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The majority of bacteria are organized in surface-associated communities, the so called biofilms. Crucial processes that drive the formation of such biofilms are the motility of bacteria on a substrate, enabling cells to reach each others vicinity, and attractive cell-cell-interactions, driving the formation of microcolonies. These colonies, aggregates consisting of thousands of cells, are the precursors of biofilms. In this thesis we investigate the role of cell appendages, called type IV pili, in the substrate motion of bacteria and the formation of bacterial microcolonies. Therefore, we study the bacterial dynamics with the help of experiments and theoretical models. We introduce a novel simulation tool in the tradition of Brownian dynamics simulations. In this computational model, that was developed alongside experimental observations, we study how explicit pili dynamics, pili-substrate and pili–pili interactions drive the cell dynamics. First, we apply our model to investigate how individual cells move on a substrate due to cycles of protrusion and retraction of type IV pili. We show that the characteristic features, in particular persistent motion, can solely originate from collective interactions of pili. Next, we perform experiments to study the coalescence of bacterial microcolonies. With the help of experiments and our computational model, we identify a spatially-dependent gradient of motility of cells within the colony as the origin of a separation of time scale, a feature which is in disagreement with the coalescence dynamics of fluid droplets. Additionally, we show that altering the force generation of pili can cause demixing of cells within bacterial aggregates. Finally, we combine our knowledge of the substrate motion of cells and of the pili-mediated interactions of colonies to identify the main processes (aggregation, fragmentation and cell divisions) that drive assembly of colonies. Starting from experiments, we develop a mathematical model and observe excellent qualitative and quantitative agreement to experimental data of the density of colonies of different sizes. In summary, hand in hand with experiments, we develop theoretical frameworks to unravel the role of type IV pili in bacterial surface motility, microcolony dynamics and colony formation.

During tissue invasion individual tumor cells exhibit two interconvertible migration modes, namely mesenchymal and amoeboid migration. The cellular microenvironment triggers the switch between both modes, thereby allowing adaptation to dynamic conditions. It is, however, unclear if this amoeboid-mesenchymal migration plasticity contributes to a more effective tumor invasion. We address this question with a mathematical model, where the amoeboid-mesenchymal migration plasticity is regulated in response to local extracellular matrix resistance. Our numerical analysis reveals that extracellular matrix structure and presence of a chemotactic gradient are key determinants of the model behavior. Only in complex microenvironments, if the extracellular matrix is highly heterogeneous and a chemotactic gradient directs migration, the amoeboid-mesenchymal migration plasticity allows a more widespread invasion compared to the non-switching amoeboid and mesenchymal modes. Importantly, these specific conditions are characteristic for in vivo tumor invasion. Thus, our study suggests that in vitro systems aiming at unraveling the underlying molecular mechanisms of tumor invasion should take into account the complexity of the microenvironment by considering the combined effects of structural heterogeneities and chemical gradients on cell migration.

