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Optimizing image acquisition NRAMM - 2017 John Rubinstein Molecular Medicine Program The Hospital for Sick Children Research Institute Departments of Biochemistry and Medical Biophysics The University of Toronto

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Optimizing image acquisition NRAMM - 2017

John Rubinstein Molecular Medicine Program The Hospital for Sick Children Research Institute Departments of Biochemistry and Medical Biophysics The University of Toronto www.sickkids.ca/research/rubinstein @RubinsteinJohn

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Voltage Gun Stage Detector Negative stain 100/120 kV Thermionic Side entry RT holder CCD

Screening Cryo-EM

  • f >300 kDa

100/120 kV Thermionic Side entry cryoholder (anticontaminor) CCD Screening Cryo- EM of <300 kDa (100 kV) 200 kV FEG Side entry cryoholder (anticontaminor) DDD Good resolution cryo-EM 200 kV FEG Side entry cryoholder

  • r autoloader-type

holder DDD Best resolution cryo-EM 300 kV + FEG Side entry cryoholder

  • r autoloader-type

holder DDD Best resolution high-throughput cryo-EM 300 kV + FEG autoloader-type holder DDD

Equipment needed for single particle EM

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SLIDE 3

Everything is easier with a Krios! (~2014)

2007 to present: Tecnai F20 (K2 summit 2013) 2017: Titan Krios with Falcon3 (Quantum K2/K3??)

Cryo-EM in Toronto

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SLIDE 4

Time needed for each experiment

Negative stain specimen screening

Cryo-EM specimen screening and preliminary structure determination

High-res structure determination

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SLIDE 5

Use your FEG/DDD microscope appropriately…

Voltage Stage Obtaining Parallel beam Avoiding lens hysterisis F20 200 kV Side Entry Cryoholder Use C2 aperture and lens setting that minimizes beam divergence Use over-focused diffraction for search mode Talos/ Talos Arctica/ Glacios 200 kV Side entry holder/ Autoloader Use C2 aperture and lens setting that minimizes beam divergence Constant power lenses F30/Polara 300 kV Side entry holder/ Stable stage Use C2 aperture and lens setting that minimizes beam divergence Use over-focused diffraction for search mode Titan Halo 300 kV Side entry holder 3rd Condenser Lens Constant power lenses Titan Krios 300 kV Autoloader 3rd Condenser Lens Constant power lenses

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Must match exposure/defocus at different voltages

100 kV 200 kV 300 kV 100 kV 1 1.5 1.8 200 kV 0.68 1 1.2 300 kV 0.56 0.82 1 100 kV 200 kV 300 kV 100 kV 1 1.47 1.88 200 kV 0.678 1 1.27 300 kV 0.532 0.785 1

New defocus must keep product of λ and Δz constant

Voltage at which exposure known Voltage at which exposure wanted Voltage at which defocus wanted

Equivalent exposure calculator Equivalent defocus calculator

Based on linear energy transfers from Glaeser (2007)

Voltage at which defocus known

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SLIDE 7

Decision Relevant concepts Magnification or pixel size (Å/pixel) DQE, Nyquist Limit, Aliasing, Anisotropic magnification Exposure rate (electrons/pixel/second) Coincidence loss (counting) Frame rate (frames/sec) Alignability of frames, movement within frames, radiation damage per frame Movie length (seconds) Total signal at different resolutions

Decisions you need to make with a DDD

frame (Gatan) = fractions (FEI)

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SLIDE 8

Fourier basics

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SLIDE 9
  • 3
  • 1
  • 2
  • 3

1 2 3 1 2

  • 1

3

  • 2

FT FT-1 Fourier array (complex value pixels)

1 2 3 4 5 6 1 2 3 4 5 6

Two dimension Fourier transforms

  • The FT of real functions (e.g. images) are Hermitian: for every point (a+bi)

there is a corresponding point (a-bi)

