Modelling shape fluctuations during cell migration

Cell migration is of crucial importance for many physiological processes, including embryonic development, wound healing and immune response. Defects in cell migration are the cause of chronic in ammatory diseases, mental retardation and cancer metastasis. Cell movement is driven by actin-mediated cell protrusion, substrate adhesion and contraction of the cell body. The emergent behaviour of the intracellular processes described above is a change in the morphology of the cell. This inspires the main hypothesis of this work which is that there is a measurable relationship between cell morphology dynamics and migratory behaviour, and that quantitative models of this relationship can create useful tools for investigating the mechanisms by which a cell regulates its own motility. Here we analyse cell shapes of migrating human retinal pigment epithelial cells with the aim to map cell shape changes to cellular behaviour. We develop a non-linear model for learning the intrinsic low-dimensional structure of cell shape space and use the resultant shape representation to analyse quantitative relationships between shape and migration behaviour. The biggest algorithmic challenge overcome in this thesis was developing a method for efficiently and appropriately measuring the shape difference between pairs of cells that may have come from independent image scenes. This difference measure must be capable of coping with the widely varying morphologies exhibited by migrating epithelial cells. We present a new, rapid, landmark-free, shape difference measure called the Best Alignment Metric (BAM). We show that BAM performs highly within our framework, generating a shape space representation of a very large dataset without any prior information on the importance of any given shape feature. We demonstrate quantitative evidence for a model of cell turning based on repolarisation and discuss the impact our proposed framework could have on the continued study of migratory mechanisms

