ABSTRACT
Title of dissertation: QUANTIFYING THE ORGANIZATION
AND DYNAMICS OF EXCITABLE
SIGNALING NETWORKS
Leonard Joseph Campanello
Doctor of Philosophy, 2020
Dissertation directed by: Professor Wolfgang Losert
Department of Physics
The transmission of extracellular information through intracellular signaling
networks is ubiquitous in biology?from single-celled organisms to complex multi-
cellular systems. Via signal-transduction machinery, cells of all types can detect
and respond to biological, chemical, and physical stimuli. Although studies of sig-
naling mechanisms and pathways traditionally involve arrays of biochemical assays,
detailed quantification of physical information is becoming an increasingly impor-
tant tool for understanding the complexities of signaling. With the rich datasets
currently being collected in biological experiments, understanding the mechanisms
that govern intracellular signaling networks is becoming a multidisciplinary problem
at the intersection of biology, computer science, physics, and applied mathematics.
In this dissertation, I focus on understanding and characterizing the physical
behavior of signaling networks. Through analysis of experimental data, statistical
modeling, and computational simulations, I explore a characteristic of signaling net-
works called excitability, and show that an excitable-systems framework is broadly
applicable for explaining the connection between intracellular behaviors and cell
functions.
One way to connect the physical behavior of signaling networks to cell func-
tion is through the structural and spatial analyses of signaling proteins. In the first
part of this dissertation, I employ an adaptive-immune-cell model with a key ac-
tivation step that is both promoted and inhibited by a microns-long, filamentous
protein complex. I introduce a novel image-based bootstrap-like resampling method
and demonstrate that the spatial organization of signaling proteins is an important
contributor to immune-cell self regulation. Furthermore, I use the bootstrap-like
resampling to demonstrate that the location of contact points between signaling
proteins can provide mechanistic insight into how signal regulation is accomplished
on the single-cell level. Finally, I probe the excitable dynamics of the system with
a Monte Carlo simulation of nucleation-limited growth and degradation. Using the
simulations, I show that careful balance between simulation parameters can elicit a
tunable response dynamic.
The spatiotemporal dynamics of signaling components are also important me-
diators of cell function. One key readout of the connection between signaling dy-
namics and cell function is the behavior of the cytoskeleton. In the second part of
this dissertation, I use innate-immune-cell and epithelial-cell models to understand
how a key cytoskeletal component, actin, is influenced by topographical features
in the extracellular environment. Engineered nanotopographic substrates similar in
size to typical extracellular-matrix structures have been shown to bias the flow of
actin, a concept known as esotaxis. To measure this bias, I introduce a generaliz-
able optical-flow-based-analysis suite that can robustly and systematically quantify
the spatiotemporal dynamics of actin in both model systems. Interestingly, despite
having wildly different migratory phenotypes and physiological functions, both cell
types exhibit quantitatively similar topography-guidance dynamics which suggests
that sensing and responding to extracellular textures is an evolutionarily-conserved
phenomena.
The signaling mechanisms that enable actin responses to the physical envi-
ronment are poorly understood. Despite experimental evidence for the enhance-
ment of actin-nucleation-promoting factors (NPFs) on extracellular features, con-
necting texture-induced signaling to overall cell behavior is an ongoing challenge.
In the third part of this dissertation, I study the topography-induced guidance
of actin in amoeboid cells on nanotopographic textures of different spacings. Us-
ing optical-flow analysis and statistical modeling, I demonstrate that topography-
induced guidance is strongest when the features are similar in size to typical actin-
rich protrusions. To probe this mechanism further, I employ a dendritic-growth
simulation of filament assembly and disassembly with realistic biochemical rates,
NPFs, and filament-network-severing dynamics. These simulations demonstrate
that topography-induced guidance is more likely the result of a redistribution, rather
than an enhancement, of NPF components.
Overall, this dissertation introduces quantitative tools for the analysis, mod-
eling, and simulations of excitable systems. I use these tools to demonstrate that an
excitable-systems framework can provide deep, phenomenological insights into the
character, organization, and dynamics of a variety of biological systems.
QUANTIFYING THE ORGANIZATION AND DYNAMICS OF
EXCITABLE SIGNALING NETWORKS
by
Leonard Joseph Campanello
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2020
Advisory Committee:
Professor Wolfgang Losert, Advisor and Chair
Professor John T. Fourkas, Dean?s Representative
Professor Michelle Girvan
Professor Brian C. Schaefer
Professor Arpita Upadhyaya
?c Copyright by
Leonard Joseph Campanello
2020

Dedication
For Dad and Poppop. I miss you very much.
ii
Acknowledgments
I owe my deepest gratitude to many people who have made this thesis possible.
You have all played important roles in my life during my career as a graduate
student, and I will cherish our experiences together forever.
Thank you to my advisor, Professor Wolfgang Losert. Your enthusiasm for sci-
ence is contagious and inspirational. Thank you for providing support and guidance
over the past several years, and for giving me the opportunity to work on challenging
and interesting projects. It has been a pleasure to work with you.
Thank you to members of my thesis committee: Professor John Fourkas, Pro-
fessor Michelle Girvan, Professor Arpita Upadhyaya, and Professor Brian Schaefer.
John, thank you for your guidance at our weekly subgroup meetings. Michelle, thank
you for your fervent support of students in the COMBINE program and for your
dedication to teaching, especially PHYS 615. Brian, thank you for collaborating
with me and Wolfgang on interesting problems over the past several years.
Thank you to all past and present members of the Losert Lab. Thank you
especially to Dr. Rachel M. Lee for your dedication to good scientific practice; Qixin
Yang for helpful and fun conversations; Professor Gabriel Frank for your example
of balancing work and life; Drs. B. U. Sebastian Schmidt and Kate M. O?Neill for
your post-doctoral guidance; Drs. Joshua Parker and Can Guven for your help; Dr.
Yang Shen, Dr. Desu Chen, and Zackery Benson for being the best officemates;
Abby Bull and Matt Hourwitz for our collaborations; and Sylvester Gates, Nick
Mennona, Corey Herr, and Stephanie Noel for all the fun and camaraderie. Thank
iii
you also to non-Losert-lab members, especially Dr. Maria Traver for your guidance.
Thank you to all of my friends whose continuous support and encouragement I
frequently relied on. Thank you especially to Alexander, Amanda, Ava, and Abigail
Proctor; Allen, Anna, and April Tan; Yidan Wang; Mikel and Erik Marshall; Marco
Sagliocca; Prahalad Reddy; Bob Scherne and family; and Ark Latt.
Thank you also to the Auteri, Ferguson, and Gallagher families for your sup-
port and encouragement, especially Jim, Irene, Jimmy, Ashley, Sean, and Brayden.
Thank you to my siblings: Christine, Anthony, and Richard. You have each
inspired me in one way or another to continue working towards completing this
goal. I am incredibly proud of all that you continue to achieve and I look forward
to celebrating your continued success.
Thank you to my grandparents: Alfio and Elaine Scammacca. Your support
of academic achievement from a very early age was inspirational, and it continues
to play an important role in the success of your children and grandchildren.
Thank you to my parents: Leonard and Pauline Campanello. This would
have not been possible without your dedication and encouragement, and I am very
grateful for you providing the four of us with the best life that you possibly could.
Finally, thank you so much to my wife, Alexis. Your love, encouragement,
and support were essential all of these years. I cannot imagine being able to finish
graduate school without you. Also, I would be remiss if I didn?t mention our dog,
Cora. You keep us on our toes, literally. We appreciate that you don?t let us sit still
for more than 1?2 hours at a time. Your companionship could not be repaid even
with a lifetime of dog treats, but we will try anyway.
iv
Table of Contents
Dedication ii
Acknowledgements iii
Table of Contents v
List of Abbreviations ix
Chapter 1:Introduction 1
Chapter 2:Background 8
2.1 Excitable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Mathematics of Excitable Systems . . . . . . . . . . . . . . . 8
2.1.2 Models and Simulations of Excitable Systems . . . . . . . . . 11
2.2 Signal Transduction During Immune Response . . . . . . . . . . . . . 14
2.2.1 Basic Operations of the Immune System . . . . . . . . . . . . 14
2.2.2 Signal Transduction in Effector T Cells . . . . . . . . . . . . . 16
2.2.3 Bcl10 Self-Assembly During Signal Transduction . . . . . . . . 18
2.3 Cytoskeletal Excitability and Signal Transduction . . . . . . . . . . . 20
2.3.1 Actin and Cell Functions . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Models and Simulations of Actin Excitability . . . . . . . . . . 22
2.3.3 Actin Sensing of the Physical Environment . . . . . . . . . . . 24
2.4 Quantitative Measurements of Biological Images . . . . . . . . . . . . 25
2.4.1 Connecting Bioimage Data and Cell Behavior . . . . . . . . . 25
2.4.2 Image-Based Measurements of Biological Flows . . . . . . . . 26
Chapter 3:T-cell activation mediated by Bcl10 31
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Measuring Bcl10 Filament Lengths . . . . . . . . . . . . . . . 36
3.3.2 Examining Autophagosome-Bcl10-Filament Interactions . . . . 39
3.3.3 Modeling Bcl10 Filament Dynamics . . . . . . . . . . . . . . . 47
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 T-Cell Stimulation and Imaging . . . . . . . . . . . . . . . . . 61
v
3.5.2 Segmentation of Bcl10 and LC3 . . . . . . . . . . . . . . . . . 62
3.5.3 Skeletonization and Skeleton Measurements of Bcl10 . . . . . 63
3.5.4 Random Rearrangement and Resampling of Segmented Struc-
tures for Statistical Assessment . . . . . . . . . . . . . . . . . 64
3.5.5 Simulations of Bcl10 Filament Growth and Degradation . . . . 65
Chapter 4:Quantifying Topography-Guided Actin Dynamics Across
Scales Using Optical Flow 68
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.5.1 Cell culture and imaging . . . . . . . . . . . . . . . . . . . . . 93
4.5.2 Surface fabrication . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5.3 Kymographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.5.4 Optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.5.5 von Mises model of flow distribution . . . . . . . . . . . . . . 98
4.5.6 Cluster-tracking analysis . . . . . . . . . . . . . . . . . . . . . 99
4.5.7 Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . 100
Chapter 5:Systematic Analysis and Simulations of Actin Waves 101
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.1 Actin-Wave Guidance Measured by Optical Flow . . . . . . . 105
5.3.2 Modeling of Optical Flow from Different Ridge Spacings . . . 108
5.3.3 Patterning NPF Activity to Simulate Ridges . . . . . . . . . . 110
5.3.4 Ridge Spacing and Actin-Wave Speeds . . . . . . . . . . . . . 114
5.3.5 Effects of Latrunculin on Experiments and Simulations . . . . 117
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.5 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.5.1 Cell Culture and Imaging . . . . . . . . . . . . . . . . . . . . 123
5.5.2 Ridge Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5.3 Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5.4 Actin Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 125
Chapter 6:Actin Dynamics During Cancer Metastasis 126
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3.1 Mammary tumor implantation as a model system . . . . . . . 128
6.3.2 Intravital microscopy of invasion and individualization . . . . 129
6.3.3 Investigating dynamics during individualization . . . . . . . . 132
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
vi
6.5 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.5.1 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 140
6.5.2 Analysis of actin and cell-shape dynamics . . . . . . . . . . . 140
6.5.3 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Chapter 7:Summary and Future Directions 143
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2.1 Extracting Biological Information from Waves and Oscillations 147
7.2.2 Connecting Biological Excitability to Models and Simulations 153
7.2.3 Insights from the Spatial Organization of Biological Structures 156
7.2.4 Enhancement, Segmentation, and Skeletonization . . . . . . . 157
Bibliography 161
vii
List of Figures
2.1 FitzHugh-Naguno Model of Excitability . . . . . . . . . . . . . . . . . 10
2.2 Phase transitions in Forest-Fire Models . . . . . . . . . . . . . . . . . 12
2.3 Response time of adaptive and innate immunity . . . . . . . . . . . . 15
2.4 TCR-to-NF-?B signaling pathway . . . . . . . . . . . . . . . . . . . . 17
2.5 Formation of filamentous Bcl10 . . . . . . . . . . . . . . . . . . . . . 19
2.6 Biochemical Model of Cytoskeleton Excitability . . . . . . . . . . . . 23
2.7 The Aperture Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 Shortening of Bcl10 filaments after T cell activation . . . . . . . . . . 38
3.2 Bcl10 filaments are preferentially in contact with autophagosomes . . 42
3.3 Autophagosome shape and size statistics . . . . . . . . . . . . . . . . 43
3.4 Autophagosomes attach to Bcl10-filament ends and puncta . . . . . . 45
3.5 Theoretical predictions of nucleation-limited growth . . . . . . . . . . 48
3.6 Simulations of Bcl10 growth . . . . . . . . . . . . . . . . . . . . . . . 51
3.7 Simulations of Bcl10 growth and degradation . . . . . . . . . . . . . . 55
4.1 Nanotopography prompts distinct actin morphology . . . . . . . . . . 73
4.2 Nanotopography leads to distinct actin morphodynamics . . . . . . . 76
4.3 Optical flow captures the dynamics in movies of actin fluorescence . . 78
4.4 Optical-flow measurements of pixel-scale dynamics . . . . . . . . . . . 82
4.5 Optical-flow-clustering workflow . . . . . . . . . . . . . . . . . . . . . 83
4.6 Optical-flow clustering and tracking of micron-scale dynamics . . . . 86
4.7 Validation of optical-flow clustering with kymographs . . . . . . . . . 88
5.1 Increased ridge spacings induced chaotic dynamics . . . . . . . . . . . 106
5.2 Actin waves were strongly guided by narrow spacings . . . . . . . . . 109
5.3 NPF Patterning Guided Actin in Simulations . . . . . . . . . . . . . 112
5.4 Effects of Latrunculin A on Experiments and Simulations . . . . . . . 116
5.5 Effects of Latrunculin on Experiments and Simulations . . . . . . . . 119
6.1 Microimplantation of tumor spheroids . . . . . . . . . . . . . . . . . . 130
6.2 Collective invasion patterns of tumor strands . . . . . . . . . . . . . . 131
6.3 Actin dynamics during collective and single-cell invasion . . . . . . . 134
6.4 Cell-shape dynamics during collective and single-cell invasion . . . . . 137
7.1 LoG Cylinders on Filamentous Shapes . . . . . . . . . . . . . . . . . 159
viii
List of Abbreviations
Dicty Dictyoselium Discoideum
cAMP Cyclic adenosine monophosphate
TCR T-cell receptor
NF-?B Nuclear factor kappa-light-chain-enhancer of activated B cells
Bcl10 B-cell lymphoma/leukemia 10
Carma1 Caspase-recruitment-domain-containing membrane-associated guanylate
kinase protein-1
Malt1 Mucosa-associated lymphoid tissue lymphoma translocation protein 1
CBM Carma1/Malt1/Bcl10
NPFs Nucleation-promoting factors
ECM Extracellular matrix
FHN FitzHugh-Naguno model
iSIM Instant-Structured-Illumination Microscope
IVM Intravital microscopy
LoG Laplacian of Gaussian
MAP Multiphoton Absorption Polymerization
PIV Particle Image Velocimetry
STICS Spatiotemporal Image Correlation Spectroscopy
ix
Chapter 1: Introduction
Cells actively detect and respond to physical, chemical, and biological cues in
the extracellular environment. Amoeboid Dictyostelium discoideum (Dicty) sense
chemical gradients to migrate towards nutrients [1], and immune cells respond to
biochemical agonists and collagen structures in the extracellular matrix to respond
to potential sites of pathogen invasion [2].
The transmission of extracellular information is carried out by complex in-
tracellular signaling networks. In Dicty, membrane sensors detect increased cross-
cell concentrations of the chemoattractant cAMP (cyclic adenosine monophosphate)
and the internal signal-transduction machinery reorients the cytoskeleton towards
the direction of highest cAMP concentration [3]. Similarly, bioelectric sensors in
epithelial cells sense wound-induced electric fields that override other guidance cues
to close the wound [4]. Although mechanisms by which cells detect, transmit in-
formation, and respond to extracellular stimuli are often studied at a biochemical
level, biophysical information regarding intracellular signaling networks, such as the
geometry, organization, and spatiotemporal dynamics of network components, can
also provide testable, and often simpler, explanations of cell behavior.
Many intracellular signaling networks exhibit properties of an excitable sys-
1
tem. Excitability is the phenomenon in which the behavior of a system can rapidly
transition between different dynamic states, such as steady-state equilibrium, oscil-
lations, and propagating waves. Excitable behavior is often observed in biological
systems across spatiotemporal scales, from multicellular, microsecond-long neuron-
firing patterns [5], to micron-scale, minute-long polymerization and depolymeriza-
tion of cytoskeletal proteins [6].
The excitable nature of biochemical signaling pathways can lead to complex,
nonlinear relationships between input signals and cell function. On the whole-cell
scale, T-cell-receptor activation in immune cells results in digital responses (i.e.,
the cell responds in an all-or-nothing manner) [7], and competing excitatory and
inhibitory signals in Dicty result in whole-cell polarization [3]. Within these cells,
the nonlinear dynamics of biochemical signaling networks play a role in response
dynamics: amplification of T cell receptor (TCR) signals in immune cells occurs
via interactions between signaling proteins [8], which may be responsible for digital
responses, and the polymerization-depolymerization dynamics of the cytoskeleton
can be modulated by slight changes in biochemical concentrations [9].
Coupled with the excitable behavior of signaling networks, the ability of cells to
quickly and efficiently respond to stimuli indicates that signaling networks are at or
near critical points between two or more dynamic states. Indeed, criticality-induced
behavior may be responsible for cytoskeletal organization [10] and dynamics [11],
and can also induce structural changes to intracellular protein complexes via phase
separation [12]. This tendency towards criticality could allow for the maximum
amount of information to be encoded in the network [13].
2
The self-organized critical states of intracellular signaling networks also make
cells sensitive to subtle changes in the extracellular environment. Dicty can detect
and respond to changes in cAMP concentration as small as 10?3 nM/?m [14], and
cytoskeletal dynamics can be tuned via the texture of the extracellular environ-
ment [15, 16] or small changes to chemical concentrations of signaling proteins [9].
Cell sensitivity to extracellular conditions also extends beyond nearby physical and
chemical perturbations. For example, numerous ion pumps and gap junctions build
up a potential difference across the cell membrane, and make the cell sensitive to
the external electrical environment [17]. This capability plays a role in physiologi-
cal functions such as adaptive immunity [18]. Changes to the dynamic behavior of
cells before and after small extracellular perturbations have many similarities with
systems undergoing a phase transition, such as the adjustment of parameters in a
forest-fire model near a critical point [19].
The sensory mechanisms within excitable intracellular signaling networks can
be harnessed in a variety clinical applications. Potential differences across the cell
membrane can help accelerate wound healing [4] and can be engineered to control di-
abetes upon stimulation from bioelectronic devices [20]; chemical activation or inhi-
bition of immune-cell signals can help inform the development of cancer immunother-
apies [21]; and extracellular textures can steer the function of stem cells [22,23] and
help to reveal metastatic potential in cancers [24].
Biochemical models of signaling networks provide frameworks to understand
cell behavior. Gene-inactivation studies have elucidated the necessity of different
signaling proteins for the activation of immune cells [25], and drug-induced changes
3
to biochemical feedback loops modulate the cytoskeleton during migration [9]. Fur-
ther, more physical inputs can be integrated into biochemical models to explain
changes in signal transduction. For example, substrate stiffness leads to changes in
immune-cell activation [26, 27], substrate-fiber density can modulate stem-cell dif-
ferentiation [23] and morphology [28], and extracellular nanostructures can guide
cell migration [29] and facilitate more efficient cytoskeletal polymerization [16].
Understanding the mechanisms that govern the integrated physical and bio-
chemical characteristics of intracellular signaling networks is now a multidisciplinary
problem at the intersection of biology, computer science, physics, and applied math-
ematics. In this dissertation, I focus on the spatial organization, excitable self
assembly and disassembly mechanisms, and multiscale spatiotemporal dynamics of
excitable signaling networks. Integrating physical characteristics with biochemical
models of signaling networks requires detailed quantification of physical information;
thus, I introduce a variety of quantitative measures and techniques to shed light on
spatial and dynamic characteristics of physical information.
One important system that operates in a highly critical state with a signaling
network that integrates both biochemical and physical information is the effector
T cell. Within the immune system, effector T cells actively respond to pathogenic
stimuli to activate other immune cells, attack virus-infected cells, and suppress ongo-
ing activation and autoreactivity (the cause of autoimmune diseases). The activity
of individual effector T cells is regulated by a complex biochemical signaling network
that is initiated at the membrane-bound TCR and results in the nuclear transloca-
tion of the transcription factor NF-?B. Termination of NF-?B activation is a crucial
4
mechanism to maintain healthy homeostasis; improper NF-?B regulation has been
associated with primary immunodeficiency disorders [30?32], cancer [33], and au-
toimmune diseases [34, 35]. Thus, the TCR-to-NF-?B signaling pathway contains
many regulatory mechanisms [36, 37]. In Chapter 3, I assess the spatial organiza-
tion, assembly, and degradation of a key protein in the TCR-to-NF-?B signaling
network and discuss how spatial colocalization between signaling components and
an excitable-systems framework can help elucidate the mechanisms that ensure rapid
immune responses yet prevent ongoing immune-system activation.
Spatial organization, assembly-disassembly characteristics, and excitability are
also important aspects of the mechanical machinery within the cytoskeleton. Cells,
including immune cells, encounter a range of physical conditions in the extracellular
environment while carrying out normal functions. These conditions have been shown
to influence cell signaling and function. However, cell responses to extracellular en-
vironments in vivo are difficult study systematically due to issues of consistency
and reproducibility. In contrast, in vitro studies designed to elucidate the influence
of the extracellular environment on cell signaling can be more carefully controlled
and replicated. For example, nanoscale ridges and sawteeth can modulate cell mi-
gration [24,29,38], morphology [28], and signaling [39], and the stiffness of the sub-
strate can influence TCR activation [40] and T-cell signaling [27]. In Chapter 4, I
introduce a novel quantification method to systematically analyze the spatiotempo-
ral dynamics and assembly-disassembly mechanisms of the cell cytoskeleton across
length scales and timescales. Although this method was initially developed to study
assembly and disassembly mechanisms, the model is generalizable for the quantifi-
5
cation of the spatiotemporal dynamics of cytoskeleton-associated signaling proteins
that are both upstream to and downstream from actin in the signaling network.
Despite the ubiquity of extracellular textures in vivo and experimental ev-
idence that textures modulate cytoskeletal dynamics, the mechanisms by which
texture can bias both small-scale signaling networks and cell-scale behaviors is not
well understood. One way to probe changes in cytoskeletal signaling on extracellu-
lar topography is through computational simulations. In Chapter 5, I employ the
quantitative tools from Chapter 4 for the systematic comparison of experimentally
derived actin dynamics in Dicty with those in a dendritic-growth model of filament
assembly and disassembly with realistic biochemical rates, nucleation-promoting
factors (NPFs), and filament-network-severing dynamics [41]. To probe real actin
dynamics, Dicty is imaged on differently spaced nanoridges centered around the
characteristic length scale of actin protrusions (?2 ?m) [29]. Recent evidence has
shown that the activity of cytoskeletal signaling components can be enhanced on
high-curvature substrates [15, 16]; thus, nanotopographic ridges in the simulations
are mimicked via the enhancement of nucleation-promoting factors in striped pat-
terns. I show that systematic experiments and simulations of topography-induced
guidance provides a robust framework for the probing the mechanisms which lead
to texture sensing.
The tools that I developed to characterize and quantify structures and dynam-
ics of intracellular signaling networks can also be applied to the analysis of dynamic
systems in vivo. In Chapter 6, I measure and characterize actin activity during
the epithelial-to-mesenchymal transition in vivo, a key step in cancer metastasis. I
6
demonstrate that cells that detach from cancerous tumors, which are thus suspended
in collagen-rich matrices, exhibit highly variable and protrusive dynamics compared
to cells which remain attached to the tumor.
The tools that I developed for measuring and characterizing spatial organiza-
tion, waves and oscillations, and excitable-systems dynamics are broadly applicable
to other systems. For example, the methods I introduce in Chapters 4 and 5 to study
assembly and disassembly mechanisms can be generalized to quantify the spatiotem-
poral dynamics of cytoskeleton-associated signaling proteins that are both upstream
and downstream from actin in the cytoskeletal signaling network. In Chapter 7, I
discuss the different quantification techniques presented in this dissertation and pro-
vide an outlook regarding how these methods could be applied in future studies of
excitable signaling networks.
7
Chapter 2: Background
2.1 Excitable Systems
2.1.1 Mathematics of Excitable Systems
Excitability is observed in a wide variety of biological systems across spa-
tiotemporal scales, from intracellular and minutes-long cascades in biochemical sig-
naling networks to multicellular and microseconds-long firing in neurons. Excitabil-
ity is characterized by the rapid switching of system evolution between different
dynamic states such as a ?rest?state, an ?excited?state (e.g., periodic excitations or
traveling waves), and a refractory period during which excitations cannot occur [42].
The FitzHugh-Nagumo (FHN) model is an instructional example of how ex-
citable behavior can be induced in media that must undergo a quiescent recovery
period between excitations [43]. For a given excitation readout v(t) (e.g., membrane
voltage in neurons, filament length of signaling complexes, speed or position of cy-
toskeletal waves), and recovery or refractory variable w(t), an FHN system evolves
8
according to the coupled differential equations
1
v?(t) = v(t)? v3(t)? w(t) + Vext
3 (2.1)
cw?(t) = v(t) + a? bw(t).
The constants a, b, and c are chosen empirically and Vext is an external perturbation
on v(t).
An FHN system can dynamically evolve in a variety of ways, including steady-
state equilibrium, a single-spike dynamic, and an oscillatory dynamic state (all seen
in Figure 2.1). The excitability characteristic of the system is contained within
the balance among parameters. If the external activation of the system is not
sufficiently large then the system will not reach an excited state (Figure 2.1A), a
concept known as ?digital activation?. Conversely, if the system undergoes slight
changes due to external perturbations, dynamic evolution of the system can rapidly
change character, such as the transition from a single-spike dynamic to an oscillatory
state (Figure 2.1B).
Excitability is indicative of a system being near a phase transition, referred
to as the system being at or near a critical point. Noncritical systems can still
display complex dynamics, but a perturbation on a noncritical system may cause
a response to differ in strength but not in character. Meanwhile, a critical system
that is perturbed in slightly different ways can evolve in drastically different man-
ners. As a result, excitable systems allow for highly nonlinear relationships to arise
between system inputs (e.g., signals, perturbations, textures) and outputs (e.g., cell
9
Figure 2.1: Excitability in the FitzHugh-Naguno model. (A) An FHN model with
parameters a = 0.1, b = 1.5, and c = 1.6. External perturbations were set at Vext =
0, 0.15, and 0.20. Vext = 0 and 0.15 were insufficient to switch the system into an
excited state whereas Vext = 0.2 was, a concept known as digital activation. (B) Two
FHN models with slightly different parameters. Dark red: a = 0.2, b = 1.05, c = 10,
and Vext = 0.5, which has a single-spike dynamic evolution. Light red: a = 0.24,
b = 1.03, c = 10, and Vext = 0.5, which has an oscillatory-state dynamic evolution.
