10,000 images of random noise noise images aligned to a reference image Janet Vonck
79 Reference bias 10,000 images of random noise Janet Vonck aligned noise images averaged
80 Reference bias 10,000 images of random noise Janet Vonck aligned noise images averaged
81 Reference bias 10,000 images of random noise Janet Vonck aligned noise images averaged
82 Reference bias 10,000 images of random noise Janet Vonck aligned noise images averaged
83 Reference bias 10,000 images of random noise Janet Vonck aligned noise images averaged
84 Gold standard Fourier shell correlation avoids reference bias compare Fourier transforms in resolution shells particle set 1 model 1 3D FT of model 1 Fourier shell correlation (FSC) independent particle set 2 model 2 3D FT of model 2
85 Resolution from FSC plot FSC = 0.5 resolution threshold for gold standard comparison FSC = (FOM = 0.5) (Rosenthal & Henderson JMB 2003) 4.1 Å 3.4 Å
86 Film vs. direct detector Fourier Shell Correlation Film, particles: 5.55 Å Falcon-II, particles: 3.95 Å FSC Resolu'on (Å - 1 ) Allegretti et al, elife 2014
87 Frh at 5.5 Å by cryo-em Mills et al, elife 2013
88 3.4 Å map of Frh complex Allegretti et al, elife 2014
89 3.4 Å map of Frh complex Allegretti et al, elife 2014
90 3.4 Å map of Frh complex Allegretti et al, elife 2014
91 3.4 Å map of Frh complex Allegretti et al, elife 2014
92 Science, 28 March 2014
93 Science, 28 March 2014
94 Three flavours of cryo-em Single-particle cryo-em! complexes > 200 kda up to 3 Å resolution Electron crystallography kda membrane proteins up to 3 Å resolution Electron cryo-tomography whole cells, organelles, membranes up to 8 Å resolution (by subtomogram averaging)
95 macromolecular complexes 2D crystals membranes, organelles, cells Frh ChR2 mito- mitochondrion single-particle processing electron crystallography electron tomography
96 macromolecular complexes 2D crystals membranes, organelles, cells Frh ChR2 mito- mitochondrion single-particle processing electron crystallography electron tomography
97 Electron crystallography
98 Purple membrane and bacteriorhodopsin Freeze-fractured H. halobium purple membranes Blaurock & Stoeckenius, Nature 1971 Henderson & Unwin, Nature 1975
99 2D crystals of LHC-II Kühlbrandt, Nature 1984
100 2D crystals of LHC-II Kühlbrandt et al, JCB 1983
101 Large 2D crystal of LHC-II
102 Electron diffraction patter of LHC-II 3.2 Å
103 Cryo image of LHC-II 2D crystal
104 Fourier transform of 2D crystal 3.28 Å
105 Reciprocal lattice of 2D crystal
106 Amplitudes and phases along lattice lines
107 3.4 Å EM structure of LHC-II Kühlbrandt et al, Nature 1994
108 3.4 Å EM structure of LHC-II Kühlbrandt et al, Nature 1994
109 Electron tomography
110 Two steps in electron tomography Achilleas Frangakis, Frankfurt University
111 Two steps in electron tomography 1. Imaging: convert 3D object into a set of 2D projections Achilleas Frangakis, Frankfurt University
112 Two steps in electron tomography 1. Imaging: convert 3D object into a set of 2D projections Achilleas Frangakis, Frankfurt University
113 Two steps in electron tomography 1. Imaging: convert 3D object into a set of 2D projections 2. reconstruction: generate 3D volume from set of 2D projections Achilleas Frangakis, Frankfurt University
114 Two steps in electron tomography 1. Imaging: convert 3D object into a set of 2D projections 2. reconstruction: generate 3D volume from set of 2D projections Achilleas Frangakis, Frankfurt University
115 Tomographic tilt series of mitochondrion 100 nm
116 Tomographic volume of mitochondrion 100 nm
117 Tomogram of a mouse heart mitochondrion outer membrane intermembrane space inner boundary membrane matrix cristae cristae junctions Tobias Brandt
118 Tomogram of a mouse heart mitochondrion outer membrane intermembrane space inner boundary membrane matrix cristae cristae junctions Tobias Brandt
119 Tomogram of a mouse heart mitochondrion outer membrane intermembrane space inner boundary membrane matrix cristae cristae junctions cristae junctions Tobias Brandt
120 Cryo-ET of Podospora mitochondrion ATP synthase dimers inner membrane outer membrane Davies et al, PNAS 2011
121 Sub-tomogram average of ATP synthase dimer Davies et al, PNAS 2012
122 Fitted X-ray structures F1 head peripheral stalk central stalk rotor ring Davies et al, PNAS 2012
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