Central European Institute of Technology BRNO | CZECH REPUBLIC
Single-particle reconstruction
With an emphasis on Random Conical Tilt in SPIDER
March 9th, 2015
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What information do we need for 3D reconstruction?
1. different orientations
2. known orientations
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What happens when we don't have enough views?
What happens when we're missing views?
sparse sampling
missing sparse missing
good views sampling views
Baumeister et al. (1999), Trends in Cell Biol., 9: 81-5.
Your sample isn't guaranteed to adopt different orientations, in which case you many need to explicitly tilt the microscope stage.
(more later...)
What information do we need for 3D reconstruction?
1. different orientations |2. known orientations
J^CEITEC
Required orientation parameters
Two translational:
■ Ax
■ Ay
Three orientational (Euler angles):
■ phi (about z axis)
■ theta (about y)
■ psi (about new z)
From http://www.wadsworth.org/spider_doc/spider/docs/euler.html
How do we used those orientation parameters?
Now that you know the Euler angles for each image, you can compute a back-projection.
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Getting different views: Tomography vs. single-particle
Tomography
From Ken Downing
We have:
■ known orientations
■ different views
BUT...
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What happens when we image the sample?
Baker et al. (1999) Microbiol. Mol. Biol. Rev. 63: 862
We are destroying the sample as we image it. c^ite
Consequences of repeated exposure
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From Ken Downing
Accumulated beam damage
If number of views is limited, then distortions
Solution:
Qf)we have manyl identical Inolecules, and if we can determine the orientations, we can use one exposure per molecule and use these images in the reconstruction.
"Single-particle reconstruction"
What information do we need for 3D reconstruction?
1. different orientations
2. known orientations
What information do we need for 3D reconstruction?
1. different orientations
2. known orientations [3. many particles
J^CEITEC
What happens as we include more particles?
n=1 n=4       n=16      n=256     n=1024 n=4096
Signal-to-noise ratio increases with Vn
But wait
Qf)we have manyl identical tnolecules, and if we can determine the orientations, we can use one exposure per molecule and use these images in the reconstruction.
							
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http://spider.wadsworth.org/spider_docte
A more realistic (but still fake) example
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From Nicolas Boisset
Synthetic images of worm hemoglobin
Shaikh etal., (2008) Nature Protocols 3: 1941-74.
What information do we need for 3D reconstruction?
1. different orientations
2. known orientations
3. many particles
J^CEITEC
What information do we need for 3D reconstruction?
1. different orientations
2. known orientations
3. many particles [4. identical particles
Now we need to find the orientations for each particle.
How to determine orientation?
Two scenarios*
1. You have a reference.
2. You don't have a reference.
Reference-based alignment
You will record the direction of projection (the Euler angles), such that if you encounter an experimental image that resembles a reference projection, you will assign that reference projection's Euler angles to the experimental image.
Step 1: Generation of projections of the reference.
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x
From Penczek etal. (1994), Ultramicroscopy 53: 251-70. Assumption: reference is similar enough to the sample that it can be used to determine orientation.
The extra features helped determine handedness in noisy reconstructions
V I V
phi=000
theta=0 00
psi=000
phi=000
theta=000
psi=000
: I
phi=000
theta=000
psi=000
phi=000
theta=0 00
psi=000
phi=000
theta=000
psi=000
^^^l ^^^l ^^^l ^^^l
phi=000
thet a=0 00
psi=000
phi=000
theta=000
psi=000
phi=000
thet a=0 00
psi=000
phi=000
thet a=0 00
psi=000
phi=000
theta=000
psi=000
theta=0 00
phi=192
thet a=045
psi=000
phi=000
theta=045
psi=000
phi=048
theta=045
psi=000
		%
phi=016		phi=115
theta=075		theta=075
psi=000		psi=000
phi=	= 072
theta=045	
psi=	= 000
i	
phi=131
theta=090
psi=000
Reference-based alignment
Stack of projections
Experimental
Stack of rotational CCF's
projection ^J^
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z
5   x r*s*r\ = _i
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i i —*— coeff's
From Penczek et al. (1994), Ultramicroscopy 53: 251-70.
Steps:
1. Compare the experimental image to all of the reference projections.
2. Find the reference projection with which the experimental image matches best.
3. Assign the Euler angles of that reference projection to the experimental image. 0^EITE
be novo reconstruction
If we don't have a reference reconstruction, how do we proceed?
1. Common lines
2. Random conical tilt
Brief summary of Fourier transforms
■ A Fourier transform is an alternative representation of image or volumetric data.
■ A Fourier transformation is a fully reversible mathematical transformation.
Projection theorem (or Central Section Theorem)
A central section through the
3D Fourier transform is the Fourier transform of the projection in that direction.
Common lines
(or Angular ReConstitution)
Summary:
■ A central section through the 3D Fourier transform is the Fourier transform of the projection in that direction
■ Two central sections will intersect along a line through the origin of the 3D Fourier transform
■ With two central sections, there is still one degree of freedom to relate the orientations, but a
third projection (i.e., central
Section) Will fiX the relative     Frank, J. (2006) 3D Electron Microscopy of Macromolecular Assemblies
orientations of all three.