The images were created by Leonard Campanello for use in this dissertation.
10
function).
2.1.2 Models and Simulations of Excitable Systems
Models and simulations of dynamic systems can capture excitable and critical
behavior. A cellular automaton that is instructional in studies of criticality is the
Abelian sandpile model [44]. Although Abelian sandpiles display complex dynamics
such as fractal-pattern generation, these models are not amenable to recreating
biologically-relevant time-series phenomena.
Another class of models that exhibit self-organized criticality and phase tran-
sitions are forest-fire models. First introduced as one- or two-parameter models
that exhibit self-organized criticality [45], forest-fire models contain a grid of loca-
tions (i.e., pixels) that represent ?trees?or small coarse-grained regions of a forest:
0 is empty and 1 represents the presence of a tree. If a tree is on fire, the tree will
?burn?(the value will be switched from 1 to 0) and the fire will also spread to nearby
trees. Thus, the typical rules of a forest fire model are: (1) all cells containing burn-
ing trees are set to 0; (2) fire from a burned tree spreads to all neighboring trees;
(3) infrequently and randomly there is a ?lightning strike?in a random cell and, if
occupied by a tree, that tree is set on fire; and (4) empty cells have a probability of
growing into a tree.
Standard forest-fire models are capable of displaying different dynamic charac-
teristics based on small changes to control parameters (Figure 2.2A). Furthermore,
modified forest-fire models have also been adapted to undergo phase transitions near
11
Figure 2.2: Dynamic phases of forest-fire models exhibit similar behaviors to bio-
physical models of cytoskeletal dynamics. (A) Different phases in a standard forest-
fire model: global traveling waves (left); and local isolated patches of activity (right).
(B) Phases in a conserved forest-fire model (constant density of trees): increasing
(1)
the density beyond the first critical point, ?critical = 0.547, causes the transition
from small-scale patches to spiral waves (left to middle); and increasing the den-
(2)
sity beyond the second critical point, ?critical = 0.592, causes the transition from
spiral waves to large-scale patches (middle to right). (C) Schematic of a traveling
wave through an excitable medium (blue) that must undergo a refractory period be-
fore subsequent excitations. (D) The signal-transduction excitable network (STEN)
model of cytoskeletal waves. The excitable cytoskeletal medium has occasional burst
of actin activity (blue puncta) but also facilitates large-scale spiral waves. The im-
ages in A were adapted with permission from forest-fire models by Ms. Melissa
Kissling, images in B were adapted from [19] with permission by the American
Physical Society, and C and D were adapted from [3] with permission by Annual
Reviews.
12
critical values of control parameters [19] (Figure 2.2B). For the two snapshots in Fig-
ure 2.2A, the left side has a higher probability of tree growth but lower lightning
probability than the right side, causing different behavior phenotypes. The modified
forest fire in Figure 2.2B is constrained by two conditions: (1) lightning will strike
in one random location only if there is no other fire in the simulation; and (2) there
is a fixed number of trees in the field of view (i.e., when a tree is burned then a new
tree will populate elsewhere to replace it).
The models presented in Figure 2.2A?B are simple, but capture essential qual-
ities of signal transduction through excitable media, e.g. wave-like propagation.
During biological signal transduction, cascades of biochemical and biophysical in-
teractions are triggered in sequence. In forest-fire models, these sequential signal-
transduction events are recapitulated via local communication between neighboring
pixels. To put Figure 2.2A?B in context, current biophysical models of cytoskeletal
dynamics incorporate traveling waves and refractory periods (Figure 2.2C). More-
over, the transition from patches of local activity (i.e., puncta) to traveling waves
in Figure 2.2B upon small perturbations to the system almost exactly mirrors the
excitable puncta-to-traveling-waves transition observed in the cytoskeleton (Fig-
ure 2.2D).
The connection between experimentally observed cytoskeletal dynamics and
physical models of excitability is introduced in Subsection 2.3.2.
13
2.2 Signal Transduction During Immune Response
2.2.1 Basic Operations of the Immune System
The immune system defends the body against pathogens via two complimen-
tary mechanisms: rapid innate immunity and pathogen-specific adaptive immunity.
Cells involved in innate immunity detect chemical signatures of homeostatic im-
balances caused by pathogen infection and rapidly respond within several hours.
Innate-immune responses have no memory of prior infections, so the anti-pathogen
capabilites of this response are one-size-fits all and are limited in strength and scope.
Thus, one additional and crucial function of the innate immune system is to activate
the adaptive immune system [46].
Adaptive immunity is the potent and highly specific response to pathogens.
Upon recognition of pathogenic material (e.g., antigens), the adaptive immune sys-
tem initiates a multicellular signaling cascade leading to the clonal expansion of
adaptive immune cells. Whereas the innate immune system responds within several
hours, the adaptive immune systems requires several days to mobilize (Figure 2.3).
Although adaptive immune response is slower than innate immune response, its
anti-pathogen capabilities are extremely potent. Due to its potency, adaptive im-
munity must be carefully regulated [46], but can also be engineered and controlled
for clinical applications.
Activation and regulation of adaptive immunity are of interest to prevent or
treat diseases. Activating the adaptive immune system to recognize and fight can-
14
Figure 2.3: Innate immune cells respond to pathogens within several hours of the
initial infection (left). Adaptive immune cells respond to pathogens within several
days of infection (right). This figure was adapted from Science Online under a
Creative Commons Attribution 4.0 International License.
15
cer has long been a goal for immunologists and oncologists, and work over the past
decade has demonstrated the promise of stimulating an immune response to fight
cancer via immunotherapies [47, 48]. On the other hand, overactive and uncontrol-
lable adaptive immune responses have been implicated in the development of some
cancers [49], autoimmune diseases [50], and allergies [51?53]. Although the body
has multiple programmed shutdown mechanisms to combat the deleterious conse-
quences of an overactive adaptive immune response, these mechanisms can also be
harnessed to treat disease [54].
2.2.2 Signal Transduction in Effector T Cells
One important component of the adaptive immune system is effector T cells,
which are terminally differentiated T cells that can generate rapid anti-pathogen
responses. Effector T cells engage in a wide variety of behaviors, including immune
regulation to prevent auto-reactivity (i.e., preventing autoimmune disorders), help-
ing in the maturation and activation of other leukocytes (i.e., accelerating immune
response), and destroying pathogen-infected cells. Effector T cells are activated via
an internal signal-transduction pathway that begins at the T-cell receptor (TCR)
and results in the nuclear translocation of several transcription factors, including
NF-?B (nuclear factor kappa-light-chain-enhancer of activated B cells), ultimately
leading to cell activation and function [55].
Tightly controlled regulation of NF-?B activation is relevant to human health.
Improper regulation of TCR-to-NF-?B signaling is associated with primary immun-
16
Figure 2.4: Positive and negative regulation of the TCR-to-NF-?B signaling path-
way. Reproduced from [37] with permission from Elsevier.
odeficiency disorders [30?32], cancer [33], and autoimmune diseases [34, 35]. Thus,
the TCR-to-NF-?B signaling pathway is subject to numerous positive and negative
feedback mechanisms [37] (Figure 2.4).
One important protein that participates in both positive and negative regu-
lation of NF-?B is Bcl10 (B-cell lymphoma/leukemia 10) [56]. Gene inactivation
studies have shown that T cells without Bcl10 are highly impaired in their response
to TCR stimulation [25]. Interestingly, although Bcl10 is critical for the transmis-
sion of activation signals through the TCR, it also participates in the self regulation
17
of T cell activation via several self-limiting mechanisms. Stimulation of the TCR
(i.e., the initiating step for cell activation) has also been shown to induce Bcl10
degradation [36, 57?60], and this degradation plays a role in downstream signaling
processes [61]. This dual purpose in both the activation and regulation of NF-?B
make Bcl10 of interest for its role in controlling system-wide immune response.
2.2.3 Bcl10 Self-Assembly During Signal Transduction
One component of Bcl10-mediated NF-?B activation is Bcl10 self-assembly in
microns-long filaments during signal transduction. Upon TCR engagement, Bcl10
polymerizes into filament structures [62] that are nucleated by Carma1 (caspase re-
cruitment domain-containing membrane-associate guanylate kinase protein-1) and
scaffolded by Malt1 (Mucosa-associated lymphoid tissue lymphoma translocation
protein 1) [8, 63, 64] (Figure 2.5). Bcl10, together with Carma1 and Malt1 (re-
ferred to as the CBM complex), form the core of a micron-scale assembly called
the POLKADOTS signalosome, which is the site of the final steps of the NF-?B
signaling cascade [7, 8, 36, 37]. The structure of Bcl10 is important for its role in
the activation of the T-cell signaling network. For example, the polymerization
of Bcl10 accelerates the growth of the CBM complex [64], and the scaffold struc-
ture of Bcl10 and Malt1 allow for downstream signal transduction such as Traf6
recruitment [8, 65].
Although Bcl10 is essential for signal activation, the structural and kinetic fea-
tures that limit and ultimately reverse Bcl10-filament polymerization are unclear.
18
Figure 2.5: Formation of filamentous Bcl10. (A) The biochemical mechanism for
Bcl10-Malt1 filament formation: active Carma1 nucleates the Bcl10-Malt1 filaments.
(B) Bcl10 core of filaments. (C) Bcl10 core with Malt1 on the surface. A and C
were derived from [8] under a CC BY-NC-ND license and B was derived from [62]
with permission from Elsevier.
19
Bcl10 is selectively degraded within the multi-protein complex [36] despite its assem-
bly into filaments decorated with other CBM and POLKADOTS components [8].
One possible mechanism for the degradation of Bcl10 is autophagy via autophago-
somes [36]. The traditional models of autophagosome-led autophagy involve com-
plete envelopment of intracellular cargo. Notably, such a mechanism could not be
reasonably applied to Bcl10 degradation due to geometric limitations (i.e., Bcl10
are much larger and thus cannot be enveloped by a much smaller autophagosome).
Despite the limitations, autophagosome-led degradation of Bcl10 is still considered
valid [36,37,56]. Thus, the biophysical and biochemical mechanisms that participate
in the self-limiting properties of Bcl10 cannot only be assessed using biochemical ap-
proaches and must also include geometry, self-assembly, and organization of protein
complexes.
In Chapter 3, simulations and analysis of super-resolution micrographs are
used to gain mechanistic insights into this self-limiting process. Further, we discuss
how components of the T-cell-activation pathway, including Carma1 nucleation of
Bcl10 filaments and Bcl10 degradation, indicate that the TCR-to-NF-?B pathway
forms an excitable system.
2.3 Cytoskeletal Excitability and Signal Transduction
2.3.1 Actin and Cell Functions
The cytoskeleton is a dynamic network of proteins responsible for the struc-
tural and mechanical properties of the cell. Through the formation of an interlocking
20
and interconnected filament network, the cytoskeleton exerts forces to participate in
cell and physiological functions such as polarization and migration [3], immune-cell
activation [39,66], and wound healing [67].
One important and abundant component of the cytoskeleton is actin. Through
continuous polymerization and depolymerization, actin, together with actin-binding
proteins such as the Arp2/3 complex and cofilin, facilitates the formation of mem-
brane protrusions and the generation of intracellular forces. The dynamic behavior
of actin has been linked to many cytoskeleton-driven phenomena such as the for-
mation of focal adhesions [68], immune-cell activation [27], and protrusions and cell
polarization [3]. Thus, understanding the dynamic rearrangements and organization
of actin is essential to developing a complete picture of many cellular processes.
The continuous polymerization and depolymerization of actin can manifest
wave-like propagations. Through polymerization on the leading edge and depoly-
merization of from trailing edge, propagating actin waves enable cell functions
such as chemotaxis in Dicty [69] and polarization of dendritic cells in search of
pathogens [70]. Current perspectives on the mechanisms that enable actin waves
are shown in Figure 2.2C. An activation wave of actin (blue) inhibits an inhibition
wave (red). If, for some reason, the blue actin wave were to encounter an obstacle or
run out of polymerization material (i.e., monomers), then the inhibition wave would
?catch up?and cause all polymerization activity to cease.
Actin waves are excitable. As introduced in Section 2.1, excitability enables
the dynamic behavior of a system to rapidly change character either spontaneously
or due to external perturbation. The STEN (signal transduction excitable network)
21
model of actin-network dynamics in Figure 2.2D predicts a critical point above
which puncta of actin activity can manifest of wave-like propagations. Recently,
it was demonstrated that the excitability of actin and actin-associated signaling
proteins can enable switching between migratory modes in Dicty from chemical
stimulation [9].
2.3.2 Models and Simulations of Actin Excitability
Models and simulations of actin excitability can be used to gain qualitative
and quantitative insights into the coupling of actin and cell behavior. For example,
the switching between migratory modes in Dicty shown in [9] can be explained
using an excitable-signal-transduction network model (shortened to ?STEN?in the
figure) [3, 71] (Figure 2.6).
Signal-transduction events (red) promote actin polymerization (green), lead-
ing to propagation of actin-polymerization waves (blue) (Figure 2.6A). Importantly,
the polymerization of actin is a postive feedback mechanism for further signal-
transduction events, which in turn leads to further actin polymeriation. In typical
(i.e., wild-type) cells, these waves could propagate over time in any direction. Con-
versely, if impeded or subjected to depletion of available actin, waves in one or both
directions could terminate (Figure 2.6B). Furthermore, chemical perturbations can
modify the character of actin-wave propagation and the shape of membrane protru-
sions (Figure 2.6C).
Other computational models and simulations also capture actin-wave dynam-
22
Figure 2.6: Biochemical Model of Cytoskeleton Excitability. (A) A propagating
wave of actin and actin-associated signaling proteins. Actin polymerization (green)
leads to increased signaling (red), which in turn promotes further actin polymer-
ization. (B) Baseline over-time schematic of typical actin-polymerization waves. If,
for some reason, signaling or actin polymerization is inhibited (e.g., depletion of
monomers, physical boundary), then signaling and polymerization will terminate.
(C) Chemical perturbations modify the character of actin-polymerization waves and
propagation of signals. Representative repercussions include broad, actin-rich pro-
trusions, narrow and sharp protrusions, or a semistable actin cortex without any
dynamics. This figure was derived from [71] under an Open Access License by
Molecular Systems Biology.
23
ics. One-dimensional models of actin and signaling proteins have been used to
connect actin flow to polarity, persistence, and migration [72], two- and three-
dimensional simulations of coupled phase and auxiliary fields can recapitulate cell-
migration phenotypes without explicit cytoskeletal components [73], and fine- and
coarse-grained simulations of the cytoskeleton have shown that actin force genera-
tion can cause large-scale reorganization via force amplification [11] and bundling
dynamics [74].
2.3.3 Actin Sensing of the Physical Environment
The actin cytoskeleton can detect and respond to physical properties of the
extracellular environment. Textures much smaller than the size of the cell can influ-
ence actin-mediated behaviors. Symmetric and uniformly spaced nanotopographic
ridges bidirectionally bias actin-driven migration [29] and modulate actin-driven
B-cell activation [39]. Asymmetric surface textures (e.g., sawteeth patterns) can
induce unidirectional bias of cell migration in pitch-dependent [38] and cell-type-
specific manners [24]. Furthermore, the stiffness of cell substrates can modulate
T-cell activation via actin-generated forces [27].
Biochemical components involved in waves of actin polymerization are im-
pacted by features in the extracellular environment. High-curvature textures in the
extracellular environment can facilitate Arp2/3 branching [15] and upregulate the
activity of N-WASP, Cortactin, and Arp2/3 [16].
Despite the connection between actin-polymerization dynamics and the ex-
24
citability of actin and actin-associated signaling proteins, we currently do not have
a detailed understand of the connection between actin-based texture sensing, cy-
toskeletal signaling, and whole-cell behavior. In Chapter 5, I link the frameworks
of cytoskeletal excitability with physical models of cytoskeletal dynamics to address
this open question.
2.4 Quantitative Measurements of Biological Images
2.4.1 Connecting Bioimage Data and Cell Behavior
Quantitative measurements of dynamic cellular processes are crucial for the
full understanding of cell behavior. Although genomics and proteomics have led
to connections between molecular signatures and cell function, these efforts have
not produced a complete biological mapping between transcription and behavior.
In fact, it has been argued that if all molecular measurements inside of a cell are
available, the complexity of the data may make their integration and interpretation
impossible [75].
One prominent tool for building a quantitative understanding of cellular pro-
cesses is through image analysis. Integrating quantitative computer vision tech-
niques with a variety of imaging modalities has exposed the mechanisms behind
actin-driven protrusions [76] and membrane fluctuations in amoeboid cells during
collective streaming [77]. Additionally, image-analysis techniques from physics have
been an important tool for extracting biological information from images. Particle
image velocimetry (PIV) originated in fluid dynamics, and is now implemented in
25
many bioimage-analysis workflows [78, 79]. Particle tracking that was designed to
study flows in colloids is now ubiquitous in studies ranging from the tracking of
f-actin speckles [76] to the swarming of fruit flies [80].
2.4.2 Image-Based Measurements of Biological Flows
The flow of biological material during cellular processes is ubiquitous, including
during development [81] and wound healing [67], and in cytoskeletal dynamics [82].
The measurement of biological flows from image data typically relies on informa-
tion contained within a single-pixel or few-pixel region. One widely-used pixel-scale
technique is PIV, which was originally designed by physicists to study fluid flows.
PIV uses correlations within a few-pixel region to create a spatial mapping between
two sequential images in a time-series. If the frame rate of the time-series is suffi-
ciently high, this mapping theoretically converges on the ground-truth-deformation
field that frames undergo in the time series.
PIV also enables a variety of downstream analysis capabilities in studies of
biological behavior. For example, PIV-driven analysis of chaos in flow fields can
distinguish between benign and malignant breast-cancer cells [79]. Although PIV
is a powerful technique, it?s effective use requires a series of conditions to be met,
including an abundance of features in the time-series (which is not typical in fluores-
cence imaging) and small changes between frames. Thus, PIV is typically limited to
phase-contrast and DIC images in which there is an abundance of features and rapid
imaging frame rates are available. Although extensions of PIV, e.g. spatiotempo-
26
ral image correlation spectroscopy (STICS), can provide better performance at a
higher computational cost [83], PIV is still correlation-based, and thus is limited to
the analysis of images with an abundance of features.
One technique that outperforms correlation-based reconstruction of flow fields
from fluorescent time-series of biological images is optical flow [84]. Originally devel-
oped for applications in robotics and stereo vision, optical flow is currently used in
a variety of modern technologies, such as self-driving cars [85] and facial-recognition
algorithms [86].
Optical flow uses spatial and temporal gradients in sequential images to create
a mapping between adjacent frames [87]. In a (2 + t)-dimensional time-series of
images, a moving object that is originally located at voxel with indices (x, y, t) will
translate to some new voxel with indices (x + ?x, y + ?y, t + ?t). If the intensity
of the object is the same at both coordinates in the time-series then
I(x, y, t) = I(x+ ?x, y + ?y, t+ ?t). (2.2)
The primary objective of optical flow is to solve for translation fields ?x and ?y
that provide the spatial mapping between each pair of adjacent frames in the time-
series. If I(x, y, t) represents a continuous field of (2D+t)-dimensional voxels, then
a Taylor-expansion of the RHS of Equation 2.2 yields
?I ?x ?I ?y ?I
+ + = 0 (2.3)
?x ?t ?y ?t ?t
27
and, if ~v =< ?x , ?y >, then
?t ?t
?~ I ? ??I~v = (2.4)
?t
where ~v is a vector-field of velocities.
Equation 2.4 is a manifestation of the aperture problem: a class of computer-
vision problems in which a small subsection of a field is visible. In Figure 2.7, there
are infinitely many ways to interpret the motion of the black and white pattern if
you are restricted to looking only through the inner circle. In the case of optical flow,
only having one set of gradients for a voxel provides similar limitations?there are
infinitely many solutions to Equation 2.4. Thus, solving the optical-flow equation
requires additional constraints.
There are many solution to Equation 2.4 that add additional constraints to
acquire an estimate for optical flow. Global methods maximize the smoothness of
the field [87], or minimize shear [88]. However, such approaches produce dense and
continuous flow fields that are not realistic in biological applications (i.e., flow in one
part of a field likely does not depend upon or affect flow at distant locations). An
alternative set of approaches to estimating optical flow is through local, gradient-
based methods. Local methods integrate information from small regions of interest.
One popular method and foundational local methos was developed by Lucas and
Kanade [89]. Specifically, for a local region of n pixels there are n linear equations
28
that must be solved to estimate optical flow:
?? ? ? ??? ( ?I ) v ?I1 x1 + ( ) v ?I? ?x ?y 1 y1 ??? ???
( )
?t 1?
? ???? ( ?I ) v + (?I ? ? ?I ?? ?x 2 x2
)
?y 2
vy2 ? ( )??? ? ?t 2???? .
.
. ???
= ????? ? . (2.5)? ?? .
.
. ????
( ?I )nv
?I
xn + ( ) v (
?I )
?x ?y n yn ?t n
For the purposes of solving for the central pixel in the local region, the Lucas-Kanade
method assumes that all ~vi are equal, thus
?? ? ? ???( ?I ) (?I )? ?x 1 ?y 1???? ? ? ?
?(?I )?t 1??
??( ?I )2 (?I ) ? v? ?x ?y 2? ??
?????? x?
? ?
?? ??(?I ) ??t 2?= ????? ???? . (2.6)?? .
.
. .
. .
. ?? vy ?? .. ??
( ?I ) (?I ) ?I
?x n ?y n
( )
?t n
The resulting system of equations is overdetermined (two variables for n equations),
and thus a typically good solution minimizes the sum of the inner product of the
residuals (i.e., least-squares minimization). Notably, despite having more equations
than degrees of freedom, the Lucas-Kanade formulation could still suffer from the
aperture problem if all spatial gradients are parallel. In such a case, the ATA matrix
will be singular (i.e., not invertible) and not yield a solution.
In Chapters 4 and 5, I use the Lucas-Kanade optical-flow formulation in an
image-analysis workflow to quantify and characterize actin-wave dynamics from flu-
orescent time series.
29
Figure 2.7: (A) A schematic representation of the aperture problem. If the field-
of-view is confined to the interior cut-out circle, it is impossible to distinguish the
different types of motion in the schematic. Adapted from [90].
30
Chapter 3: Signaling Through Polymerization and Degradation: Anal-
ysis and Simulations of T-Cell Activation Mediated by
Bcl10
This chapter was adapted from Campanello, Traver, Shroff, Schaefer,
and Losert [91]. Maria Traver performed the experiments, Leonard Cam-
panello performed the analysis, Leonard Campanello built the simula-
tions, and Leonard Campanello and Maria Traver wrote the paper.
3.1 Overview
The adaptive immune system serves as a potent and highly specific defense
mechanism against pathogen infection. One component of this system, the effector
T cell, facilitates pathogen clearance upon detection of specific antigens by the T-cell
receptor (TCR). A critical process in effector T cell=activation is transmission of
signals from the TCR to a key transcriptional regulator, NF-?B. The transmission
of this signal involves a highly dynamic process in which helical filaments of Bcl10, a
key protein constituent of the TCR signaling cascade, undergo competing processes
of polymeric assembly and macroautophagy-dependent degradation. Through com-
31
putational analysis of three-dimensional, super-resolution micrographs, we quanti-
tatively characterize TCR-stimulated Bcl10 filament assembly and length dynamics,
demonstrating that filaments become shorter over time. Additionally, we develop an
image-based, bootstrap-like resampling method to demonstrate quantitatively the
preferred association between autophagosomes and either Bcl10-filament ends or
punctate-Bcl10 structures, implying that autophagosome-driven macroautophagy is
directly responsible for Bcl10 filament shortening. We probe Bcl10 polymerization-
depolymerization dynamics with a stochastic Monte-Carlo simulation of nucleation-
limited filament assembly and degradation, and we show that high probabilities
of filament nucleation in response to TCR engagement could provide the observed
robust, homogeneous, and tunable response dynamic. Furthermore, the speed of au-
tophagic degradation of filaments preferentially at filament ends provides effective
regulatory control. Taken together, these data suggest that Bcl10 filament growth
and degradation act as an excitable system that provides a digital response mecha-
nism and the reliable timing critical for T-cell activation and regulatory processes.
3.2 Background
The vertebrate adaptive immune system consists of billions of T and B lym-
phocytes, which serve as a potent and highly specific host defense mechanism
against pathogen infection. Once an antigen, an immune-activating component of a
pathogen, has been recognized by the T-cell receptor (TCR), an intracellular signal-
ing cascade is initiated that leads to the clonal expansion of T cells responsive to this
32
antigen. This anti-pathogen immune response, including the T-cell component, will
cause damage to healthy tissue if not temporally limited [49]. Indeed, unregulated
adaptive immune responses have been implicated in the development of certain can-
cers [49] and autoimmune diseases [50]. Thus, adaptive immune responses include
programmed shutdown mechanisms to maintain homeostasis and prevent damage
to host tissues [50,54]. In this study, we introduce novel image-analysis tools for the
robust analysis of a component signaling pathway of the adaptive immune response
from a biophysical perspective, specifically focusing on the spatial organization of a
key signaling structure that contributes to adaptive immunity.
The many classes of effector T cells are the main cell types that control adap-
tive immunity. Effector T cells are terminally differentiated T lymphocytes with
previous antigen exposure, and can generate rapid anti-pathogen responses. Antigen
engagement of the TCR in effector T cells initiates an internal signal-transduction
pathway that leads to the translocation of NF-?B from the cytoplasm to the nucleus.
NF-?B is a heterodimeric protein complex in both vertebrates and invertebrates [92]
that controls gene transcription in response to a diverse array of receptors [93]. In
effector T cells, the nuclear translocation of NF-?B results in the de novo or in-
creased expression of a large number of genes involved in T-cell proliferation and
immune response mechanisms [92, 94]. Improper regulation of NF-?B signaling in
T cells is mechanistically associated with primary immunodeficiency [30?32] and
autoimmune disease [34, 35]. Thus, the regulation of the TCR-to-NF-?B pathway
is critically important for proper immune function.
A key signaling protein in the TCR-to-NF-?B pathway is Bcl10 [56]. Upon
33
TCR stimulation, Bcl10 assembles with its signaling partners Carma1 and Malt1
to form the micron-scale CBM complex [8, 37, 65, 95, 96]. In effector T cells, the
CBM complex forms the core of a filamentous assembly called the POLKADOTS
signalosome, which serves as the cytoplasmic site of the terminal steps of the NF-?B-
activation cascade [7,8,36,37,62,64]. At the same time that Bcl10 is being assembled
into microns-long filaments, it is also being degraded [37,57?61]. We have previously
shown that proteolysis of Bcl10 occurs within the POLKADOTS signalosome via
TCR-dependent selective autophagy [36]. In this degradative process, autophago-
somes associate with POLKADOTS filaments, resulting in selective destruction of
Bcl10 and thus terminating signals to NF-?B. Data suggest that the balance be-
tween assembly of filamentous Bcl10 in POLKADOTS and proteolytic degradation
of Bcl10 via selective autophagy determines the extent of NF-?B activation [36,37].
