alignment of cryo-electron tomography images using markov random fields a dissertation ...

180 Pages·2010·15.63 MB·English

ALIGNMENT OF CRYO-ELECTRON TOMOGRAPHY IMAGES
USING MARKOV RANDOM FIELDS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Fernando Amat Gil
May 2010
(cid:13)c Copyright by Fernando Amat Gil 2010
All Rights Reserved
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I certify that I have read this dissertation and that, in my opinion, it is fully
adequate in scope and quality as a dissertation for the degree of Doctor of
Philosophy.
(Mark A. Horowitz) Principal Advisor
I certify that I have read this dissertation and that, in my opinion, it is fully
adequate in scope and quality as a dissertation for the degree of Doctor of
Philosophy.
(Daphne Koller)
I certify that I have read this dissertation and that, in my opinion, it is fully
adequate in scope and quality as a dissertation for the degree of Doctor of
Philosophy.
(Kenneth H. Downing)
Approved for the University Committee on Graduate Studies.
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Abstract
Cryo-Electrontomography(CET)istheonlyimagingtechnologycapableofvisualizingthe
3D organization of intact bacterial whole cells at nanometer resolution in situ. However,
quantitativeimageanalysisofCETdatasetsisextremelychallengingduetoverylowsignal
to noise ratio (well below 0dB), missing data and heterogeneity of biological structures.
In this thesis, we present a probabilistic framework to align CET images in order to
improve resolution and create structural models of different biological structures. The
alignment problem of 2D and 3D CET images is cast as a Markov Random Field (MRF),
where each node in the graph represents a landmark in the image. We connect pairs
of nodes based on local spatial correlations and we find the “best” correspondence be-
tween the two graphs. In this correspondence problem, the “best” solution maximizes
the probability score in the MRF. This probability is the product of singleton potentials
thatmeasureimagesimilaritybetweennodesandthepairwisepotentialsthatmeasurede-
formations between edges. Well-known approximate inference algorithms such as Loopy
Belief Propagation (LBP) are used to obtain the “best” solution.
We present results in two specific applications: automatic alignment of tilt series using
fiducial markers and subtomogram alignment. In the first case we present RAPTOR,
which is being used in several labs to enable real high-throughput tomography. In the
second case our approach is able to reach the contrast transfer function limit in low SNR
samples from whole cells as well as revealing atomic resolution details invisible to the
naked eye through nanogold labeling.
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Acknowledgments
Writingthispageisthelaststepofajourneythatstartedsixyearsago. Itisagreatfeeling
to reach a conclusion, but it is even better knowing that this is just the beginning of my
career. The experiences I have had during my PhD at Stanford will follow me wherever I
go, and all of those experiences have names and faces associated with them that I would
like to thank here.
First and foremost, I would like to thank my principle advisor Mark Horowitz. He has
been a real mentor in all aspects of a PhD, from showing which questions are important
to answer to how to exchange knowledge better. Through his example, he has shown me
that it is possible to seek knowledge forever. No matter how many things you know, there
are still many things to be discovered. Finally, I am grateful to him for giving me the
opportunity to apply my engineering and mathematical background in a new field for me
and for opening the door to a great group of collaborators from many different disciplines,
which dramatically enriched my experience at Stanford.
One of those collaborators is my co-advisor Daphne Koller, who I would like to thank
for guiding me through the rich subject of graphical models and the complicated world
of research. Daphne’s advice is always sharp and stimulating, pushing me to elevate my
own standards. She set an example for me with her brilliance, high standards and drive
for excellence.
Kenneth H. Downing is another of those collaborators and he is responsible for ev-
erything I know about electron microscopy. I would like to thank him for opening the
doors of Donner Lab at LBL for me and for showing me the nuts and bolts of the electron
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microscope over informal discussion sessions. I am also grateful that he kindly accepted
to be in my reading committee for this thesis.
I would also like to acknowledge my office mate and great friend Farshid Moussavi.
