Microtubule associated molecular motors are involved in a multitude of fundamental cellular processes such as intracellular transport and spindle positioning. During these movements multiple motor proteins often work together and are, therefore, able to exert high forces. Thus force generation and sensing are common mechanisms for controlling motor driven movement. These mechanisms play a pivotal role when motor proteins antagonize each other, e.g. to facilitate oscillations of the spindle or the nucleus. Single motor proteins have been characterized in depth over the last two decades, our understanding of the collective behavior of molecular motors remains, however, poor. Since motor proteins often cooperate while they walk along microtubules, it is necessary to describe their collective reaction to a load quantitatively in order to understand the mechanism of many motor-driven processes. I studied the antagonistic action of many molecular motors (of one kind) in a gliding geometry. For this purpose I crosslinked two microtubules in an antiparallel fashion, so that they formed \"doublets\". Then I observed the gliding motility of these antiparallel doublets and analyzed the gliding velocity with respect to the relative number of motors pulling or pushing against each other. I observed that the antiparallel doublets gliding on conventional kinesin-1 (from Drosophila melanogaster) as well as cytoplasmic dynein (from Saccharomyces cerevisae) exhibited two distinct modes of movement, slow and fast, which were well separated. Furthermore I found a bistability, meaning, that both kinds of movement, slow and fast, occurred at the same ratio of antagonizing motors. Antiparallel doublets gliding on the non-processive motor protein Ncd (the kinesin-14 from D. melanogaster) showed, however, no bistability. The collective dynamics of all three motor proteins were described with a quantitative theory based on single-motor properties. Furthermore the response of multiple dynein motors towards an external, well-defined load was measured in a gliding geometry by magnetic tweezing. Examples of multi-motor force-velocity relationships are presented and discussed. I established, furthermore, a method for counting single surface immobilized motors to guide the evaluation of the tweezing experiments.

Developing tissues are out-of-equilibrium systems that grow and reshape to form organs in adult animals. They are typically composed of a large number of cells. The constitutive cells of a tissue perform different roles in tissue development and contribute to the overall tissue shape changes. In this thesis, we construct a hydrodynamic theory of developing epithelial tissues. We use it to investigate the developing wing of the fruit fly Drosophila melanogaster. This theory relates the coarse-grained cell scale properties to the large-scale tissue flows. We explicitly account for the active cellular processes in the tissue that drive tissue flows. In our description of the tissue, we also include the memory effects that are necessary to account for the experimental observations. These memory effects have a significant influence on the tissue rheology. Using this hydrodynamic theory we analyze shear flow in a developing fruit fly wing tissue. We find that the active cellular processes contribute to overall tissue flows and that memory effects are present in the wing tissue. We investigate consequences of these findings on the rheology of tissue shear flow. We find that the memory effects give rise to an inertial response that leads to oscillations in the tissue but it does not stem from the wing mass. Finally, we describe how the tissue rheology is affected by different boundary conditions. We then investigate the area changes during the pupal wing development and we construct a mechanosensitive model for the cell extrusion rate in the pupal wing. Analysis of cell extrusions in the context of this model also allows us to extract information about the cell division properties. Boundary connections between the wing tissue and surrounding cuticle are crucial for the proper development of the pupal wing. A dumpy mutant wing is strongly misshaped during the pupal wing morphogenesis. We use a simple model for the wing to show that the dumpy mutant wing can be described as a wild type wing with compromised boundary conditions. Finally, we analyze cell properties and tissue flows in a developing wing disc epithelium. Motivated by the observation of radially oriented active T1 transitions in the wing disc epithelium, we use the hydrodynamic theory to investigate the influence of such T1 transitions on stresses in the tissue. We show that sufficiently strong radially oriented active T1 transitions can contribute to the control of the tissue size. Results obtained in this thesis extend our understanding of the fly wing tissue rheology and the role of internal and external forces in the proper shaping of the wing epithelium. The hydrodynamic theory we use to describe the fly wing development provides a set of phenomenological parameters that characterize the tissue mechanics and can be experimentally measured. Therefore, we expect that future research will include and extend the hydrodynamic theory presented in this thesis.