Notably, many outputs of TCR signaling exhibit nonlinear response profiles,
including all-or-nothing (i.e., digital) responses. Although not every T cell re-
sponse has digital characteristics [97], studies have demonstrated that specific TCR-
triggered events are digital, including activation of the extracellular regulated kinase-
mitogen activated protein kinase (ERK-MAPK) signaling cascade [98?100], signal-
ing via the Protein kinase D2-protein kinase C (PKD2-PKC) cascade [101], release
of cytokines [102], and activation of cytolytic capacity [103]. Additionally, we have
previously shown that TCR activation of NF-?B is digital in nature, with formation
of and signal transmission by the POLKADOTS signalosome occurring in an all-
or-nothing manner [104]. Mechanistically, how nucleation, growth and eventual au-
tophagic degradation of POLKADOTS filaments are connected to the digital nature
34
of the NF-?B cascade is unclear. In this manuscript, we link the nonlinear character
of the signaling cascade to the spatial organization, assembly, and degradation of
filamentous Bcl10. We propose that highly nonlinear self-assembly and degradation
processes comprise an excitable system, enabling a rapid yet self-limiting response.
Several key details of this polymerization process are known: recent cell-free
cryo-electron-microscopy studies revealed that Bcl10 polymerizes into filaments with
a geometrically confined, helical arrangement with other POLKADOTS components
[8, 62, 64]. Although the core of the POLKADOTS filament is composed primarily
of Bcl10, polymerization of Bcl10 is nucleated by short oligomers of Carma1, and
the Carma1-driven nucleation of Bcl10 can act as an amplifier of activation signals
from the T-cell receptor to NF-?B [8]. In contrast to the above parameters driving
filament growth and signal propagation, autophagic degradation of Bcl10 opposes
this amplification process. However, the geometric and kinetic features that limit,
and ultimately reverse, filament growth in living T cells are unclear. These opposing
effects on filament growth and degradation are not well understood, and cannot
be assessed via traditional biochemical approaches and signaling pathway models,
which exclude spatial organization.
In this study, we quantify the spatial arrangement of Bcl10, its colocalization
with autophagosomes, and the randomness of their relative spatial distributions.
Our analysis introduces a novel computational workflow that combines bootstrap-
like resampling methods adapted for image features and medial-axis-thinning skele-
tonization for the robust analysis of the structure and organization of Bcl10 filaments
in relation to autophagosomes. The methods we present are broadly applicable to
35
studies of biologically encoded spatial colocalizations and self-assembly, such as toll-
like receptor-stimulated assembly of the myddosome, RIG-I-like receptor triggering
of mitochondrial antiviral-signaling protein oligomerization, and activation of the
various sensor proteins that promote assembly of micron-scale inflammasomes [105].
To gain further mechanistic insights into the assembly and degradation dynamics
of POLKADOTS filaments, we complement the analysis of super-resolution images
with stochastic Monte Carlo simulations of POLKADOTS dynamics that include
the nucleation, growth, and degradation of Bcl10. In sum, we show that spatial
assembly and degradation of protein complexes in the TCR-to-NF-?B-activation
cascade are key design elements to ensure a rapid response while preventing ongo-
ing immune activation. These elements may also contribute to the digital nature of
this crucial signaling pathway.
3.3 Results
3.3.1 Measuring Bcl10 Filament Lengths
Utilizing a long-term murine-effector-T-cell clone, D10.G4.1 (henceforth re-
ferred to as D10), we engineered a cell line that stably expressed GFP-tagged Bcl10.
Using the D10 cell line, we imaged Bcl10 filaments in cells fixed at 20- and 40-min
post-TCR activation using a super-resolution instant structured illumination micro-
scope (iSIM) [106] (Figure 3.1A). The earliest evidence of formation of POLKA-
DOTS structures is at 10 min post-TCR activation. These polymers are maximally
evident by 20 min post-activation, at which point initial activation with autophago-
36
somes is also apparent. Association with autophagosomes and degradation of Bcl10
persists through 2 hr post-stimulation, by which time Bcl10-containing polymers
can no longer be found in any cells. Indeed, these polymers are rare even by 60 min
post-activation [37, 95]. Thus, 40 min post-activation is a reasonable time point at
which to assess intermediate consequences of autophagosome association with Bcl10
filaments.
To analyze these data, we developed a semiautomatic segmentation and skele-
tonization algorithm based on medial-axis thinning, and used the resultant skeletons
to obtain various structural measurements (Methods). Bcl10-rich regions with skele-
ton lengths less than 150 nm (the approximate spatial resolution of the iSIM) were
designated as punctate structures, labeled by ?P?in these data. The punctate struc-
tures were analyzed separately from micron-scale filaments (Figure 3.1B), the latter
of which ranged in length from 0?5 ?m (Figure 3.1C). Between 20 min and 40 min
post-activation, the relative number of Bcl10 puncta increased, and the number of
long Bcl10 filaments correspondingly decreased (Figure 3.1D).
We define a correlation measure ? to assess the relationship between the num-
ber of Bcl10 puncta and distribution of Bcl10-filament lengths. At both time points,
a moderate negative correlation (? < ?0.6) existed between the overall number of
Bcl10 puncta and the distribution of Bcl10-filament lengths. Thus, cells with fewer
puncta were more likely to have long filaments, and cells with more puncta were more
likely to have shorter filaments (Figure 3.1D). The negative correlation between the
average number of puncta and average filament length was statistically significant at
the single-cell level: cells at 40 min post-stimulation were more likely to have both
37
Figure 3.1: Bcl10 filaments shorten between 20 min and 40 min post-T cell receptor
activation. (A) Representative image of an activated T cell 20 min after TCR stim-
ulation. (B) Representative Bcl10 filaments within the activated T cell. Filament
outlines and skeletons were calculated using a semiautomatic segmentation method
and medial axis thinning. The upper image exemplifies the filamentous form of Bcl10
and the lower image is representative of punctate Bcl10. (C) Representative distri-
bution of Bcl10 lengths from all Bcl10 filaments from (A). Punctate Bcl10 structures
were separately counted and binned as P. (D) Cumulative length distributions of
Bcl10 filaments from all T cells at 20 min (47 cells from 2 experiments) after TCR
stimulation and 40 min (53 cells from 2 experiments). Each row is a length distri-
bution for a cell sorted by the percentage of punctate Bcl10 structures in each cell.
The correlations between the number of punctate structures and average filament
lengths are -0.657 and -0.695 at 20 min and 40 min post-activation, respectively.
(E) Scatter plot of the proportion of punctate Bcl10 structures at 20 and 40 min
after TCR stimulation. (F) Scatter plot of the proportion of Bcl10 filaments longer
than 1 ?m at 20 min and 40 min after TCR stimulation. Correlations are the Pear-
son product-moment correlation. Error bars are the 95% confidence interval of the
mean. p-values were calculated using a two-sample t-test were considered significant
if less than 0.05.
38
a larger relative proportion of punctate structures (Figure 3.1E, p = 0.0010), and a
decrease in the relative number of Bcl10 filaments longer than 1 ?m (Figure 3.1F,
p = 0.00039). Taken together, these results are consistent with the interpretation
that between 20 min and 40 min post-activation Bcl10 filaments decrease in length
and the proportion of punctate structures increases. This increase in the number
of punctate structures and decrease in the number of long filaments could indicate:
(i) ongoing nucleation of new filaments; (ii) disassembly or end-directed degrada-
tion of existing filaments; (iii) scission of existing filaments, which would create two
daughter filaments with each scission event; or (iv) some combination of the above
processes.
3.3.2 Examining Autophagosome-Bcl10-Filament Interactions
Our previous work has demonstrated that Bcl10 within the filamentous POLKA-
DOTS signalosome is targeted for degradation by macroautophagy (henceforth re-
ferred to as autophagy) [36], an intracellular degradative process involving the
envelopment of cargo by double-membraned vesicles called autophagosomes. Au-
tophagic degradation of Bcl10 leads to a dampening of NF-?B activation and NF-
?B-dependent T-cell responses [36]. To examine whether autophagy is responsible
for the observed decrease in Bcl10 filament length, we expressed an RFP-tagged
form of the autophagosome membrane protein LC3 in our Bcl10-GFP-expressing
D10 cell line, then imaged static interactions between Bcl10 filaments and LC3-
labeled autophagosomes at 20 min and 40 min post-TCR activation (Figure 3.2A).
39
Consistent with our previous data [36], these experiments indicated that filamen-
tous Bcl10 and LC3-positive autophagosomes existed simultaneously in activated
T cells. A large number of autophagosome contacts with Bcl10 filaments were
observed. Thus, independent semiautomatic segmentation of Bcl10 filaments and
autophagosomes was used to determine the number and location of contacts (Fig-
ure 3.2B). Interestingly, we observed that activated T cells have significantly fewer
Bcl10-autophagosome contacts at 20 min post-TCR stimulation than at 40 min post-
stimulation (Figure 3.2C, p = 0.000145). However, this fact alone is not sufficient
to conclude that contact formation is preferred. To assess whether autophagosome
contacts with Bcl10 filaments form preferentially or randomly, we developed an
image-based-resampling method analogous to statistical bootstrapping (Methods).
We randomly rearranged the segmented autophagosomes throughout the cell cytosol
and recalculated the resulting filament-autophagosome contacts (Figure 3.2D). The
cell-averaged number of colocalizations in these rearrangements was significantly
fewer than the number in the experimental observations (Figure 3.2E). As an addi-
tional test, we conducted 100 rearrangements of each individual cell and constructed
a confidence interval for the number of randomized contacts. The actual number
of autophagosome contacts in 45 of 47 cells at 20 min post-activation, and 52 of
53 cells at 40 min post-activation, was greater than the 95% confidence interval
for random LC3 contacts (3.2F). Thus, we concluded that contact between Bcl10
and autophagosomes was non-random, and that there were indeed more Bcl10-
autophagosome interactions at 40 min post-activation.
Our results thus far indicate that at 40 min post-activation, Bcl10 filaments
40
41
Figure 3.2: Bcl10 filaments are preferentially in contact with autophagosomes rel-
ative to a random null model. (A) Representative image of an activated T cell 20
min after TCR stimulation. Bcl10 filaments (green) and LC3 vesicles (autophago-
somes, red) are within the yellow cell boundary. The outlined ROI contains a Bcl10
structure with two in-contact autophagosomes. (B) Representative Bcl10 filament-
autophagosome contacts. Segmentation and skeletonization analyses identify the
number and location of contacts highlighted by blue arrows. (C) Cumulative num-
ber of contacts in all T cells (20 min: 47 cells from 2 experiments; 40 min: 53
cells from 2 experiments). There is a statistically significant difference in the num-
ber of Bcl10-autophagosome contacts at 20 min and 40 min post-stimulation (p =
0.00014). (D) Three representative trials of the resampling from the cell in (A).
Contacts that formed after resampling are highlighted with arrows. (E) The cu-
mulative distribution of the number of Bcl10 filament-autophagosome contacts in
the random rearrangement trials. (F) Difference between the true number of Bcl10
filament-autophagosome contacts and the number of contacts found in each of the
100 trials per cell. Positive values indicate a greater number of true contacts than
found in the trials. There is statistically significant difference in the number of
contacts between the true and rearranged data in 45 of 47 T cells imaged 20 min
post-activation, and 52 of 53 T cells imaged 40 min post-activation. Error bars are
the 95% confidence interval of the mean and were calculated independently for each
cell. p-values were calculated using two-tailed t-tests. p-values less than 0.05 were
considered significant.
42
Figure 3.3: Shape and size statistics of autophagosomes 20 min and 40 min post-
activation. (A) Distribution of autophagosome 3-D volumes. (B) Distribution of
autophagosome 3-D surface areas. (C) Distribution of autophagosome sphericities.
A sphericity of 1 corresponds to a sphere and sphericity of 0 corresponds to a flat
disk.
are both shorter and have increased contact with autophagosomes, consistent with
the interpretation that autophagosomes degrade the filaments over time. How-
ever, a mechanistic problem arises from these data: autophagy occurs when double-
membraned vesicles completely surround and envelop intracellular cargo, yet Bcl10
structures are larger than autophagosomesthe majority of autophagosome structures
are smaller than (0.2 ?m)3 in volume at both 20 min and 40 min post-activation
(Figure Figure 3.3).
The traditional biophysical understanding of mechanisms of autophagy may
not be viable as an explanation for Bcl10-filament degradation. To examine the
mechanism whereby autophagosomes degrade Bcl10 filaments, we examined the
location of autophagosome colocalizations along each filament. Biochemical and
structural studies have demonstrated that Bcl10 filaments have two distinct end
points and no junctions along the main body [8]. However, due to the resolution
43
limits of this imaging method, some filaments appear joined. Thus, employing
the same super-resolution dataset used for Figure 3.2, we extracted Bcl10 filament
skeletons and fragmented them to eliminate high-degree junctions such that the re-
sulting skeleton configurations minimized the total bending energy (Figure 3.4A,
Methods). After processing the skeletons, each Bcl10 filament was segmented based
on the distance from the nearest skeleton endpoint (Figure 3.4B). Finally, we ex-
amined each colocalization event between an autophagosome and a Bcl10 structure.
If the Bcl10 structure was punctate, the event was designated P, and if the Bcl10
structure was filamentous, the event was characterized by the shortest distance
between the autophagosome and the skeleton endpoint (Figure 3.4C). Excluding
puncta, the distance-from-end distributions at 20 min and 40 min were not statis-
tically distinguishable (Figure 3.4C, p = 0.085), and we found a marked preference
for autophagosomes to localize near filament ends at both time points. Interest-
ingly, a greater proportion of autophagosomes were in contact with Bcl10 puncta
(as opposed to filaments) at 40 min post-activation than at 20 min post-activation
(Figure 3.4C, p = 2.03?10?9). Although the proportion of punctate Bcl10 approxi-
mately doubled between 20 and 40 min post-activation (Figure 3.1E), the proportion
of autophagosomes that localized to puncta approximately quadrupled over the same
period (Figure 3.4C), indicating a distinct preference for autophagosomes to localize
with punctate Bcl10 at the later time point.
Our observations thus far indicate that autophagosomes are more likely to
localize to the ends of filaments and, by 40 min post-activation, to Bcl10 puncta.
To assess whether these localizations are truly preferred, as opposed to random, we
44
Figure 3.4: Autophagosomes preferentially localize to Bcl10-filament ends and, at
later timepoints, to Bcl10 puncta relative to a random null model. (A) Repre-
sentative segmented Bcl10 filaments (green) and autophagosomes (red) after post-
processing, overlaid with the pruned medial-axis skeleton of Bcl10 (black). Filament
skeletons were fragmented to minimize the bending energy at junctions. (B) Using
the skeleton of the representative Bcl10 filament, the filament volume was segmented
into sections based on the nearest distance from skeleton ends. (C) Distribution of
autophagosome-Bcl10 contacts by distance from endpoint (filamentous Bcl10) or
punctate Bcl10 (P). (D) Scatter-bar plot of the proportion of Bcl10 puncta per
cell in contact with an autophagosome in experimental and randomized data. (E)
Distribution of autophagosome-filamentous Bcl10 colocalizations by distance from
endpoint in experimental and randomized data. p-values in C and E were calcu-
lated using two-sample KS tests and p-values in D were calculated using paired
two-sample t-tests. p-values less than 0.05 were considered significant.
45
again employed the randomized images from the image-based resampling shown in
Figure 3.2D. First, we compared the number of colocalizations of Bcl10 puncta with
autophagosomes in the true versus the randomized images (Figure 3.4D). At 20 min
post-activation, the true and random distributions of contacts were indistinguishable
(Figure 3.4D, p = 0.079), indicating that autophagosome-puncta contacts could be
the result of random co-localization. However, at 40 min post-activation, the number
of true puncta contacts was greater than the number of such contacts in the ran-
domized images, and this enrichment was statistically significant (Figure 3.4D, p =
2.15?10?16), indicating that punctate Bcl10 structures were preferentially in contact
with autophagosomes at this time point. Next, we compared the distance-from-end
distributions of autophagosome-filament contacts for the experimental versus ran-
domized data at both time points (Figure 3.4E). The randomized distributions at
both time points demonstrated fewer end-localizations and increased numbers of
contacts along the body of the filament in comparison to quantification of local-
ization data from true images (Figure 3.4E, p = 1.10 ? 10?11 and 2.01 ? 10?16 at
20 min and 40 min, respectively). These results indicate that the preference for
autophagosomes to localize at or near filament ends is non-random.
Taken together, the results from Figure 3.2 and Figure 3.4 indicate that fol-
lowing TCR engagement and activation, autophagosomes formed attachments with
Bcl10 filaments, the number of attachments increased over time, and these attach-
ments occurred near the ends of Bcl10 filaments. Furthermore, by 40 min post-
activation, autophagosomes also formed attachments with Bcl10 punctate struc-
tures in a biologically targeted (i.e., non-random) manner. Together, these results
46
are consistent with the hypothesis that autophagosomes are responsible for the pro-
gressive shortening of Bcl10 filaments over time, and that this process is directed
by a biologically encoded targeting process. Further, the accumulation of punctate
Bcl10 structures at 40 min post-activation may be the result of the degradation
of longer Bcl10 filaments. Complete degradation of Bcl10 may follow nonlinear ki-
netics, with the final remnant, visualized as puncta, undergoing slower degradation
than filamentous regions of these structures.
3.3.3 Modeling Bcl10 Filament Dynamics
Our previously published observations demonstrate that macroautophagy con-
tributes to Bcl10 filament degradation [36], and the above analysis of imaging data
supports and extends these conclusions. This degradation occurs simultaneously
with Bcl10 polymerization, and the interplay between these processes serves to con-
trol T-cell activation states. However, our understanding of the dynamics of fila-
ment polymerization and degradation, and the interaction between these processes,
remains limited.
To explore the interplay between simultaneous Bcl10 polymerization and degra-
dation further, as well as the implications of this interplay, for control of T-cell
activation states, we designed a stochastic Monte Carlo simulation to model Bcl10
polymerization (Methods). Previous studies have indicated that growth of Bcl10
filaments is nucleated by short cytosolic oligomers of Carma1 [8, 62], and that this
nucleation is the rate-limiting step for filament growth [8]. Thus, we used nucleation-
47
Figure 3.5: Theoretical predictions of nucleation-limited growth. (A) Expected
length of filaments undergoing nucleation-limited growth in damped (red) and un-
damped (green) environments. (B) Expected growth rate of of filaments undergoing
nucleation-limited growth in damped (red) and undamped (green) environments.
limited filament assembly as the basis for our simulation. The growth rates of fil-
aments that undergo nucleation-limited growth are governed by whether filament
lengths are less than or greater than the nucleation barrier. Short filaments grow
slowly until they reach the critical length.. In effect, growth rates of such filaments
can be understood as a sequence of Bernoulli processes whose probability parameter
is modified based on current filament length. Under these conditions, theoretical
predictions of filament growth rate indicate a dramatic transition between slow, ini-
tial growth, to fast, steady-state growth, as outlined in Equation 3.1 and Figure 3.5.
??????( )n px qn?x? x attach( attac)h
x < L0
P (x|n) = ???? ? ( ) (3.1)n?(x?L0) i?1 (n?i)?(x?L )? pL0 i?L0 n?i x?L0 0L0 1 attachqattach ? px L grow qgrow x ? L00
i=L0
Filament growth is further mediated by a kinetic process whereby monomers
48
collide with, or are recruited to, the site of the growing filament. Our simulation
began with the generation of cells, which were each given a random size that was
used to generate the initial conditions, including numbers of monomeric nucleation-
site components (mimicking monomeric Carma1), Bcl10, autophagosomes, and the
size of the immunological synapse (i.e., the portion of the cell membrane with the
potential to activate the Bcl10-nucleation sites). As this cell evolved in time over
each iteration of the simulation, the growth of Bcl10 filaments was governed by
three independent and tunable parameters (visually represented in Figure 3.6A):
the activation probability of the nucleation sites (pactivate), the growth probability of
the initial layer of Bcl10 monomers before the nucleation barrier has been overcome
(pattach), and the steady-state growth probability after the filament overcomes the
nucleation barrier (pgrow).
We first sought to determine whether the value of each parameter should re-
main constant throughout each iteration of the simulation, or whether the results
of each iteration would affect parameter values. For instance, if the concentration
of free Bcl10 monomers decreases over time (i.e., if resynthesis of Bcl10 monomers
is outpaced by their degradation), the probability of monomer collisions with the
growing filament end decreases over time, thus decreasing pgrow, in a process known
as damping. To determine whether Bcl10 filament growth is damped, we tested
100 simulated T cells, each with a different size, and thus initialized with a unique
number of nucleation sites and Bcl10 monomers, representing the evolution of a
heterogeneous population of T cells with varying initial conditions (Figure 3.6B).
When our simulation were employed in an undamped environment, growth contin-
49
50
Figure 3.6: Simulations of Bcl10 filament growth reveal properties of real Bcl10
nucleation rates and concentrations, but fail to match observed values for ?. (A)
Representative segmented Bcl10 filaments (green) and autophagosomes (red) after
post-processing overlaid with the pruned medial-axis skeleton of Bcl10 (black). Fil-
ament skeletons were fragmented to minimize the bending energy at junctions. (B)
Using the skeleton of the representative Bcl10 filament, the filament volume was
segmented into sections based on the nearest distance from skeleton ends. (C) Dis-
tribution of autophagosome-Bcl10 contacts by distance from endpoint (filamentous
Bcl10) or punctate Bcl10 (P). (D) Scatter-bar plot of the proportion of Bcl10 puncta
per cell in contact with an autophagosome in experimental and randomized data.
(E) Distribution of autophagosome-filamentous Bcl10 colocalizations by distance
from endpoint in experimental and randomized data. p-values in (C) and (E) were
calculated using two-sample K-S tests and p-values in (D) were calculated using
paired two-sample t-tests. p-values less than 0.05 were considered significant.
51
ued perpetually and, by the end of the simulation, punctate structures all grew into
filaments and all Carma1-mimicking nucleation sites were filled. The same simu-
lation in a damped environment, with a finite supply of Bcl10 monomers, led to a
heterogeneous distribution of Bcl10 puncta and filaments of varying lengths. The
results of the damped growth simulation were more representative of observed Bcl10
filament lengths (Figure 3.1D), leading us to conclude that Bcl10 filament growth
is limited by Bcl10 monomer supply. This conclusion is supported by biochemical
analyses of Bcl10 levels over time in activated T cells [36]. Thus, in all subsequent
simulations, we allowed the decreasing availability of monomeric Bcl10 to cause
an effective stochastic reduction in the Bcl10-nucleation probabilities, pattach and
pgrow, because fewer monomeric Bcl10 will lead to a reduced number of attempted
attachments.
Next, we tested whether changes in the value of pgrow would provide useful
information regarding the response dynamics. Previous work by David et al. [8]
indicated that nucleation (pactivate) and/or the initial attachment of Bcl10 filaments
(pattach) is the rate-limiting step in filament growth. Thus, varying the value of pgrow
would likely provide little in the way of relevant biological information. Furthermore,
increasing the growth rate would more quickly deplete the monomer concentration,
thus ending the simulation after fewer iterations and limiting the sampling of the
activation and attachment probabilities. Thus, we chose to assign pgrow a fixed value
that allowed the simulations to run for a reasonable number of iterations (here, we
chose p = 0.4 as described in the Methods), and we only modulated pactivate and
pattach.
52
Finally, we examined the effect of various values for pactivate and pattach on fil-
ament lengths resulting from the simulation (Figure 3.6C). The observed filament
lengths in our cell images (Figure 3.1D) demonstrate a moderately negative corre-
lations between the relative numbers of puncta and length of Bcl10 filaments, ? ?
-0.6. We therefore explored which combinations of parameters applied to the same
heterogenous population of 100 simulated T cells could generate an equivalent cor-
relation. Each simulation was repeated 10 times, and each trial was terminated
when the number of free monomers of Bcl10 reached zero. The filament-length
distributions we report represent the cumulative distribution from each of the 10
trials. There is a complex interplay between pactivate and pattach: when pactivate is
small, there are few simulated filaments, and simulated filament length distributions
appear to be unchanged with increasing pattach (Figure 3.6C left). On the other
hand, when pactivate is large, there are many activated nucleation sites in each simu-
lated cell, which results in heterogeneity in the preferred filament length. Increased
pattach results in decreased average-filament length (Figure 3.6C right). Interest-
ingly, intermediate values of pactivate in the simulations results in nonlinear behavior
(Figure 3.6C center). In particular, the preferred filament length appears to be
independent of pattach for small pattach, similar to Figure 3.6C left, but decreases for
large pattach, similar to Figure 3.6C right. Careful tuning of simulations parameters
resulted in correlations between ? = [-0.5, -0.4] in subsections of the simulation?s
parameter space in which pactivate was 0.5, and pattach was 0.075. However, the min-
imum ? value in the simulation was unable to reach observed levels of ? less than
-0.6. This failure to match the model to experimental observations points to a need
53
to include Bcl10 degradation in the simulations.
To understand the effect of degradation on Bcl10 filament size, we added a pro-
cess in the simulation in which an autophagosome attaches to a filament and cause
degradation with probability pdegrade (Figure 3.7A). As in Figure 3.6, we simulated
100 cells with random initial conditions and repeated each simulation 10 times. A
comparison of twelve representative parameter sets is instructive for determining
the effects of each individual parameter, as well as of the interplay among the pa-
rameters, on the concentration of filamentous Bcl10 (Figure 3.7B). For this set, we
chose a small vs a large value for both pattach (Figure 3.7B, top vs bottom) and
pactivate (Figure 3.7B, left vs right). For each of these four parameter subspaces, we
compared a small, medium, and large value for pdegrade, which was varied over the
same range as pattach. As expected, increasing values of pdegrade in each parameter
space led to a smaller concentration of filamentous Bcl10. Interestingly, an increase
in the rate of nucleation-site generation (represented by a greater pactivate) led to a
faster decline in filamentous Bcl10 (Figure 3.7B, left vs right). This result makes
intuitive sense, as a greater number of activation sites would lead to a greater num-
ber of filaments, and thus a greater number of sites where degradation can occur.
In contrast, a lower activation barrier (represented by a greater pattach) had a much
smaller effect on the rate of decline in filamentous Bcl10, promoting only a slight
increase in filament stability. When combined, a lower activation barrier and a
greater activation of nucleation sites created a dynamic in which slight variations in
degradation had a large effect on the concentration of filamentous Bcl10.
We further explored how each of the three parameters in our simulation af-
54
Figure 3.7: Simulations of Bcl10-filament growth and decay demonstrate that
changes in the response dynamic due to increasing degradation by autophagy were
stabilized by increasing pattach but emphasized by increased pactivate. (A) Bcl10-
filament degradation was simulated in conjunction with filament growth. Degra-
dation was modulated by pdegrade, the probability of degradation by an autophago-
some. (B) The average normalized concentration of filamentous Bcl10 as simulations
evolved. Concentration is relative to the maximum-average concentration of all sim-
ulations with the same parameters. Each line represents the average of 100 cells,
repeated 10 times each, and shaded bars are the 95% CI of the mean. Simulations
were repeated with small and large values for pactivate and pattach. (C) The number
of iterations needed to reach the maximum relative concentration vs. the number
of iterations to reach half of the maximum concentration due to degradation. Each
entry represents the average nmax and nhalf for the 10 trials of each of the 100 cells.
Low pdegrade is 0.05, moderate pdegrade is 0.10, and high pdegrade is 0.20. Ellipses
represent one standard error of the mean.
