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EXPLORING CRYO-ET WITH DYNAMO: TILT SERIES ALIGNMENT, TEMPLATE MATCHING, AND PCA

RAFFAELE CORAY,

NUMERICAL METHODS OF CRYO ELECTRON TOMOGRAPHY LAB

MADRID, 2025

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TILT SERIES ALIGNMENT IN DYNAMO

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AUTOMATIC TILT SERIES ALIGNMENT

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e^-

Idealization

Reality

50 nm

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AUTOMATIC TILT SERIES ALIGNMENT

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Micrograph i-2

Micrograph i-1

Micrograph i

Micrograph i+1

Micrograph i+2

chain

observations

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AUTOMATIC TILT SERIES ALIGNMENT

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Marker observation

Estimated

marker projection

Computation of marker projection

Indexing of observations

Model of the alignment geometry

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AUTOMATIC TILT SERIES ALIGNMENT: DETECTION

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AUTOMATIC TILT SERIES ALIGNMENT: INDEXING

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Micrograph

Neighboring Micrograph

Initial matches create chains

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AUTOMATIC TILT SERIES ALIGNMENT: INDEXING

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Initial chains

Estimation in 3D

Reprojection

Re-Indexing

Incorrect indexing

Incomplete indexing

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AUTOMATIC TILT SERIES ALIGNMENT: INDEXING

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Missing chains

Apply current alignment

Reprojection

New chains

Reconstruction and inspection

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HANDS-ON TUTORIAL

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Walkthrough on manual marker clicking

Familiarization to observation/chain logic.
Tool useful for manual corrections.

Walkthrough on GUI based tilt series alignment

Familiarization to the automatic alignment algorithm.
Results visualization by GUI and figures.

Walkthrough on command line based tilt series alignment

Example of scripting for large dataset processing.

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TEMPLATE MATCHING IN DYNAMO

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PARTICLE PICKING

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Template Matching

Manual

Automated

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TEMPLATE MATCHING: OVERVIEW

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Cross-correlation map

Assembled cross-correlation map

Best template rotations

Angle i

Angle i+1

Angle i+2

Template matching in cryoet for intifying copies of a template in a volume.

Example in 2D

Temlatr and image, a cross correlation amp can be computed. It shows positions were the image is most similar to the template

This computations is efficient thanks to fourier acceleration.

However, the temp,ate may be in different poses. SO this porcess need to be repeated for each pose.

CC maps are computed for each and the information is merged.

This creates an assembles cross-correlation map that can be used to determine both the most likely positions and orientation of compies of the template in an image.

However, in tomo, this process needs to be done in 3D. rotating 3D volume multiple times, cross-correlated against 3D volume, and then assemble. As three Euler angles arer equired to describe all template poses, the number of angualr combinations quickly become impractical, especially for fine angular scanning.

Unfortunately, fine angualr scanning is preferable for accurate identification. However, this type of computations become rapidly unfeasible.

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TEMPLATE MATCHING: HIGH RESOLUTION

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200 nm

10 nm

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TEMPLATE MATCHING: DIVIDE AND CONQUER

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Template

Informations to reduced scanning requirements:

Spatial locality

chunks

Angular restrictions

cones

However, in many cases, most combinations of tempate posiitons and rotations are not needed.

Here is a simple example with a spherical viral particle in which we are interested to identify the positions of the template on the spherical lattice.

In the highlighted area,, only a limited set of orientations are feasable for the target to be in. This defines a angular cone with which to rotate the template.

This can be repeated in othe regions, chunks, untilla all meaningful posiitons and orientations of the template are scanned while reducing computing time..

This is a process of divide and conquer by using spatial locality and angular restrictions.

I call this geometry-aware TM. As the biological context of the sample is used to improve computing times. the way to split this analysis by divide and conquer is what I describe as a tessellation.

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TEMPLATE MATCHING: DIVIDE AND CONQUER

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TEMPLATE MATCHING: IMPLEMENTATION

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VIDEO?

On-the-fly reconstruction

Manual tesselation

Peak extraction

Chunk peak extraction

Single chunk modus

Automatic tesselation

Running time estimator

Model-aware template match module

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HANDS-ON TUTORIAL

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Walkthrough for template matching

Familiarization to syntax and parameters.
Creation of template.
Parallel computing and chunks.
Analysis of cross-correlation maps.
Selection of TM particles.