Stochastic dynamics of migrating cells

Cell migration is critical in many physiological phenomena, including embryogenesis, immune response, and cancer. In all these processes, cells face a common physical challenge: they navigate confining extra-cellular environments, in which they squeeze through thin constrictions. The motion of cells is powered by a complex machinery whose molecular basis is increasingly well understood. However, a quantitative understanding of the functional cell behaviours that emerge at the cellular scale remains elusive. This raises a central question, which acts as a common thread throughout the projects in this thesis: do migrating cells exhibit emergent dynamical 'laws' that describe their behavioural dynamics in confining environments? To address this question, we develop data-driven approaches to infer the dynamics of migrating cells directly from experimental data. We study the migration of cells in artificial confinements featuring a thin constriction across which cells repeatedly squeeze. From the experimental cell trajectories, we infer an equation of cell motion, which decomposes the dynamics into deterministic and stochastic contributions. This approach reveals that cells deterministically drive themselves into the thin constriction, which is in contrast to the intuition that constrictions act as effective barriers. This active driving leads to intricate non-linear dynamics that are poised close to a bifurcation between a bistable system and a limit cycle oscillator. We further generalize this data-driven framework to detect and characterize the variance of migration behaviour within a cell population and to investigate how cells respond to varying confinement size, shape, and orientation. We next investigate the mechanistic basis of these dynamics. Cell migration relies on the concerted dynamics of several cellular components, including cell protrusions and adhesive connections to the environment. Based on the experimental data, we systematically constrain a mechanistic model for confined cell migration. This model indicates that the observed deterministic driving is a consequence of the combined effects of the variable adhesiveness of the environment and a self-reinforcement of cell polarity in response to thin constrictions. These results suggest polarity feedback adaptation as a key mechanism in confined cell migration. Finally, we investigate the dynamics of interacting cells. To enable inference of cell-cell interactions, we develop Underdamped Langevin Inference, an inference method for stochastic high-dimensional and interacting systems. We apply this method to experiments of confined pairs of cells, which repeatedly collide with one another. This reveals that non-cancerous (MCF10A) and cancerous (MDA-MB-231) cells exhibit distinct interactions: while the non-cancerous cells exhibit repulsion and effective friction, the cancerous cells exhibit attraction and a surprising 'anti-friction' interaction. These interactions lead to non-cancerous cells predominantly reversing upon collision, while the cancer cells are able to efficiently move past one another by relative sliding. Furthermore, we investigate the effects of cadherin-mediated molecular contacts on cell-cell interactions in collective migration. Taken together, the data-driven approaches presented in this thesis may help to provide a new avenue to uncover the emergent laws governing the stochastic dynamics of migrating cells. We demonstrate how these approaches can provide key insights both into underlying mechanisms as well as emergent cell behaviours at larger scales.Zellmigration ist ein Kernelement vieler physiologischer Phänomene wie der Embryogenese, dem Immunsystem und der Krebsmetastase. In all diesen Prozessen stehen Zellen vor einer physikalischen Herausforderung: Sie bewegen sich in beengten Umgebungen, in denen sie Engstellen passieren müssen. Die Zellbewegung wird von einer komplexen Maschinerie an- getrieben, deren molekulare Komponenten immer besser verstanden werden. Demgegenüber fehlt ein quantitatives Verständnis des funktionalen Migrationsverhaltens der Zelle als Ganzes. Die verbindende Fragestellung der Projekte in dieser Arbeit lautet daher: gibt es emergente dynamische 'Gesetze', die die Verhaltensdynamik migrierender Zellen in beengten Umgebungen beschreiben? Um dieser Frage nachzugehen, entwickeln wir datengetriebene Ansätze, die es uns erlauben, die Dynamik migrierender Zellen direkt aus experimentellen Daten zu inferieren. Wir untersuchen Zellmigration in künstlichen Systemen, in denen Zellen Engstellen wiederholt passieren müssen. Aus den experimentellen Zelltrajektorien inferieren wir eine Bewegungsgleichung, die die Dynamik in deterministische und stochastische Komponenten trennt. Diese Methode zeigt, dass sich Zellen deterministisch 'aktiv' in die Engstellen hineinbewegen, ganz entgegen der intuitiven Erwartung, dass Engstellen als Hindernis fungieren könnten. Dieser aktive Antrieb führt zu einer komplexen nichtlinearen Dynamik im Übergangsbereich zwischen einem bistabilen System und einem Grenzzyklus-Oszillator. Wir verallgemeinern diesen datenbasierten Ansatz, um die Varianz des Migrationsverhaltens innerhalb einer Zellpopulation zu quantifizieren, und analysieren, wie Zellen auf die Größe, Form und Orientierung ihrer Umgebung reagieren. Darauf aufbauend untersuchen wir die zugrundeliegenden Mechanismen dieser Dynamik. Zellmigration basiert auf verschiedenen zellulären Komponenten, wie unter Anderem den Zellprotrusionen und der Adhäsion mit der Umgebung. Auf Basis der experimentellen Daten entwickeln wir ein mechanistisches Modell für Zellmigration in beengten Systemen, welches zeigt, dass der beobachtete aktive Antrieb eine Konsequenz zweier Effekte ist: Einer variierenden Adhäsion mit der Umgebung und einer Zellpolarität, die sich in Engstellen selbst verstärkt. Diese Ergebnisse deuten darauf hin, dass die Anpassung der Zellpolarität an die lokale Geometrie ein Schlüsselmechanismus in beengter Zellmigration ist. Schließlich analysieren wir die Dynamik interagierender Zellen. Um Zell-Zell Interaktionen zu inferieren, entwickeln wir die Underdamped Langevin Inference, eine Inferenzmethode für stochastische hochdimensionale und interagierende Systeme. Wir wenden diese Methode auf Daten von eingeschlossenen Zellpaaren an, welche wiederholt miteinander kollidieren. Dies zeigt, dass gesunde (MCF10A) und krebsartige (MDA-MB-231) Zellen unterschiedliche Interaktionen aufweisen: Während gesunde Zellen mit Abstoßung und effektiver Reibung interagieren, zeigen Krebszellen Anziehung und eine überraschende 'Anti-Reibung'. Diese Interaktionen führen dazu, dass gesunde Zellen nach Kollisionen primär umkehren, während Krebszellen effizient aneinander vorbeigleiten. Darüberhinaus analysieren wir die Effekte von Cadherin-basierten Molekularkontakten auf Zell-Zell Interaktionen in kollektiver Migration. Zusammenfassend könnten die in dieser Arbeit präsentierten datengetriebenen Ans ̈atze dabei helfen, ein besseres Verständnis der emergenten stochastischen Dynamik migrierender Zellen zu erlangen. Wir zeigen, wie diese Methoden wichtige Erkenntnisse sowohl über die zugrundeliegenden Mechanismen als auch über das emergente Zellverhalten liefern können