A highly structured tissue is formed from an unstructured accumulation of cells during morphogenesis. The pioneering works by Thompson, Turing and Meinhardt introduced physical principles allowing the breaking of symmetry, i.e. the emergence of patterns. This started an ongoing effort to understand the physics behind morphogenesis. In this thesis I will analyze spatial and temporal aspects of morphogenesis for different biological systems in separate parts. The planarian is an ideal model animal to understand mechanisms of spatial body axis formation. This is due to the possibility to measure its body orientation field which utilizes the orientation of the cilia of the planarian’s ventral tissue. Moreover, their astonishing regeneration capabilities allow extensive perturbation experiments. I propose a minimal model which demonstrates the emergence of the wild type body orientation as well as the development of dual-head body orientation due to beta-Catenin RNAi treatment. The topological defects of the body orientation field are calculated on a lattice for simulations and lattice-free for experimental data. These topological defects are a robust way to analyze and compare experiments with simulations. My minimal model reveals sufficient components and mechanisms for robust body axis regeneration. The second important aspect of morphogenesis is the growth regulation of tissues which is often driven by cell proliferation. The regulation of growth is not only important during growth, but also to maintain homeostasis. As fast renewing tissues are very dynamic they may have more pathways of morphogenesis active than non-renewing tissues which points to mechanisms of morphogenesis. The in vivo measurement of this proliferation rate is a challenging task. In this thesis the analysis of DNA labelling assays and the carbon 14 dating method are extended. The carbon 14 dating method can be used to determine cell renewal rates on time scales as long as the lifetime of organism last. Moreover, this method can be applied for tissues in any terrestrial organism because it utilizes the change of carbon 14 in the atmosphere due to atmospheric nuclear bomb tests in the 1960s. The method is extended to gain a better understanding of the tissue dynamics of liver, muscles and amygdala. On the other hand, the DNA labelling assays are used to estimate cell cycle parameters for fast cycling cells. The measurements are fatal to the samples and involve plenty of labor resulting in few sampled data for a time series. The deterministic Nowakowski model is extended to a stochastic model accounting for cell-to-cell and sample-to-sample variability to fully exploit the information contained even in the fluctuations of the data points. A comprehensive parameter recovery study with synthetic ground truth data is performed to evaluate the models. The new stochastic model shows no bias, a good accuracy and scales well with the number of measurements in contrast to the deterministic text-book method. I conclude with proposed applications of my new models and methods that can advance our understanding of growth and pattern formation during morphogenesis. All python software developed in this thesis is shared as open source and a website makes the stochastic analysis of DNA labelling assays available to experimentalists in a user-friendly way.

It has been known for almost two decades that the water proton NMR signal of diffusing water molecules in brain white matter undergoes a non-monoexponential decay with increasing diffusion gradient factor b. With the help of numerical simulations and analytical expressions, much effort has been directed to describing the signal decay and to extracting relevant biophysical features of the system under investigation. However, the physical basis of such nonmonoexponential behavior is still not properly understood. The primary difficulty in characterizing this phenomenon is the variation in behavior in the different directions of diffusion measurement. A combined framework that accounts for the diffusion process in all directions requires several parameters. Addition of many such parameters renders a model to be unwieldy and over-complicated, but over-simplifications can be shown to miss crucially relevant information in the data. In this thesis, I have attempted to handle this problem with simple measurements that span a wide range of parameter space. Compared to often-performed measurements that probe diffusion over a time-scale of 50-100 ms with relatively low diffusion weighting, the measurements here have been done for very short diffusion times of 2 ms and also very long diffusion times up to 2 s. The temperature dependence of the diffusion coefficients has also been extensively probed. To avoid problems related to gross tissue heterogeneity, diffusion-weighted MR imaging in vivo was performed with ultra-high resolution. These simple measurements allowed sequential assessment of many possible arguments that could have led to such non-monoexponential decay curves. Finally, it was concluded that the water in the glial processes was the major contributor to the non-exponential decay, giving rise to a \''slow\'' component both along the axonal fibers and transverse to them.