Walkthrough for GUI-based template matching

Familiarization with GUI tools for tessellation creation.
Tomogram investigation with template matching.
Use of tessellation for template matching speed-up.

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PRINCIPAL COMPONENT ANALYSIS IN DYNAMO

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PCA: WHAT IS IT?

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PCA is a dimensionality reduction technique.

… we cannot approximate it

with only one component

r

r_x

r_y

X

Y

Let us consider a data sets of points in the plane.

Each point has two components.

We can describe them with the ”regular”

x,y system of coordinates,

which is unaware of the data structure

if we consider a generic data point r

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PCA: WHAT IS IT?

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can be (better) approximated

by its projection along U, i.e. r_u

U

V

r_u

r

let’s try again.

Now we tailor a system of reference

for this data set

dimensionality reduction

an axis U along the direction of maximal variance

an axis V orthogonal to U

now, our generic data point r

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PCA: WHAT IS IT?

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dimensionality

reduction

we go from 2 dimensions (x,y)

to 1 dimension (u)

How do we go from 256^ˆ3 dimensions to, say, 10?

Each subtomogram has (for example) a sidelength of 256 voxels

In subtomogram averaging, each data point would be a particle

pay a price: approximation

figure out a data-aware representation

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PCA: WHAT IS IT?

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x²_i

1005	1021
1021	1053

2029	0
0	29

Matrix diagonalization <-> redundancy reduction

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PCA: CROSS-CORRELATION MATRIX

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Missing wedge-aware cross-correlation coefficients for all possible particle couples

Element m(i,j)

similarity

of particle i

and particle j

Constrained

cross correlation

aligned particles

Förster et al, JSB, 2008

Castaño-Díez et al, JSB, 2012

aligned particles

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PCA: MISSING WEDGE

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each pair of particles are filtered to

their common Fourier components for a fair comparison!

“perfect” particle

Missing wedge compensation

when measuring particle similarity

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PCA: MATRIX DIAGONALIZATION

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A systematic way to create eigenvolumes as linear combinations of particles:

≈ p_1,1 •

+ p_1,2 •

≈ p_2,1 •

≈ p_3,1 •

≈ p_4,1 •

+ p_1,3 •

+ p_2,2 •

+ p_3,2 •

+ p_4,2 •

+ p_2,3 •

+ p_3,3 •

+ p_4,3 •

+ p_1,N-1 •

+ p_1,N •

+ p_2,N-1 •

+ p_3,N-1 •

+ p_4,,N-1 •

+ • • •

+ p_2,N •

+ p_3,N •

+ p_4,N •

L eigenvectors (eigenvolumes)

N particles

<<

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PCA: A NEW BASIS TO REPRESENT THE PARTICLES

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≈ λ_1,1 •

+ λ_1,2 •

+ λ_1,3 •

+ λ_1,4 •

≈ λ_N-2,1 •

≈ λ_3,1 •

≈ λ_2,1 •

≈ λ_N,1 •

≈ λ_1N-1,1 •

+ λ_2,2 •

+ λ_3,2 •

+ λ_N-2,2 •

+ λ_N-1,2 •

+ λ_N,2 •

+ λ_2,3 •

+ λ_2,4 •

+ λ_3,4 •

+ λ_N-2,4 •

+ λ_N-1,4 •

+ λ_N,4 •

+ λ_3,3 •

+ λ_N-2,3 •

+ λ_N-1,3 •

+ λ_N,3 •

λ_i,j : “weight”

of eigenvolume j in particle I

“eigencomponents”

…

Particles

most relevant

eigenvector

less relevant

eigenvector

particles

eigenvectors

λ_i,j :

representation of the full data set as a single matrix

tailored to capture variance

across particles

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PCA: A NEW REPRESENTATION TO IDENTIFY CLASSES

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Each point represents a particle in a L-dimensional space

λ_1,_•

λ_2,_•

λ_3,_•

K-means: clustering on L-dimensional spaces provided by L Principal Components

Each axis represents

a column of the matrix

(i.e.: the distribution of a feature)

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HANDS-ON TUTORIAL

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Walkthrough on PCA through the command line

PCA computation: particle alignment, constrained cross-correlation matrix, matrix diagonalization.
Management of computing resources.
Inspection of eigencomponent and eigenvolumes.
Munual and automatic clustering.
GUI-based inspection of classes