Molecular Mechanisms of Cell Migration Inhibition by Synthetic Triterpenoids

Cell migration is an important mediator of cancer metastasis and invasion, which is responsible for 90% of cancer-related premature deaths in Canada. Synthetic triterpenoids are a class of promising anti-cancer compounds that have shown considerable efficacy in targeting various cellular functions including apoptosis, growth, inflammation and cytoprotection in both cell culture and animal tumor models. However, their effect on cell migration, an important event in metastasis, remains poorly understood. This thesis focuses on deciphering the molecular mechanisms whereby the synthetic triterpenoids affect cell migration. I observed that the imidazolide and methyl ester derivatives of the synthetic triterpenoid, 2-cyano-3,12-dioxooleana-1,9-dien-28-oic aic acid (CDDO-Im and CDDO-Me), inhibit cell migration by disrupting microtubule dynamics. In addition, I found that these triterpenoids disrupt cell polarity by displacing proteins at the leading edge of migrating cells. Furthermore, using a two-pronged proteomic approach involving protein arrays and mass spectrometry, I identified numerous triterpenoid-binding targets involved in actin polymerization and focal adhesion maintenance. My data further revealed that triterpenoids inhibit branched actin polymerization by targeting Arp3 in the Arp2/3 complex and target GSK3b activity to alter focal adhesion sizes. Collectively, my studies provided novel insights on the underlying molecular mechanisms by which triterpenoids act to affect cell migration. This knowledge will be important for developing a more efficacious and specific therapeutic triterpenoid compound that targets cancer metastasis

Models of the lung tissue microenvironment for studies of human myeloid cell function

Studies of the immune system requires knowledge concerning not only the perturbating event itself, i.e. specific microorganisms, and how it interacts with immune cells but also how it functions in its natural environment – tissues. The non-hematopoietic component of tissues contributes immensely to all immune responses and acknowledging its contribution have been central to immunological research during the last decade. The work in this thesis focuses on the use of a three-dimensional organotypic lung tissue model, which recapitulates many aspects of its in vivo correlate. Study I describe the properties of the organotypic tissue model and implanted monocyte-derived dendritic cells. In Study II we show how the organotypic tissue model can be used to study, not only secreted factors influenced by dendritic cells, but also a key functional property of dendritic cells – cell migration. In Study III, we used the tissue model to model a staphylococcus aureus infection, and in particular how derived toxins such as alpha-toxin and Panton-Valentine Leukocidin (PVL) contribute to tissue pathology. Immunological downstream effects of staphylococcal toxins are further explored in Study IV, where we investigate the role of ADAM10 and CX3CL1 (fractalkine) in alpha-toxin mediated pathology. In Study V, the goal was to set up a model system in which it is possible to study the interaction between immune cells, tissue model and tumor cells, analogous to Study III and IV. The studies here provide a framework for how complex, multicellular in vitro systems can be used in immunological studies in context to inflammation-driven pathologies. The validity of the model system remains to be studied, and the role for organotypic tissue models in medical research is yet to be determined. However, it is becoming increasingly clear that the study of disease mechanisms relating to inflammation will benefit from added complexity and acknowledgement that cells such as epithelial cells and fibroblast are active contributors to immune responses and tissue pathology

Amoeboid Shape Dynamics on Flat and Topographically Modified Surfaces

I present an analysis of the shape dynamics of the amoeba Dictyostelium discoideum, a model system for the study of cellular migration. To better understand cellular migration in complicated 3-D environments, cell migration was studied on simple 3-D surfaces, such as cliffs and ridges. D. discoideum interact with surfaces without forming mature focal adhesion complexes. The cellular response to the surface topography was characterized by measuring and looking for patterns in cell shape. Dynamic cell shape is a measure of the interaction between the internal biochemical state of a cell and its external environment. For D. discoideum migrating on flat surfaces, waves of high boundary curvature were observed to travel from the cell front to the cell back. Curvature waves are also easily seen in cells that do not adhere to a surface, such as cells that are electrostatically repelled from the coverslip or cells that are extended over the edge of micro-fabricated cliffs. At the leading edge of adhered cells, these curvature waves are associated with protrusive activity, suggesting that protrusive motion can be thought of as a wave-like process. The wave-like character of protrusions provides a plausible mechanism for the ability of cells to swim in viscous fluids and to navigate complex 3-D topography. Patterning of focal adhesion complexes has previously been implicated in contact guidance (polarization or migration parallel to linear topographical structures). However, significant contact guidance is observed in D. discoideum, which lack focal adhesion complexes. Analyzing the migration of cells on nanogratings of ridges spaced various distances apart, ridges spaced about 1.5 micrometers apart were found to guide cells best. Contact guidance was modeled as an interaction between wave-like processes internal to the cell and the periodicity of the nanograting. The observed wavelength and speed of the oscillations that best couple to the surface are consistent with those of protrusive dynamics. Dynamic sensing via actin or protrusive dynamics might then play a role in contact guidance