  • For an N ⨉ N pixel image, Fourier transform is N/2+1 ⨉ N

a

a+bi a-bi c

Image array (real value pixels)

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SLIDE 10

Representing waves as vectors

phase (Φ) wavelength (λ) amplitude (|F|)

  • Wavelength
  • Amplitude
  • Phase

Real Imaginary a b

φ |F|

For waves of a specified wavelength

F=a+bi

i = √ −1

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SLIDE 11

The FT represents functions in terms of waves

Function wave 27 wave 28 wave 29 = … + + + + …

+ + + ... = ... +

FT frequency

F=a+bi F=a+bi F=a+bi

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SLIDE 12

Shifting waves causes a phase change

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SLIDE 13

Phase change of Fourier components from shifting

Shifting in real space causes phase changes in Fourier space

+ + + ... = ... + + + + ... = ... +

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Two dimension Fourier transforms

1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5

a+bi a+bi a+bi

Position of pixel determines sine wave frequency and direction

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Detective quantum efficiency

(What pixel size/magnification should you use?)

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McMullan et al. (2014), Ultramicroscopy 147, 156-63.

Detective Quantum Efficiency Fraction of Nyquist frequency

[SNRout(res’n)]2 [SNRin(res’n)]2 DQE(res’n)=

Detective quantum efficiency

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SLIDE 17

McMullan et al. (2009), Ultramicroscopy 109, 1144-7.

Electron counting can boost DQE

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SLIDE 18

Integration

Electron counting

1 1 1 1 Counting

Counting electrons normalizes the signal from each electron on the sensor

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SLIDE 19

Aliasing

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Sampling To capture signal of frequency ‘f’, must sample at 2f (e.g. 1 Å pixels allows 2 Å resolution) ‘Nyquist frequency’

Nyquist frequency and aliasing

This ‘critical sampling’ can also miss signals Sampling of signals that are higher-frequency than Nyquist produces lower-frequent power ‘Aliasing’

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SLIDE 21

Spectral power Frequency Nyquist frequency

Effect of aliasing on spectral power

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SLIDE 22

In reality, pixelated detector don’t sample analogue signal but integrate over pixel

Aliasing for real electron sensors

Aliasing limits DQE of perfect detector to (2/π)2

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SLIDE 23

Avoiding the effects of Aliasing - approach 1 (K2/K3)

  • Try to localize electron impacts to a corner of a pixel

}

Physical pixel size

}Super-res

pixel

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SLIDE 24

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 1 2 3 4 5 6

FT-1 FT

extract central region put in new array Collect data in “super-resolution mode”

Four ‘super-resolution’ pixels per physical pixel

Avoiding the effects of Aliasing - approach 1 (K2/K3)

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SLIDE 25

McMullan et al. (2014), Ultramicroscopy 147, 156-63.

Detective Quantum Efficiency Fraction of Nyquist frequency

Super-resolution signal from K2 summit has super-low DQE

Don’t try to use super-resolution signal for structure determination Super-resolution data collection followed by Fourier truncation may help reduce aliasing Super-resolution data collection takes additional time/disc space Reduced aliasing probably isn’t worth the extra time it takes (get more particle images instead) Averaging pixels 2⨉2 after super-resolution data collection re-aliases image

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SLIDE 26

Avoiding the effects of Aliasing - approach 2 (Falcon3)

  • Acquire a frame with ~1 el/100 pixels
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SLIDE 27

Avoiding the effects of Aliasing - approach 2 (Falcon3)

  • Acquire a frame with ~1 el/100 pixels
  • Localize electron to a sub-pixel (corner of a physical pixel)
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SLIDE 28

Avoiding the effects of Aliasing - approach 2 (Falcon3)

  • Acquire a frame with ~1 el/100 pixels
  • Localize electron to a sub-pixel (corner of a physical pixel)
  • Replace electron with a function (e.g. Gaussian) that covers multiple pixels
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SLIDE 29

Avoiding the effects of Aliasing - approach 2 (Falcon3)