Jamming' ist ein faszinierender, nicht vollständig verstandener Prozess in der Physik der weichen Materie. Zelluläres Jamming' tritt auch in biologischem Gewebe auf und muss sich im Fall von Krebszellen im Tumorgewebe aufgrund der dichten Packung der Zellen über der dichtesten Kugelpackung anders verhalten als die bekannten 'Jamming' Systeme. In meiner Dissertation skizziere ich wesentliche Ergebnisse zum Verständnis dieses neuen physikalischen Phänomens. Meine Erkenntnisse tragen dazu bei die Dichotomie zwischen den Theorien der dichteinduzierten und der forminduzierten 'Zelljamming' aufzulösen. Die gewonnenen Erkenntnisse weisen auf die Möglichkeit hin Krebszellformen und deren Zellkernformen als Tumormarker für die Metastasierung zu verwenden. Ich fand ein kritisches Skalierungsverhalten für die Dynamik der Neuanordnung von Zellen in der Nähe des Jamming-Übergangs, abhängig von der Zellform der Nachbarschaft. Dies ist der bisher stärkste Beweis dafür, dass die Zellformen als Kontrollparameter für das 'Zelljamming' fungieren können. Die Zellanzahldichte beeinflusst ebenfalls das 'Jamming', ihr Einfluss kann jedoch als eine Verlangsamung der Eigengeschwindigkeit der Zellen beschrieben werden. Eine hohe Zellanzahldichte allein würde also nur die Viskosität des Gewebes erhöhen und es nicht verfestigen. Darüber hinaus habe ich gezeigt, dass es in dicht gepackten dreidimensionalen Zellsphäroiden sowie in Primärtumorstücken einen mit der Zellform verbundenen 'Jamming'-Übergang gibt. Ich verbinde das 'Unjamming' von Zellen mit dem Fortschreiten des Krebses, indem ich zeigte, dass die Herunterregulierung des Adhäsionsmoleküls E-Cadherin, die ein typischer Schritt während der Krebentwicklung ist, einen 'Unjamming'-Übergang verursacht. Bei diesem 'Unjamming'-Übergang kommt es zu einem ausgeprägten Verlust der Kohäsion und einem reduzierten Volumenanteil der Zellen, was zeigt, dass das 'Zelljamming' einen hohen Volumenanteil erfordert.

Die mechanischen Eigenschaften von Zellen charakterisieren und beeinflussen deren Zustand. Die vorliegende Arbeit zielt auf ein besseres Verständnis der biomechanischen Eigenschaften von Zellen ab. Der Fokus lag dabei auf der Biegesteifigkeit von Zellmembranen und der Deformierbarkeit der Zellen. Es werden drei Studien vorgestellt in der diese Materialparameter untersucht wurden. Die erste Studie befasst sich mit der Temperaturabhängigkeit der mechanischen Eigenschaften. Hierbei wurden acht verschieden Zelllienien bei jeweils fünf Temperaturen rheologisch vermessen. Zur Messung wurde der sog. \"optical stretcher\" verwendet der gleichzeitig die Zellen deformieren und aufheizen kann. Die Versuche zeigen, dass eine Zeit-Temperatur superposition dabei nicht für alle Zelltypen funktioniert. In der zweiten Studie wurden die Membransteifigkeit von Gewebeproben von Brust- und Gebärmutterhalskrebspatienten untersucht. Als Kontrollsystem wurde gutartiges Gewebe aus dem Umfeld des Tumors verwendet. Es konnte gezeigt werden, dass die Zellmembranen von Tumorzellen weicher waren als von gesundem Vergleichsgewebe. Die Änderung der Membrankomposition wurde dabei als mögliche Ursache massenspektroskopisch Untersucht und verschieden Ursachen der weichen Membrane diskutiert. Für die dritte Studie wurde der chemische Wirkstoff Soraphen A eingesetzt um die Membransteifigkeit von zwei Zelllienien zu erhöhen. Dies zeigte eine Verringerung von Zellbeweglichkeit und Invasivität.