Cell-migration in two-state micropatterns

Migrating cells are key players during development and immune response, and also in cancer metastasis. Cells actively adapt their mode of migration to constraints imposed by their microenvironment. To provide standardized and tunable microenvironments for the study of cell organization and migration, micropatterning techniques were developed. Micropatterning allows the controlled deposition of cell-adhesive proteins in defined geometries on a surface while rendering the surrounding areas cell-repellent. The spreading dynamics of cells on micropatterns has previously been successfully modelled and several theoretical models exist for cell migration on homogeneous substrates. In contrast, little is known about the dynamics of cells in confining microenvironments. In particular, it is an open question how the dynamics changes as a function of the geometry of the confinement. In this thesis, I developed an artificial micrometre-scale two-state system for the study of cell migration in confinement. Furthermore, I identified several geometric determinants affecting the migration dynamics and quantified their effect. The micropatterned system consists of two cell-sized adhesion sites at either end of a connecting stripe. MDA-MB-231 human breast cancer cells, and several other cell lines, responded to the dumbbell-like geometry by migrating back and forth between the adhesion sites. The migration can be characterized by direct readouts from the cell trajectories such as accelerations, dwell times and occupation probabilities. In collaboration with the Broedersz group, we found a novel theoretical description for cell migration in confinement that is entirely based on short-timescale readouts. We showed that the cell migration in the two-state micropattern is captured by a stochastic equation of motion consisting of a deterministic and a stochastic term. Both terms were inferred from the data and a good agreement between model prediction and experimental data was found. In particular, we established that highly metastatic MDA-MB-231 breast cancer cells and non-tumourigenic MCF10A breast epithelial cells have distinct deterministic dynamics on two-state patterns with a bridge width of 7.2 μm. The two-state setup was further used to systematically probe the influence of geometrical cues presented to the cells within the micropatterns. Thus, the migration dynamics of cells was found to be sensitive to bridge length and width, adhesion site area and adhesion site orientation. Specifically, the escape rates of cells from differently shaped adhesion sites were determined. For isotropic shapes, it was found that the escape rates linearly depend on adhesion site area only. When adhesion sites extend significantly into the direction orthogonal to the micropattern’s bridge, cell polarisation on the adhesion sites biases occupation probabilities. Consequently, the two-state system is a suitable assay to study cell dynamics as a function of the confining microenvironment. In this particular confinement, cells have to deform in order to transition between the two adhesion sites. As cell lines of different metastatic potential exhibit different dynamic behaviour, the measured escape dynamics may possibly be connected to clinical parameters like invasiveness.Die Hauptakteure in der (Embryonal-)Entwicklung und bei Immunreaktionen, sowie bei Krebsmetastasen sind migrierende Zellen. Zellen passen ihre Art der Migration aktiv den von ihrer mikroskopischen Umgebung gesetzten Randbedingungen an. Um standardisierte und justierbare Mikro-Umgebungen für die Untersuchung von Zellorganisation und -migration bereitstellen zu können, wurden Mikrostrukturierungstechniken entwickelt. Die Mikrostrukturierung erlaubt es, zelladhäsive Proteine in definierten Geometrien an einer Oberfläche anzubinden, während die umgebenden Flächen zellabweisend funktionalisiert werden. Die Spreit-Dynamik von Zellen auf Mikrostrukturen wurde schon zuvor erfolgreich modelliert; und eine Vielzahl an theoretischen Modellen existieren, die die Zellmigration auf homogenen Substraten beschreiben. Im Gegensatz dazu ist wenig über die Dynamik von Zellen in einengenden Geometrien bekannt. Insbesondere ist die Frage, wie sich die Dynamik als Funktion der Geometrie der Einengung verändert, noch unbeantwortet. In dieser Dissertation habe ich ein artifizielles mikrometerskaliges Zweizustandssystem für die Untersuchung der Zellmigration bei Einengung entwickelt. Weiterhin habe ich mehrere geometrische Bestimmungsgrößen identifiziert, die die Migrationsdynamik beeinflussen, und habe ihren Effekt quantifiziert. Das mikrostrukturierte System besteht aus zwei zellgroßen Adhäsionsflächen, die an den beiden Enden eines verbindenden Streifens liegen. Menschliche Brustkrebszellen MDA-MB-231, sowie verschiedene andere Zelllinien, migrieren in dieser Hantelgeometrie zwischen den Adhäsionsflächen hin und her. Die Migration kann durch aus den Zelltrajektorien direkt auslesbare Größen wie Beschleunigungen, Aufenthaltsdauern und Aufenthaltswahrscheinlichkeiten charakterisiert werden. In Kollaboration mit der Arbeitsgruppe Broedersz haben wir eine neuartige theoretische Beschreibung der Zellmigration in beengten Geometrien entwickelt, die ausschließlich auf der Kurzzeitdynamik basiert. Wir haben gezeigt, dass die Zellmigration in Zweizustands-Mikrostrukturen von einer stochastischen Bewegungsgleichung, die aus einem deterministischen und einem stochastischen Term besteht, beschrieben wird. Beide Terme wurden aus den Daten inferiert und eine gute Übereinstimmung zwischen Modellvorhersagen und Experimentaldaten wurde beobachtet. Insbesondere haben wir herausgefunden, dass hochmetastatische MDA-MB-231 Brustkrebszellen und nicht maligne Zellen aus Brustgewebe (MCF10A) auf Zweizustandssystemen mit Brückenbreite 7.2 μm verschiedene deterministische Dynamiken aufzeigen. Das Zweizustandssystem wurde weiterhin genutzt, um systematisch den Einfluss der Geometrie der Mikrostruktur auf die Zellmigration zu studieren. Dabei haben wir herausgefunden, dass die Migrationsdynamik der Zellen sensitiv gegenüber der Brückenlänge und -breite, sowie der Adhäsionsflächengröße und -orientierung ist. Insbesondere wurden die Austrittsraten der Zellen aus Adhäsionsflächen mit verschiedenen Formen bestimmt. Wir haben festgestellt, dass die Austrittsraten für isotrope Formen ausschließlich von der Adhäsionsfläche linear abhängen. Wenn die Adhäsionsflächen eine signifikante, zur Brücke der Mikrostruktur orthogonale, Ausdehnung haben, beeinflusst die Zellpolarisation die Aufenthaltswahrscheinlichkeiten. Daraus folgend ist das Zweizustandssystem ein geeigneter Testaufbau um Zelldynamik als Funktion der einengenden mikroskopischen Umgebung zu studieren. In dieser beengten Geometrie müssen Zellen ihre Form verändern um Übergänge zwischen den zwei Adhäsionsflächen zu bewerkstelligen. Da Zelllinien mit unterschiedlichem metastatischem Potential unterschiedliche dynamische Verhalten aufzeigen, kann man potentiell die gemessene Austrittsdynamik mit klinischen Parametern wie Invasivität verbinden