364 214

214 105 23 55 5 55 23

364

5 55 23 214 105 23 214 55

364 214

55 23 105 214 5 23 55

364 55

23 5 214 105 23 214 55

  • Acquire a frame with ~1 el/100 pixels
  • Localize electron to a sub-pixel (corner of a physical pixel)
  • Replace electron with a function (e.g. Gaussian) that covers multiple pixels
  • Determine contribute of Gaussian to 9 physical pixels and record
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SLIDE 30

Avoiding the effects of Aliasing - approach 2 (Falcon3)

  • Acquire a frame with ~1 el/100 pixels
  • Localize electron to a sub-pixel (corner of a physical pixel)
  • Replace electron with a function (e.g. Gaussian) that covers multiple pixels
  • Determine contribute of Gaussian to 9 physical pixels and record

364 214

214 105 23 55 5 55 23

364

5 55 23 214 105 23 214 55

364 214

55 23 105 214 5 23 55

364 55

23 5 214 105 23 214 55

Advantage: benefits

  • f anti-aliasing without

problems of recording super-resolution image Disadvantage: may complicate data compression

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SLIDE 31

Coincidence loss

(What exposure rate should you use?)

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SLIDE 32

Integration

Electron counting

1 1 1 1 Counting

Counting electrons normalizes the signal from each electron on the sensor

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SLIDE 33

Too many electrons in a frame for counting… Missed electrons = coincidence loss Ideal for counting: 1 electron/100 pixels

Camera Frame rate (fps) Exp rate (e/pix/s) K2 400 4 K3 1500 15 Falcon 3 40 0.4 DE-20 32 0.32

Conditions for achieving 1 el/100 pix/frame

Camera Frame rate (fps) Exp rate (e/pix/s) K2 400 4-12 K3 1500 15-45 Falcon 3 40 0.4-1.2 DE-20 32 0.32-0.96

Conditions for achieving acceptable coincidence loss

Coincidence loss

Microscope stage must be stable enough to allow counting!

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SLIDE 34

Frame alignment

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SLIDE 35
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SLIDE 36

Unaligned movie Aligned movie

Frame 1 2 3 4

  • Define Frame 1 as “unshifted” (0,0)
  • Calculate vectors (xshift,yshift) that bring two frames into register
  • Can use cross correlation to estimate 6 unique vectors for 4 frame movie:

Frame 1 vs Frame 2 Frame 1 vs Frame 3 Frame 1 vs Frame 4 Frame 2 vs Frame 3 Frame 2 vs Frame 4 Frame 3 vs Frame 4

The MotionCorr algorithm: least squares

Li … Cheng (2013). Nat Methods 10, 584-90.

Can calculate (Z/2) ⨉ (Z-1) cross-correlation functions for a movie with Z frames (e.g. 30 frame movie yields 435 CCFs)

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SLIDE 37

= ·

tNM means true shift vector between frames N and M mNM means measured shift vector (by cross correlation) between frames N and M

t12 t23 t34 m12 1 0 0 m14 m13 1 1 0 m23 m24 m34

m12≃1·t12+0·t23+0·t34 m13≃1·t12+1·t23+0·t34

1 1 1

m14≃1·t12+1·t23+1·t34

1 1 1 1 0 0

m23≃0·t12+1·t23+0·t34 m24≃0·t12+1·t23+1·t34 m34≃0·t12+0·t23+1·t34

MotionCorr: least squares method for aligning frames

Li…Cheng, Nature Methods

Once matrices are filled in standard linear algebra can be used to find values that best fit the data for t12, t23, t34

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SLIDE 38

The Unblur algorithm: Iterative sum & align (with splines)

Grant & Grigorieff (2015) eLife 4:e06980

Take movie Remove a frame Align removed frame to sum Calculate sum Fit trajectories of frames to a (smooth) spline repeat for all frames repeat until convergence

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SLIDE 39

Alignframes_lmbfgs: Gradient-based optimization

  • ptimum

(minimum)

O(𝚺)

θa O(θ)

  • Conjugate gradients
  • Broyden-Fletcher-Goldfarb-Shanno

Use an objective function that, when minimized, maximizes the sum

  • f the correlations of each shifted frame with the sum of the shifted

frames.

