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)

• ML classification (Sigworth)
• ML-like restraints & classification
• Continuous deformation models (Sigworth)

– Continuous vs. discrete models – Reconstructing continuous models using morphings--2D results.

Heterogeneity in Single Particles…

Degrees of Right and Wrong

Yu et al. 2008

Cytoplasmic Polyhedrosis Virus

3.88 Å resolution Atomic structure visible Degrees of Right and Wrong

Rabl et al. 2008

20S Proteasome

Resolution between 6 and 8 Å Secondary structure visible Correlation with existing atomic models Degrees of Right and Wrong

Villa et al. 2009

80S Ribosome

6.7 Å Resolution Secondary structure visible Correlation with existing atomic models Degrees of Right and Wrong

L-Type Ca2+ Channel

100 Å Wolf et al. 2003 23 Å Resolution Secondary structure NOT visible No existing atomic models available Neg. stain Cryo Degrees of Right and Wrong hollow

Wolf et al. 2003

Interpretation

Degrees of Right and Wrong

0.1 0.2 0.3 0.4 Fourier Shell Correlation 0.5 0.6 0.7 0.8 Resolution [Å] 0.9 1 ฀ 20 10 6.7 9.2 Å

Over-Refinement

∞

Wolf et al. 2002, unpublished Degrees of Right and Wrong

Resolution FSC

Images of Particles Alignment Averaging

Resolution Measurement

Degrees of Right and Wrong

100 Images 1000 Images Reference

Seeing is NOT Always Believing

Degrees of Right and Wrong

Ways to Increase Reliability

N = 30000 SNR = 1/50

Computer Simulation

Different Refinement Targets

0.2 0.4 0.6 0.8 1 FSC 0.1 0.2 0.3 0.4 0.5

PRES CC

Resolution [pixel-1]

Weighted

Estimated resolution

0.2 0.4 0.6 0.8 1 FSC 0.1 0.2 0.3 0.4 0.5

True Estimated

Resolution [pixel-1] 0.2 0.4 0.6 0.8 1 0.1 FSC 0.2 0.3 0.4 0.5

PRES CC Weighted

Resolution [pixel-1]

True resolution

Target functions: Phase residual Linear correlation coefficient Weighted correlation coefficient (signal-to-noise weighting) Ways to Increase Reliability

“The resolution reported by RMEASURE […] was more consistent with the details

• bserved in the reconstructions.”

Stagg et al. 2008

Resolution Measurement

FSC0.5 RMEASURE Ways to Increase Reliability

More RMEASURE Tests

0.2 0.4 0.6 0.8 1 0.02 0.04 0.06 0.08 0.1 0.12 0.14

• Pred. FSC

FSC FSC Resolution [Å-1]

Gabashvili et al. 2000 Samso et al. 2005

0.2 0.4 0.6 0.8 1 0.02 0.04 0.06 0.08 0.1 0.12 0.14

• Pred. FSC

FSC FSC Resolution [Å-1]

Ways to Increase Reliability

RMEAS. FSC0.5 RMEAS. FSC0.5

The Many Faces

• f a Channel

Murata et al. 2001

100 Å 100 Å

Serysheva et al. 2002 Wang et al. 2002

50 Å 50 Å

100 100 Å Wolf et al. 2003

Degrees of Right and Wrong

Jiang et al. 2002 da Fonseca et al. 2003 Serysheva et al. 2003 Sato et al. 2004

IP3 Receptor

Degrees of Right and Wrong

Spliceosome

100Å

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

Untilted

Random Conical Tilt

Structures 40° tilt Class Averages

Jurica et al. 2003 Ways to Increase Reliability

Classification

Jurica et al. 2003 Ways to Increase Reliability

Two Methods - Two Structures

Jurica et al. 2003 Ways to Increase Reliability

Angular reconstitution (no tilts) Random conical tilt

90 90

Rosenthal & Henderson 2003

Tilt Experiments

Ways to Increase Reliability

α-SNAP NAP

Rice& Br Brünge ger (1999) (1999)

SNARE co complex ex

Sutton

• n et al. (1998)

(1998)

N D1 D2

NS NSF

AAA domain AAA domain

NS NSF

Yu et al. (1999) (1999) May et a

• al. (1999)

(1999) Yu et al. (1998) (1998) Lenzen et a

• al. (1998)

(1998)

D2 D2 N

N-ethylmaleimide Sensitive Factor

Ways to Increase Reliability

Reconstruction

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

Matching References

Ways to Increase Reliability

D1 N N D2

Interpretation?