Single cell migration in artificial collagen gels as an in vitro model system in the context of cancer are studied. Cell and matrix mechanical properties are determined using atomic force microscopy and an advanced analysis method. Matrix pore-size is studied using a novel approach and analysis method. A novel, minimally invasive approach to determine the amount of displacement of the cell microenvironment due to force generation of single cells during migration in artificial 3D collagen gels is introduced. An automated analysis and user friendly software to analyze high-throughput cell invasion is introduced. These methods are used to study cell migration and mechanical properties of the breast cancer cell lines MDA-MB-231 and MCF-7 and the influence of cell nuclear elasticity is investigated. Using mouse embryonic fibroblasts, the role of focal adhesion kinase (FAK) during cell migration is studied using FAK deficient knock-out cell lines FAK-/- and control FAK+/+ as well as kinase-dead mutants FAKR454/R454 and control FAKWT/WT.:Abstract i Acknowledgements iii 1 Introduction 1 2 Background 5 2.1 Cancer — An ever-changing Disease 5 2.1.1 Carcinogenesis and Neoplasm 6 2.1.2 Hallmarks of Cancer 7 2.1.3 Metastasis— The malignant Progression of Cancer 7 2.1.4 Metastatic Cascade 9 2.2 The Cell— Where it begins 10 2.2.1 Actomyosin Complex 12 2.2.1.1 Actin Monomer 12 2.2.1.2 Polymerization 12 2.2.1.3 Structures 14 2.2.1.4 Actin Cortex 15 2.2.1.5 Filopodia 16 2.2.1.6 Lamellipodium 16 2.2.1.7 Invadopodium 17 2.2.1.8 Stress Fibers 17 2.2.1.9 Actin in Cancer and Metastasis 17 2.2.1.10 Myosin and Actin 18 2.2.2 Focal Adhesions 19 2.2.3 Microtubules 20 2.2.4 Intermediate Filaments 21 2.2.5 Cellular Stiffness 22 2.2.6 Nuclear Deformability 23 2.3 The Extracellular Matrix— Where it happens 24 2.3.1 Components and Structure 25 2.3.2 Collagen as a Model System 26 2.3.2.1 Collagen I Fibril Formation 27 2.3.2.2 The Rat/Bovine-Collagen-Mix Model System 28 2.4 Single Cell Migration— Why it spreads 29 3 Materials and Methods 31 3.1 Cell Culture 31 3.1.1 Cancer Cells 31 3.1.2 Mouse fibroblasts 32 3.1.3 Pharmacological treatment 34 3.2 Collagen matrices 34 3.3 Cell Elasticity 36 3.3.1 Atomic Force Microscopy 36 3.3.2 Preparation 37 3.3.3 Data Aquisition 38 3.3.4 Data Analysis 38 3.4 Matrix Stiffness 40 3.4.1 Preparation 40 3.4.2 Data Aquisition 41 3.4.3 Data Analysis 41 3.5 Invasion Assay 42 3.5.1 Preparation 42 3.5.2 Data aquisition 44 3.5.3 Data Analysis 44 3.6 Matrix Topology 48 3.6.1 Preparation 49 3.6.2 Data Acquisition 50 3.6.3 Data Analysis 51 3.6.3.1 Binarization 51 3.6.3.2 Pore-Size 53 3.6.3.3 Fiber Thickness 54 3.7 Fiber Displacement 55 3.7.1 Preparation 56 3.7.2 Data Aquisition 56 3.7.3 Data analysis 57 3.7.3.1 Fiber Displacement 59 3.7.3.2 Cell Segmentation 60 3.7.3.3 Shell Analysis 61 3.8 A toolset to understand Single Cell Migration and what influences it 62 4 Results 65 4.1 Cell Elasticity 65 4.1.1 Example Force-Distance Curves 66 4.1.2 Single Cell Elasticity 67 4.2 Matrix Stiffness 69 4.3 Invasion 71 4.4 Matrix Topology 75 4.5 Influence of Cell Nucleus on Cell Migration 79 4.5.1 Cellular Elasticity 79 4.5.2 Invasion 81 4.6 Fiber Displacement 89 4.7 Effect of FAK on Cell Invasion and Fiber Displacement 93 4.7.1 FAK Knock-Out 93 4.7.2 Kinase-dead FAK Mutant 96 5 Discussion 103 References 107 / Die Einzelzellmigration in künstlichen Kollagennetzwerken als ein in vitro Modellsystem im Kontext von Krebs wurde studiert. Mechanische Eigenschaften von Zellen