𝞊O(𝚺)/𝞊𝚺a

Calculate the partial derivatives of the objective function to quickly and accurately find the best value of the objective/best shifts.

Rubinstein and Brubaker (2015) J Struct Biol 192, 188-95. (arXiv 2014)

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SLIDE 40

1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5 1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5 1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5 1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5 1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5 1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5

z=1 … Z

FTs of shifted frames

1 2 3 4 5 6

  • 1
  • 2
  • 3
  • 4
  • 5

6/-6 1 2 3 4 5

Sum of FTs

Fjz(cos jz + i sin jz) FjzSjz Sjz = (cos jz + i sin jz)

a+bi

Z

X

z=1

FjzSjz

a+bi

Overall objective function and its derivatives:

O(Θ) = −Re

Z

X

z=1 J

X

j=1

" F*

jzS* jz Z

X

z0=1

Fjz0Sjz0 # 6 ∂O(Θ) ∂xa = Re

J

X

j=1

2πikx(j) N " FjaSja

Z

X

z=1

F*

jzS* jz F* jaS* ja Z

X

z=1

FjzSjz # ∂O(Θ) ∂ya = Re

J

X

j=1

2πiky(j) N " FjaSja

Z

X

z=1

F*

jzS* jz F* jaS* ja Z

X

z=1

FjzSjz #

Alignframes_lmbfgs: Gradient-based optimization

Rubinstein and Brubaker (2015) J Struct Biol 192, 188-95. (arXiv 2014)

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SLIDE 41

500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500 5 10 15 20 25 30

y-position (pixels)

x-position (pixels)

Particle/patch-based motion correction

Alignparts_lmbfgs (Rubinstein & Brubaker, 2015, JSB 192, 188-95) MotionCor2 (Zheng…Agard, 2017, Nat Meth 14, 331-2) Relion Polishing (Scheres, 2014, eLife 3:e03665)

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SLIDE 42

Particle polishing in Relion

Relion Polishing (Scheres, 2014, eLife 3:e03665)

Align rolling frame averages to projections of reference map Do whole-frame alignment

Frame2’=ave(Frame1,2,3) Frame3’=ave(Frame2,3,4) Frame4’=ave(Frame2,3,4) FrameN’=ave(FrameN-1,N,N+1) . . .

Rolling average of frames Fit trajectories to a straight line position=(x0,y0)+(Δx,Δy)*frame Local averaging

  • f speed & direction
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SLIDE 43

MotionCor2

Align whole frames with Unblur-type approach Divide image into grid of patches (e.g. 5⨉5) Align each patch with Unblur-type approach Fit shift at centre of patches to a polynomial model Use polynomial model to find pixel shifts between patch centres Deform image so that each pixel is appropriately shifted

MotionCor2 (Zheng…Agard, 2017, Nat Meth 14, 331-2)

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SLIDE 44

500 1000 1500 2500 3500 2000 3000 position (x-direction) 500 1000 1500 2500 3500 2000 3000 position (y-direction)

500 550 600 650 700 750 2700 2750 2850 2950 2800 2900 3100 3200 3300 3350 3250 3150 550 600 650 750 700

Trajectories x5

alignparts_lmbfgs: gradient-based optimization

Like alignframes_lmbfgs but use particle boxes and force smoothness and local averaging

Rubinstein and Brubaker (2015) J Struct Biol 192, 188-95. (arXiv 2014)

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SLIDE 45

High-throughput structure determination pipeline

Unpublished

cryoSPARC: 3.4 Å Sample (from collaborator) Optimize specimen on F20/K2 Alignframes/Alignparts small dataset cryoSPARC: ~ 5Å 24h Titan Krios/K2 (NRAMM/SEMC) MotionCor2 large dataset