Complexity in Developmental Systems: Toward an Integrated Understanding of Organ Formation

During animal development, embryonic cells assemble into intricately structured organs by working together in organized groups capable of implementing tightly coordinated collective behaviors, including patterning, morphogenesis and migration. Although many of the molecular components and basic mechanisms underlying such collective phenomena are known, the complexity emerging from their interplay still represents a major challenge for developmental biology. Here, we first clarify the nature of this challenge and outline three key strategies for addressing it: precision perturbation, synthetic developmental biology, and data-driven inference. We then present the results of our effort to develop a set of tools rooted in two of these strategies and to apply them to uncover new mechanisms and principles underlying the coordination of collective cell behaviors during organogenesis, using the zebrafish posterior lateral line primordium as a model system. To enable precision perturbation of migration and morphogenesis, we sought to adapt optogenetic tools to control chemokine and actin signaling. This endeavor proved far from trivial and we were ultimately unable to derive functional optogenetic constructs. However, our work toward this goal led to a useful new way of perturbing cortical contractility, which in turn revealed a potential role for cell surface tension in lateral line organogenesis. Independently, we hypothesized that the lateral line primordium might employ plithotaxis to coordinate organ formation with collective migration. We tested this hypothesis using a novel optical tool that allows targeted arrest of cell migration, finding that contrary to previous assumptions plithotaxis does not substantially contribute to primordium guidance. Finally, we developed a computational framework for automated single-cell segmentation, latent feature extraction and quantitative analysis of cellular architecture. We identified the key factors defining shape heterogeneity across primordium cells and went on to use this shape space as a reference for mapping the results of multiple experiments into a quantitative atlas of primordium cell architecture. We also propose a number of data-driven approaches to help bridge the gap from big data to mechanistic models. Overall, this study presents several conceptual and methodological advances toward an integrated understanding of complex multi-cellular systems