55
fected the variability of the response across the heterogeneous initial population of
cells (Figure 3.7C). For each of the 100 cells, we calculated the average number of
iterations for the filament-length distribution to reach its maximum average size,
nmax, and compared this to the average number of iterations required for the aver-
age size to be half of the max, nhalf (Figure 3.7C), for each of the twelve parameter
configurations. Increasing the value of pattach, pactivate, or pdegrade independently of
the others led to decreased variability in outcomes, with a lower nucleation barrier
(an increase in pattach) having the greatest effect on variability in the response to an
activation signal (i.e., heterogeneity in the time to peak response), and an increase
in pactivate emphasizing changes in pdegrade. The introduction of degradation into
the simulations reduced the already negative correlations ? between the number of
puncta and average filament length. Each of the simulations reached values of ? ?
-0.5 during system evolution, close to the experimental value of ? < ?0.6.
In summary, we have developed a refined model of a critical TCR signaling pro-
cess that quantitatively captured the growth and decay dynamics of Bcl10 filaments
and their heterogeneous length distribution. We determined that a high activation
potential of nucleation sites can, when combined with a low Bcl10-nucleation barrier,
provide the most predictable and homogeneous response to T-cell activation. Fur-
thermore, we found that the rate of degradation of Bcl10 filaments had the largest
effect on the percentage of Bcl10 in filamentous form when nucleation sites have a
high activation potential and Bcl10 has a low nucleation barrier. These conditions
ultimately allow the response dynamic to be maximally tunable via changes in the
degradation rate. These data offer a mechanistic explanation for the opposition of
56
Bcl10 polymerization by simultaneous autophagic degradation of Bcl10 polymers.
3.4 Discussion
In this work, we explored the mechanism and dynamics of Bcl10 filament
degradation, a process that is a key regulatory element in the T cell receptor-to-
NF-?B signal transduction pathway. Through computational analysis of super-
resolution images, we demonstrated that Bcl10 filaments are shorter in length at 40
min post-TCR engagement than at 20 min, with an increase in punctate Bcl10 and
a decrease in filaments longer than 1 ?m. We demonstrated that autophagosomes
were preferentially in contact with Bcl10 filaments, that these contacts increased
over time, that at both 20 min and 40 min post-TCR engagement there was a
preference for the contacts to occur near filament ends, and that by 40 min post-
TCR engagement, autophagosomes colocalize with Bcl10 puncta in non-random,
significant manner. Together, these findings, along with our previous biochemical
studies [36], imply that autophagosomes drive a degradative process that progres-
sively shortens Bcl10 filaments, leaving behind remnants visualized as puncta that
undergo slower degradation. Furthermore, we developed a stochastic Monte Carlo
simulation of nucleation-limited filament growth and degradation, which we used
to probe aspects of regulatory control of filamentous signal transduction bodies.We
ascertained that the rate of degradation was the most important element controlling
the magnitude and dynamics of the response function, particularly when the homo-
geneity of the response has been maximized via a high activation potential and a
57
low nucleation barrier.
Importantly, these results shed light on possible mechanisms of autophagic
degradation in the poorly understood scenario in which the structures to be de-
graded are larger than the autophagosomes performing the degradation. We found
that increased contact between autophagosomes and Bcl10 filaments corresponded
to a progressive shortening of Bcl10 filament length, implying that autophagosomes
degrade these large structures through a piecewise mechanism rather than by en-
closure of the entire volume of a given cargo. Furthermore, we determined that
filaments to which autophagosomes attached were more likely to experience attach-
ment near filament ends, and that degradation models that target the ends of fila-
ments rather than the mid-region best fit the experimental observations. However,
we were unable to establish whether this degradation might occur via end-based dis-
assembly at the molecular scale, or via scission of larger regions near the end. The
observation that the number of punctate structures in contact with autophagosomes
increases significantly at 40 min vs 20 min could not be recapitulated in our model,
indicating that the final degradation of Bcl10 filaments once they reach lengths less
than 150 nm, and thus appear as punctae, is inhibited or occurs by an independent
mechanism.
The analysis methods that we developed for this study have broad applicability
to computational image analysis and the study of dynamic signaling processes. Typ-
ically, radial-distribution functions are used to measure and statistically assess con-
tacts and/or colocalizations between structures. However, because contacts between
Bcl10 filaments and autophagosomes involve close-range contact and significant vol-
58
umetric overlap, such an analysis was not suitable. Our image-based bootstrap-like
method of random rearrangement and reanalysis of segmented objects could prove
to be widely applicable in assessing colocalizations between structures in an image.
Furthermore, filamentous signaling structures, particularly those whose core con-
stituent protein contains a death domain superfamily element (as Bcl10 does), are a
common motif in immunological signal transduction pathways [107?109], and many
are downregulated via macroautophagy [110?112]. Thus, our model of nucleation-
limited filament growth and degradation, with its multiple tunable parameters that
can be used to fit the model to observed imaging data, may be applicable to a
variety of autophagy-regulated signal transduction pathways and reveal common
mechanistic principles of immune regulation.
The simulations we developed offer intriguing insight into the regulatory con-
trol of T cell activation states. Higher values of pactivate in the model led to in-
creased heterogeneity in filament lengths. Because our experimental observations
include heterogeneous filament lengths, it is implied that the probability of activation
of Carma1 in response to TCR engagement is realistic biologically. Furthermore,
higher values of pactivate in the model led to increased responsiveness to variations in
degradation speed, along with decreased variability of the response from a variety
of initial states; outcomes that are both beneficial to the overall control of T cell
activation. Thus, it appears that in activated T cells, Carma1 in the vicinity of
the immunological synapse has a high likelihood of promoting Bcl10 filament nucle-
ation, and further regulatory control of the activation potential of Carma1 would
provide little overall benefit. In contrast, variations in the size of the nucleation
59
barrier (represented by pattach) had little effect on the dynamics of the response,
although a smaller nucleation barrier (higher pattach) led to slightly stabilized fila-
ments over time and increased homogeneity of the response dynamic. Regulatory
control of the nucleation barrier does not appear to provide substantial benefit to
the response dynamic. Interestingly, based on the results of the simulations, govern-
ing the rate of filament degradation via control of autophagy has the greatest effect
on the response dynamic. Indeed, autophagy has many regulatory control points
and processes feedback from a wide variety of signaling pathways [113], providing
myriad opportunities for crosstalk among T-cell signaling inputs.
The results of our simulations indicate that POLKADOTS filament growth
and degradation exhibit the characteristics of an excitable system. Excitability is
a phenomenon by which a system can undergo dramatic changes in behavior in
response to small perturbations. Components of such a system typically include
nonlinear thresholded/digital activation that initiates a fast, amplifying, positive
feedback loop, and a slower, delayed, response-limiting negative feedback loop [3].
Excitable systems characteristics are observed in a variety of biological processes,
including in the polymerization and depolymerization of cytoskeletal proteins dur-
ing migration [9], and in ion channels during neuronal firing cascades [114]. Further,
excitability is often observed when signaling networks reach a critical, near-phase-
transition state [5,13], which induces dramatic changes to system dynamics, includ-
ing the oligomerization of protein complexes via phase separation [12]. We have
previously reported that the Bcl10-dependent TCR-to-NF-?B signaling pathway is
characterized by digital activation, with increased stimulus beyond a certain thresh-
60
old having little effect on the signaling response of individual T cells [104]. Thus,
the predictions of behavior of POLKADOTS filament growth and degradation re-
sulting from these simulations are consistent with our previous observations of the
biological behavior of these signaling elements in T cells.
Our analysis of Bcl10 filament formation and degradation suggest that this
self-limiting, all-or-nothing response is enabled by nucleation-limited filament as-
sembly with a high probability of Carma1 activation in response to even minimal
TCR engagement and a low nucleation barrier. The system is self-limiting via au-
tophagy operating on filament ends, which extends the lifetime of filaments and thus
signal activation (a result not inconsistent with autophagy limiting the intensity of
the signal by limiting the amount of Bcl10 in POLKADOTS filaments [36]). Disas-
sembly via autophagy results in a long refractory period due to protein degradation.
More broadly, our results, when considered in combination with existing structural
data [105], offer the possibility that spatial organization of signaling components,
specifically filament assembly and degradation, may be used in other biological sig-
naling networks to enable robust all-or-nothing responses and/or self-limiting dy-
namics.
3.5 Materials and Methods
3.5.1 T-Cell Stimulation and Imaging
D10.G4.1 T cells were transduced with retroviruses-expressing Bcl10-GFP and
TagRFP-T-LC3 (referred to as RFP-LC3) as previously described [115]. Following
61
antibiotic selection, cells were subcloned to ensure uniform imaging characteristics.
The resultant D10 cell line was activated via plating on coverslips coated with anti-
CD3 antibody (clone 145-2C11, BioXCell). Cells were fixed with 3% paraformalde-
hyde after the indicated incubation times and mounted for imaging on a custom-built
instant structured illumination microscope (iSIM) with a 1.45 NA oil-immersion ob-
jective [106]. Images were collected as z-stacks inclusive of the entire volume of the
cells with a 200 nm distance between z planes. Following collection, images were
deconvolved using the Richardson-Lucy algorithm as previously described [106] and
converted to a new isotropically-distributed 3-D coordinate grid via 3-D spline in-
terpolation.
3.5.2 Segmentation of Bcl10 and LC3
Fluorescent iSIM images of Bcl10 and LC3 were binarized using an intensity
threshold on a cell-by-cell and channel-by-channel basis due to fluctuations in ex-
pression and intensity. Each binarized image was convolved with a 3? 3? 3 kernel
with values 13 and again binarized with a threshold of (
2)3 so that pixels with at
3 3
least 8 occupied nearest neighbor locations were considered. All small binary pixel-
noise was removed. Colocalizations between Bcl10 and LC3 were determined by
identifying the voxels which directly overlap in the two binary channels.
62
3.5.3 Skeletonization and Skeleton Measurements of Bcl10
Each of the structures in the binary Bcl10 images was individually skeletonized
using a MATLAB implementation of medial-axis thinning skeletonization [116,117].
Bcl10 skeletons sometimes contained erroneous spurs due to fluctuations in the vol-
ume from sensitivity to the intensity threshold. Thus, filament skeletons were pro-
cessed by iteratively removing spurs less than 6 voxels (150 nm) in end-to-end length,
the approximate optical resolution of the iSIM. Structurally isolated skeletons less
than 6 pixels (150 nm) in length were labeled as punctate as indicated in Figure 3.1.
Where multiple Bcl10 filaments overlapped, skeletons developed high-degree
nodes in which multiple filament branches converged or intersected at a single branch
point. This type of Bcl10 filament structure is inconsistent with current perspec-
tives [8], and was treated as an imaging artifact. To estimate the appropriate skele-
ton segmentation in these regions, we instituted a minimum-bending-energy scheme
under the assumption that filaments are less likely to develop large curvature, and
thus chose the configuration that resulted in the smallest net bending energy. Bend-
ing energy for a simple elastic beam is proportional to 12 , where R is the radius ofR
curvature of the bent region. Thus, we fit an 11-pixel segment centered at the high-
degree junction between multiple skeletons to the surface of a sphere to calculate R
for the segment.
Measurements from the ends of skeletons were calculated using the Floyd-
Warshall algorithm where the reference point was the nearest degree-one node.
Colocalizations between Bcl10 and LC3 were assigned the end-distance value from
63
the nearest skeleton points in all overlapping voxels.
3.5.4 Random Rearrangement and Resampling of Segmented Struc-
tures for Statistical Assessment
Bootstrapping is a statistical resampling procedure that allows for the esti-
mate of a sampling distribution. Because resampling of a single fixed T cell at
20 min or 40 min post-activation is impossible, we developed an image-based re-
sampling method to assess the sample distributions for the number and location of
Bcl10-autophagosome contacts if the underlying biological processes are driven by
randomness.
To implement the procedure, we identified three relevant cell structures from
the 3-D super-resolution iSIM image: the cell boundary, binary Bcl10, and binary
autophagosomes. For the resampling, we kept the location of the cell boundary and
Bcl10 fixed. Then, we removed all autophagosomes from the image and separately
saved each individual 3-D structure. Each 3-D autophagosome was then rotated by
three randomly generated angles between 0 degrees and 360 degrees about the x-,
y-, and z-axes. Finally, each randomly rotated autophagosome was placed one at a
time in a random location within the cell boundary. If any voxel in the currently
selected autophagosome fell outside of the boundary or overlapped with an existing
autophagosome, then a new location was chosen. The procedure was repeated until
all autophagosomes were placed. Upon completion, the contact calculations were
repeated, including the number of Bcl10-autophagosome contacts per cell, and the
64
location of each of the contacts along connected Bcl10-filament skeletons.
3.5.5 Simulations of Bcl10 Filament Growth and Degradation
Simulated cells were initialized with a variable amount of monomeric Bcl10,
monomeric Carma1, and autophagosomes. To determine initial levels, each cell was
assigned four random radii, R1, R2, R3, and R4, from a normal distribution with
parameters ? = 1 and ? = 0.2. The initial amount of Carma1 was a0?R31, Bcl10 was
b 30 ? R2, autophagosomes were c0 ? R33, and the size of the immunological synapse
was d0 ? R22, where a0 = 10, b0 = 500, c0 = 5, and d0 = 0.2, were each chosen
empirically.
The simulated evolution of filament growth and degradation was controlled by
the activation of Carma1 by the engaged TCR, the nucleation of Bcl10 filaments by
an active Carma1, the attachment of monomeric Bcl10 to nucleated Bcl10 filaments,
the attachment of autophagosomes to Bcl10 filaments, and the degradation of Bcl10
filaments by autophagosomes. Each step in the evolution was mediated by both
fixed and variable probabilities.
1. Activation of Carma1 by the engaged TCR.
(a) Probability that Carma1 will collide with the TCR, pcollide = 0.1.
(b) Probability that the TCR was part of the immunological synapse, psynapse =
d0 ?R24.
(c) Probability of Carma1 activation, pactivate (variable).
2. Growth of Bcl10 on activated Carma1.
65
(a) Probability that Bcl10 will collide with Carma1, pcollide = 0.01.
(b) Probability of attachment before the nucleation barrier has been reached,
pattach (variable).
(c) Size of the nucleation barrier (i.e., the number of attachments before the
attachment probability switches from pattach to pgrow), nbarrier = 20.
(d) Probability of attachment after the nucleation barrier has been reached,
pgrow = 0.4.
3. The degradation of Bcl10 by an attached autophagosome.
(a) Probability of autophagosomes colliding with a Bcl10 filament, pcollide =
0.01.
(b) Probability of autophagosomes attaching to a Bcl10 filament, pattach =
0.1.
(c) Probability of autophagosomes degrading attached-to filaments, pdegrade
(variable).
(d) If attached autophagosomes do not degrade, the probability that they
fall off the attached-to filament, pdetach = 0.1
We used physical properties of Carma1 and Bcl10 to inform the interaction
probabilities in the simulations. Bcl10 has a mass of 33 kDa and its cytosolic
2
diffusion constant is on the order of DBcl10 ? 10?m , whereas Carma1 has a mass ofs
2
130 kDa, and thus has a cytosolic diffusion constant on the order of D ?mCarma1 ? 1 s
[118]. The time required to traverse some mean-squared displacement d via diffusion
66
? d2is t . T-cell diameters are on the order of dTcell ? 10?m, and thus the time6D
it takes for Bcl10 and Carma1 molecules to traverse the cytosol are approximately
0.2 sec and 2 sec, respectively. Thus, the collision probability for Bcl10 was chosen
to be 10? larger than that of Carma1. The other rate constants, such as pgrow and
pattach, have not been determined experimentally, to our knowledge.
Simulations from Figure 3.6 were performed without autophagosomes and ter-
minated upon monomeric Bcl10 being completely converted to filamentous Bcl10.
Simulations from Figure 3.7 were performed for either 10,000 iterations or when the
number of monomeric and filamentous Bcl10 reached zero, whichever came first.
67
Chapter 4: Quantifying Topography-Guided Actin Dynamics Across
Scales Using Optical Flow
This chapter was adapted from Lee?, Campanello?, Hourwitz, Alvarez,
Omidvar, Fourkas, and Losert [6]. Text and figures were reproduced
under a Creative CommonsNoncommercialShare Alike 3.0 Unported li-
cense. Rachel Lee, Matt Hourwitz, and Phillip Alvarez performed the
MCF10A experiments, Matt Hourwitz and Ava Omidvar performed the
HL60 experiments, Leonard Campanello designed and performed the
optical-flow analysis, and Rachel Lee and Leonard Campanello wrote
the paper.
4.1 Overview
The dynamic rearrangement of the actin cytoskeleton is an essential component
of many mechanotransduction and cellular force generation pathways. Here we use
periodic surface topographies with feature sizes comparable to those of in vivo colla-
gen fibers to measure and compare actin dynamics for two representative cell types
that have markedly different migratory modes and physiological purposes: slowly
migrating epithelial MCF10A cells, and polarizing, fast-migrating, neutrophil-like
68
HL60 cells. Both cell types exhibit reproducible guidance of actin waves (esotaxis)
on these topographies, enabling quantitative comparisons of actin dynamics. We
adapt a computer-vision algorithm, optical flow, to measure the directions of actin
waves at the submicron scale. Clustering the optical flow into regions that move in
similar directions enables micron-scale measurements of actin-wave speed and direc-
tion. Although the speed and morphology of actin waves differ between MCF10A
and HL60 cells, the underlying actin guidance by nanotopography is similar in both
cell types at the micron and submicron scales.
4.2 Background
Understanding the rearrangements of the cytoskeleton is essential to develop-
ing a complete picture of the dynamic forces involved in cellular processes such as
migration, division, and differentiation. Cytoskeletal dynamics, and in particular
actin dynamics, have been shown to be important for the growth of cell junctions
and focal adhesions [68] and for immune-cell activation [27]. The formation of actin
waves through directional polymerization and depolymerization of filaments drives
many types of cell migration [119], and has been associated with the establishment
of polarity in a variety of cell types [120].
Forces from the extracellular environment are an important modulator of actin
dynamics. Physical and chemical characteristics of the extracellular environment,
such as rigidity, biochemical composition, and topography, have been shown to
influence actin dynamics and associated cell behavior [121?124]. One mechanism
69
for this modulation is mechanosensing via focal adhesions [39]. In addition, actin
waves respond when cells encounter obstacles [125]. It has been established that
ridges of width comparable to fibers in the extracellular matrix (ECM) can alter
actin dynamics significantly [29, 38, 39] and bias the localization of focal adhesions
[126, 127]. Thus, in vivo, the topography of the ECM, such as collagen networks
[128,129], is likely to modulate actin dynamics.
Periodic nanotopographic surfaces provide the opportunity to obtain system-
atic data on the modulation of such intracellular dynamics. In prior work, we have
shown that actin waves can be nucleated near, and guided along, periodic nanotopog-
raphy, in a phenomenon termed esotaxis. Actin-wave guidance has been observed in
cell types that exhibit distinct physiological functions and migration phenotypes, in-
cluding Dictyostelium discoideum [29,38], neutrophil-like HL60 cells [38], B cells [39],
and breast-cancer cell lines [24]. However, there are clear differences in the responses
of each of these cell types to nanotopography. For example, although both D. dis-
coideum and HL60 cells exhibit esotaxis, these two types of cells have been found to
move preferentially in different directions on specific nanoscale asymmetric sawtooth
textures [38]. Furthermore, different breast cancer cell lines preferentially move in
different directions on asymmetric sawtooth nanotopography [24].
Here we introduce a method for performing quantitative measurements of the
influence of nanotopography on intracellular dynamics at both the submicron and
the micron scales. This approach enables the detection of subtle differences in cy-
toskeletal dynamics, and allows for in-depth analysis of both the differences and the
similarities of these dynamics across cell types and phyla. Our method of quantifi-
70
cation of actin dynamics across scales is based on optical flow, an image-analysis
technique developed in the fields of robotics and navigation control that uses changes
in pixel intensities to detect motion in image sequences [87,89]. Because of the pop-
ularity of particle image velocimetry (PIV), optical flow has seen limited use on
biological images. However, PIV is poorly suited for the variety of features that can
be exhibited in fluorescence images of amorphous concentration fields. Indeed, a
recent study indicated that optical flow may be better suited for analysis of fluores-
cence images, as it provides a more accurate estimate of ground-truth flow fields [84].
Here, we use optical flow to measure the dynamics of actin polymerization with sub-
micron precision, and we further expand the utility of optical flow by introducing
modeling and fitting approaches to the analysis of optical-flow vector fields. Clus-
tering of the optical-flow data further allows us to quantify actin dynamics on the
micron scale. This optical-flow-based analysis enables the identification of similari-
ties and differences between esotaxis in neutrophil-like HL60 cells and human breast
epithelial MCF10A cells across length scales.
4.3 Results
Esotaxis has been observed in a wide range of cell types that are known to
respond to their in vivo microenvironment through processes such as directed mi-
gration or immune-system activation [29, 38, 39]. More recently, esotaxis has also
been observed in epithelial cells, which are not motile [24]. Here we contrast the
actin dynamics of epithelial MCF10A cells with those of neutrophil-like HL60 cells.
71
LifeAct-GFP-labeled epithelial MCF10A cells were plated on a 900 ?m ? 900
?m region patterned with parallel nanoridges with a spacing of 1.5 ?m, as well as
on the surrounding flat regions. Confocal imaging near the surface revealed distinct
actin morphologies on nanoridges as compared to on the flat region (Figure 4.1). On
the flat regions the phenotype was a common one for MCF10A, with a broad lamel-
lipodium at the cell front and stress fibers throughout the cell body (Figure 4.1A).
In contrast, MCF10A on nanoridges exhibited actin streaks aligned with the ridges
throughout the cell area (Figure 4.1B). The local nature of the responses of actin
to the surface texture is illustrated in Figure 4.1C, which shows a cell that was par-
tially on the nanoridges and partially on the flat region. On the nanoridged region,
the cell showed the same types of actin streaks as a cell that was fully on a ridged
surface, whereas the same cell maintained a broad lamellipodium on the flat region.
Ridged and flat regions also engender distinct actin dynamics. Kymographs
were used to visualize dynamics in regions of interest in one spatial direction over
time. The left side of Figure 4.2A compares an MCF10A cell on a flat region with one
on a nanoridged region. The cell on the nanoridged region exhibited actin streaks
that are characteristic of esotaxis. Actin kymographs from two perpendicular re-
gions (Figure 4.2A) in an MCF10A cell on a flat surface show oscillatory dynamics
in all directions at the cell boundary. These oscillations in the kymographs indicate
the presence of fanlike protrusions and retractions across each region over 30 min
(Figure 4.2B). In contrast, on the nanoridged region, the actin dynamics parallel and
perpendicular to the ridges were different (Figure 4.2C). Parallel to the nanoridges,
MCF10A cells exhibited oscillatory actin dynamics. As shown in the bottom left
72
(A) (B) (C)
Flat Ridges Flat Ridges
Figure 4.1: Nanotopography prompts distinct actin morphology. The actin cy-
toskeleton of an epithelial MCF10A cell on (A) a flat surface had an actin morphol-
ogy that was distinct from that of a cell on (B) a nanoridged surface. (C) A cell that
was partially on a nanoridged region and partially on a flat region exhibited local
actin morphologies that were driven by the underlying topography. The blue line in
(C) indicates the boundary between the flat region and the nanoridged region. All
scale bars are 10 ?m.
73
of Figure 4.2C, a representative kymograph of a region perpendicular to the ridges
shows actin structures that persisted for tens of minutes and did not move perpen-
dicular to the ridges. This behavior was typical for kymographs perpendicular to
the ridges, although perpendicular motion was observed in some cases, as discussed
below.
The behavior of motile, neutrophil-like HL60 cells on flat and nanoridged re-
gions is illustrated in Figure 4.2D?F. Figure 4.2D indicates the regions from which
kymographs were generated. In HL60 cells on flat regions, actin was concentrated
near the cell front. This localization was largely preserved on the ridged surfaces, al-
though the morphology of the actin changed such that streaks of actin were aligned
with the ridges. On flat surfaces, the HL60 cells showed regions of protrusions and
retractions (Figure 4.2E), similar to the actin dynamics seen in MCF10A cells (Fig-
ure 4.2B). We note that protrusions occured on a scale of seconds in HL60 cells
and on a scale of minutes in MCF10A cells. Kymographs of the HL60 cells in the
direction parallel to the nanoridges showed protrusive dynamics, although often in
the form of single persistent waves (Figure 4.2F, top), in contrast to the oscilla-
tory behavior seen on flat surfaces (Figure 4.2E). A representative kymograph of
an HL60 cell in the direction perpendicular to the nanoridges shows streaks (Fig-
ure 4.2F, bottom) that indicate that actin waves did not move perpendicular to
the ridges. However, the streaks were shorter in duration than those in a typical
MCF10A cell (Figure 4.2C). This behavior was typical for kymographs of actin in
HL60 perpendicular to the ridges. Unlike in MCF10A cells, in which actin streaks on
the ridges localized throughout the cell (Figure 4.2C, bottom), in the HL60 cells the
74
streaks occured near the cell front (Figure 4.2F, bottom). Groups of actin streaks
propagated together at the front of the HL60 cells, suggesting that there may have
been a large-scale organization of actin dynamics (spanning many ridges) in these
cells. It is unclear whether there was large-scale organization of actin dynamics in
the MCF10A cells. The full range of actin dynamics was more complex than what
was revealed by kymographs. MCF10A cells on the ridged regions exhibited actin
dynamics throughout the substrate contact area, whereas actin dynamics on flat
surfaces were largely confined to the cell boundary. In both cell types, nanoridges
stimulated reproducible, dynamic, linear actin structures.
Time-lapse fluorescence images of actin waves are difficult to interpret by vi-
sual inspection or kymographs alone, because the observed dynamics arise from a
complex spatio-temporal concentration field. To measure these wavelike dynamics
quantitatively, we must first define a wave (size and shape) and then capture its
propagation (e.g., splitting, recombination, and changes in direction). Here, we
address these challenges by introducing an automated approach to quantify actin-
wave dynamics across length scales for unbiased comparison in different cell types
and extracellular environments.
Our method is based on a computer-vision algorithm from robotics and nav-
igation control called optical flow [87, 89], which provides pixel-based information
about the direction and magnitude of intensity flux in a series of time-lapse images.
Fields of optical-flow vectors are calculated by integrating changes of intensity in
space and time, as shown schematically in Figure 4.3. For example, two images of a
migrating HL60 cell taken 8 sec apart are shown, with changes in time highlighted
75
(A) MCF10A (D) HL60
(B) (E)
10 10
5 Flat 5
0 0
10 10
5 Flat 5
0 0
0 10 20 30 0 10
Time (min) Time (min)
(C) (F)
10 10
5 Ridges 5
0 0
10 10
5 Ridges 5
0 0
0 10 20 30 0 10
Time (min) Time (min)
Figure 4.2: Nanotopography leads to distinct actin morphodynamics. (A) Optical
micrographs of MCF10A cells in (left) bright-field and (right) fluorescence on (top) a
flat region and (bottom) a nanoridged region. All scale bars are 10 ?m. Kymographs
for the areas denoted in A are shown in B for the flat region and in C for the
nanoridges. D-F are the same as A-C, respectively, but for HL60 cells.