The mechanical parameters of biological cells are relevant indicators of their function or of disease. For example, certain cancerous cells are more deformable than healthy cells. The challenge consists in developing methods that can measure these parameters while not affecting the cell. The Optical Stretcher is a microfluidic system that deforms single suspended cells without contact using lasers and determines the cells’ viscoelastic properties. The advantage compared to standard methods of molecular biology is that cells do not need to be treated with additional markers. Basic versions of the Optical Stretcher have existed for some years. These allow the measurement of homogeneous cell populations. Up until now, it was only possible to calculate average population values of compliance. To characterize inhomogeneous populations however, it is necessary to consider each single cell and measure additional mechanical or optical parameters such as the refractive index. This work highlights various extensions of the Optical Stretcher. A novel procedure, including an improved image processing algorithm, is presented to analyze mechanical data in real time. In combination with measurements of the optical refractive index, single cells can now be characterized in more detail. Moreover, it is now possible to extract interesting subpopulations that can be further examined with molecular biology techniques. Depending on the intended purpose, novel devices for cell measurements, based on microfluidic and optical considerations, are presented. The fundamental concept involves microstructured chips that can be integrated into a commercial microscope. These chips offer the possibility of separating measured cell populations according to their mechanical properties. This separation, including mathematical classification, is demonstrated. These methods are tested with cell types of differing mechanical properties to prove their applicability in practice. Single cells are sorted into their respective population of origin. These novel methods offer the possibility of a versatile device to be applied in biophysical research.

Developing tissues are out-of-equilibrium systems that grow and reshape to form organs in adult animals. They are typically composed of a large number of cells. The constitutive cells of a tissue perform different roles in tissue development and contribute to the overall tissue shape changes. In this thesis, we construct a hydrodynamic theory of developing epithelial tissues. We use it to investigate the developing wing of the fruit fly Drosophila melanogaster. This theory relates the coarse-grained cell scale properties to the large-scale tissue flows. We explicitly account for the active cellular processes in the tissue that drive tissue flows. In our description of the tissue, we also include the memory effects that are necessary to account for the experimental observations. These memory effects have a significant influence on the tissue rheology. Using this hydrodynamic theory we analyze shear flow in a developing fruit fly wing tissue. We find that the active cellular processes contribute to overall tissue flows and that memory effects are present in the wing tissue. We investigate consequences of these findings on the rheology of tissue shear flow. We find that the memory effects give rise to an inertial response that leads to oscillations in the tissue but it does not stem from the wing mass. Finally, we describe how the tissue rheology is affected by different boundary conditions. We then investigate the area changes during the pupal wing development and we construct a mechanosensitive model for the cell extrusion rate in the pupal wing. Analysis of cell extrusions in the context of this model also allows us to extract information about the cell division properties. Boundary connections between the wing tissue and surrounding cuticle are crucial for the proper development of the pupal wing. A dumpy mutant wing is strongly misshaped during the pupal wing morphogenesis. We use a simple model for the wing to show that the dumpy mutant wing can be described as a wild type wing with compromised boundary conditions. Finally, we analyze cell properties and tissue flows in a developing wing disc epithelium. Motivated by the observation of radially oriented active T1 transitions in the wing disc epithelium, we use the hydrodynamic theory to investigate the influence of such T1 transitions on stresses in the tissue. We show that sufficiently strong radially oriented active T1 transitions can contribute to the control of the tissue size. Results obtained in this thesis extend our understanding of the fly wing tissue rheology and the role of internal and external forces in the proper shaping of the wing epithelium. The hydrodynamic theory we use to describe the fly wing development provides a set of phenomenological parameters that characterize the tissue mechanics and can be experimentally measured. Therefore, we expect that future research will include and extend the hydrodynamic theory presented in this thesis.