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SLIDE 46

One size does not fit all… (Hui Guo)

Initial dataset: F20/K2, 239159 particle images, alignparts_lmbfgs (4.4 Å)

1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 16.5 8.4 5.6 4.2 3.4 2.8 2.4

Resolution (Å) Fourier Shell Correlation

0.143

NRAMM dataset: Titan Krios/Quantum K2, 470036 particle images, MotionCor2 (4.5 Å) 4.5 Å NRAMM: Hui (Alex) Wei, Bridget Carragher, Clint Potter NRAMM dataset: Titan Krios/Quantum K2, 446259 particle images, alignparts_lmbfgs (3.6 Å) 3.6 Å

g b e f k a 8 d c-ring i/j

Mitochondrial matrix Intermembrane space

Guo et al. (2017) Science, In Press

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SLIDE 47

Comparison of motion correction methods

Approach Frames/ Particles/ Regions Correlation Smoothing Advantages/Disadvantage Motioncorr (least squares) Frames Noisy images to noisy images Over-determined problem (least squares fit) Over-determined/low signal- to-noise in comparisons Unblur (iterative sum & align) Frames Noisy images to sums of noisy images Trajectory fitted to spline Robust/whole frame only Alignframes_lmbfgs (gradient-based) Frames Noisy images to sums of noisy images Penalize changes in trajectory (second

  • rder smoothing)

Relatively fast and robust/ whole frame only Polishing in Relion (projection matching) Particles Noisy images to high SNR map projections Linear fit, rolling averages, enforce local correlation Map projection v. high SNR/ map projection may not match image Alignparts_lmbfgs (gradient-based) Particles Noisy particle images to sums of noisy images Penalize changes in trajectory, enforce local correlation Non-linear trajectories/Map projections have higher SNR MotionCor2 (model-based) Regions Noisy patch images to sums of noisy images Polynomial model Fast and efficient/May be trying to align empty patches

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SLIDE 48

Exposure weighting

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SLIDE 49

ky

kx

ky

kx

ky

kx

ky

kx

a c b d

0-8 e-/Å2 8-16 e-/Å2 46-54 e-/Å2 78-96 e-/Å2 Baker, Smith, Bueler and Rubinstein (2010). J Struct Biol 169, 431-7.

Optimizing signal-to-noise ratios in images

Electron exposure (multiples of Ne) Relative SNR at resolution k Hayward and Glaeser (1979). Ultramicroscopy 4, 201-10.

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SLIDE 50

Optimal weighting for radiation damage

Baker, Smith, Bueler, and Rubinstein (2010), J. Struct. Biol., 169, 431-7. Baker and Rubinstein (2010), Method Enzymol 481, 373-90.

0.05 0.10 0.15 0.20 0.25 0.30 0.35 5 30 25 20 15 10

Radius (Å-1) E x p

  • s

u r e ( e

  • /

Å

2

)

Use this exposure For this resolution Use this exposure For this resolution

Hayward and Glaeser (1979). Ultramicroscopy 4, 201-10.

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SLIDE 51

Baker, Smith, Bueler and Rubinstein (2010). J Struct Biol 169, 431-7.

10 20 30 40 50 60 70 80 90 100 20 40 60 80 100

Electron exposure (e-/Å2) Relative SNR (%)

2 Å 3 Å 5 Å 10 Å 15 Å 20 Å

Physics based exposure weighting

Physics-based exposure weighting

Better exposure curves measured by: Grant & Grigorieff (2015) eLife 4:e06980 Used in: Alignparts_lmbfgs (Rubinstein & Brubaker, 2015, JSB 192, 188-95) Unblur (Grant & Grigorieff, 2015, eLife 4:e06980) MotionCor2 (Zheng…Agard, 2017, Nat Meth 14, 331-2)

20S Proteasome

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SLIDE 52

A

γ-secretase

movie frame number frequency (1/Å) r e l a t i v e w e i g h t

Ct Bt ( Å2 )

β-galactosidase

Data-driven exposure weighting

Scheres (2014). eLife 3:e03665.