J^CEITEC
Common lines
(or Angular ReConstitution)
Summary:
■ A central section through the 3D Fourier transform is the Fourier transform of the projection in that direction
■ Two central sections will intersect along a line through the origin of the 3D Fourier transform
■ With two central sections, there is still one degree of freedom to relate the orientations, but a third projection (i.e., central section) will fix the relative orientations of all three.
de novo reconstruction
If we don't have a reference reconstruction, how do we proceed?
1. Common lines [2. Random conical tilt |
Random-conical tilt:
Determination of Euler angles
/-		.jft^^i   Jät triff H in *      • * ^#     jT^v 45° Tilt			
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This scenario describes a worst case, when there is exactly one orientation in the 0° image. Since the in-plane angle varies, in the tilted image, we have different views available.
From Nicolas Boisset
Random-conical tilt: Geometry
Two images are taken: one at 0° and one tilted at an angle of 45°.
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Radermacher, M., Wagenknecht, T., Verschoor, A. & Frank, J. Three-dimensional reconstruction from a single-exposure, random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli. J Microsc 146, 113-36 (1987).
From Nicolas Boisset
See movie rct-part1 .avi
See movie rct-part2.avi
One problem though:
We can't tilt the stage all the way to 90 degrees.
Projection theorem
Random-conical tilt:
The "missing cone"
Representation of the distribution of views, if we display a plane perpendicular to each projection direction
The missing information, in the shape of a cone, elongates features in the direction of the cone's axis.
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From Nicolas Boisset
Random-conical tilt:
Filling the missing cone
If there are multiple preferred orientations, or if there is symmetry that fills the missing cone, you can cover all orientations.
Reconstruction
Distribution of orientation
From Nicolas Boisset
SPIDER
SPIDER
S ystem for P rocessing I mage D ata from
E lectron microscopy and R elated fields
SPIDER   & WEB
Wadsworth Center
Random Info Future of EM Software, MRC Image Stacks Harmful, GPU's and Snake Oil
Documentation Whats Hew Availability Download Installation Getting Started User Guide Tutorial_
SPIDER (System for Processing Image Data from Electron microscopy and Related fields) is an image processing system for electron microscopy.
• News:
• SPIDER is now an open source project maintained by unpaid volunteers. We invite contribution of code, documentation, and funding.
• Emphasis on:
• 3D reconstruction
• Averaging of single particle macromolecule specimens
• Multivariate statistical classification
• Electron tomography.
• Features:
• Interactive command line interface.
• Hierarchical modular design for scripting.
• Graphical User Interface, Web, for visualizing and interacting with images.
• File format interchangeable with other scientific imaging systems.
• Extensive documentation of operations and techniques.
• Includes source code.
• Includes PubSub for use on clusters.
• Available for Linux, OSX, and Aix. (OSX support will be discontinued in 2014.)
• History:
• Originated by: Joachim Frank. Availab
http://spider.wadsworth.org
Interacting with SPIDER:
The classic way
spiro nodupes/em2em 96> spider spi
\_^0 □'_/ SPIDER -- COPYRIGHT
,_xXXXx_ HEALTH RESEARCH INC., ALBANY, NY.
_xXXXx_
/   /xxx\   \ VERSION:    UNIX   21.13 ISSUED: 12/16/2013
/ \ DATE: 17-SEP-2014       AT 12:44:11
If SPIDER is useful, please cite:
Frank J, Radermacher M, Penczek P, Zhu J, Li Y, Ladjadj M,   Leith A. SPIDER and WEB: Processing and visualization of images in 3D electron microscopy and related fields.   J. Struct. Biol. 1996; 116: 190-199.
Results file: results.spi.6
Running : /home/tapu/local/spide r/bin/spide r_linux_mp_intel64
.OPERATION: WI WI
.INPUT FILE: testimg testimg testimg
(R )      230     230 CREATED 17-SEP-2014 AT 12:44:04   0 HEADER BYTES: 1840 .OUTPUT FILE: testwin testwin
.X S Y DIMENSIONS: 128,128
128 128 testwin
(R ) 128 128 CREATED 17-SEP-2014 AT 12:44:59 N HEADER BYTES: 1024 .TOP LEFT COORDINATES: 52,52
52 52 .OPERATION: f
Tilt-pair selection
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File   Edit Analysis
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From Nicolas Boisset Synthetic images of worm hemoglobin Shaikh etal., (2008) Nature Protocols 3: 1941-74.
Classification of 0° images
O^At Web - A SPIDER image viewer and analyzer     COPYRIGHT (c) 1992-2011 Health Research Inc., Menands, NY
Worm hemoglobin (phantom data)
Worm hemoglobin (side view)
IT
Central European Institute of Technology
Masaryk University
Kamenice 753/5
625 00 Brno, Czech Republic
www.ceitec.muni.cz | info@ceitec.muni.cz
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