76
Ridges Flat
Distance (?m) Distance (?m)
Ridges Flat
Distance (?m) Distance (?m)
by a green-to-magenta montage (Figure 4.3A). The magenta region indicates growth
of the actin front (which, as expected, occured at the leading edge of the cell), and
the green region indicates a decrease in actin intensity.
The general objective of calculating optical flow is to solve for the unknowns
?x and ?y in Equation 2.2, where I(x, y, t) represents the actin fluorescence inten-
sity at frame t. The intensity I that exists at point (x, y) at time t translates to a
new point (x + ?x, y + ?y) at some future time t + ?t. Expanding about small
?x and ?y and neglecting second-order derivatives yields the master optical-flow
expression in Equation 2.4. This governing equation is underdetermined, and so the
Lucas-Kanade optical-flow constraint [89] was applied to calculate flow fields. This
constraint prescribes that all pixels in a small window centered at (x, y) have the
same translational optical-flow vector. The equation can then be solved using the
least-squares criterion (an explicit derivation is given in the Materials and Methods)
to yield the intensity flow, ~v (Figure 4.3B, center panel). Solving for ~v requires use
of the negative spatial gradient, ??~ I (Figure 4.3B, left panel), which forms a vector
field oriented away from regions of highest local intensity, and the time derivative, ?I
?t
(Figure 4.3B, right panel), as shown in Equation 2.2. Using the pair of images from
Figure 4.3A as a representative example, the spatial and temporal gradients were
used to calculate the optical-flow vector field, which approximated the flow of actin
between the two frames. In this example, the vector field captured the translational
motion on the leading edge of the cell (Figure 4.3C).
Optical-flow measurements of actin intensity translation enabled the quan-
tification of the pixel-scale response of actin dynamics to nanoridge topographies
77
(A) First frame Second frame
(t = 0 seconds) (t = 8 seconds) Overlay
Time
(B) Spatial Gradient Optical Flow Difference Image
(C) Spatial Gradient Optical Flow Difference Image
Figure 4.3: Optical flow captured the dynamics in movies of actin fluorescence.
(A) Two frames of a representative HL60 cell obtained 8 sec apart and a merged
image show the dynamics of cell behavior over time. (B) The procedure used to
carry out optical-flow calculations combined the spatial gradient of an image (left)
and the difference image/temporal gradient (right) to yield the optical-flow vector
field (center). (C) Calculations from (B) were applied to the images in (A). The
spatial gradient (left) and temporal gradient (right) resulted in the output optical-
flow vector field (center). Blue pixels in the right panel of (C) indicate positive
changes (increases) in the pixel brightness from the first frame to the second frame,
and red pixels in the right panel indicate negative changes (decreases) in the pixel
brightness from the first frame to the second frame. All scale bars are 5 ?m.
78
(Figure 4.4). The green-to-magenta montages of representative HL60 and MCF10A
cells show dynamic and protrusive actin behavior at the leading edge of the cell
(Figure 4.4A). Coloring the calculated flow fields based on direction relative to the
nanoridges (Figure 4.4B) reveals the clear bias of actin wave guidance in the direc-
tion parallel to the ridges, which is consistent with the qualitative features of the
montage images in Figure 4.4A. Measurements of the optical-flow directions in all
HL60 and MCF10A cells on both flat and ridged surface topographies are shown
in the histograms of Figure 4.4C. In both cell types, the cumulative distribution of
flow in cells on flat surfaces showed no appreciable bias in any direction. However,
cells on ridges exhibited a clear preference for flow along the ridge direction.
We note that the images for the MCF10A and HL60 were obtained with dif-
ferent objectives (100? and 60?, respectively) and at different acquisition rates (10
and 2 sec between frames, respectively). Nevertheless, the optical-flow algorithm
performed well on each set of data, emphasizing the broad applicability of this ap-
proach. The two cell types also used different actin-labeling approaches (LifeAct for
the MCF10A and Actin-YFP for the HL60), which may have different overexpres-
sion effects on actin dynamics [130], but in both cases produced reliable optical-flow
results that were indicative of nanotopography-guided actin dynamics.
For further quantification, we fit the distribution of flow directions from each
cell to a bimodal von Mises model with a constant offset (Materials and Methods).
The distribution consists of a uniform component and two peaked components that
are 180? apart. The five parameters of the bimodal model are illustrated in Fig-
ure 4.4D. The angle ?? indicates the direction of the main component, and
1 is
?
79
proportional to the width of the distribution. The values of ? on ridged regions
were significantly higher than those than on flat regions for both the MCF10A and
the HL60 cells (Figure 4.4E, p = 0.0001583 and p = 0.0040), indicating that the
ridges strongly guided the actin flows in a bidirectional manner. A comparison of
? and ?? shows that cells with a bidirectional actin flow (i.e., high ? values) were
more likely to be guided along the ridge direction (Figure 4.4F).
Although the optical-flow vector field indicates preferred directions of actin
flow, it does not directly yield propagation speeds of actin polymerization waves.
The magnitude of an optical-flow vector incorporates both the shift of actin in space
and the change in actin intensity over time. This submicron-scale (i.e., pixel-scale)
flux of intensity does not translate directly into characteristics of the dynamics
that are notable on the micron scale (i.e., tens of pixels), such as the organization of
waves across ridges that were seen in neutrophils in Figure 4.2F or the speed of wave
propagation. To quantify these micron-scale characteristics, we combined similarly
oriented optical-flow vectors into clusters (Figure 4.5). To ensure that we tracked
robust clusters, we applied additional constraints, such as requiring sufficiently large
intensity changes (see Materials and Methods). The result of this clustering was the
identification of broad regions of actin that moved collectively.
To quantify these micron-scale structures further, we applied peak-finding and
tracking algorithms [131] to follow the locations of maximum alignment of these
optical-flow clusters on the micron scale. Although the optical-flow results shown
in Figure 4.4 followed motion on the pixel scale, by following the peak alignment
of the optical flow, we were able to track larger coordinated clusters of actin. Our
80
(A) (B) (C) Fractional count of flow angles
120? 0.04 60?
150? 0.02 30?
180? 0?
210? 330?
Time 240? 300?
270?
120? 0.04 60?
150? 0.02 30?
180? 0?
210? 330?
240? 300?
270?
(D) Fractional count of flow angles (E) p = 1.583?10-4 p = 0.0040
20
120? 60? 19
9
150? 30? ??: Mean direction of motion
-1 8
?-1 ? :Concentration of motion in ??? % of motion in ?
180? 0? % of motion in ? + 180? 6
% uniformly distributed
210? 330? 4
240? 300?
270?
2
(F) ? vs. ??
120? ? 60? 120? 60? 0
MCF10A HL60
150? 30? 150? 30?
?? Flat Ridges
180? MCF10A 0? 180? HL60 0? MCF10A
HL60
210? 330? 210? 330?
240? 300? 240? 300?
270? 270?
81
HL60 MCF10A
Concentration of motion, ?
Figure 4.4: Using optical flow to measure pixel-scale actin dynamics. (A) Rep-
resentative merged images of an MCF10A cell (top, 100 sec apart) and an HL60
cell (bottom, 8 sec apart). (B) Optical-flow vectors colored by direction relative
to the horizontal ridges. All scale bars are 5 ?m. (C) Cumulative distributions
of the optical-flow vector directions for multiple HL60 and MCF10A cells on flat
and ridged surfaces; all cells were weighted equally in the distribution. (D) The
distribution of angles were fit to a mixture of two von Mises distributions with five
fitting parameters: ?? (primary direction of motion), ? (inversely related to dis-
tribution width), and three coefficients indicating the strength of motion in the ??
and ?? + 180
? directions and the strength of the uniform distribution. (E) In both
MCF10A and HL60 cells, the distribution widths, parameterized by ?, were signifi-
cantly different (p = 0.0001583 and p = 0.0040) on flat versus ridged surfaces. (F)
?? (angular axis) vs. ? (radial axis). Values of ? < 2 (indicated by the dashed line)
were cells with direction distributions that are statistically indistinguishable from a
uniform distribution. We note that ? = 19.6 for one HL60 cell, which is not visible
in this figure.
82
Input Smoothed Difference Image Mask
Gradients
Optical Flow Alignment
Cluster
Reliability Reliability Mask
Figure 4.5: Finding clusters using optical flow. Input time-lapse images (upper left,
scale bar is 5 ?m.) were used to generate a series of masks along two independent
work flows to generate three outputs: a difference-image mask, an alignment ma-
trix, and a reliability mask. To generate the difference image mask, images were
smoothed and subtracted from adjacent frames. The difference-image mask was
calculated by applying a threshold (in this work, the threshold is 0). To generate
the alignment and reliability masks, spatiotemporal intensity gradients were calcu-
lated and used to estimate optical flow and reliability. Alignment was calculated
by taking the dot product between vectors and their local neighborhood (in this
work, the neighborhood was a Gaussian with a standard deviation of 0.63 ?m). The
reliability mask was calculated by applying a threshold (in this work, the threshold
was 10? the median of the reliability distribution). Taken together, the difference
image mask, alignment matrix, and reliability mask were multiplied in an element-
wise fashion to generate the final cluster image. In this work, the cluster image was
used as an input to peak finding and tracking algorithms.
83
tracking is consistent with the actin dynamics seen in kymographs, as shown by the
representative kymographs of MCF10A (Figure 4.6C) and HL60 (Figure 4.6D) cells
overlaid with the tracked location of actin waves. Unlike kymographs, which were
sensitive to motion along a chosen direction, tracks of clustered flow vectors revealed
the micron-scale motion of actin in two dimensions. The benefits of our approach
are illustrated in Figure 4.6C for an MCF10A cell. For the initial frames, the
kymograph indicates a stationary actin structure (Figure 4.6C, left), but when the
actin dynamics are viewed in two dimensions (Figure 4.6C, right), it is evident that
in the early frames this wave is moving perpendicular to the ridges, a motion that
cannot be captured in this one-dimensional kymograph. Thus, the combination of
optical flow, clustering, and tracking allowed us to follow actin waves without being
limited to tracking motion that only occured along a straight line.
The speeds of the tracked actin clusters (Figure 4.6E) were similar to speeds
derived from actin kymographs (Figures 4.6C, 4.6D, and 4.7), despite an approx-
imately order-of-magnitude difference in speed between the two cell types that is
consistent with their distinct in vivo functions and with previously reported cell-
migration speeds [79,132]. For both cell types we found no significant difference (p
= 0.5529 and p = 0.0586) between actin-wave speeds on flat and ridged surfaces
(Figure 4.6E), implying that topography steered actin dynamics but did not alter
wave speeds. On flat surfaces, the directions of the clusters were distributed uni-
formly for MCF10A cells, but showed distinct peaks in multiple directions for HL60
cells (Figure 4.6F). This observation is consistent with the polarized character of
actin in several of the HL60 cells on flat surfaces, corresponding to ? values greater
84
(A) (B) 10 sec 30 sec 50 sec
(C) 8 MCF10A
6
4 4.5 ?m 
1.5 ?m/min
2
3 min
Time
0
0 1 2 3 4 5
Time (min)
(D) HL60
6
4 8.1 ?m/min
2.7 ?m 
2
20 sec
Time
0
10 20 30
(E) p = 0.0586 (F) Fractional count of cluster track angles
14 120? 0.1 60? 120? 0.1 60?
12
10 150? 30? 150? 30?0.05 0.05
8
6 180? 0? 180? 0?
3 p = 0.5529
2 210? 330? 210? 330?
1 240? 300? 240? 300?
0 270? 270?
MCF10A HL60 MCF10A HL60
85
Track velocity (?m/min)
Figure 4.6: Clustering of optical-flow vectors to measure micron-scale dynamics. (A)
Similar flow vectors were grouped into clusters. (B) Clusters contain optical-flow
vectors with a wide array of orientations, resulting in micron-scale structures. All
scale bars are 5 ?m. (C, D) Particle-tracking algorithms were applied to the tracked
clusters. The cluster tracks were consistent with the motion at the leading edge
of the actin waves seen in the kymographs in both HL60 (C, left) and MCF10A
(D, left). Panels to the right of each kymograph show the same track in the 2D
context of the cells; clusters found throughout the cell over time are indicated by
colored regions. (E) The cluster tracks were used to determine speed distributions
of actin waves on the ridges in the MCF10A and HL60 cells, which showed no
significant difference (p = 0.5529 and p = 0.0586) between flat surfaces and ridges.
(F) Cumulative angle distributions of cluster track directions for multiple HL60
and MCF10A cells on flat and ridged surfaces; all cells were weighted equally in
the distribution. (N = 4 MCF10A cells on flat surfaces from three independent
experiments, N = 17 MCF10A cells on ridges from four independent experiments,
N = 9 HL60 cells on flat surfaces from two independent experiments, and N = 16
HL60 cells on ridges from three independent experiments.)
86
than 2 in Figures 4.4E and 4.4F.
4.4 Discussion
Extracellular texture, which is an important component of the 3-D, in vivo
environment, is capable of spatially patterning actin and modulating actin dynam-
ics. Using nanoridge structures in conjunction with optical-flow analysis, we were
able to probe and quantify this intracellular response to extracellular textures in a
systematic manner.
Previous studies of D. discoideum [29, 38], B cells [39], and tumor-associated
fibroblasts [133] showed similarity in actin response to texture, which suggests that
guidance of actin driven by texture (esotaxis) is broadly conserved across cell types.
Controlled textures are thus a useful model microenvironment for the systematic,
reproducible, and quantitative study of intracellular dynamics and force regulation.
Here we demonstrated the analysis of time-lapse images of two cell types that have
distinct physiological function. Neutrophil-like HL60 cells are polarized and highly
motile, and respond to a variety of cues as they fulfill their role in the immune sys-
tem, whereas epithelial MCF10A cells have a nonmotile physiological function. Nev-
ertheless, both cell types showed clear, and quantitatively similar, actin dynamics
in response to surface textures. Consistent with our and other prior results [29,133],
we find that nanoridges lead to persistent streaks of actin that are not seen on flat
surfaces.
Optical flow enables the quantification of both the reproducible streaks of actin
87
(A) MCF10A (B) HL60
0 0
0.52 ?m/min 1.3 ?m/min
5 0.50 ?m/min 5 2.8 ?m/min
0.36 ?m/min 3.0 ?m/min
10 10 4.3 ?m/min
10 20 30 0 10
Time (min) Time (min)
0 0
0.47 ?m/min 2.4 ?m/min
5 0.39 ?m/min 5 4.9 ?m/min
0.39 ?m/min 12 ?m/min
10  10 5.6 ?m/min
10 20 30 0 10
Time (min) Time (min)
(C) MCF10A (D) HL60
0 0
0.42 ?m/min 5.2 ?m/min
5 1.4 ?m/min 5  
10 3.8 ?m/min 10
10 20 30 0 10
Time (min) Time (min)
0
5
10
10 20 30
Time (min)
Figure 4.7: Actin-wave speeds measured by kymographs to validate optical-flow
clustering. Actin-wave speeds were calculated from the kymographs shown in Fig-
ure 4.2 by manually selecting two points on the kymograph and calculating the slope
between the points. The speeds shown here agreed with the distribution of speeds
found using optical-flow-based tracking (Figure 4.6) for a MCF10A on a flat surface
(A), an HL60 cell on a flat surface (B), a MCF10A cell on a ridged surface (C), and
an HL60 cell on a ridged surface (D). The bottom panel of (C) shows a saturated
version of the underlying kymograph to emphasize protrusions.
88
?m ?m ?m ?m
?m ?m ?m
seen on nanoridged surfaces and the more chaotic actin waves seen on flat surfaces.
The latter waves are typically much wider than guided actin waves. On flat surfaces
the waves often change direction, and can also grow wider and split. Such motion
phenotypes are not easily captured with standard techniques such as kymographs.
Optical flow enables us to follow these dynamics, and thus yields insights beyond
those derived from kymograph-based techniques.
We note that optical flow is suitable for comparisons of systems imaged under
different conditions (e.g., 60? vs. 100? objectives), enabling comparisons of cells
with widely varying sizes and migration speeds. The use of varying acquisition
rates (i.e., 2 and 10 sec) in this work was based on the differences in cell migration
speeds of the two cell lines studied. In general, optical flow requires a frame rate
such that changes in fluorescence intensity between frames are small, but larger
than noise. Our use of the Lucas-Kanade optical-flow constraint also requires that
there is a smoothness to the flow field over a certain neighborhood, which is a
length-scale parameter in the optical-flow analysis. This assumption is met by a
wide variety of biological imaging data sets, and thus the use of our optical-flow
approach is not limited to actin dynamics. Optical flow could provide insights into
the motion of other cytoskeletal proteins, such as tubulin, or into the dynamics of
other fluorescent markers that exhibit a spatially and temporally changing intensity
field. Our use of clustering to study larger-scale actin dynamics could similarly be
adapted to other fluorescent markers under the assumption that there are larger-
scale dynamics that move together in similar directions. In this work, we used a
spinning-disk confocal microscope for image acquisition, but our analysis pipeline
89
would also be appropriate for other imaging techniques, such as epifluorescence.
When working with other imaging techniques or fluorescent markers, the size of
the Lucas-Kanade neighborhood and the threshold for vector reproducibility (see
Materials and Methods and Figure 4.5) can be adapted to only include robust results
in further analysis.
Using submicron-scale optical flow and associated micron-scale analysis, we
showed that both MCF10A and HL60 cells had actin flows that were biased along
nanoridges. By clustering similarly oriented optical-flow vectors, we were able to
measure the speed of actin waves within the cells. The measured speeds were compa-
rable to speeds calculated from actin kymographs. Optical-flow analysis allowed us
to determine that the speeds did not differ significantly on flat versus ridged regions.
This finding indicates that nanotopography guides, but does not fundamentally al-
ter the speed of, actin dynamics. We measured actin-wave speeds on the order of
1 ?m/min in the MCF10A cells, consistent with previously reported cell migration
speeds of approximately 0.5 ?m/min [79]. In the HL60 cells we found actin speeds
ranging from approximately 8 to 14 ?m/min, consistent with the 8 ?m/min speed
for cell migration previously reported [132].
Fitting the optical-flow vectors to a bimodal von Mises distribution enabled
quantification of the differences in the directionality of actin flows on flat and ridged
surfaces in both cell lines. The fit parameters also showed differences in actin po-
larization in these two cell lines. HL60 cells occasionally exhibited coordinated and
directed actin flows even on flat surfaces, whereas MCF10A cells on flat surfaces
showed uniform direction distributions of actin waves. On the micron scale, actin-
90
wave tracks from individual HL60 cells on flat surfaces generally polarized and had
a preferred direction, consistent with the behavior of immune cells, which tend to
polarize and migrate in a directed manner. Tracks from MCF10A cells on a flat
surface, on the other hand, were more directionally uniform for each cell. In both
cell types, ridges guided actin waves in a bidirectional manner.
The quantitative actin responses in MCF10A and HL60 cells support a model
in which surface texture provides a symmetry-breaking cue that leads to nucleation
of actin polymerization. Under flat tissue-culture conditions, which lack symmetry-
breaking cues, actin polymerization relies on spontaneous nucleation or edge effects
[134]. Edge effects may lead to morphological features such as the lamellipodia
seen in HL60 cells on flat surfaces in Figure 4.2B. By changing the landscape on
which nucleation occurs, surface texture can lead to actin polymerization in other
locations of the cell, such as the persistent streaks seen in the center of MCF10A
cells on ridges in Figure 4.2A.
There are multiple mechanisms by which cells may respond to local forces
and geometry [135], including sensing mechanisms that can respond to membrane
curvature on a variety of scales [136]. Our finding that nanoridges changed the
direction, rather than the speed, of actin waves suggests that growth of existing
actin filaments away from the surface is the rate-limiting step of actin polymerization
wave propagation. In some cases, sensing mechanisms may rely on the preferential
formation of focal adhesions. This hypothesis is consistent with previous results on
focal adhesion localization and orientation in response to surface texture [126,127].
Although MCF10A cells form strong focal adhesions that may align with texture
91
cues [127], the HL60 cells form weaker adhesions, and the previously studied D.
discoideum cells [29, 38] are known to not form integrin-mediated focal adhesions.
Thus, the dominant mechanism of surface texture response likely depends on both
the cell type and the extracellular environment.
Known surface-sensing mechanisms also include cytoskeletal components such
as septins, which respond to micron-scale curvatures [137], and BAR domains, which
sense nanoscale curvature [138]. Proteins with BAR domains have been linked to
actin assembly [139], as well as to key components of actin-regulating pathways, such
as WAVE and Rac [140,141]. Recent work has suggested that nucleation of new actin
filaments is enhanced by nanotopography. Specifically, curved nanopillars activate
the nucleation-promoting factors Arp2/3 and N-WASP through enhanced binding
of an F-BAR domain containing protein [16]. Additionally, evidence suggests that
topography is capable of shifting multiple gene-expression pathways [142], which
implies that longer-term exposure to topography may mediate additional surface-
sensing pathways. As in vivo microenvironments contain a variety of textures, it is
likely that multiple mechanisms respond to distinct features of extracellular texture,
and future work on the response of actin regulators to controlled topographies such
as those investigated here will help elucidate the contributions of distinct signaling
pathways in topography-guided actin dynamics.
Although the systematic modulation and interrogation of all possible molec-
ular factors of esotaxis is beyond the scope of this chapter, our analysis yields two
remarkable constraints on the molecular sources of esotaxis. First, the speed of
actin waves is not altered by esotaxis. Second, the directional guidance provided
92
by nanotopography is comparable in the two cell types investigated, despite their
disparate functions and migratory phenotypes. Quantitative analysis of esotaxis as
a physical phenotype could yield crucial prognostic disease insights, especially in the
case of cancer, in which changes in the texture of the microenvironment correlate
with disease progression.
4.5 Materials and Methods
4.5.1 Cell culture and imaging
HL60 YFP-actin cells were a gift from Orion Weiner of the University of
California, San Francisco. The cells were cultured in RPMI 1640 medium, Glu-
tamax (Life Technologies) supplemented with 10% heat-inactivated fetal bovine
serum (Gemini Bio). Cells were passaged every 2-3 days and kept between 3?105
and 1?106 cells/mL. For differentiation, cell media was additionally supplemented
with 1.3% dimethyl sulfoxide Hybri-Max (Sigma Aldrich) for 5 days before imaging.
Actin dynamics of HL-60 YFPactin cells were observed by confocal fluorescence and
brightfield time-lapse imaging using a PerkinElmer spinning-disk confocal micro-
scope with a water immersion 60? objective (0.21 ?m/pixel). Images were recorded
every 2 sec. We note that this method of plating resulted in the imaging of some
multicellular clusters of HL60 cells; these clusters were not considered for further
analysis.
Preparation for imaging included a 10 ?g/mL coating of fibronectin on the
substrates. Cells were plated and allowed to settle. After approximately 30 min,
93
N-Formyl-Met-Leu-Phe (fMLF; Sigma Aldrich) was added to 1 ?m. HL-60 cells
were imaged on flat resin and ridged nanotopographies beginning between 10 and
15 sec after fMLF stimulation. All images analyzed in this work were obtained after
fMLF stimulation.
MCF10A LifeAct-EGFP cells were a gift from Carole A. Parent. These cells
were cultured in DMEM/F12 media supplemented with 5% horse serum, 10 ?g/mL
insulin (ThermoFisher Scientific), 10 ng/mL EGF (Peprotech, Rocky Hill, NJ), 0.5
?g/mL hydrocortisone, and 100 ng/mL cholera toxin (both Sigma, St. Louis, MO).
The media were additionally supplemented with 2 ?g/ml puromycin dihydrochlo-
ride (ThermoFisher Scientific) to select for EGFP-positive cells. Before imaging,
cells were plated on a nanoridged surface coated with collagen IV and were allowed
to adhere to the surface overnight. Actin dynamics were studied by confocal flu-
orescence and bright-field, time-lapse imaging using a PerkinElmer spinning-disk
confocal microscope with a 100? objective (0.14 ?m/pixel). Images were recorded
every 10 sec. For both cell types, data were collected using PerkinElmers Volocity
software (version 6.4.0). The spinning-disk confocal microscope was equipped with
a Hamamatsu ImagEM X2 EM-CCD camera (C9100-23B) which recorded 12-bit
images. Cells used in this study tested mycoplasma negative using the MycoAlert
(Lonza) testing system.
94
4.5.2 Surface fabrication
The nanotopographies were designed and fabricated using multiphoton absorp-
tion polymerization (MAP), as described previously [127]. A drop of prepolymer
resin (1:1 wt/wt Tris [2-hydroxy ethyl] isocyanurate triacrylate [SR368]: ethoxylated
(6) trimethylolpropane triacrylate [SR499], both from Sartomer; 3% Lucirin TPO-L
[BASF]) was sandwiched between a coverslip and a plasma-treated microscope slide
that had been functionalized with acrylate groups [127,143,144]. The coverslip was
mounted onto the stage of an inverted microscope (Zeiss Axiovert 135). A beam
of 150-fs pulses centered at 800 nm from a Ti:sapphire oscillator (Coherent Mira
900) was directed into the microscope and through a highnumerical aperture ob-
jective (Zeiss alpha-Plan Fluar 100; NA 1.45). The stage motion and shutter were
controlled using a program written in LabVIEW (National Instruments). Once the
pattern was fabricated, the sample was developed in ethanol and baked at 110?C
for 1 h.
A replica-molding approach was then used to mold the chemically functional-
ized pattern [127]. This step included the initial casting of a hard-poly dimethyl-
siloxane (h-PDMS) layer (1000 rpm, 40 sec) for better resolution of nanoscale fea-
tures of the topographical pattern. This layer was allowed to sit on the pattern
at room temperature for 2 hrs and was then baked at 60?C for an additional 1 hr.
Finally, Sylgard 184 was mixed (10:1 elastomer base:curing agent) and poured onto
the initial h-PDMS layer. The PDMS was cured at 60degC for 1 hr 10 min.
The MAP-fabricated structure was then reproduced through a soft litho-
95
graphic technique. A drop of the aforementioned resin was sandwiched between
the PDMS mold and an acrylate functionalized coverslip and was then exposed to
UV radiation from a lamp for a desired amount of time. After the resin cured, the
coverslip was peeled off the mold. This process was repeated many times to produce
enough replicas to perform the necessary experiments. The replicas were soaked in
ethanol for at least 4 h and subsequently baked/dried in an oven at 110?C for 1
hour. Samples used to study MCF10A cells were also soaked in UltraPure water
(ThermoFisher) for approximately 12 hours.
4.5.3 Kymographs
Kymographs were created in MATLAB by manually selecting a rectangular
region in an actin image. Fluorescence intensities inside the region were averaged
across the short axis of the region; this process was repeated for each image in
the time-lapse sequence, and the resulting intensity data were combined into the
kymographs shown in Figures 4.2 and 4.7.