During development, cells consume energy, divide, rearrange, and die. Bulk properties such as viscosity and elasticity emerge from cell-scale mechanics and dynamics. Order appears, for example in patterns of hair outgrowth, or in the predominately hexagonal pattern of cell boundaries in the wing of a fruit fly. In the past fifty years, much progress has been made in understanding tissues as living materials. However, the physical mechanisms underlying tissue-scale behaviour are not completely understood. Here we apply theories from statistical physics and fluid dynamics to understand mechanics and order in two-dimensional tissues. We restrict our attention to the mechanics and dynamics of cell boundaries and vertices, and to planar polarity, a type of long-ranged order visible in anisotropic patterns of proteins and hair outgrowth. Our principle tool for understanding mechanics and dynamics is a vertex model where cell shapes are represented using polygons. We analytically derive the ground-state diagram of this vertex model, finding it to be dominated by the geometric requirement that cells be polygons, and the topological requirement that those polygons tile the plane. We present a simplified algorithm for cell division and growth, and furthermore derive a dynamic equation for the vertex model, which we use to demonstrate the emergence of quasistatic behaviour in the limit of slow growth. All our results relating to the vertex model are consistent with and build off past calculations and experiments. To investigate the emergence of planar polarity, we develop quantification methods for cell flow and planar polarity based on confocal microscope images of developing fly wings. We analyze cell flow using a velocity gradient tensor, which is uniquely decomposed into terms corresponding to local compression, shear, and rotations. We argue that a pattern in an inhomogeneously flowing tissue will necessarily be reorganized, motivating a hydrodynamic theory of polarity reorientation. Using such a coarse-grained theory of polarity reorientation, we show that the quantified patterns of shear and rotation in the wing are consistent with the observed polarity reorganization, and conclude that cell flow reorients planar polarity in the wing of the fruit fly. Finally, we present a cell-scale model of planar polarity based on the vertex model, unifying the themes of this thesis.

Microtubule associated molecular motors are involved in a multitude of fundamental cellular processes such as intracellular transport and spindle positioning. During these movements multiple motor proteins often work together and are, therefore, able to exert high forces. Thus force generation and sensing are common mechanisms for controlling motor driven movement. These mechanisms play a pivotal role when motor proteins antagonize each other, e.g. to facilitate oscillations of the spindle or the nucleus. Single motor proteins have been characterized in depth over the last two decades, our understanding of the collective behavior of molecular motors remains, however, poor. Since motor proteins often cooperate while they walk along microtubules, it is necessary to describe their collective reaction to a load quantitatively in order to understand the mechanism of many motor-driven processes. I studied the antagonistic action of many molecular motors (of one kind) in a gliding geometry. For this purpose I crosslinked two microtubules in an antiparallel fashion, so that they formed \"doublets\". Then I observed the gliding motility of these antiparallel doublets and analyzed the gliding velocity with respect to the relative number of motors pulling or pushing against each other. I observed that the antiparallel doublets gliding on conventional kinesin-1 (from Drosophila melanogaster) as well as cytoplasmic dynein (from Saccharomyces cerevisae) exhibited two distinct modes of movement, slow and fast, which were well separated. Furthermore I found a bistability, meaning, that both kinds of movement, slow and fast, occurred at the same ratio of antagonizing motors. Antiparallel doublets gliding on the non-processive motor protein Ncd (the kinesin-14 from D. melanogaster) showed, however, no bistability. The collective dynamics of all three motor proteins were described with a quantitative theory based on single-motor properties. Furthermore