Heterogeneity in Single Particles Degrees of right and wrong Ways - PowerPoint PPT Presentation

Heterogeneity in Single Particles • Degrees of right and wrong • Ways to increase reliability • Detecting problems • Different types of heterogeneity • Overview of classification methods (Sigworth) – Classification as a problem of clustering in factor space – Brief intro to supervised classification – ML and the EM algorithm – ML with a prior probability (MAP estimation)

Heterogeneity in Single Particles… • ML classification (Sigworth) • ML-like restraints & classification • Continuous deformation models (Sigworth) – Continuous vs. discrete models – Reconstructing continuous models using morphings--2D results.

Degrees of Right and Wrong

Degrees of Right and Wrong Cytoplasmic Polyhedrosis Virus 3.88 Å resolution Atomic structure visible Yu et al. 2008

Degrees of Right and Wrong 20S Proteasome Resolution between 6 and 8 Å Secondary structure visible Correlation with existing atomic models Rabl et al. 2008

Degrees of Right and Wrong 80S Ribosome 6.7 Å Resolution Secondary structure visible Correlation with existing atomic models Villa et al. 2009

Degrees of Right and Wrong L-Type Ca 2+ Channel Neg. Cryo stain hollow 100 Å 23 Å Resolution Secondary structure NOT visible No existing atomic models available Wolf et al. 2003

Degrees of Right and Wrong Interpretation Wolf et al. 2003

Degrees of Right and Wrong Over-Refinement 1 0.9 0.8 Fourier Shell Correlation 0.7 0.6 0.5 0.4 9.2 Å 0.3 0.2 0.1 0 ∞ ฀ 20 10 6.7 Resolution [Å] Wolf et al. 2002, unpublished

Degrees of Right and Wrong Resolution Measurement . Images of Particles Alignment Averaging FSC Resolution

Degrees of Right and Wrong Seeing is NOT Always Believing 100 Images 1000 Images Reference

Ways to Increase Reliability

Computer Simulation N = 30000 SNR = 1/50

Ways to Increase Reliability Different Refinement Targets Estimated resolution True resolution 1 1 PRES 0.8 0.8 CC Weighted 0.6 0.6 FSC FSC 0.4 0.4 PRES 0.2 0.2 CC Weighted 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Resolution [pixel -1 ] Resolution [pixel -1 ] Target functions: 1 Estimated 0.8 True Phase residual 0.6 FSC Linear correlation coefficient 0.4 0.2 Weighted correlation coefficient (signal-to-noise weighting) 0 0 0.1 0.2 0.3 0.4 0.5 Resolution [pixel -1 ]

Ways to Increase Reliability Resolution Measurement RMEASURE FSC 0.5 “The resolution reported by RMEASURE […] was more consistent with the details observed in the reconstructions.” Stagg et al. 2008

Ways to Increase Reliability More RMEASURE Tests 1 RMEAS. Pred. FSC FSC FSC 0.5 0.8 0.6 FSC 0.4 0.2 0 Gabashvili et al. 2000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Resolution [Å -1 ] 1 RMEAS. Pred. FSC FSC 0.8 FSC 0.5 0.6 FSC 0.4 0.2 0 Samso et al. 2005 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Resolution [Å -1 ]

Degrees of Right and Wrong 100 Å 100 Å Serysheva et al. 2002 Murata et al. 2001 Wang et al. 2002 50 Å 50 Å The Many Faces of a Channel 100 Å Wolf et al. 2003 100

Degrees of Right and Wrong IP 3 Receptor da Fonseca et al. 2003 Jiang et al. 2002 Sato et al. 2004 Serysheva et al. 2003

Degrees of Right and Wrong Spliceosome 100Å Jurica et al. 2002, unpublished

Ways to Increase Reliability Random Conical Tilt Class Averages 40° tilt Structures Jurica et al. 2003 Untilted

Ways to Increase Reliability Classification Jurica et al. 2003

Ways to Increase Reliability Two Methods - Two Structures Angular reconstitution (no tilts) 90 Random conical tilt 90 Jurica et al. 2003