4.5.4 Optical flow
The Lucas-Kanade optical-flow method [89] was used to capture the direc-
tion and strength of intensity flow of fluorescent actin and to produce vector fields
indicating actin motion. The optical-flow vector field of an image series is the
field of apparent translation in the image plane, as is shown schematically in Fig-
ure 4.3. Calculating the optical flow for two adjacent two-dimensional images in
96
an image series requires solving for the unknowns ?x and ?y in Equation 2.2,
which yields the optical-flow vectors ~v in Equation 2.4. The Lucas-Kanade method
uses a least-squares regression approach to solve for the best optical-flow vector
on a pixel-by-pixel basis under the assumption that all pixels within a neighbor-
hood move in a similar direction [89]. If solving for the optical-flow vector of some
point p with coordinate (xp, yp, ?), the master optical flow equation requires that
the optical flow vector of point p and all points in the neighborhood about p (points
1, 2, . . . , p, . . . , N) follow the underdetermined relation given in Equation 2.4.
Under the Lucas-Kanade assumption, the vector for point p is assigned to
all points in the neighborhood given in Equation 2.6. The least-squares solu-
tion to equations of the form in Equation 2.6, namely A~x = ~b, are generally
~x = (ATA)?1AT~b when ATA is invertible (i.e., when (ATA)?1 is nonsingular).
Furthermore, we implement a scheme using a Gaussian weight matrix centered at
point p to ensure that pixels near p have more influence over the result. The
? ?
general equation then takes the form wA~x = w~b and has the solution ~x =
?
T T
? ? T?
(A w wA)?1AT w w~b = (ATwA)?1ATw~b.
Optical-flow reliability is defined as the smallest eigenvalue of the ATwA ma-
trix [145, 146], and was used to remove flow vectors that were created by noise or
an ill-defined least-squares calculation. The threshold used can be adapted to best
suit the experimental data and scientific questions of interest by only keeping the
most reliable vectors while measuring the motion of more regions of the cell. The
optical-flow weight matrix for MCF10A cells was a 27 ? 27 pixel Gaussian with a
? of 4.5 pixels (0.63 ?m). The optical-flow weight matrix for HL60 cells was 19 ?
97
19 pixel Gaussian with a ? of 3 pixels (0.63 ?m). With other imaging modalities,
magnifications, or fluorescent markers, it may be appropriate to change the size of
this weight matrix based on the size of features of interest and noise in the image.
4.5.5 von Mises model of flow distribution
Optical-flow distributions were modeled with a modified bimodal von Mises
distribution (von Mises distributions are a continuous and differentiable analogue of
normal distributions on a circle with similar statistical properties). The model was
defined as
1
f(?|??, ?) = p1VM(?|??, ?) + p2VM(? + ?|??, ?) + (1? p1 ? p2) (4.1)
2?
where VM(?|??, ?) is the von Mises distribution
e? cos(????)
VM(?|??, ?) = (4.2)
2?I0(?)
and I0(?) is the modified Bessel function of the first kind. The maximum
likelihood estimates of the parameter ? were used for statistical analyses.
98
4.5.6 Cluster-tracking analysis
Regions of actin fluorescence were clustered using the direction of optical-
flow vectors together with an optical-flow reliability threshold and by requiring that
actin intensity change over time (see Figure 4.5 for a visualization of this work-
flow). The dot products between optical-flow vectors around a point p (i.e., vec-
tors ~v1, ~v2, . . . , ~vp?1, ~vp+1, . . . , ~vN) were calculated and accumulated using a Gaussian
weighting scheme to a single scalar alignment metric. The alignment metric was de-
fined as
?N
ap = wi(~vp ? ~vi) (4.3)
i=1
where w is a renormalized N ?N centered Gaussian matrix with a center manually
set to 0. This calculation was carried out for each pixel. To require that the actin
intensity change over time, a mask of the thresholded difference image between
subsequent frames was calculated. For every pair of adjacent frames, It and It+?t,
the resulting mask took value 1 where It+?t > It and 0 otherwise. For our analysis,
?t = 30 sec for MCF10A and 6 sec for HL60. To calculate the final clustered regions,
the alignment metric ap, optical-flow reliability ?p, and difference-image mask were
multiplied in an element-wise manner to create a final cluster image. The cluster
image was inputted into a peak-finding algorithm to locate peaks in the resulting
intensity profile, and the Crocker-Grier particle-tracking algorithm [131] was used
99
to track coordinates of the resulting peaks over time.
The clustering weight matrix for MCF10A was a 27 ? 27 pixel Gaussian with
a SD of 4.5 pixels (0.63 ?m). The clustering weight matrix for HL60 cells was 19
? 19 pixel Gaussian with a SD of 3 pixels (0.63 ?m). The diameter of the peaks
used during peak finding was 15 pixels (2.1 ?m) for MCF10A cells and 10 pixels
(2.1 ?m) for HL60 cells. The maximum displacement used during tracking was 11.5
pixels (1.54 ?m) for MCF10A cells and 7 pixels (1.47 ?m) for HL60 cells. Tracks
measured in the movies of MCF10A cells were considered only if they were tracked
for more than three frames (30 sec) and tracks measured in movies of HL60 cells
were only considered if they were tracked for more than three frames (6 sec).
4.5.7 Statistical methods
Measurements of for MCF10A cells (Figure 4.4) and actin-wave speeds for
both cell types (Figure 4.6) were compared on flat versus nanoridged surfaces using
two-sample t-tests with unequal variances. A two-tailed t-distribution was used to
calculate the reported p-values. As the measurements ? of for HL60 cells violated
the normality assumption for a t-test, we used a nonparametric Wilcoxon rank-sum
test to compare these values.
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Chapter 5: Systematic Analysis and Simulations of
Topography-Induced Guidance of Actin Waves
This chapter was adapted from a work in preparation by Campanello?,
Guven?, Driscoll, Sun, Carlsson, Fourkas, and Losert. Can Guven and
Xiaoyu Sun performed the experiments, Can Guven and Anders Carlsson
performed the simulations, Leonard Campanello designed and performed
the optical-flow analysis, and Leonard Campanello and Can Guven wrote
the paper.
5.1 Overview
The cytoskeleton of a living cell is one of the most versatile examples of active
matter in nature. Through polymerization and depolymerization, the continuous
remodeling of the cytoskeleton drives a multitude of biological processes, such as
cell division, migration, and the development of multicellular organisms. Although
a broad range of models aim to capture detailed biomechanical properties of the cy-
toskeleton, and especially the actin component, the experimental data and computa-
tional techniques required to perform detailed quantitative benchmarking are often
lacking. Here, we directly link experimental observations of cytoskeletal remodeling
101
in Dictyostelium discoideum to simulations that include biophysically realistic dy-
namics of actin filaments. Using an optical-flow-based analysis, we perform detailed
measurements on simulated and experimentally observed actin dynamics. To pro-
vide cells with biologically realistic extracellular environments, we employ uniformly
spaced nanotopographic ridges similar in size to collagen fibers. In both experiments
and simulations, the nanoridges generate guided waves of actin polymerization with
reproducible direction, speed, and shape, allowing for deep, quantitative compar-
isons. Analysis of the simulations reveals that a model assuming redistribution of
a fixed pool of nucleation promoting factors provides better agreement with exper-
iments than does a model that posits local enhancement of nucleation. By vary-
ing the spacing between the ridged nanotopographic features, we demonstrate that
maximum guidance by ridges occurs on spacings that are ?1 to 2 microns apart
and diminishes guidance for ridges greater than 3 microns apart. Neither the ridge
spacing nor the concentration of available actin monomers alters the speed of actin
waves, but these parameters do alter the length of actin filaments. Together, ex-
periments and simulations of topography-induced guidance of actin waves provide
a robust framework for understanding the mechanisms of texture sensing in the
natural world.
5.2 Background
Cytoskeletal rearrangements underlie many critical cell behaviors. Through
controlled polymerization and depolymerization, coordinated force generation of the
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cytoskeleton results in polarization and migration [3], immune-cell activation [27,40],
and crucial physiological functions such as tissue development, immune response,
and wound healing [147?149].
Topographic features in the extracellular environment influence cytoskeletal
dynamics and cell behavior. Collagen-fiber environments in the extracellular matrix
(ECM), which are topographically complex [150], play an important role in functions
such as differentiation [23], immune response [2], and cancer progression (Chapter 6).
In vitro topographical features that are similar in size to typical ECM structures
can also modulate morphology [28, 151] and migration [29]. Furthermore, ridge
patterns with broken symmetry along the ridge axis, e.g., sawteeth, induce cell-type-
dependent unidirectional guidance in epithelial cells [24], amoeboid Dictyostelium
discoideum cells (which feature pseudopod-driven migration), and neutrophil-like
HL60 cells (which feature lamellipod-driven migration) [38]. Despite the influence
of physical topography on cytoskeletal dynamics and cell behaviors, the coupling
between extracellular features and cytoskeletal signaling is poorly understood.
The primary cytoskeletal component responsible for remodeling and force gen-
eration is actin. In concert with other signaling proteins, such as PIP3 and PI3K, the
actin cytoskeleton operates as an excitable system that can rapidly switch among
a variety of dynamic states [9, 152, 153], such as propagating waves and oscilla-
tory bursts [9, 71]. Through continuous polymerization at the leading edge and de-
polymerization at the trailing edge, excitable actin rearrangements are manifested
in wave-like propagations that push on the cell membrane and other cytoskeletal
structures to generate forces [154,155].
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Actin excitability enables cells to respond to extracellular stimuli [9,152], and
has been implicated in the development of subcellular protrusions [156, 157] and in
whole-cell behavior such as chemotaxis and electrotaxis [158?160]. However, the
mechanisms by which actin excitability on nanotopography can guide subcellular
and whole-cell behaviors are not well understood. For example, we have previously
shown that actin flux and cell migration on nanotopographic sawteeth can change
directions based on sawtooth pitch [38] and cell type [24,38]. Although the activity
of actin nucleation-promoting factors (NPFs) contribute to topography sensing [15,
16], the connection between subcellular dynamics and whole-cell behavior is poorly
understood.
In Chapter 4, I introduced an optical-flow-based approach to quantify actin
flux. Using this method, we were able to identify quantitative similaritities of actin
wave guidance by nanotopography between neutrophil-like cells (HL60) and epithe-
lial cells (MCF10A), despite wave speeds and imaging conditions varying signifi-
cantly between cell types. In this chapter, I employ this optical-flow analysis for a
quantitative comparison of actin waves from experiments of D. discoideum to those
in a dendritic-growth model of filament assembly and disassembly with realistic
biochemical rates, NPFs, and filament-severing dynamics [41].
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5.3 Results
5.3.1 Optical-flow analysis of actin waves revealed that ridges pref-
erentially nucleate and guide actin dynamics.
Using limE-?coil-GFP D. discoideum, which overexpress the fluorescently-
labeled actin-binding reconstruct limE-?coil [161, 162], we investigated the rela-
tionship between actin polymerization and nanotopography via time-lapse imaging
on surfaces with evenly spaced, parallel ridges of different spacings (Figure 5.1).
The characteristic length scale of actin polymerization waves in D. discoideum is
between 1 and 2 ?m [29,154]. Thus, we investigated actin-wave dynamics on ridges
with spacings ranging from 0.8 ?m to 5 ?m (Figure 5.1A?B). Dark regions in the
bright-field images are ridges with a fixed width (200?300 nm) and height (0.4?1
?m), and the bright regions are the grooves between adjacent ridges. Cells were in-
cubated with 2 mM caffeine to block the intracellular activation of cAMP synthesis
and thus prohibit intercellular signal relay [163].
Topography-induced guidance of actin waves has been shown to bias the flow
of new actin polymerization (Chapter 4). Similarly, in both representative time-
lapse images from Figure 5.1A?B, the direction of actin polymerization appears to
be biased in the ridge direction, i.e., from blue to yellow, and the nucleation of
new actin polymerization appears to be enhanced at the ridges. Furthermore, as
shown in Figure 5.1A, we observed continuous nucleation of actin waves on narrowly
spaced ridges. On the other hand, as the spacing between ridges increased, as in
105
Figure 5.1: Actin-wave nucleation is enhanced at ridges and actin-wave dynamics are
more complex with increased ridge spacing. Time-lapse montage of D. discoideum
with fluorescently labeled actin-binding protein limE-?coil on (A) 1.5-?m-spaced
ridges and (B) 5 ?m spaced ridges. The polymerization of new actin waves is en-
hanced near ridges. (C) Three snapshots 10 sec apart on 1.5-?m-spaced ridges with
optical-flow vector fields superimposed on images; the actin polymerization dynam-
ics are aligned with the ridges. (D) Normalized optical-flow-direction distributions
corresponding to each frame in (C). The distributions show that actin polymeriza-
tion dynamics are polarized and strongly guided by ridges. (E) Three snapshots
8 sec apart on 5 ?m-spaced ridges with optical-flow vector fields superimposed on
images; the actin polymerization dynamics are biased in the ridge direction but are
also complex and chaotic. (F) Normalized optical-flow-direction corresponding to
each frame in (E). The distributions show that actin polymerization dynamics are
more weakly guided by the ridges and are more variable than those in (D). Ridge
directions are indicated by dashed lines and arrows. All scale bars are 5 ?m.
106
Figure 5.1B, the number of polymerization events decreased.
To quantify these dynamics, we applied a modified version of the Lucas-Kanade
optical-flow algorithm [87,89], which has been shown to perform better than compet-
ing flow-field-analysis techniques on fluorescent images [84]. Optical flow provides
pixel-scale information about the flow of intensity in a time series of images, and
we have previously shown that the distribution of optical-flow directions can be
used to quantify the guidance of actin-wave dynamics by ridges (Chapter 4). On
the narrowly spaced ridges, the direction of actin flow was more polarized by ridges
(Figure 5.1C), which resulted in flow-direction distributions having large amplitudes
and narrow peaks in the ridge direction (Figure 5.1D). On the widely spaced ridges,
actin dynamics were slightly biased by the ridges, but were also more chaotic and
variable than on the narrowly spaced ridges (Figure 5.1E). Consequently, the distri-
butions of optical-flow-direction distributions on widely spaced ridges were broad,
with a weak guidance in the ridge direction (Figure 5.1F).
Although the dominant behavior of actin waves was guidance along ridges,
freely nucleated waves (i.e., those that did not nucleate at the site of ridges) exhib-
ited a wider range of behaviors. On the 1.5-?m-spaced ridges, where nucleation of
waves mostly happened along the ridges (Figure 5.1A), the optical-flow direction dis-
tributions showed that actin dynamics were strongly guided by the nanotopography
(Figure 5.1D). On 5-?m-spaced ridges, where nucleation occurred throughout the
space between ridges (Figure 5.1B), the actin dynamics were less guided by the nan-
otopography and exhibited a wider array of dynamic behavior (Figure 5.1F). Thus,
actin waves that did not nucleate on the high-curvature regions of 5-?m-spaced
107
ridges displayed more complex dynamics.
5.3.2 Modeling optical flow of actin-wave dynamics can quantify the
influence of ridges.
The shape of the optical-flow-direction distributions indicates the strength
of actin-wave guidance caused by differently spaced ridges. We employed a sta-
tistical model of bidirectional guidance to parameterize the optical-flow-direction
distributions and quantify the strength of actin-wave guidance induced by ridges
(Figure 5.2). The actin dynamics in D. Discoideum on ridges with spacings of 0.8
(Figure 5.2A) and 1.5 ?m (Figure 5.2B) were strongly guided along the ridges, as
indicated by the cumulative distributions of optical-flow directions. On the other
hand, the actin-wave dynamics in D. Discoideum on ridges with spacings of 3 ?m
(Figure 5.2C) and 5 ?m (Figure 5.2D) were guided more weakly by the ridges.
Ridge-induced guidance can be quantified using a modified bimodal-von-Mises
model with constant offset (Chapter 4). Model fitting of the direction distributions
yielded five fit parameters: the mean direction, ?; the concentration of motion, ?;
and weights p1, p2, and p3, which are the proportions of motion that are in the ?
direction, in the ?+? direction, and uniformly distributed, respectively (Figure 5.2E,
Methods, Chapter 4). The representative fits in Figure 5.2E accurately captured the
nature of the corresponding distributions in Figure 5.2A?D. Guided actin dynamics
in D. Discoideum on ridge spacings of 0.8 and 1.5 ?m were highly concentrated in
the ridge direction, with an average ? between 10 and 15 (Figure 5.2F). On the other
108
Figure 5.2: Actin-wave dynamics were more strongly guided by narrowly spaced
ridges. (A) Representative snapshot of D. discoideum on 0.8-?m spaced ridges
and the actin-wave-direction distribution measured by optical flow for the whole
movie. The same procedure was performed for D. discoideum on (B) 1.5-?m-spaced
ridges, (C) 3-?m-spaced ridges, and (D) 5-?m-spaced ridges. Stronger guidance
was observed on narrower ridge spacings. (E) Cumulative actin-wave-direction dis-
tributions fit to a five-parameter modified-bimodal-von-Mises model. The model
captured the nature of the distributions. (F) Concentration of motion (?) in the
modified bimodal-von-Mises model for each cell. Actin on 0.8- and 1.5-?m-spaced
ridges had significantly larger ? than 3- and 5-?m-spaced ridges. ? < 2 (red dashed
line) is not statistically distinguishable from a uniform distribution. (G) Propor-
tion of actin guided by ridges (p1 + p2). p1 + p2 on 0.8- and 1.5-?m-spaced ridges
that were guided by the ridges were significantly larger than the proportions on 3-
and 5-?m-spaced ridges. Ridge directions are indicated by dashed lines and arrows.
Optical-flow-vector directions relative to the ridge direction are indicated by color:
light yellow is parallel to ridges and dark red is perpendicular to ridges. All error
bars are the 95% confidence interval and all scale bars are 5 ?m.
109
hand, guided actin dynamics on ridge spacings of 3 and 5 ?m were weakly guided
in the ridge direction with an average ? between 3 and 5. Note that fits for which
? < 2 are statistically indistinguishable from a uniform distribution (indicated by
the dashed red line).
Whereas ? indicated how concentrated the guided actin dynamics were, the
sum of the weights, p1+p2, indicated the proportion of dynamics that were subjected
to the guidance. On ridges with spacings of 0.8 and 1.5 ?m, roughly 80% of the
actin dynamics were guided by ridges (Figure 5.2G). In contrast, roughly 50% of
the actin dynamics on 3-?m-spaced ridges were guided, and about 35% of the actin
dynamics on 5-?m-spaced ridges were guided (Figure 5.2G). Taken together, the two
complementary parameters ? and p1 + p2 provide a quantitative means for making
comparisons between actin dynamics on narrowly and widely spaced ridges; actin
dynamics on narrowly spaced ridges were strongly guided with comparatively large
? and p1 + p2, whereas actin dynamics on widely spaced ridges are weakly guided
with comparatively small ? and p1 + p2.
5.3.3 Greater actin-nucleation rate in a ridge pattern recapitulated
topography-guidance behavior.
To investigate the nature of interactions between actin waves and ridges, we
employed a dendritic-growth simulation of actin-filament assembly and disassembly
with realistic biochemical rates, NPFs, and actin-filament-severing dynamics [41].
Nanotopography modulates actin dynamics via the enhancement of NPFs on regions
110
of high curvature [15,16]. Thus, to capture the observed variation in actin-filament
nucleation due to nanotopography, in the simulations we increased the activity of
NPFs along periodic stripes that were the same widths as the ridges from Figures
5.1 and 5.2. This approach attempted to mimic the effect of ridges on actin poly-
merization dynamics without requiring the explicit inclusion of nanotopography in
the simulations.
We employed the optical-flow analysis introduced in Figure 5.2 to measure the
strength of pixel-scale guidance of actin waves in the simulations (Figure 5.3). The
biomechanical simulations included individual actin monomers, filaments, branch-
ing, capping, and contacts between actin and the cell membrane. Thus, we employed
a coarse-graining technique that converted z-projections of the simulated volume to
what would be expected if the images had been acquired on a microscope with
optical resolution of ?250 nm [41] (Figure 5.3A).
Actin waves in the simulations on ridges with spacings of 1.5, 3, and 5 ?m
all had clear, leading-edge-driven waves that were identified by optical flow (Fig-
ure 5.3B). Notably, the wave fronts in Figure 5.3B were uniformly bright between
the ridges, in contrast with wave fronts in Dicty shown in Figure 5.2A?D that were
sparse. Although high-curvature textures induce increased NPF activity [15, 16],
it is unclear whether the increase of NPF activity on ridges leads to a simultane-
ous decrease in NPF activity between ridges. Thus, to probe the mechanism behind
topography-induced guidance, we performed two complementary sets of simulations,
which we labeled as unconstrained (Figure 5.3C) and constrained (Figure 5.3D).
Unconstrained simulations had an increased NPF activity along the high-curvature
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Figure 5.3: Patterning of simulated-nucleation-promoting-factors captures aspects of
experimental topography-guidance phenotypes. (A) Actin simulations were coarse-
grained to generate images akin to those expected from a microscope with ?250
nm optical resolution. (B) Representative snapshots of experimental and simulated
actin waves on ridges with spacings of 1.5, 3, and 5 ?m. Optical-flow vectors are
colored by direction: yellow is aligned with ridges and red is perpendicular. Two
types of simulation conditions were used: unconstrained (C), which used upregulated
NPF activity on ridges, and constrained (D), which used globally constrained NPF
activity, (i.e., upregulation on ridges and downregulation between ridges) to mimic
a redistribution of NPFs to ridges. Optical-flow distributions were fit to a bimodal-
von-Mises model to quantify guidance strength. (C) Parameters from unconstrained
simulations on ridges with spacings of 1.5, 3, and 5 ?m. Weak-to-moderate guidance
was observed. (D) Parameters from the constrained simulations on ridges with
spacings of 1.5, 3, and 5 ?m. The guidance in these simulations was stronger than
that in the unconstrained simulations. Error bars are the 95% confidence interval
and scale bars are 1 ?m.
112
parts of the simulated nanoridges, which resulted in an overall global increase in
NPF activity through the simulation space and thus an increase in overall actin-
polymerization activity. To balance the increased NPF activity on ridges, NPF
activity between adjacent ridges in the constrained simulations was reduced such
that the total NPF activity remained constant. In practice, these two cases mimic
two possible mechanisms for nanotopography-induced increases in polymerization
activity. Unconstrained simulations mimic an upregulation of NPF activity due to
curvature, whereas constrained simulations mimic a redistribution of NPFs, which
would lead to having fewer NPFs between high-curvature regions while leaving the
total NPF activity unchanged.
The fitting procedure used on the data in Figure 5.2 was applied to the
optical-flow-direction distributions from the unconstrained and constrained simu-
lations (Figure 5.3C and D, respectively). In the unconstrained simulations, guided
actin dynamics on ridges with spacings of 1.5 and 3 ?m exhibited weak guidance,
whereas 4 out of 6 simulations on a 3 ?m spacing and the simulation on a 5 ?m
spacing exhibited no guidance (Figure 5.3C). Around 30% of the actin dynamics
on 1.5-?m-spaced ridges were weakly biased in the ridge direction, with ? = 3.
About 15% of the actin dynamics on 3 ?m spaced ridges were moderately guided,
with ? = 6. In contrast, the constrained simulations exhibited a greater degree of
ridge-induced bias in guided dynamics (Figure 5.3D). About 25% of the simulated
actin on the 1.5 ?m spacing was guided with ? = 4, about 40% of the dynamics
on 3 ?m spacing was guided, with ? = 3, and about 10% of the dynamics on 5 ?m
spacing was guided, with ? = 6. Note that a fit with ? < 2 is statistically indistin-
113
guishable from a uniform distribution. Thus, one of the simulations for each of the
ridge spacings exhibited no bias in the ridge directions. In sum, the actin dynamics
in the simulations were not as strongly guided as those in the experimental data,
but there were some guided dynamics in simulations on each of the ridge spacings.
Constrained simulations exhibited more biologically realistic guidance phenotypes.
5.3.4 Simulated and experimental actin-wave speeds were similar,
and were unaffected by varying ridge spacing.
For further quantification of the similarities between experimental observations
and simulations, we measured the speed of the actin waves in both the experimental
and simulated images (Figure 5.4). Representative kymographs of actin waves in
D. Discoideum on ridges with 0.8 ?m and 3 ?m spacings, indicated wave speeds
on the order of 10 to 20 ?m/min (Figure 5.4A). The polymerizing edge of the
actin wave is variable and chaotic, which is especially clear on the 3 ?m spacing
where there are various protrusions that grow independently from the leading edge.
Furthermore, depolymerization on the back end of the actin waves on both 0.8 and
3 ?m spacings was slow, and thus remains bright in the kymograph. Representative
kymographs of simulated actin waves on ridges with 0.8 and 3 ?m spacings indicate
wave speeds on the order of 5 to 10 ?m/min (Figure 5.4B). The leading edge of
simulated waves appeared to be coherent and move uniformly as compared to that
in the experimental data. Furthermore, the depolymerizing (trailing) edge of the
actin wave was well constructed and moved roughly as fast as the leading edge.
114
115
Figure 5.4: Experimental actin-wave speeds were unaffected by varying ridge spac-
ings, which was recapitulated in simulations. (A) Representative time-lapses and
kymographs of actin in D. discoideum on 0.8- and 3-?m-spaced ridges. The lead-
ing edge of actin waves was variable and chaotic but moved somewhat uniformly
between ridges over time. Depolymerization at the back of the wave was slow and
remained bright. (B) Representative time-lapses and kymographs of simulated actin
on 0.8- and 3-?m-spaced ridges. The leading edge of simulated waves were uniform,
sharply pointed, and moved in a spatially coordinated manner. Depolymerization
on the back end of the wave was rapid with occasional afterburns that manifested
in bright puncta behind the depolymerized edge. (C) The speeds of the actin-wave
fronts according to optical-flow-based clustering and tracking. There was no statis-
tically significant difference between actin-wave speeds on different ridge spacings
(p = 0.9186, calculated using one-way ANOVA). (D) The speeds of the simulated-
actin-wave fronts according to optical-flow-based clustering and tracking. There
was no statistically significant difference between actin-wave speeds on different
ridge spacings in the constrained simulations (left, p = 0.1734, calculated using
one-way ANOVA), unconstrained simulations (right, p = 0.8461, calculated using
one-way ANOVA), or between the two groups (p = 0.5971, calculated using two-way
ANOVA).
116
To analyze all actin waves systematically in both the experimental and simu-
lated images, we used optical-flow-based clustering and tracking (Chapter 4). Actin-
wave speeds in D. discoideum on different ridge spacings were all centered around 8
to 9 ?m/min, and there was no statistically significant difference between speeds on
any spacings (p = 0.9186, calculated using one-way ANOVA) (Figure 5.4C). Simi-
larly, simulated-actin-wave speeds on 1.5, 3, and 5 ?m spacings were centered around
7 ?m/min in both unconstrained (Figure 5.4D Left, p = 0.1734, calculated using
one-way ANOVA) and constrained simulations (Figure 5.4D Right, p = 0.8461, cal-
culated using one-way ANOVA). Furthermore, there was no difference in actin-wave
speeds between constrained and unconstrained groups (p = 0.5871, calculated using
two-way ANOVA). Finally, there was no significant difference in speeds between
experimental data and unconstrained simulations or between the experimental data
and constrained simulations. In sum, experimental and simulated actin-waves in
all datasets moved in qualitatively different ways (i.e., polymerized edges were ei-
ther chaotic or uniform, and depolymerized edges were either nonexistent or well
formed), but at similar speeds.
5.3.5 Simulations of the actin cytoskeleton enable new quantitative
measures of, and biomechanical insights into, actin-polymerization
dynamics.