Most of the work presented here is shared with him through many hours at the office and
many hours of joy and camaraderie outside the office. I really admire his determination
and his character. I would also like to thank Luis R. Comolli for never ending discussions
aboutmicroscopy,Fourierandanyothersubjectnotstrictlyrelatedtoresearch. Iconsider
Luis a true artist of the microscope and without his talent and all his images this thesis
would not be possible. I would also like to thank Lucy Shapiro and Harley McAdams for
all their support and kindness during all these years. The list of collaborators could go
on forever, but I definitely do not want to forget to thank Albert Lawerence at UCSD,
Grant Jensen at Caltech, Puey Ounjay at LBL and John Smit at British Columbia for
working together in different projects presented in this thesis. Finally, thanks to all the
VLSI research group for support and fruitful discussions, and to Teresa and Rafael for
making visits to administration offices fun.
In my experience, the PhD journey goes beyond research and it affects all aspects of
life. Without the personal friendship of many people this would have not been possible. I
am thinking of friends and family such as Mario, Argyris, Luciana, Sewoong, Yorgos and
many others that made these years in San Francisco unforgettable. However, I would like
to dedicate this thesis to Margie Marx. For me, she represents the beginning and the end
of my years at Stanford, and she taught me many valuable lessons that can not be learned
in any university.
Last but not least, I would like to dedicate this thesis to the three most important
people in my life: my fiancee Hillary, my dad Nicolas and my mom Josefina. Hillary has
given me love and support throughoutthese years andshe is always ableto lightup a gray
day with a single smile. I am looking forward to sharing the rest of my life with her. My
parents taught me since I was little that education will open doors to fanstatic places...
they were so right.
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Contents
Abstract iv
Acknowledgments v
1 Introduction 1
1.1 Imaging in life science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Statistical image processing in CET . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Thesis outline and contributions . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Background 7
2.1 Image formation in transmission electron microscope . . . . . . . . . . . . . 8
2.2 3D reconstruction from multiple 2D TEM images . . . . . . . . . . . . . . . 22
2.3 Cryo-electron tomography pipeline and challenges. . . . . . . . . . . . . . . 26
2.4 Related work in image alignment . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Automatic alignment of CET tilt series 47
3.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Challenges in CET projections of tilt series . . . . . . . . . . . . . . . . . . 51
3.3 Pairwise image correspondence with MRF . . . . . . . . . . . . . . . . . . . 52
3.4 Global correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.6 Discussion and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
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4 Subtomogram alignment 77
4.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Pairwise subtomogram correspondence with MRF. . . . . . . . . . . . . . . 82
4.3 Alignment refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5 Discussion and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5 Analysis of Caulobacter crescentus S-layer 113
5.1 Image analysis pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6 Conclusion 134
A Materials and methods 139
A.1 Bacterial strains and growth conditions . . . . . . . . . . . . . . . . . . . . 139
A.2 Introducing unique cysteines into rsaA . . . . . . . . . . . . . . . . . . . . . 140
A.3 Protein isolation and separation . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.4 Bacterial growth media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.5 Nanogold labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.6 Cryo-electron microscopy specimen preparation . . . . . . . . . . . . . . . . 141
A.7 Cryo-electron tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
B Noise model for CET volumes 143
C Cylindrical coordinates 146
Bibliography 148
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List of Tables
4.1 Percentage of Fourier coefficients selected in synthetic data . . . . . . . . . 103
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List of Figures
1.1 Bioimaging spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 CET challenges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Transmission electron microscope components . . . . . . . . . . . . . . . . . 9
2.2 Electron trajectories in a magnetic lens field . . . . . . . . . . . . . . . . . . 10
2.3 Elastic electron-specimen interaction . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Energy filter effects to improve image quality. . . . . . . . . . . . . . . . . . 12
2.5 Notation diagram at different stages of the image formation . . . . . . . . . 14
2.6 Phase-contrast principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 Contrast transfer function plots. . . . . . . . . . . . . . . . . . . . . . . . . 19
2.8 Defocus series of ferritin molecules . . . . . . . . . . . . . . . . . . . . . . . 20
2.9 Maximum thickness t as a function of accelerating voltage.. . . . . . . . . . 21
2.10 Projection-slice theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.11 Principle of electron tomography imaging . . . . . . . . . . . . . . . . . . . 27
2.12 CET pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.13 Radiation damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.14 Dose limitation affects SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.15 Missing wedge example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.16 Heterogeneity of biological structures . . . . . . . . . . . . . . . . . . . . . . 35
2.17 Markov chain factorization example . . . . . . . . . . . . . . . . . . . . . . 41
2.18 Conditional independence encoded in an MRF . . . . . . . . . . . . . . . . 42
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