Ways to Increase Reliability Tilt Experiments Rosenthal & Henderson 2003

Ways to Increase Reliability N-ethylmaleimide Sensitive Factor NSF NS N D1 D2 AAA domain AAA domain NS NSF Yu et al. (1999) (1999) May et a al. (1999) (1999) D2 D2 N Yu et al. (1998) (1998) Lenzen et a al. (1998) (1998) α -SNAP NAP SNARE co complex ex Rice& Br Brünge ger (1999) (1999) Sutton on et al. (1998) (1998)

Ways to Increase Reliability Reconstruction 100 Å 100 Å 200 Å 200 Å Fürst et al. 2003

Ways to Increase Reliability Matching References

Degrees of Right and Wrong Interpretation? Yu et al. 1999 May et al. 1999 p97/VCP N N N N D1 D1 D2 D2 Sutton et al. 1998 Fürst et al. 2003

Detecting Problems • Often not straight forward! • Does it look like a ball? • Is it hollow? • Does the reference match the particles? • Does is correlate with known structures? • Can the high-resolution details be verified? • Does it make sense (biology, molecular mass)? • How does the structure refine? • Is there heterogeneity (variance, classification)?

Different Types of Heterogeneity

Different Types of Heterogeneity Conformational Heterogeneity NSF NSF Δ N N N D1 D2 Fürst et al. 2003

Different Types of Heterogeneity Compositional Heterogeneity Shaker α 4 Shaker α 4 β 4 50 nm 10 nm Sokolova et al. 2003

Classification Methods… Fred Sigworth

ML-Like Restraints & Classification

ML-Like Restraints & Classification Poor Man’s Maximum Likelihood p i = joint probability N ( ) ( ) ∑ ∫ Θ = φ Θ φ ln , | ( ) L p X d Θ = σ σ , , , , i i A x y 0 0 = 1 xy i If SNR high, then p i essentially zero everywhere except when particle aligned with reference ( p i similar to delta function): [ ] [ ] ( ) ( ) φ = φ Θ = φ Θ argmax , | argmax ln , | p X p X i i i i i [ ] ( ) = • + σ φ Θ 2 argmax ln | X A f i X i : image I σ : standard deviation of noise in image φ A : reference image : particle params Sigworth 1998

ML-Like Restraints & Classification Parameter Restraints [ ] ( ) φ = • + σ φ Θ 2 argmax ln | X i A f i x 0 ( ) φ , Θ f ( ) ( ) y 0   2 2 − + − 1 ( ) x x y y φ Θ = − , exp 0 0   f π 2 σ 2 σ 2 4 2     xy xy X i : image i A : reference image x 0 ,y 0 : average x , y coords in data set φ : particle params σ xy : std. deviation of x , y coords σ : standard deviation of noise in image

ML-Like Restraints & Classification Computer Simulation 1 0.8 x,y restraints no restraints 0.6 FSC 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 Resolution [pixel -1 ]

ML-Like Restraints & Classification Poor Man’s ML Classification Assume K classes with class averages A k : ( ) ( N ∑ ) φ + 1 n X q , , i i k i k + ( 1 ) = = 1 n i A ∑ ( ) + 1 k n q , i k i ( ) ( ) ( ) ( ) K ∑ ( ) ( ) ( ) ( ) ( ) + = φ Θ φ Θ 1 , | , | n n n n n n n q p X a p X a , , , , , i k i k i k i k k i k i k i k k = 1 k N ∑ ( ) n [ ] q ( ) , i k φ = • + σ φ Θ 2 argmax ln | ( ) X A f = = 1 n i a , i k i k k N

ML-Like Restraints & Classification Test Structures

ML-Like Restraints & Classification 10000 i 10000 image ges of of e each s structure i in r random om or orientation ons SNR ~ 1

ML-Like Restraints & Classification Correlation Classification Cycle 10 SNR ~ 1 ~ 1 Correct: 99.2%

ML-Like Restraints & Classification ML-Like Classification Cycle 10 SNR ~ 1 ~ 1 Correct: 94.3%

ML-Like Restraints & Classification 10000 i 10000 image ges of of e each s structure i in r random om or orientation ons SNR ~ 0.1 0.1

ML-Like Restraints & Classification Correlation Classification Cycle 20 0.1 Correct: 62.6% SNR ~ 0.1

ML-Like Restraints & Classification ML-Like Classification Cycle 20 0.1 Correct: 86.5% SNR ~ 0.1

Continuous Deformation Models… Fred Sigworth