Latrunculin A is a drug that influences actin dynamics via the sequestration
of cytosolic actin monomers. Latrunculin-A treatments have been shown to modify
117
polymerization-depolymerization dynamics [164] and impede or inhibit cell functions
such as B-cell signaling [39]. Here, we use optical-flow-based analyses to perform a
quantitative comparison of Latrunculin-A-treated and wild-type (WT) Dicty on 1.5
?m spaced ridges, and also to compare these experiments against simulations data of
varying actin monomer concentrations (Figure 5.5). Topography-induced guidance
was observed to be weaker in cells treated with Latrunculin A than in WT cells
(Figure 5.5A). In Latrunculin-A-treated cells, optical-flow-direction distributions
had an average ? on the order of 8 and p1 + p2 on the order of 0.7. Both ? and
p1 + p2 were significantly smaller than those measured in WT Dicty on 1.5-?m-
spaced ridges (p ? 1?10?3 in both cases). Furthermore, optical-flow-cluster tracking
indicated that Latrunculin A caused a significant decrease in actin-wave speeds in
treated cells (Figure 5.5C, p = 3.45? 10?4).
To compare actin in Latrunculin-A-treated Dicty to simulated actin, we tested
several maximum-free-actin concentrations in the simulations. Given that stronger
guidance phenotypes were observed in constrained simulations (Figure 5.3), we used
constrained conditions in further comparisons between simulations and experiments.
There was no statistically significant difference between the ? and p1 + p2 values
across simulated actin waves with different actin concentrations.
5.4 Discussion
In this work, we explored the dynamic behavior of the actin cytoskeleton in
D. discoideum and in simulations on differently spaced nanoridges. We employed
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Figure 5.5: Latrunculin-treated Dicty was less guided and slower that WT Dicty
on nanoridges. D. discoideum was treated with 1.25 ?M Latrunculin A and im-
aged on 1.5-?m-spaced ridges; Latrunculin A is known to bind to actin monomers,
and thus inhibits the polymerization of new actin filaments. (A) Systematic anal-
ysis of the optical-flow-direction distributions in Latrunculin-A-treated Dicty from
four experiments on two separate days. Average ? on each day was on the or-
der of 8 and p1 + p2 was on the order of 0.7. Both measures are less than those
observed in WT Dicty on ridges with the same spacing. To try to recapitulate
actin-monomer sequestration in simulations, the maximum concentration of free
actin was systematically varied. (B) The speeds of the actin-wave fronts according
to optical-flow-based clustering and tracking. Red is all WT experimental data on
all ridge spacings, green is Latrunculin-A-treated Dicty, and black, teal, and pink
are simulated actin at variable monomer concentrations. There was a statistically
significant difference between actin-wave speeds in WT and Latrunculin-A-treated
cells (p = 3.45 ? 10?4), whereas no significant difference was found between sim-
ulated actin-wave speeds and Latrunculin-A-treated cells (p = 0.7970, calculated
using one-way ANOVA). (C) Average actin-filament length in monomers measured
from simulated actin at 0.35, 0.4, and 0.45 ?M concentrations; this measurement is
only available in the simulations. As the concentration of available actin monomers
was increased the average filament length increased. Notably, the average filament
length was unaffected by the ridge spacing. Error bars in (B) and (C) are the 95%
confidence interval and in (D) are the standard error of the mean.
119
optical-flow-based modeling, clustering, and tracking to perform robust and system-
atic comparisons between experiments and simulations. We were able to quantify
actin-wave dynamics in experiments and simulations despite apparent qualitative
differences, particularly regarding the chaotic and variable leading edge in experi-
ments and lack of a trailing edge in the simulations.
We parameterized optical-flow-direction distributions utilizing a bimodal-von-
Mises model. The influence of nanoridges on actin dynamics can be assessed using
two key parameters from these fits: the concentration of motion, ?, and the guid-
ance proportion, p1 + p2. We found that nanoridges with spacings of 0.8 and 1.5
?m strongly biased the direction of actin polymerization, whereas widely-spaced
nanoridges with spacings of 3 and 5 ?m weakly biased the direction of actin poly-
merization, consistent with prior studies on whole-cell behaviors during guided cell
migration [29].
To elucidate further the biomechanical interactions between cytoskeletal dy-
namics and nanotopography, we employed dendritic-growth simulations of filament
assembly and disassembly with realistic biochemical rates, nucleation-promoting
factors (NPFs), and filament-severing dynamics [41]. To simulate the effect of nan-
otopographic ridges on cytoskeletal dynamics, we contrasted two conditions. In
unconstrained conditions, we upregulated NPF activity on ridges consistent with
previous experimental data [15, 16]. The enhanced activation of NPFs in a ridge
pattern could be altering signaling thresholds of biomechanical excitability [9, 71],
which has been shown to induce rapid changes in cytoskeletal dynamics and overall
cell behavior [3]. In constrained conditions, we both upregulated NPF activity on
120
ridges and downregulated NPF activity between ridges, which mimicked a redistri-
bution of a fixed pool of NPFs preferentially to ridge locations. Although these
simulation conditions don?t specifically allow for the direct inference of the inter-
action between nucleation and nanotopography, they provide insight into the core
mechanisms governing texture-induced guidance of actin.
Using optical flow and the bimodal-von-Mises model, we showed that actin-
wave guidance was achieved in both unconstrained and constrained conditions.
Guidance in the constrained conditions was stronger than the unconstrained con-
ditions, but in both types of simulations the actin waves were less guided than
in experiments. On the other hand, the speed of actin waves in simulations was
comparable to those measured in the experiments. This observation is particularly
noteworthy because (1) the simulations were adopted without substantial changes
to the parameters from prior studies and (2) although speeds are determined by
micron-scale motion, the biochemical rates and components in the simulations are
on the order of several nanometers. In effect, because small errors in the biochem-
istry lead to substantive changes in micron-scale motion, quantitative agreement of
actin-wave speed is particularly profound.
As a further test of the agreement between experiments and simulations, we
compared responses to a chemical perturbation of the actin cytoskeleton. A de-
crease in the concentration of actin monomers?the fuel for polymerization?can be
directly simulated and also experimentally achieved through treatment of cells with
Latrunculin A. The simulations allowed for extraction of information that cannot
be obtained from the experiments. In particular, we found that the average length
121
of actin filaments decreased roughly linearly with a decrease in actin-monomer con-
centration. In both experiments and simulations, we did not see a large decrease in
the speed of actin waves, although a small decrease was noted in experiments.
In addition to this small discrepancy between simulations and experiments,
simulations systematically exhibited less guidance than experiments and the simu-
lated actin waves were typically shorter than the experimental waves (i.e., depoly-
merizing after a delay time and yielding a polymerized region of constant size).
On the other hand, in experiments the actin waves exhibited a long tail after the
leading polymerization edge. These observations suggest that that the ridges may
stabilize the actin network and inhibit depolymerization. Indeed, prior work has
demonstrated that extracellular structures can modulate micron-scale actin struc-
tures [125,165], although the effect on filament-scale actin dynamics is unclear. On
the other hand, our observations could also indicate that the dynamics of actin-
network disassembly are not yet fully captured in the model.
Linked together by the robust quantification of optical-flow-based analyses,
experiments and simulations on guided actin waves provided a robust framework
for probing the mechanisms of texture sensing and contact guidance, which are
ubiquitous processes in the natural world.
122
5.5 Materials and Methods
5.5.1 Cell Culture and Imaging
The limE-?coil overexpressing Dictyostelium discoideum cells (in an AX3
background) were cultured in HL-5 medium at 1?4? 106 cells/mL with 50 mg/mL
hygromyocin B (Sigma-Aldrich H3274). We imaged cells in the pre-aggregate state.
Cells were harvested at 4 ? 106 cells/mL and shaken at 150 rpm in a beaker with
a density of 2 ? 107 cells/mL. Cells were then developed for 4 hours in develop-
ment buffer (5 mM Na2HPO4, 5 mM NaH2PO4, pH 6.2, 2 mM MgSO4 and 0.2 mM
CaCl2). During development, cells were stimulated every 6 minutes with pulses of 50
nM cAMP. The cells were then washed twice in phosphate buffer (5 mM Na2HPO4,
5 mM NaH2PO4, pH 6.2). To inhibit cell-cell communication, cells were treated
with 2 ?M caffeine (Sigma-Aldrich C1778) for 30 min, while being shaken at 150
rpm. For imaging, 300 ?L of cell solution with density 5?105 cells/mL was added to
a multi-well plate. After waiting 5 min for the cells to adhere to the surface, 50 ?M
of cAMP (Sigma A3262) was added to cells to initiate chemokinesis. Latrunculin A
(Sigma L5163) perturbations were performed via the addition of the drug to a final
concentration of 1.25 ?M (and a final concentration of 0.05% DMSO by volume)
after cells adhered to the substrate.
Fluorescence and bright field images were obtained on a Leica TCS SP5 con-
focal microscope (Leica TCS SP2 for Latrunculin A experiments) with a 100? ob-
jective, and a frame rate of 0.5 frames/second.
123
5.5.2 Ridge Fabrication
Structures were fabricated according to the protocols described previously [29].
We used a Ti:sapphire laser (Coherent Mira 900F) to perform multiphoton absorp-
tion polymerization. A region of total size 300 ?m ? 300 ?m was patterned with
200- to 300-nm-wide ridges with uniform spacings of 0.8, 1.5, 3, or 5 ?m. The ridges
were fabricated using an acrylic resin containing 49 wt% tris-(2-hydroxyethyl) iso-
cyanurate triacrylate (SR368, Sartomer), 49 wt% dipentaerythritol pentaacrylate
(SR399, Sartomer), and 2 wt% Lucirin TPO-L (Ciba). This process yielded a mas-
ter structure, which was then developed in dimethylformamide and ethanol. In
experiments, we made replicas of the master structure using a composite PDMS
mold [166].
5.5.3 Image Analysis
Images were processed with modified MATLAB software from Chapter 4. Op-
tical flow was calculated using the Lucas-Kanade method [89] with a gaussian-
weighted window with ? = 0.642 ?m. Distributions of optical-flow-vector directions
were fit with a bimodal-von-Mises model and the fit parameters ?, p1, and p2 were
used to interpret the model output.
Actin-wave speeds were calculated according to Chapter 4 with a clustering
parameter threshold of 0.1, and global reliability threshold for each time-series image
chosen empirically.
124
5.5.4 Actin Simulations
Simulations were performed using a custom C++ program created by modi-
fying the one published previously [41]. A rectangular simulation domain of size 8
?m ? 5 ?m was used. From the simulation results, we measured the actin filament
density within 200 nm from the cell membrane with a planar resolution of 10 nm ?
10 nm and a temporal resolution of 0.5 seconds.
We compared the simulation results with recorded images of limE-?coil-GFP
polymerization by transforming the simulated F-actin density via convolution with a
Gaussian kernel matching the resolution of our confocal microscopy images of ?250
nm.
125
Chapter 6: Analysis of Actin Dynamics in a Biological Context:
Actin Dynamics During Cancer Metastasis
This chapter is an adapted excerpt from Ilina, Campanello, Gritsenko,
Vullings, Wang, Bult, Losert, and Friedl [167]. Text and figures were
adapted and reproduced under a CC BY 4.0 license. Olga Ilina and Pavlo
Gritsenko performed the experiments, Leonard Campanello performed
the image processing and analysis, and Olga Ilina, Leonard Campanello,
and Pavlo Gritsenko wrote the paper.
6.1 Overview
Cancer invasion programs adapt by switching between collective and single-
cell dissemination. However, current intravital microscopy models for epithelial
cancer in mice fail to recreate such invasion plasticity reliably. We microimplanted
breast-cancer spheroids into the murine mammary fat pad and performed live-cell
imaging of the microenvironmental conditions and cytoskeletal adaptation during
the collective-to-single-cell transition in vivo. E-cadherin-expressing 4T1 and E-
cadherin-negative MMT tumors both initiated collective invasion along stromal
structures, reflecting invasion patterns in 3-D organotypic culture and human pri-
126
mary ductal and lobular carcinoma. Collectively invading cells developed weakly
oscillatory actin dynamics, yet provided zones for single-cell transitions with ac-
centuated, more chaotic actin fluctuations. These studies indicate that collective
invasion in vivo is a dynamic niche and an efficient source for single-cell release.
6.2 Background
Progression and fatal outcome of breast-cancer disease result from the emer-
gent ability of cancerous cells to invade tissue, to cope with complex tissue mi-
croenvironments, and to adapt their metastatic dissemination by switching between
collective-migration and individual-cell-migration programs [168]. Early steps and
molecular drivers of single-cell dissemination of epithelial cancers in vivo were identi-
fied by intravital microscopy (IVM) in rodent models, including oncogenic mutations
in Wnt, EGFR, p53 (also known as Trp53) and TGF-? signaling pathways [169?171].
IVM has further revealed how tumors co-evolve, with the reactive tumor stroma and
undergo anatomic, molecular, and functional reprogramming, and had underscored
the significance of tumor-associated macrophages directing local invasion and sys-
temic dissemination [172,173].
In epithelial cancers assessed by histopathological analysis, collective cell pat-
terns are abundant at the invasion front [174?176]. Collective invasion occurs in
cell groups or strands connected and coordinated by adherens and other cell-cell
junctions that mediate multicellular polarity, actomyosin contractility, and cell-cell
signaling [172]. Subsequent to local epithelial cancer invasion, persisting cell-cell
127
interactions can support collective metastasis by tumor-cell clusters circulating in
peripheral blood and collective organ colonization [177, 178]. However, to date,
IVM models of epithelial cancers, including breast cancer and colorectal cancer,
have not been able to detect and mechanistically interrogate collective invasion re-
liably [169, 179, 180]. As a consequence, in vivo insights into collective invasion in
epithelial cancers, the guidance of collective invasion by tissue structures, and the
mechanisms enabling transitions between collective and single-cell invasion remain
lacking.
Here, we applied microsurgical implantation of multicellular breast cancer
spheroids into the mammary fat pad, followed by intravital mammary window imag-
ing. Our experiments enabled us to identify principles of collective invasion, transi-
tions to single-cell dissemination and associated modulation of cytoskeletal states.
6.3 Results
6.3.1 Implantation and window-based monitoring as a model system
of primary mammary carcinoma and metastasis
To create a model for monitoring collective invasion of breast cancer cells by
intravital microscopy, the mammary imaging model [171] was adapted for microim-
plantation of multicellular spheroids at the collagen-containing border of the 4th
mammary fat pad (Figure 6.1A). Up to 10 4T1 and MMT spheroids, which con-
tained intercellular junctions including E-cadherin (4T1), -catenin and p120 catenin
(4T1, MMT), were implanted in the same fat pad in order to mimic multifocal
128
disease [181]. The integrity of spheroids, connective and adipose tissues, and vascu-
lar networks was preserved after implantation (Figure 6.1B), consistent with min-
imally invasive microsurgery. Multifocal tumors developed spontaneous micro and
macrometastasis (Figure 6.1C) and grew exponentially for periods up to 3 weeks
(Figure 6.1D). 4T1 cells were separately injected as suspensions and established
bulky tumors without signs of collective invasion. Thus, the mammary imaging
model recapitulated the growth of primary carcinoma lesions and the subsequent
distant metastasis.
6.3.2 Intravital microscopy of invasion and individualization
Collective cell invasion in both 4T1 and MMT tumors initiated within 1-2 days
after implantation irrespective of differences in E-cadherin expression (Figure 6.2A?
B). 4T1 (i.e., E-cadherin expressing) cells invaded as solid collective strands with
detectable leader cells (Figure 6.2C). MMT cells that lacked E-cadherin but ex-
pressed N-cadherin invaded in a less-organized manner, which is consistent with
previous reports [182], but nevertheless formed collective networks with multicel-
lular organization, head-to-tail cell alignment, and actin enrichment along cell-cell
junctions (Figure 6.2D).
Both 4T1 and MMT cells were able to detach and migrate individually, with
elongated, spindle-shaped morphology that involved substantial actin activity (Fig-
ure 6.2A?B). However, individualization was more abundant in MMT compared
with 4T1 tumors, which developed more frequent tip and detached cells, despite
129
Figure 6.1: Microimplantation of tumor spheroids recapitulated the growth of pri-
mary carcinoma and subsequent distant metastasis. (A) 4T1 and MMT spheroids
were prepared in vitro and implanted in the 4th mammary fat pad, and went on
to form metastatic lesions 2?3 weeks after implantation. (B) The integrity of the
spheroids, surrounding connective and adipose tissues, and vascular networks was
preserved after the minimally invasive microsurgery. (C, D) Spheroids spontaneously
developed metastatic tumors over 2?3, weeks which grew in size exponentially.
130
Figure 6.2: Collective and individual-cell invasion patterns and angiogenesis in the
mammary tumor imaging model.Time-course of (A) 4T1- and (B) MMT-tumor
growth and angiogenesis monitored by two-photon microscopy. Images are mon-
taged maximum-intensity projections of three channels; z-stacks were obtained in 5
?m intervals. Dotted-line ROIs were used to show close-ups of collectively invad-
ing strands and single cells. Zoomed-in ROIs of (C) 4T1 and (D) MMT cells in
the mammary fat pad 4 days after spheroid implantation. Both cell types exhib-
ited collective-invasion phenotypes. Dashed lines mark the position of cross-section
planes for orthogonal views and arrowheads indicate enrichment of Lifeact-eGFP
along cell-cell junctions.
131
having an apparent reduction in actin expression. The inverse association between
cell individualization and E-cadherin expression in the spheroid implantation model
in vivo is consistent with increased single-cell release in 3-D organotypic culture of
MMT compared with 4T1 spheroids and in patient samples from human lobular
carcinoma compared with ductal breast carcinoma [176].
6.3.3 Investigating actin and cell-shape dynamics during the
collective-to-single-cell transition
Plasticity of cancer cell invasion is associated with an adaptive actin cytoskele-
ton. Cortical actin networks in vitro define the shape, polarity, and force transmis-
sion in individually moving cells [183], and further stabilize adherens junctions and
transmit long-range forces across connected cells during collective migration [184].
To address whether actin dynamics in individual and collective invasion differ in
vivo, the intensity fluctuations of Lifeact-eGFP in 4T1 tumors transiting from col-
lective to single-cell migration were quantified (Figure 6.3).
Individual cells in and around the tumor were identified and categorized as
detached (1), tip (2), or bulk (3) (Figure 6.3A). Boundary outlines were traced
and analyzed using a semi-automatic cell-shape-analysis workflow to measure the
dynamic behavior of actin along the cell boundary [29, 185] (Figure 6.3B). Actin-
intensity profiles were captured in equally spaced wedges along the cell boundary.
Wedges were associated frame-to-frame with a minimum-squared-distance criterion
to create time-lapse profiles of actin intensity on a per-wedge-per-frame basis (Fig-
132
133
Figure 6.3: Actin dynamics during collective and single-cell invasion. The time-
dependent shape of each cell was extracted by semi-automatic shape segmentation
from sequential single-imaging planes, and the Lifeact-eGFP intensity along the cell
periphery was obtained from equal segments 2.07 ?m inward from the cell bound-
ary. (A) 4T1 cells at different invasion position in vivo 4 days after implantation.
Segmented cells were categorized as detached (1), tip (2), and bulk (3), and series of
boundary wedges were calculated and tracked for time-dependent analysis of actin
intensity. (C) Mean-actin-intensity kymographs from wedges. Wedges were asso-
ciated frame-to-frame using a minimum-squared-distance criterion. Detached cells
exhibited rapid fluctuations, whereas tip and bulk cells exhibited slower and less-
intense fluctuations. (D) Time-delay autocorrelation of the actin-intensity profile for
the detached cell from (B). Time-delay autocorrelations indicate how correlated an
intensity profile is with a time-shifted copy of itself. The time-delay autocorrelation
equals 1 when the time-delay parameter, ?t is 0, and decays based on how quickly
the two intensity profiles diverge. The black line is the mean and the gray region
is the standard deviation calculated at each time delay, ?t. (E) Aggregated time-
delay-autocorrelation curves of actin intensity from 4 detached (green), 8 tip (red),
and 15 (bulk) cells, respectively, from 3 independent tumors. Intensity profiles from
detached cells diverged more quickly than tip and bulk cells. (F) Intensity variabil-
ity for intervals of 10 s (representing fast fluctuations) and 60 s (slow fluctuations)
within detached (green), tip (red), and bulk cells (blue). Significant differences were
found when comparing the mean variability between detached and bulk cells. The
box plots in (F) are of the median (black line), IQR (box), and range (whiskers).
P-values were obtained with the Tukey-Kramer multiple comparisons test. Scale
bars were 50 ?m in (A) and 10 ?m in (B).
134
ure 6.3C). Intensity-over-time profiles in detached cells exhibited rapid fluctuations
at different times and spatial locations along the cell periphery. Tip and bulk cells
exhibited slower and less frequent intensity spikes (6.3C).
The extracted actin-intensity profiles were characterized and parameterized by
time-delay autocorrelations in a wedge-by-wedge manner (Figure 6.3D). The error
bars represent the standard deviation of the time-delay autocorrelation for each
value of ?t. Time-delay autocorrelations indicate how similar an intensity profile
is with a time-delayed replica of itself. When the time-delay parameter, ?t, is
equal to zero then the correlation value is 1, and the autocorrelation decay rate
indicates how quickly the intensity profiles diverge. Time-delay autocorrelations
for the representative cells in Figure 6.3A?C demonstrate how rapidly intensity
fluctuations decorrelate over time. Detached cells quickly diverge in actin-intensity
behavior, whereas tip and bulk cells do not (Figure 6.3E).
Amoeboid cells moving along extracellular-matrix-like substrates in vitro de-
veloped actin waves reaching speeds of ? 10?m/min [29], with calculated changes
in polymerization on timescales of seconds [186]. On the other hand, cell protru-
sions, such as ruffles or pseudopods, remodel on a timescale of minutes [186]. To
test whether actin dynamics in vivo have similar dynamic properties, we probed the
intensity variations for 10 and 60 sec time delays in collective and single-cell migra-
tion in vivo. Systematic measures of variability, which were defined as 1 minus the
time-delay autocorrelation for a particular time-delay, ?t, indicated that autocorre-
lations at 10 and 60 sec were significantly different between detached cells and bulk
cells (Figure 6.3F). Taken together, the data in Figure 6.3 indicate an upregulation
135
of actin variability after collective-to-single-cell individualization from the invasion
zone.
To connect the dynamic behavior of actin to cell shape, we measured and ana-
lyzed fluctuations in the extracted cell boundaries over time (Figure 6.4). Detached
cells exhibited a significant amount of protrusive motion, whereas bulk cells were
more quiescent (Figure 6.4A). Interactions between the cytoskeleton and ECM are
most efficient for protrusions and features on the order of 2 ?m in size [29]. We
observed that detached cells exhibited many protrusions greater than 2 ?m in size
between adjacent frames, whereas bulk cells were relatively quiescent and had few
large protrusions (Figure 6.4B). The gray regions indicate the standard deviation
of boundary motion, thus when the gray regions fall above the 2 ?m line, at least
15% of the boundary motion is of magnitude greater than 2 ?m. The aggregate and
high-percentile behavior in all detached, tip, and bulk cells is similar (Figure 6.4C),
which indicates that boundary fluctuations are roughly the same size in all cases.
However, boundary motion with magnitude ? 2 ?m occurred significantly more
frequently in detached and tip cells than in bulk cells (Figure 6.4D).
6.4 Discussion
Although collective invasion patterns are abundant in clinical samples of ep-
ithelial cancers, including breast carcinoma [174?176], current intravital-microscopy
models of breast cancer were insufficient to detect and mechanistically interrogate
collective invasion reliably [170, 171, 179]. Reasons for this model insufficiency are
136
Figure 6.4: Detached and tip cells exhibited significantly more large-amplitude mem-
brane fluctuations. (A) Cell boundary motion traces and their obtained from time-
lapse sequences for detached (1), tip (2) and bulk (3) cells. (B) Boundary motion
distributions over time for the representative cells in (A). Each cell exhibited simi-
lar background behavior, but detached and tip cells experienced a higher frequency
of large-amplitude protrusion events than bulk cells. (C) Box plots of background
(median) and high-percentile behavior (95th percentile). Both background and high-
percentile behavior is similar in all cell types. (D) The percentages of motion with
a magnitude greater than 2 ?m, the characteristic length scale of membrane fluc-
tuations, for all detached, tip, and bulk cells. There are significantly more > 2 ?m
events in detached an tip cells than in bulk cells. Box plots in (C), (E) and (F) show
the median (black line), IQR (boxes), and range (whiskers). P-values were obtained
with the Tukey-Kramer test for multiple comparisons.
137
likely multifactorial, based on (1) lack of cell-cell junctions when tumor-cell sus-
pensions are implanted; (2) excessive growth, which might cause circular tissue
compression and disable multicellular invasion; and (3) a bias in genetic mouse mod-
els, which disable or minimize cadherin-based cell-cell junctions and possibly favor
individual-cell, but not collective, behaviors. To overcome this problem, we used or-
thotopic microimplantation of multicellular spheroids of murine breast cancer cells
into the mammary fat pad/stroma interface, monitored by intravital microscopy,
as a reliable model of collective invasion followed by a transition to individual cell
detachment in vivo.
Using spheroid microimplantation at the edge of the mammary fat pad, this
intravital microscopy approach captured critical early steps of collective invasion and
cytoskeletal plasticity in breast-cancer tumors. With transition from collective to
single-cell migration, individually disseminating cells exhibited oscillatory behavior
of the actin cytoskeleton and abandoned strict alignment along collagen fibers. Such
collective-to-single-cell transitions arguably broaden the ability of tumor cells to cope
with different tissue topologies and escape from the primary site [172].
In both E-cadherin-positive and E-cadherin-negative cells, implanted spheroids
supported tumor-like topology and cell-cell cohesion for emerging collective invasion
followed by gradual individualization. E-cadherin is considered an important gate-
keeper of epithelial functions. Because single-cell events are enhanced in epithelial
tumors when E-cadherin is downregulated [176], E-cadherin was initially considered
to counteract local tissue invasion and metastatic spread [187]. However, in clinical
breast cancer, the E-cadherin status does not predict metastatic outcome and prog-
138
nosis [176, 188]. Similar to these clinical data, E-cadherin-negative MMT tumors,
albeit developing more frequent cell individualization compared with E-cadherin-
expressing 4T1 tumors, did not give rise to increased rates of distant metastasis.
Beyond mechanical cell-cell cohesion, other pathways might control the metastatic
outcome in MMT and 4T1 cells, including oncogenic signaling, sensitivity to growth
factors and mechanoregulation [170,172,173].
Our data further reveal plasticity of the actin cytoskeleton during the collective-
to-single-cell transition in vivo, as predicted from in vitro and in silico models
[183, 189]. A relatively quiescent actin cytoskeleton in the collective invasion zone
possibly fulfills a dual function in (1) controlling both the stability and turnover of
cell-cell junctions, and (2) providing a starting point for actin-rich protrusions at the
invasion front. Leader cells that extended outwards to the stroma still retained over-
all quiescent actin dynamics comparable to those of bulk cells, but developed large
protrusions at rates comparable to those in individual cells. Likely as a consequence
of detachment, actin dynamics in individually moving cells rapidly switch dynamic
character, suggesting that the actin cytoskeleton in invading tumor cells is an ex-
citable system with dynamic focalization and protrusive bursts similar to traveling
actin waves in moving Dictyostelium discoideum amoebae and fibroblasts migrating
on 2D substrate in vitro [185, 186]. We consider spheroid microimplantation, com-
bined with fate tracing of distinct invasion modes, as a potentially suitable model
to barcode invasion mechanisms and stromal niches in primary lesions, and assess
the relevance of these mechanisms for distant metastasis formation and resistance
to therapy [190,191].
