Optimizing Image Acquisition Getting the most out of your microscope - PowerPoint PPT Presentation

Optimizing Image Acquisition Getting the most out of your microscope and detectors and the math you need to do it John Rubinstein Molecular Structure and Function Program The Hospital for Sick Children Research Institute Departments of Biochemistry and Medical Biophysics The University of Toronto

Outline Image optimization • Compare F20 to Titan Krios • Mysterious optimization for DDDs • Math for DDDs • Exposure weighting • Introduce problem of frame alignment • Refresher: waves and Fourier transforms • Padding and truncating in Fourier Space • Fourier shift theorem • Cross correlation functions • Applications of FFTs: • Downsampling images • (matrix multiplication review) • Aligning whole frames • Shifting frames • Aligning individual particles •

Getting good images

The NRAMM website … http://nramm.scripps.edu/2012-workshop-lectures/

Use your microscope appropriately … Tecnai F20 Titan Krios Use C2 aperture and lens setting that Parallel 3rd Condensor Lens minimizes beam divergence Avoiding Lens Use over-focused diffraction for search Constant power lenses Hystersis mode Stage Side Entry Cryoholder Cryo-autoloader Voltage 200 kV 300 kV

F20/Titan Krios cost analysis Titan Krios/DDD: USD $5M Tecnai F20/DDD: USD $2M —————————— Difference: USD $3M ” I think my time is worth ~£20/hr” - Richard Henderson (2001) £20/hr in 2001 ≃ £29/hr in 2014 (£1 ≃ USD$1.68) ≃ $49/hr in 2014 62,000 hours of Richard’s time “Official” work week = 35 h (34 years with Richard) “Machines don’t make discoveries, people do.” - Lewis Kay

Mysterious additional optimization with some microscopes Acknowledgments: Tim Grant (JFRC) Alexis Rohou (JFRC) Niko Grigorieff (JFRC) Jianhua Zhao (Toronto) Samir Benlekbir (Toronto)

Thallous chloride crystal - 25 kx magnification setting d=3.842 Å

FT of thallous chloride crystal image

Average of many thallous chloride FTs

Fitting of measured radius to an ellipse 1585 ’anisotropy3.txt’ f1(x) f2(x) 1580 r 1 =1577 pixels radius (pixels) 1575 r 2 =1547 pixels 1570 𝜮 off =1.3° 1565 1560 1555 1550 1545 -200 -150 -100 -50 0 50 100 150 200 angle (°) radius ( θ ) = r 1 + r 2 + cos (2 · ( θ − θ off )) ( r 1 − r 2 ) 2

FT of thallous chloride crystal image

Corrected FT(sinc interpolations)

Thallous chloride crystal

Corrected thallous chloride crystal

Average of many corrected thallous chloride FTs

Anisotropic magnification affects CTF estimation Anisotropic magnification • appear different (worse) at DF2 low magnification DF1 Will look like objective lens • astigmatism in power spectra

Easy way to check for anisotropic magnification (Jianhua Zhao) 35000 Original CTF parameters 30000 Defocus 2 (Å) 25000 20000 15000 10000 10000 15000 20000 25000 30000 35000 Defocus 1 (Å)

Easy way to check for anisotropic magnification (Jianhua Zhao) 35000 CTF parameters after anisotropy correction 30000 Defocus 2 (Å) 25000 20000 15000 10000 10000 15000 20000 25000 30000 35000 Defocus 1 (Å)

Is the problem widespread? (Yifan Cheng/Jianhua Zhao) 35000 TRPv1 CTF parameters 30000 Defocus 2 (Å) 25000 20000 15000 10000 10000 15000 20000 25000 30000 35000 Defocus 1 (Å)

Math for DDDs

Signal to Noise ratio in averages and frames A B Average of 30 frames: Individual frame 30 e - /Å 2 1 e - /Å 2

Exposure weighting 1.0 80 Å 50 Å Relative signal-to-noise ratio 27 Å 16 Å 0.5 8 Å 3 Å 0 0 10 20 30 40 50 Exposure (e - / Å 2 ) Hayward and Glaeser (1979).Ultramicroscopy 4 , 201-10. Baker, Smith, Bueler, and Rubinstein (2010), J. Struct. Biol. , 169 , 431-7. Baker and Rubinstein (2010), Method Enzymol 481 , 373-90.