und der verwendeten Kollagennetzwerke wurden mithilfe der Atomic Force Microscopy (AFM) und weiterentwickelten Analysemethoden bestimmt. Die Porengröße der verwendeten Kollagennetzwerke wurde mit einer neuentwickelten Auswertemethode analysiert. Eine neuartige, minimal-invasive Methode zur Bestimmung der Verformung der Mikroumgebung von Zellen während der Migration verursacht durch Kräftegenerierung der Zelle wird beschrieben. Die Analyse des Invasions-Assays wurde automatisiert und eine nutzerfreundliche Software entwickelt, mit der große Datenmengen ausgewertet werden können. Diese Methoden wurden verwendet, um mechanische Eigenschaften und Migration der humanen Brustkrebszellinien MDA-MB-231 und MCF-7 zu studieren. Die Rolle der focal adhesion kinase (FAK) wurde mithilfe von embryonalen Maus-Fibroblasten studiert. Sowohl eine FAK knock-out Zellinie FAK-/- und Kontrolle FAK+/+, als auch eine kinase-dead Mutante FAKR454/R454 und Kontrolle FAKWT/WT wurden hinsichtlich ihrer Invasion und Verformung der Mikroumgebung analysiert.:Abstract i Acknowledgements iii 1 Introduction 1 2 Background 5 2.1 Cancer — An ever-changing Disease 5 2.1.1 Carcinogenesis and Neoplasm 6 2.1.2 Hallmarks of Cancer 7 2.1.3 Metastasis— The malignant Progression of Cancer 7 2.1.4 Metastatic Cascade 9 2.2 The Cell— Where it begins 10 2.2.1 Actomyosin Complex 12 2.2.1.1 Actin Monomer 12 2.2.1.2 Polymerization 12 2.2.1.3 Structures 14 2.2.1.4 Actin Cortex 15 2.2.1.5 Filopodia 16 2.2.1.6 Lamellipodium 16 2.2.1.7 Invadopodium 17 2.2.1.8 Stress Fibers 17 2.2.1.9 Actin in Cancer and Metastasis 17 2.2.1.10 Myosin and Actin 18 2.2.2 Focal Adhesions 19 2.2.3 Microtubules 20 2.2.4 Intermediate Filaments 21 2.2.5 Cellular Stiffness 22 2.2.6 Nuclear Deformability 23 2.3 The Extracellular Matrix— Where it happens 24 2.3.1 Components and Structure 25 2.3.2 Collagen as a Model System 26 2.3.2.1 Collagen I Fibril Formation 27 2.3.2.2 The Rat/Bovine-Collagen-Mix Model System 28 2.4 Single Cell Migration— Why it spreads 29 3 Materials and Methods 31 3.1 Cell Culture 31 3.1.1 Cancer Cells 31 3.1.2 Mouse fibroblasts 32 3.1.3 Pharmacological treatment 34 3.2 Collagen matrices 34 3.3 Cell Elasticity 36 3.3.1 Atomic Force Microscopy 36 3.3.2 Preparation 37 3.3.3 Data Aquisition 38 3.3.4 Data Analysis 38 3.4 Matrix Stiffness 40 3.4.1 Preparation 40 3.4.2 Data Aquisition 41 3.4.3 Data Analysis 41 3.5 Invasion Assay 42 3.5.1 Preparation 42 3.5.2 Data aquisition 44 3.5.3 Data Analysis 44 3.6 Matrix Topology 48 3.6.1 Preparation 49 3.6.2 Data Acquisition 50 3.6.3 Data Analysis 51 3.6.3.1 Binarization 51 3.6.3.2 Pore-Size 53 3.6.3.3 Fiber Thickness 54 3.7 Fiber Displacement 55 3.7.1 Preparation 56 3.7.2 Data Aquisition 56 3.7.3 Data analysis 57 3.7.3.1 Fiber Displacement 59 3.7.3.2 Cell Segmentation 60 3.7.3.3 Shell Analysis 61 3.8 A toolset to understand Single Cell Migration and what influences it 62 4 Results 65 4.1 Cell Elasticity 65 4.1.1 Example Force-Distance Curves 66 4.1.2 Single Cell Elasticity 67 4.2 Matrix Stiffness 69 4.3 Invasion 71 4.4 Matrix Topology 75 4.5 Influence of Cell Nucleus on Cell Migration 79 4.5.1 Cellular Elasticity 79 4.5.2 Invasion 81 4.6 Fiber Displacement 89 4.7 Effect of FAK on Cell Invasion and Fiber Displacement 93 4.7.1 FAK Knock-Out 93 4.7.2 Kinase-dead FAK Mutant 96 5 Discussion 103 References 107