D2 D1 N N

p97/VCP

Sutton et al. 1998 Yu et al. 1999 May et al. 1999 Fürst et al. 2003 Degrees of Right and Wrong

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

D1 N N D2

Conformational Heterogeneity

NSF NSFΔN Fürst et al. 2003 Different Types of Heterogeneity

Compositional Heterogeneity

10 nm 50 nm

Shaker α4 Shaker α4β4 Sokolova et al. 2003 Different Types of Heterogeneity

Classification Methods…

Fred Sigworth

ML-Like Restraints & Classification

Poor Man’s Maximum Likelihood

Sigworth 1998

pi = joint probability

( ) ( )

∑ ∫

=

φ Θ φ = Θ

N i i i

d X p L

1

| , ln

If SNR high, then pi essentially zero everywhere except when particle aligned with reference (pi similar to delta function):

( )

[ ]

( )

[ ]

( )

[ ]

Θ φ σ +

• =

Θ φ = Θ φ = φ | ln argmax | , ln argmax | , argmax

2

f A X X p X p

i i i i i i

( )

xy

y x A σ σ = Θ , , , ,

ML-Like Restraints & Classification

X

i : image I

σ : standard deviation of noise in image A : reference image : particle params φ

Parameter Restraints

X

i : image i

A : reference image x0,y0: average x,y coords in data set : particle params σxy : std. deviation of x,y coords σ : standard deviation of noise in image

( ) ( ) ( )

        σ − + − − σ π = Θ φ

2 2 2 2 2

2 exp 4 1 ,

xy xy

y y x x f x0

( )

Θ φ, f y0 φ

( )

[ ]

Θ φ σ +

• =

φ | ln argmax

2

f A X i

i ML-Like Restraints & Classification

Computer Simulation

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5

FSC Resolution [pixel-1]

x,y restraints no restraints

ML-Like Restraints & Classification

Poor Man’s ML Classification

( ) (

) ( )

∑ ∑

+ = + +

φ =

i n k i N i n k i k i i n k

q q X A

1 , 1 1 , , ) 1 (

( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

∑

= +

Θ φ Θ φ =

K k n k n k i k i n k i n k n k i k i n k i n k i

a X p a X p q

1 , , , , 1 ,

| , | ,

Assume K classes with class averages A

k:

( )

[ ]

Θ φ σ +

• =

φ | ln argmax

2 ,

f A X

k i k i

ML-Like Restraints & Classification

( ) ( )

N q a

N i n k i n k

∑

=

=

1 ,

ML-Like Restraints & Classification

Test Structures

10000 i 10000 image ges of

• f e

each s structure i in r random

• m or
• rientation
• ns SNR ~ 1

ML-Like Restraints & Classification

ML-Like Restraints & Classification

Correlation Classification

SNR ~ 1 ~ 1 Correct: 99.2%

Cycle 10

ML-Like Restraints & Classification

ML-Like Classification

SNR ~ 1 ~ 1 Correct: 94.3%

Cycle 10

10000 i 10000 image ges of

• f e

each s structure i in r random

• m or
• rientation
• ns SNR ~ 0.1

0.1

ML-Like Restraints & Classification

ML-Like Restraints & Classification

Correlation Classification

SNR ~ 0.1 0.1 Correct: 62.6%

Cycle 20

ML-Like Restraints & Classification

ML-Like Classification

Cycle 20

SNR ~ 0.1 0.1 Correct: 86.5%

Continuous Deformation Models…

Fred Sigworth