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SLIDE 53

Anisotropic magnification

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SLIDE 54

magnification(x) ≠ magnification(y)

Anisotropic magnification detected numerous microscopes at low magnification Affects small pixel detectors (Gatan K2/K3, DirectElectron) Several papers describe (e.g.) Baldwin, J., Henderson, R., 1984. Ultramicroscopy 14 (4), 319–335. Grant, T., Grigorieff, N (2015) J Struct Biol (2015) 192(2):204-8. Zhao, J., Brubaker, M. A., Benlekbir, S., Rubinstein, J.L. (2015). J Struc Biol 192(2):209-15

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SLIDE 55

Thallous chloride crystal - 25 kx magnification setting

d=3.842 Å

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SLIDE 56

FT of thallous chloride crystal image

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SLIDE 57

Average of many thallous chloride FTs

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SLIDE 58

1545 1550 1555 1560 1565 1570 1575 1580 1585

  • 200
  • 150
  • 100
  • 50

50 100 150 200 ’anisotropy3.txt’ f1(x) f2(x)

angle (°) radius (pixels)

radius(θ) = r1 + r2 + cos (2 · (θ − θoff)) (r1 − r2) 2

r1=1577 pixels r2=1547 pixels 𝜮off=1.3°

Fitting of measured radius to an ellipse

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SLIDE 59

Anisotropic magnification degrades resolution

Stretch Distorted particles are no longer identical

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SLIDE 60

Thallous chloride crystal

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SLIDE 61

Corrected thallous chloride crystal

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SLIDE 62

Average of many corrected thallous chloride FTs

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SLIDE 63

Anisotropic magnification affects CTF estimation

  • Anisotropic magnification

appear different (worse) at low magnification

DF1 DF2

  • Will look like objective lens

astigmatism in power spectra

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SLIDE 64

Easy way to check for anisotropic magnification (Jianhua Zhao)

Defocus 1 (Å) Defocus 2 (Å)

Original CTF parameters

10000 15000 20000 25000 30000 35000 10000 15000 20000 25000 30000 35000

Astigmatism: DF1 ≃ DF2 + Const Anisotropic mag: DF1 ≃ Const*DF2

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SLIDE 65

CTF parameters after anisotropy correction

10000 15000 20000 25000 30000 35000 10000 15000 20000 25000 30000 35000

Defocus 1 (Å) Defocus 2 (Å)

Easy way to check for anisotropic magnification (Jianhua Zhao)

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SLIDE 66

Is the problem widespread? (Yifan Cheng/Jianhua Zhao)

TRPv1 CTF parameters

10000 15000 20000 25000 30000 35000 10000 15000 20000 25000 30000 35000

Defocus 1 (Å) Defocus 2 (Å)

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SLIDE 67

Decision Relevant concepts Conclusion Pixel size/magnification (Å/pixel) DQE, Nyquist Limit, Aliasing, Anisotropic magnification Resolution of interest must be within Nyquist limit and have good DQE Exposure rate (electrons/ pixel/second) Coincidence loss Minimize coincidence loss while keeping exposure time reasonable Frame rate (frames/sec) Alignability of frames, movement within frames, radiation damage per frame Ensure enough signal to align frames but exposure weight properly Movie length (seconds) Total signal at different resolutions Ensure enough signal to align and classify particles

Decisions you need to make with a DDD

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SLIDE 68

Acknowledgements:

Current members: Yazan Abbas Samir Benlekbir Stephanie Bueler Hui Guo Zev Ripstein Thamiya Vasanthakumar Toronto Collaborators Marcus Brubaker (York U) Past members: Jianhua Zhao Lindsay Baker Hui (Alex) Wei (NRAMM) Bridget Carragher (NRAMM) Clint Potter (NRAMM)