Computational methods for single-particle cryo-electron ... · Computational methods for single-particle cryo-electron microscopy Daniel Hogan and Hugo Kitano ... but easier reconstruction

CryoEM

Daniel HoganHugo Kitano

Introduction

Bayesianrefinement

Ribosometrajectories

Computational methods for single-particle cryo-electronmicroscopy

Daniel Hogan and Hugo Kitano

CS371 presentation

15 February 2017

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


1 IntroductionBasicsThe ProcessDifficultiesClusteringBack projectionOverfitting

2 Bayesian refinement

3 Ribosome trajectories

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


What is Cryo-EM?

Gaining traction in recent years due to better cameras

Crystallization avoided!

can change conformation

difficult for larger molecules

Lower resolution, but easier reconstruction problems

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


What is Cryo-EM?

Gaining traction in recent years due to better camerasCrystallization avoided!




CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


What is Cryo-EM?





CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


What is Cryo-EM?





CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Setup

Nature

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Two Steps to Reconstruct a 3D structure

Refine the 2D images

align movie frames to account for movement

cluster images that look similar together to average them

3D reconstructions

Combine our 2D projections into a 3D structure

Back-projection is difficult!

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement






3D reconstructions



CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement






3D reconstructions



CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement






3D reconstructions



CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement






3D reconstructions



CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Bunny

From Joachim Frank, Three-dimensional electron microscopy of macromolecular assemblies: Visualization of biological molecules in their nativestate, 2006

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Analysis difficulties

noisy images

random protein orientations

3D reconstruction

risk of overfitting data

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement



noisy images


3D reconstruction


CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement



noisy images


3D reconstruction


CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement



noisy images


3D reconstruction


CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Clustering

In order to create a 3D reconstruction, the 2D projections need to be clustered

Chicken and egg problem (“ill-posed”):

orientation information is necessary for cluster determination

cluster information makes orientation determination tractable

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Clustering

In order to create a 3D reconstruction, the 2D projections need to be clusteredChicken and egg problem (“ill-posed”):



CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Clustering




CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Clustering




CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Clustering

Pintilie http://people.csail.mit.edu/gdp/cryoem.html

http://people.csail.mit.edu/gdp/cryoem.html

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Back projection

Pintilie http://people.csail.mit.edu/gdp/cryoem.html

http://people.csail.mit.edu/gdp/cryoem.html

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Overfitting

Random noise becomes part of the model

Wikipedia https://en.wikipedia.org/wiki/File:Overfitting.svg

https://en.wikipedia.org/wiki/File:Overfitting.svg

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Smoothing

Smoothing is a powerful way to reduce overfitting, but it’s currently done via adhoc filtering

arbritary decisions using unstandardized heuristics, causes overfitting as well

separate steps of particle alignment, class averaging, filtering, and 3Dreconstruction

CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Smoothing




CryoEM


Introduction

Basics

The Process

Difficulties

Clustering

Back projection

Overfitting

Bayesianrefinement


Smoothing




CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement

Results of MAPestimation


1 Introduction

2 Bayesian refinementBayesian refinementResults of MAP estimation

3 Ribosome trajectories

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



MAP estimator

We will try to maximize a single probability function that takes into accountall of the steps

Maximum a priori estimation, which uses prior information to make ourprediction:

θ̂MAP = argmaxθ

P (θ|D)

θ̂MAP = argmaxθ

P (D|θ)P (θ)

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



MAP estimator

We will try to maximize a single probability function that takes into accountall of the steps

Maximum a priori estimation, which uses prior information to make ourprediction:

θ̂MAP = argmaxθ

P (θ|D)

θ̂MAP = argmaxθ

P (D|θ)P (θ)

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Bayesian refinement algorithm

This is very difficult!

V(n+1)l =

∑Ni=1

∫φ Γ

(n)iφ

∑Jj=1 P

φTljCTFijXij

σ2(n)ij

dφ∑Ni=1

∫φ Γ

(n)iφ

∑Jj=1 P

φTljCTFijXij

σ2(n)ij

dφ+ 1

τ2(n)l

σ2(n+1)ij =

1

2

∫φΓ(n)iφ

∣∣∣∣∣Xij − CTFij

L∑l=1

PφjlV

(n)l

∣∣∣∣∣2

dφ

τ2(n+1)l =

1

2

∣∣∣V (n+1)l

∣∣∣2where

Γ(n)iφ =

P(Xi |φ,Θ(n),Y

)P(φ|Θ(n),Y

)∫φ′ P

(Xi |φ′,Θ(n),Y

)P(φ′|Θ(n),Y

)dφ′

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Less overfitting

Overfitted vs. MAP

Scheres http://dx.doi.org/10.1016/j.jmb.2011.11.010

http://dx.doi.org/10.1016/j.jmb.2011.11.010

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Greater objectivity

The new approach (red) has higher resolution and greater objectivity than the old(green)

Scheres http://dx.doi.org/10.1016/j.jmb.2011.11.010

http://dx.doi.org/10.1016/j.jmb.2011.11.010

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Future improvements

Better microscopes and detectors will lead to less noise

More information about the relative orientations (especially for symmetricmolecules)

Regularization and the use of prior information (used here!)

CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Future improvements




CryoEM


Introduction

Bayesianrefinement

Bayesianrefinement



Future improvements




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

1 Introduction

2 Bayesian refinement

3 Ribosome trajectoriesIntroductionDataAnalysisResultsDiscussion

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Ribosomes

Responsible for the synthesis of protein using a mRNA template

Two subunits

Large subunit, composed of three rRNAs and 46 proteinsSmall subunit, composed of one rRNA and 33 proteins

The subunits rotate during each step elongation

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Ribosomes


Two subunits



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Ribosomes


Two subunits



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series

Objective: a series of structures of the ribosome to construct a time series

Purify ribosomes

Cryofix and image

Categorize by orientation and conformation

Determine structures

Construct a time series

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series


Purify ribosomes

Cryofix and image




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series


Purify ribosomes

Cryofix and image




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series


Purify ribosomes

Cryofix and image




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series


Purify ribosomes

Cryofix and image




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Time series


Purify ribosomes

Cryofix and image




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Raw images

Dashti, et al. http://dx.doi.org/10.1073/pnas.1419276111

http://dx.doi.org/10.1073/pnas.1419276111

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Data

∼4,700 micrographs

∼1,100,000 particles found algorithmically

∼850,000 particles after manual selection

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Data




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Data




CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Oriented image



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Analysis procedure



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Conformational manifold

Determined by a non-linear analog of PCA



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Analysis details

50 distinct conformations were identified

Ordering was inferred from similarity

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Analysis details

50 distinct conformations were identified

Ordering was inferred from similarity

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Structures



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Ribosome trajectory

Free energy inferred by relative populations



CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Concerns

Lack of detail on the preparation of ribosomes

The imaged ribosomes were “not engaged in translation”But ribosomal subunits do not bind together in the absence of mRNA

The ribosomes were manually selected from the micrographs, introducing apotential source of bias

Selecting images based on orientation before conformation

CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Concerns





CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Concerns





CryoEM


Introduction

Bayesianrefinement


Introduction

Data

Analysis

Results

Discussion

Concerns





Documents

Computational methods for single-particle cryo-electron ... · Computational methods for single-particle cryo-electron microscopy Daniel Hogan and Hugo Kitano ... but easier reconstruction