Beta-barrel outer membrane proteins (OMPs) present on the outer membrane of Gram-negative bacteria are vital to cell survival. Their biogenesis is a challenging process which is tightly regulated by protein-chaperone interactions at various stages. Upon secretion from the inner membrane, OMPs are solubilized by periplasmic chaperones seventeen kilodalton protein (Skp) and survival factor A (SurA) and maintained in a folding competent state until they reach the outer membrane. As periplasm has an energy deficient environment, thermodynamics plays an important role in fine tuning these chaperone-OMP interactions. Thus, a complete understanding of such associations necessitates an investigation into both structural and thermodynamic aspects of the underlying intercommunication. Yet, they have been difficult to discern because of the conformational heterogeneity of the bound substrates, fast chain dynamics and the aggregation prone nature of OMPs. This demands for use of single molecule spectroscopy techniques, specifically, single molecule Förster resonance energy transfer (smFRET). In this thesis, upon leveraging the conformational and temporal resolution offered by smFRET, an exciting insight is obtained into the mechanistic and functional features of unfolded and Skp/SurA - bound states of two differently sized OMPs: OmpX (8 β-strands) and outer membrane phospholipase A (OmpLA – 12 β-strands). First, it was elucidated that the unfolded states of both the proteins exhibit slow interconversion within their sub-populations. Remarkably, upon complexing with chaperones, irrespective of the chosen OMP, the bound substrates expanded with localised chain reconfiguration on a sub-millisecond timescale. Yet, due to the different interaction mechanisms employed by Skp (encapsulation) and SurA (multivalent binding), their clients were found to be characterised by distinct conformational ensembles. Importantly, the extracted thermodynamic parameters of change in enthalpy and entropy exemplified the mechanistically dissimilar functionalities of the two chaperones. Furthermore, both Skp and SurA were found to be capable of disintegrating aggregated OMPs rather cooperatively, highlighting their multifaceted chaperone activity. This work is of significant fundamental value towards understanding the ubiquitous chaperone-protein interactions and opens up the possibility to design drugs targeting the chaperone-OMP complex itself, one step ahead of the OMP assembly on the outer membrane.

This work is a numerical examination of a semiflexible polymer exposed to a disorder landscape consisting of hard disks. For a small parameter range and simple constraints it is known that disorder leads to structural transitions of the equilibrium properties of polymers. The scope of this work strongly extends this range by going to both high disorder densities and large stiffnesses of the polymers. The competing length scales of polymer stiffness and average distance between the obstacles of the potential along with the way of assembling the disorder lead to a wide range of effects such as crumpling and stretching of polymer configurations due to the disorder or a modulation of the polymer’s characterizing observables with the correlation function of the potential. The high accuracy results presented in this work have been obtained by means of sophisticated Monte Carlo simulations. The refinement of a rarely applied but highly promising method to a state of the art algorithm in connection with latest numerical techniques made it possible to investigate the impact of hard-disk disorder on semiflexible polymer conformations on a broad scale.