Exposure weighting The resolution dependence of optimal exposures in liquid nitrogen temperature electron cryomicroscopy of catalase crystals Baker et al. the first few frames could be used to build high-resolution models. Journal of Structural Biology 169 (2010) 431–437 An even more sophisticated approach would be to use the optimal exposures measured here to calculate weighted averages of frames in order to maximize the SNR at each spatial frequency. Publication Conditions Conclusion Veesler et al. (2013) 200 kV, 20.6 e - /Å 2 , ~4-6 Å, groups of frames small effect JSB 184, 193-202 Scheres (2014) Estimate B-factor for each frame effect ELife 3:e03665. Wang et al. (2014) Baker et al. 2010 measured values + 30 % effect Nat Comm 5:5808

Drift of movie frames Unaligned movie Aligned movie Frame 1 2 3 4 Sources of movement: Specimen stage drift • Long exposures necessary for Gatan K2 summit in counting mode (>5 sec) • Side entry cryoholders may have drift rates of ~1 Å/s • Beam-induced movement • May cause shift of whole frame • May not be uniform within an image • Harder problem to solve •

Waves and FFTs

Representing waves a vectors phase ( Φ ) amplitude (|F|) For waves of a specified wavelength √ Imaginary i = − 1 F =a+bi b wavelength ( λ ) |F| • Wavelength φ • Amplitude a Real • Phase

The FT represents functions in terms of waves Function = = ... … + + wave 27 F= a+bi FT F= a+bi F= a+bi + + frequency wave 28 + + wave 29 + + ... …

Shifting waves causes a phase change

Phase change of Fourier components from shifting = = ... ... + + + + + + + + ... ... Shifting in real space causes phase changes in Fourier space

Resolution encoded by different pixels in a FFT Real image The FFT of an N pixel line 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å image will have N/2+1 complex pixels Fourier transform 2.6 -1 8 Å -1 4 Å ∞ Å -1 2 Å -1 Å -1 t (1 Å)*8/0 resolution ( k x ) = pixelsize · FTsize (1 Å)*8/1 radius (1 Å)*8/2 (1 Å)*8/3 (1 Å)*8/4

Manipulating FTs: truncating in Fourier space Real image The FFT of an N pixel line 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å image will have N/2+1 complex pixels Fourier transform 2.6 -1 8 Å -1 4 Å ∞ Å -1 2 Å -1 Å -1 Fourier transform 2.6 -1 8 Å -1 4 Å (now corresponds to 4 pixel image) ∞ Å -1 2 Å -1 Å -1 { removed values Real image 2 Å 2 Å 2 Å 2 Å Truncating in Fourier space leads to downsampling in Real space

Manipulating FTs: padding in Fourier space t resolution ( k x ) = pixelsize · FTsize The FFT of an N pixel line radius image will have N/2+1 complex pixels Real image 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å 1 Å Fourier transform 2.6 -1 8 Å -1 4 Å ∞ Å -1 2 Å -1 Å -1 Fourier transform 2.6 1.6 1.3 1.1 (now corresponds to 16 pixel image) -1 8 Å -1 4 Å ∞ Å 2 Å 1 Å -1 -1 -1 Å Å Å Å -1 -1 -1 -1 { padding 0s Real image 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å 0.5 Å { interpolated values Padding in Fourier space leads to interpolation in Real space

Two dimension Fourier transforms c 6 3 a+bi 2 5 1 a 4 -3 -2 -1 0 1 2 3 3 -1 2 a-bi -2 1 -3 c 1 2 3 4 5 6 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 • The positive Nyquist and negative Nyquist values are the same •

Two dimension Fourier transforms 6/-6 5 4 3 2 a+bi 1 0 1 2 a+bi 3 4 5 a+bi 6 -1 -2 -3 -4 -5

Phase change in 2D FFT upon shifting and image 6 3/-3 Imaginary 5 2 a+bi F b 4 1 | F | φ FT position (k y ) 3 0 a Real 2 -1 -2 1 2 3 1 FT position (k x ) 1 2 3 4 F shifted = F unshifted (cos � + i sin � ) � = k x ( j ) · ∆ x 2 ⇡ N + k y ( j ) · ∆ y 2 ⇡ N where ∆ x and ∆ y are the x and y shifts, respectively. N is the extent in pixels in both the x and y direction of the N × N image. k x ( j ) and k y ( j ) are the distance of the Fourier component from the origin in the k x and k y directions, respectively.

Applying knowledge of FFTs to DDD images

Sometimes you may want to downsample your images Ruskin, Yu, and Grigorieff (2013). JSB 184 , 385-93.

Downsampling in Fourier space 12 12 11 11 extract 10 10 central 9 9 FT region 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 put in 1 2 3 4 5 6 7 7 8 8 9 9 10 10 11 11 12 12 1 2 3 4 5 6 new array 6 FT -1 5 4 3 2 1 1 2 3 4 5 6

Cross correlation functions Cross-correlation Image 1 Image 2 function 6 6 6 3/-3 5 5 5 2 4 4 4 1 3 3 3 0 2 2 2 -1 1 1 1 -2 -1 0 1 2 3/-3 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 FT 3/-3 6 5 2 FT -1 4 1 a+bi FT FT position (k y ) 3 0 2 -1 -2 1 2 3 1 FT position (k x ) 1 2 3 4 take complex conjugate 6 3/-3 6 3/-3 6 3/-3 = × 5 2 5 2 5 2 4 1 4 4 1 a-bi 1 FT position (k y ) 3 0 FT position (k y ) FT position (k y ) 3 3 0 0 2 -1 2 2 -1 -1 -2 1 2 3 1 -2 1 2 3 -2 1 2 3 1 1 FT position (k x ) FT position (k x ) FT position (k x ) 1 2 3 4 1 2 3 4 1 2 3 4

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