139
When benchmarking in vitro and in vivo analyses of cancer cell invasion, the
spheroid microimplantation strategy closes a validation gap by reflecting invasion
types and plasticity derived from both 3-D organotypic culture and clinical sam-
ples [174, 176]. Multiple spheroids can be implanted in the same mouse to increase
the surface area of the tumor-stroma interface and collect larger data sets. Multiple
microlesions further increase the tumor mass, and enable spontaneous distant metas-
tasis from these lesions, and this reduces animal consumption and improves data
quality from the same mouse. Because intact spheroids are implanted, the strat-
egy will be amenable for epithelial cancer organoids or dissected tumor microtissues
from patients to create mouse avatars for personalized medicine.
6.5 Materials and Methods
6.5.1 Experimental methods
For a detailed explanation of experimental methods, including the antibodies
and reagents, cell lines and culture, spheroid generation, immunohistochemistry, and
confocal and two-photon microscopy, please refer to [167].
6.5.2 Analysis of actin and cell-shape dynamics
Actin dynamics were measured via Lifeact-eGFP fluorescence intensity in
space and time from single imaging planes through the center of the cell body with-
out signs of drift. Using a custom MATLAB code based on [29, 185], cell outlines
were semiautomatically segmented from source images, and the boundary traces
140
were calculated on a subpixel basis using 200 boundary points using an active-
contour algorithm. Source images had a pixel resolution of either 3.02 ?m or 1.45
?m and an adjusted signal-to-noise ratio.
Wedges based on the cell boundary were calculated by applying morphological
erosion on the segmented cell boundaries, using an active-counter algorithm with 200
boundary points to generate a boundary trace, and generating a mapping between
the original boundary and eroded boundary in a minimum-least-squares fashion
[185]. Separations between wedges were 1.73 ?m, which was larger than the average
fluctuation in measured boundary position. Thus, this separation was sufficient
to capture cortical actin with accuracy. The mean intensity per wedge boundary
region was plotted over time on a wedge-by-wedge basis as a kymograph and used
for calculating the time-delay autocorrelation.
For the nth boundary index with average background intensity I?, time-delay
autocorrelation for time delay ?t was defined as
?T
? [In(t+ ?t)? I?] ? [In(t)? I?]cn(?t) = ?t=0 ? . (6.1)T T
[In(t+ ?t)? I?]2 ? [I 2n(t)? I?]
t=0 t=0
The mean background fluorescence of the cell, I?, was determined based on the
eroded cell boundary which was the dimmest part of the intensity image. Thus, the
time-delay autocorrelation is limited to [0, 1]. The time-delay autocorrelations for
each cell were used to calculate the mean and standard deviation independently at
each ?t. Intensity variability was defined as 1 minus the time-delay autocorrelation.
141
cn(?t) = 1 indicates complete stability of cortical actin dynamics over time, and
this is therefore equivalent to variability equal to zero.
6.5.3 Statistics
Statistical analysis was performed with one-way ANOVA and the Tukey-
Kramer test for multiple comparisons. P-values were subjected to a Bonferroni
correction for multiple comparisons where necessary. P-values less than 0.05 were
considered significant.
142
Chapter 7: Summary and Future Directions
7.1 Summary
Cells actively detect and respond to physical, chemical, and biological stim-
uli in extracellular environments. In this dissertation, I combined experimental
data, image analysis, statistical models, and computational simulations to link the
geometry, organization, and dynamics of intracellular signaling networks with cell
function.
Activation mechanisms of effector T cells must be highly sensitive to biochem-
ical cues to ensure a rapid immune response, but must also be self-regulating to
prevent the deleterious consequences of immune-system autoreactivity. In Chap-
ter 3, I explored the organization and geometry of Bcl10 self-assembly and degra-
dation, which are key mediating steps in effector-T-cell activation and regulation.
By using computational image-analysis tools to quantify Bcl10-filament lengths and
Bcl10-autophagosome contacts, I demonstrated that Bcl10 filaments shortened over
time and that autophagosomes were more likely to be attached to Bcl10-filament
ends or Bcl10 puncta. To assess the statistical validity of these results, I intro-
duced a novel bootstrap-like resampling method for image data and showed that
the number of Bcl10-autophagosome contacts and their spatial distributions were
143
highly non random. To probe Bcl10 dynamics further, I developed a stochastic
Monte Carlo simulation of nucleation-limited growth and degradation, and showed
that tuning the simulations parameters modulated both the heterogeneity and char-
acter of the simulation outputs. The results of these studies demonstrated that the
TCR-to-NF-?B signaling pathway exhibits characteristics of an excitable system,
including a digital activation facilitated by Carma1 nucleation of Bcl10, and the
coupled positive- and negative-feedback loops between Bcl10-filament growth, cell
activation, and Bcl10 degradation.
Other cell functions also rely on physical and biochemical cues in the extra-
cellular environment. During wound healing, cells in the immune system, such as
neutrophils, become activated and migrate towards the site of wounds to detect and
eliminate pathogens, and epithelial cells migrate in a collective fashion to close the
wound. In Chapter 4, I explored the effect of nanotopographic ridged substrates on
cytoskeletal dynamics in both neutrophil-like HL60 and epithelial MCF10A. Nan-
otopographies such as collagen fibers are ubiquitous in vivo. To explore the dynamic
behavior of the cytoskeleton on and off the nanotopographies, I developed an image-
analysis suite based on optical flow. Using the raw, pixel-based optical-flow-direction
distributions, I systematically measured the influence of nanoridges on cytoskeletal
dynamics and showed that nanoridges bias waves of cytoskeletal polymerization
in both cell types. To parameterize these distributions, I designed a statistical
bimodal-von-Mises model and showed that both immune cells and epithelial cells
were similarly affected by ridged substrates despite having different migratory modes
and phenotypes (epithelial vs. amoeboid). To quantify the influence of ridges on the
144
micron scale, I clustered and tracked similarly-oriented optical-flow vectors. Using
optical-flow-cluster tracking, I showed that the speed of actin polymerization waves
were unchanged on and off ridges.
Although I demonstrated that nanotopographic ridges bias cytoskeletal dy-
namics, the mechanisms that facilitate this bias are not completely understood.
In Chapter 5, I utilized the optical-flow-analysis suite introduced in Chapter 4 to
probe the interaction between textures and the cytoskeleton via the use of differently
spaced nanoridges and Dictyostelium discoideum. In Dicty, I showed that ridges of
narrow spacings biased the direction of actin-wave polymerization along the ridges,
but that actin-wave speeds were unaffected by ridge spacing. Motivated by recent
experimental data which showed that curvature promotes actin nucleation [15,16], I
showed that evenly spaced ridge-like patterns of upregulated nucleation-promoting-
factor activity are sufficient to generate biased actin waves in the ridge direction.
Interestingly, upregulating NPF activity on ridges coupled with a downregulation
of NPF activity off ridges produced better actin-wave guidance than upregulation
alone, which suggests that a redistribution of NPFs rather than enhancement is re-
sponsible for topography-induced guidance. Remarkably, the actin-wave speeds in
the experiments and simulations were similar despite simulation parameters being
developed under different experimental conditions. Lastly, although full quantita-
tive agreement wasn?t achieved, the simulations also provided additional measure-
ments of actin-filament length that would not be possible to measure experimentally.
Taken together, robust quantification with optical-flow-based analyses and guided
actin waves on nanotopographic ridges provided a robust framework for probing the
145
mechanisms of texture sensing and contact guidance.
The tools and techniques that I developed can also be applied to detect and
quantify dynamics in vivo. In Chapter 6, I shared an in vivo application for measure-
ments of self-assembly and disassembly and how they can provide deep insight into
cell behavior. I used a modified cell-shape-analysis framework [29, 185] to measure
the dynamics of actin waves before, during, and after the epithelial-to-mesenchymal
transition in cancer metastasis. I showed that mesenchymal cancer cells exhib-
ited distinguishable dynamic hallmarks: rapid periods of actin activity in seemingly
random locations around the cell periphery and large but short-lived protrusions
around 2 ?m in size. Interestingly, cells which were on the leading edge of a tumor
exhibited a mix of both hallmarks, which indicated that cells with mesenchymal-
like qualities either tended to migrate towards the edge of the tumor, or that the
epithelial-to-mesenchymal transition led to more variable and dynamic cytoskeletal
activity.
In sum, the work presented in this dissertation introduced ways that an ex-
citable systems framework and quantification of the organization and dynamics of
signaling-network components can provide deep, phenomenological, and quantita-
tive insights into variety of biological systems.
146
7.2 Future Directions
7.2.1 Extracting Biological Information from Waves and Oscillations
The actin-polymerization dynamics studied in Chapters 4, 5, and 6 all demon-
strated that amorphous concentration fields of actin encode biological information
in the form of waves and oscillations. In each chapter, I presented computational
techniques to measure the dynamic behavior of actin, and connected these measure-
ments to cell behavior. One recurring technique that I used was optical flow. Here,
I expand upon the future directions of optical-flow-based analysis techniques and
suggest other applications for their use.
In Chapters 4 and 5, I showed that optical flow uses image gradients to measure
the dynamics of actin in a time series of images. In both chapters, I parameterized
the distribution of optical-flow directions, however, the fhe fit parameters that were
analyzed in Chapters 4 and 5 were derived from accumulated-over-time data. Thus,
the fit parameters did not include how actin, and overall cell behavior, might be
changing in time. One way to expanding the capabilities of the optical-flow analysis
is to fit the direction distributions for each frame in the time series independently
(or moving window of frames in a given time interval). This over-time extension of
the current analysis technique can provide insight into how a system dynamically
responds to a static or changing environment. Due to the piecewise nature of such
an analysis, the over-time behavior of model parameters will need to be interpreted
carefully and/or fit to their own time-series model.
147
In independently fitting the von-Mises model in a frame-by-frame manner,
the model can also be adapted to parameterize directly the time-series behavior
of optical-flow distributions. The model, which for a single distribution of optical-
flow directions (i.e., without considering time) is shown in Equation 4.5.5, can be
a?ugmented via substitutions for each of the model parameters of the form ? = ?(t) =
i fi(t, ?~i). The set of functions f(t, ?~ ) can be simple (e.g., at + b) or complex
(e.g., terms of a Fourier series). Each of the other parameters, including ?, p1, p2,
and p3 would undergo a similar transformation with their own set of functions and
parameters. Under such a substitution, the components of ?~ would vary to maximize
the likelihood function, and optimum values for the components of ?~ will produce
over-time functions for the interpretable von-Mises-model parameters. Notably, such
a model can also include nonlinear functions such as Heaviside functions, which could
parameterize discrete switches in external environments, such as a switching electric
field.
Building statistical models of optical-flow direction distributions can also pro-
vide insight into coarse-grained behavior within flow fields. As described previously,
the Lucas-Kanade optical-flow method utilizes a window of predetermined size, and
it is crucial that the span of the window is within the confines of the desired region.
Once optical flow is calculated, optical-flow modeling can also be performed in a
coarse-grain manner whereby the optical-flow directions in a moving-N -?-N win-
dow are independently fit to some chosen model (e.g., von Mises distribution plus a
constant offset). Upon such a calculation, the model-parameter field (e.g., field of ?,
p1, etc.) would contain information about coarse-grained uniformity or randomness
148
in the flow field. Such an advancement could augment, or be combined with, optical-
flow-based-detection algorithms [192] to provide additional information about the
motion of discrete objects in images.
Optical flow can also be used to connect, correlate, or causally relate dynamics
that occur in different spatial regions. In the actin-wave dynamics in HL60 or Dicty
(in Chapters 4 and 5, respectively) correlation-length or correlation-time measure-
ments could be performed on actin waves that evolve in statistically similar ways.
These measurements could address questions of actin-wave persistence on and off
ridges, the spatial distance over which actin waves are correlated on and off ridges,
and the effect of different ridge spacings on actin-wave correlation over a fixed dis-
tance. Beyond bioimage analysis, correlation of optical flow across spatial distances
can help identify structures moving in ways that optical flow cannot determine eas-
ily. For example, the Lucas-Kanade optical-flow solution cannot distinguish global
circular motion (e.g., a rotating wheel). However, the spatial correlation of optical
flow between any pair of coordinates in a circularly moving region would be con-
stant (e.g., opposite sides of the wheel would be maximally anticorrelated). Thus,
spatial correlations of optical flow can provide insights into the structure or spatial
connection between moving objects in a field of view.
The use of optical flow also extends beyond single-channel analyses. Although
the techniques used in Chapters 4, 5, and 6 were performed on images of actin, they
can also be used to measure, and elucidate relationships between, other cytoskeletal
proteins and signaling molecules. For example, waves of signaling molecules like
PTEN, PIP3, and PI3K all play a role in actin dynamics [9], and the dynamic
149
relationships between actin and upstream signaling components control a variety of
cell functions and behaviors [3,71]. Because the waves and oscillations in fluorescent
images of signaling molecules can also be measured with optical flow and downstream
optical-flow techniques, simultaneously analyzing actin alongside other signaling
molecules can measure spatial and temporal relationships, and assess the role of
biochemical dynamics in overall cell behavior.
In addition to the analysis of biological images, there are numerous industry
applications for optical flow that are currently in development or use. For example,
optical-flow-based methods are being used in autonomous vehicles to segment and
extract discrete objects in the foreground and background of images in a time series
[193], and optical flow is being combined with neural-network models to predict
emotional states from facial expressions [194,195].
Adapting the optical-flow-based algorithms developed for industry applica-
tions can provide new ways to analyze and interpret bioimage data. For example,
one common set of bioimage challenges are related to microscope jitter and drift,
whereby the stationary background of an image series moves in random or regu-
lar patterns. Using foreground-background separation techniques outlined in [193],
which was developed to identify vehicles, pedestrians, or other obstacles from a
moving viewpoint, can help identify the true motion of cell that is being imaged in
jittery conditions. Moreover, using optical-flow vectors (along with raw intensity)
to train a convolutional-neural-network (CNN) can provide the network with ad-
ditional information for training, and, ultimately, could yield better performance.
Using training techniques similar to those outlined in [194,195], which used optical
150
flow for the recognition of facial expressions, can allow for machine-learning models
to classify images of WT versus perturbed cells, such as those in [9, 71].
One challenge in using optical-flow-based tools from industry (e.g., from au-
tonomous vehicles [193]) is that industrial applications of optical flow often involve
combining images, or a time series of images, from multiple viewing angles. The
combination of two or more views of the same field allows for the deduction of 3-D
motion [89,90] that cannot be measured directly in real-world conditions (i.e., mobile
cameras often produce 2-D projections rather than 3-D volumetric scans). Realistic
cell behaviors are not confined to two-dimensional planes (e.g., those seen in [196]),
and, thus, require the analysis of 3-D motion. However, unlike industrial appli-
cations, advances in bioimaging technology have enabled isotropic, fast-frame-rate,
3-D imaging [197?200]. Despite such imaging advances, cutting-edge techniques on
the analysis of 3-D objects is limited to the tracking and measurement of segmented
volumes [201] and organization (shown in Chapter 3). Since optical flow relies on
fast frame rates and accurate gradients, extending the optical-flow-based tools pre-
sented in this dissertation into 3-D can provide a substantial amount of new dynamic
information and, ultimately, lead to new insights into 3-D biological behavior.
Extending optical flow to efficiently compute higher-dimensional motion is not
trivial. For one, the eigenvalue problem for a 3 ? 3 matrix is equivalent to finding
the roots of a cubic polynomial, for which general solutions are complicated. Note
that numerical solutions are slow and must be computed ijkl times for a 3-D time
series with dimension i? j? k? l where i, j, k, l > 500 is typical. Thus, hard-coded
solutions are strongly preferred for efficient implementations.
151
One additional challenge lies in the Lucas-Kanade equations during the cal-
culation of 3-D optical flow. During 3-D calculations, moving 3-D planes or two
intersecting 3-D planes will produce low reliabilities [202]. Although such solutions
are valid and realistic, the least-squares formulation of the Lucas-Kanade method
will project all 3-D optical-flow calculations onto a 2-D plane, and the eigenvalue as-
sociated with the eigenvector normal to the plane will be small. Thus, all reliability
measures must be carefully considered, and the traditional definition of reliability,
the smallest eigenvalue of the structure tensor, may need to be redefined. One pos-
sible solution is to use the set of eigenvalues and eigenvectors of the structure tensor
from the 3-D extension of Equation 2.6 to determine the high-reliability subspace
of optical flow (i.e., the one- or two-dimensional eigenspace with large eigenvalues).
Once the subspace is found, the structure tensor can be rotated such that one or two
of the eigenvalues will be zero, and then optical-flow calculations can be repeated
on the lower dimensional subspace.
If the challenges associated with 3-D optical flow are solved, then the exten-
sion of the optical-flow tools introduced in this dissertation can provide additional
capabilities. One such capability is the 3-D extension of the von-Mises model. A
3-D von-Mises distribution would require two angles to parameterize the mean di-
rection of flow, and theoretical calculations of the indistinguishable-from-uniform
cutoff, which is ? = 2 in 2-D. Notably, there may even need to be two independent
? parameters that define the distribution widths in perpendicular directions. For-
tunately, the clustering and tracking introduced in Chapter 4 could remain largely
unchanged except to add an additional spatial dimension to the clustering kernel
152
in Equation 4.5.6, and to the tracking, which has already been implemented [131].
Notably, 3-D optical-flow clustering allows for the identification of similarly moving
mesoscale structures in 3-D. In the context of bioimage analysis, optical-flow clus-
tering can provide motion-based metrics to augment challenging tasks like object
segmentation, which I will discuss at the end of Subsection 7.2.4.
7.2.2 Connecting Biological Excitability to Models and Simulations
As demonstrated in Chapters 3 and 5, models and simulations provide a way
to probe the dynamics of a biological system that may not be able to be studied
experimentally. In Chapter 3, I showed that different simulations parameters can
alter the character and heterogeneity of outputs, and in Chapter 5, I showed that
different configurations of biochemical-signaling components can be compared to
and benchmarked against experimental data.
One simple, yet powerful, way to probe biological excitable-systems dynamics
is through the use of forest-fire models. Although reaction-diffusion equations are
not explicitly included in forest-fire models, the dynamic patterns observed exhibit
many apparent similarities with observed reaction-diffusion systems [9, 71]. Such
patterns include clearly-defined leading edges of a wave and slowly diffusing trailing
edges, which in a forest-fire model is the growth of a tree in an empty region on the
trailing edge.
With new understandings of the excitability of the actin signaling network
[3, 9, 71], there are many ways in which a forest-fire model can be augmented to
153
be more biologically realistic. For example, one missing component is an inhibi-
tion signal/wave. Recapitulating a traveling wave in a forest-fire model minimally
requires an activator (i.e., fire) and refractory period (i.e., regrowing of trees). How-
ever, experimental evidence and theoretical predictions suggest the existence of a
mutual-inhibition-feedback loop between signaling molecules that promote versus
inhibit actin polymerization [3, 9, 71, 158, 160]. The three primary challenges to
incorporating an inhibition wave in a forest-fire model are: (1) determining the
medium in which the inhibition wave travels (i.e., the fires travel on trees, so is
there another set of trees for inhibition waves?); (2) determining the mechanisms by
which inhibition waves are initiated; and (3) determining the result of the inhibition
wave coming in contact with a tree and/or a fire. One possible way to incorporate
inhibition of excitatory waves is through local excitation and global inhibition [203].
One drawback in the use of forest-fire models to recapitulate biological phe-
nomena is the requirement that a fire will spread from neighboring pixels. During
a cascade of actin-wave polymerization, there is no guarantee that polymerization
will continue an additional step even if all biochemical components are in place.
Thus, modifying a forest-fire model to facilitate more randomness in the spread-
ing of fire can be accomplished with a spreading probability. Furthermore, inclu-
sion of a spreading probability could allow a modified forest-fire model to recre-
ate spatially patterned substrates. For example, because data suggest that biased
actin-wave propagation on nanotopographic surfaces is facilitated by large-curvature
regions [15, 16], the forest-fire substrate can upregulate the spreading parameter
along equally-spaced stripes and leave it unchanged elsewhere. Alternatively, three-
154
dimensional forest-fire models could also be used to enable more complexities in
the texture. In that case, such models could also incorporate the shapes of 3-D
nanotopography in the simulations, such as sawteeth [24,38].
Finally, exploring a large range of dynamic behavior in a forest fire could be
accomplished via the inclusion of a cell membrane. Although it is unclear how the
membrane will deform, and if/how there will be conservation of quantities such
as cytosolic volume or surface area, solving these challenges could yield an easily
implementable toy model for an excitable reaction-diffusion-like dynamic system
that mimic aspects of cell behavior.
One alternative class of models that explicitly incorporate reaction-diffusion
dynamics is phase-field models. Phase-field models were initially designed to capture
the growth dynamics of crystals, but have recently been shown to capture cell-
migration phenotypes accurately [73]. All suggested future directions for a forest-
fire model could also be considered for a phase-field model. Notably, phase-field
models implicitly include a cell membrane, and thus can incorporate additional
membrane-dependent terms such as curvature and tension, albeit at a significantly
greater computational cost (minutes-long phase-field simulations take hours to run
on modern hardware).
An additional bonus is that a phase-field contains explicit polarity for separate
coarse-grained regions through the simulated cell. This polarity could enable addi-
tional simulations in which external forces on the cell or intracellular component is
directional, e.g. electric fields.
One important issue in both forest-fire and phase-field models is the analysis of
155
model outputs. Although the outputs are rich and dynamic, similar to image data,
these outputs are difficult to quantify and analyze in a statistically robust way.
Thus, the analysis techniques that were introduced in this dissertation can prove to
be widely applicable in the analysis experimentally-derived and simulations-derived
data.
7.2.3 Insights from the Spatial Organization of Biological Structures
Intracellular structures are organized into a wide range of shapes and sizes.
In Chapter 3, I demonstrated how image-based bootstrap-like resampling is a pow-
erful and generalizable way to determine whether a given arrangement of struc-
tures should be considered random or biased, e.g., preferentially co-localized with
other structures. In essence, if measurements from an image are determined and
image-based resampling is performed, a comparison of the measured and resam-
pled distributions can determine whether the measurement results were a product
of randomness.
In general, the bootstrap-like resampling of image structures can provide a
baseline of what any type of spatial distribution would look like if the underlying
driver of the distribution is uniformly random. Moreover, the random distribution
of image structures can be augmented based on other distribution types, such as
simple Gaussians or complex structure-based distributions based on other image
features (e.g., Gaussians centered at the nearest objects in other imaging channels).
Notably, the resampling can be augmented to such that only certain regions of the
156
space are eligible for placement of image structures, which could be particularly
useful if there are restricted regions in the image. For example, in Chapter 3, I
forced all random placements of autophagosomes to occur within the cell volume;
one might also find it useful to exclude other biologically restricted regions, such as
the cell nucleus.
7.2.4 Enhancement, Segmentation, and Skeletonization of 3-D Fila-
ments, Planes, and Spheroids
The practice of segmenting three-dimensional objects with distinguishable ge-
ometric features is widely applicable in the image analysis of biological systems.
Although sophisticated segmentation techniques can perform well on high-quality
image data, such as those of Bcl10 and autophagosomes in Chapter 3 [201, 204],
these algorithms can underperform when structures are not continuous or uniformly
bright (e.g., similar to those seen in [205,206] where segmentation and tracing were
performed by hand).
One generalizable way to improve and enhance raw image data is through
the use of carefully constructed filters, such as Laplacian-of-Gaussian (LoG) filters
(Figure 7.1). In the case of a 2-D Laplacian and a 3-D Gaussian, the LoG filter
takes the form of a cylinder (cylindrical LoG). Parameterized by radial and length
parameters (Figure 7.1A), filamentous objects can be extracted from images by
tuning the radius parameter to an appropriate value to match the size of the object
of interest. Note, this tuning could be used to segment thick and thin filaments
157
separately by tuning the radius range. Furthermore, tuning can also be customized
to match the unique shape of some biological structures, such as 3-way (shaped like
a ?T?) or 4-way (?X?) junctions. Ultimately, enhancing images can be achieved by
taking a max projection through the newly introduced angular degrees of freedom
(Figure 7.1B). As a representative example of this method, the data from [205,
206] were enhanced with LoG cylinders by identifying the argmax over all possible
filter angles, segmented via empirically chosen thresholds, and then skeletonized
(Figure 7.1C). The difference between automatically traced data and hand-traced
data was small.
In addition to enhancing the image, carefully constructed filters that span a
filter-parameter space can also be used to extract geometric information about the
objects of interest. For example, in the case of the cylindrical Laplacian-of-Gaussian
filters, the filter-parameter space consisted of angles ? and ?, which represented the
orientation of the cylinder. Given an image I, and filter f , a filtered image J can
be expressed as J(x, y, z) = I(x, y, z) ? f(x, y, z|?, ?). Thus, at a chosen voxel
(x, y, z), if the filter spans an entire (?, ?) subspace, the output will be a 2-D, ?
vs. ? heatmap where the global maximum in the 2-D heatmap is located at the
(?, ?) coordinate that represents alignment with the structure centered around the
(x, y, z) voxel (similar to the heatmap in Figure 7.1B). This process could be relevant
to extracting angular information (i.e. the orientation of filaments or orientations
normal to surfaces) or geometric information like the radii of filaments or thicknesses
of membranes. However, the most impactful and powerful use of this method could
be to generate medial-axis skeletons from grayscale images, which is an ongoing
158
Figure 7.1: Using LoG cylinders to filter, segment, and trace filamentous objects.
(A) A representative segment of a typical LoG cylinder and a xy cross section.
The filter size is parameterized by radial and length parameters, ?xy and ?z. The
orientation of the filter is parameterized by the polar and azimuthal angles, ? and
?. (B) (?,?) heatmap produced by filtering with the LoG cylinder in A at all
angles in the space. The semi-sphere representation indicates direction of maximum
correlation with image features. (C) Representative skeletonization from enhanced
images using the LoG-cylinder filtering.
159
challenge with no clear general solution. In all cases, in addition to cylinders where
?2 = D2x + D2y, LoG filters could also be used to extract and measure planes or
spheroids, where ?2 = D2x or D2x + D2y + D2z , respectively. The robustness of this
scheme can be widely applied to the analysis of 3-D volumes of sparse or densely
packed filament networks, such as axons and dendritic spines.
Enhancement of 2-D and 3-D structures can also be used as a preprocessing
step before calculating optical flow. In estimating the optical flow of a discrete
object, enhancing the object via carefully constructed filters can increase the accu-
racy and continuity of image gradients, and, thus, make the optical-flow calculation
more robust. Furthermore, the mesoscale clustering described in Chapter 4 and
Subsection 7.2.2 can also be combined with spatial information from Laplacian-
of-Gaussian filtering to ensure that optical-flow vectors and mesoscale clusters are
properly contained with the object volume.
160
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