Zu den Eigenschaften eukaryotischer Zellen gehört ihre Kompartimentierung, welche durch die Abtrennung verschiedener Reaktionsräume durch Lipiddoppelschichten erreicht wird. Verschiedene Vesikel-Transportwege verbinden diese Kompartimente miteinander, einer dieser Wege in der Hefe Saccharomyces cerevisiae ist der sogenannte ALP-Weg. Dieser gehört zu den biosynthetischen Wegen, über die neue Proteine an ihren Bestimmungsort gebracht werden, in diesem Falle die Vakuole. Ausgehend vom Golgi-Apparat werden die Vesikel dieses Weges mit Hilfe des Adaptorproteinkomplexes-3 (AP-3) gebildet. Ein weiteres Protein, das eine spezifische Funktion in diesem Weg übernimmt, ist Vps41. Ein aktuelles Modell beschreibt seine Funktion in der Aufnahme der Vesikel an der Vakuole. Es konnte gezeigt werden, das Vps41 mit der sogenannten ear-Domäne von Apl5, einer Untereinheit des AP-3- Komplexes, interagiert. In dieser Arbeit konnte ich nachweisen, dass die Interaktionsstelle im Vps41 innerhalb einer konservierten PEST-Domäne liegt. Eine Deletion dieser Domäne beeinflußte die Funktion des Proteins im ALP-Weg jedoch nicht die in der homotypischen Vakuolenfusion und im CPY-Weg. Eine weitere Eingrenzung des deletierten Bereiches zeigte, dass die PEST-Domäne eine Sequenz enthält, die einem Di-Leucin- Sortierungssignal ähnlich ist. Dieses konnte ich als minimal notwendigen Bereich für die Wechselwirkung mit der Apl5-ear-Domäne bestimmen. Meine Daten zeigen, dass dieser Bereich des Proteins notwendig ist für das Docking der AP-3-Vesikel an der Vakuole. Weiterhin konnte ich eine kompetitive Bindung von Liposomen und Apl5 an die N-terminale Hälfte von Vps41 zeigen. Zusammengefasst und mit aktuellen Veröffentlichungen in Zusammhang gebracht, ergänzen meine Daten das Modell der Funktion von Vps41 in der Vesikelaufnahme an der Vakuole: Vps41 wird durch die Rab-GTPase Ypt7, als deren Effektorprotein, an späte Endosomen gebunden. An dieser stark gekrümmten Membran taucht ein kürzlich identifiziertes ALPS (amphipathic lipid packing sensor)-Motiv im Vps41 in die Membran des Organells ein und zieht so den N-terminalen Bereich mit der Bindestelle für die AP-3-Vesikel an die Oberfläche des Organells wodurch eine verfrühte Fusion der AP-3-Vesikel mit dem Endosom verhindert wird. Erst nach der Reifung zur Vakuole wird die PEST-Domäne für die Bindung an Apl5 verfügbar, da sich die Membrankrümmung ändert. Zusätzlich wird das ALPS-Motiv phosphoryliert, so dass dieses nicht mehr in die Membran eintauchen kann. Erst jetzt ist eine Interaktion zwischen Apl5 und Vps41 und damit eine Fusion der AP-3-Vesikel mit der Vakuole möglich. Der zweite Teil dieser Arbeit beschäftigt sich mit der Protonentranslokation durch den Fo-Teil der ATP-Synthase aus Escherichia coli. Durch Mutagenese wurden ATP-Synthasen hergestellt, in denen die beiden für den Protonentransport essentiellen Aminosäurereste D61 in der Untereinheit c und R210 in der Untereinheit a in der α-Helix in der sie liegen, entweder einzeln oder beide zusammen, um je eine Helixwindung nach oben oder unten verschoben wurden. Dies führt zu einer Verlängerung bzw. Verkürzung der Protonenzu- und austrittskanäle. Durch die Untersuchung der Funktionalität dieser ATPasen auf sowohl aktives und passives Protonenpumpen, als auch ATP-Synthese konnte ich zeigen, daß die Position der beiden essentiellen Aminosäurereste cD61 und aR210 zueinander nicht entscheidend ist. Werden beide Reste in die gleiche Richtung verschoben, so daß ihre Position zueinander gleich bleibt, kommt es unabhängig von der Richtung immer zu einem kompletten Funktionsverlust. Weiterhin läßt sich aus meinen Daten folgern, daß die Position des Restes aR210 in der Mitte der Membran wichtig ist. Beim Verschieben des Restes auf die Position 206 (a-up) geht die gesamte Funktion des Fo-Teiles verloren, während das Verschieben auf die Position 214 (a-down) zu einem passiven Ausströmen der Protonen durch den Fo-Teil führt. Die Position des Restes cD61 in der Membran ist flexibler. Obwohl die Repositionierung des Aspartats auf die Position 57 (c-up) jegliche Funktionalität des Fo-Teiles beeinträchtigt, ermöglicht ein Verschieben auf die Position 65 (c-down) aktives und passives Protonenpumpen, sowie die Synthese von ATP.