the response of multiple dynein motors towards an external, well-defined load was measured in a gliding geometry by magnetic tweezing. Examples of multi-motor force-velocity relationships are presented and discussed. I established, furthermore, a method for counting single surface immobilized motors to guide the evaluation of the tweezing experiments.:1 Introduction to the functions of molecular motors 1 1.1 How molecular motors move 1 1.1.1 Of muscles and molecules 1 1.1.2 Kinesin-1, the working horse of single-molecule research 3 1.1.3 Kinesin-14, an unusual kinesin with a new twist 6 1.1.4 Cytoplasmic dynein, the molecule with many qualities 7 1.2 Structure and function of microtubules 8 1.3 The directionality of molecular motors 9 1.4 Force regulation in cell biology via molecular motors 10 1.4.1 Bidirectional cargo transport 10 1.4.2 Dynein drives intracellular oscillations 13 1.4.3 Control of spindle length 15 2 Introduction to the collective behavior of molecular motors in vitro 19 2.1 Cooperativity of molecular motors 19 2.2 How multiple motors work against a load 21 2.2.1 Theoretical concepts 21 2.2.2 Optical tweezing of multiple motors 22 2.2.3 Alternative experimental approaches 23 2.2.4 Membrane tube dynamics 24 2.3 Antagonizing molecular motors 25 2.3.1 Competition between dissimilar motors 25 2.3.2 Competition between identical motors 26 2.4 Aim of the project 28 3 Characterization of molecular motors 31 3.1 Results: The run length of processive motors 31 3.1.1 Run length of kinesin-1 at different ATP concentrations 31 3.1.2 The run length of cytoplasmic dynein 34 3.2 Results for multi-motor gliding assays 37 3.2.1 The effect of ATP on the gliding motility 37 3.2.2 The effect of temperature on the gliding motility 39 3.2.3 Bead transport does not influence gliding motility 42 3.3 Discussion 43 4 Magnetic tweezing of multiple molecular motors 45 4.1 Concepts of the magnetic tweezing setup 45 4.1.1 Theoretical concepts 45 4.1.2 Implementation 48 4.1.3 Calibration 51 4.2 Results of multi-motor force measurements 53 4.2.1 External force leads to microtubule re-orientation 53 4.2.2 Cytoplasmic dynein is able to withstand high opposing loads 55 4.2.3 Force-velocity curves at very low motor densities 56 4.2.4 Averaging of multi-motor force-velocity relationships 58 4.3 Discussion 60 5 Reconstitution of antagonizing motor activity 63 5.1 The doublet assay 63 5.2 Experimental results of the doublet assay 65 5.2.1 Kinesin-1 driven doublets move in discrete velocity regimes 65 5.2.2 Velocity affects the shape of the bistability curve 68 5.2.3 Dynein\'s processivity allows bistability at low velocity 69 5.2.4 Ncd does not exhibit a bistability curve 70 5.3 Theoretical results of the doublets assay 71 5.3.1 General concepts 71 5.3.2 Theory for processive motors 73 5.3.3 Theory for non-processive motors 75 5.3.4 The emergence of bistability 78 5.3.5 Model for single-motor force-velocity relationships 81 5.4 Comparison between theoretical and experiment results 83 5.5 Discussion 87 6 Materials and Methods 91 6.1 List of chemicals and equipment 91 6.2 Buffer recipes 92 6.3 Protein purification 93 6.4 Preparation of microtubules 95 6.5 Preparation of flow cells 96 6.6 Fluorescence microscopy 98 6.7 Errors computation 100 6.8 Software 100 7 References 103 8 Acknowledgement 113

During embryonic development, precursor germ cells contain aggregates of protein and RNA known as germ granules. These germ granules are important in the specifi- cation of a functioning germ line, i.e. functioning sex cells within mature organisms. In the single cell fertilized embryo of the nematode worm C.elegans, germ granules (referred to as P granules) localize to the posterior side of the cell. After cell division occurs, they are found only in the posterior daughter cell. The localization behav- ior of P granules has been a topic of much interest, and considered an important aspect of symmetry breaking during development. We learn the fundamental prop- erties of P granule localization, and determine possible parameters and features of this biological system by developing theory in close collaboration with experimental evidence. In this study, experimental evidence is presented which shows that P granules are liquid droplets, and that their localization occurs through preferential nucleation and growth behavior on one side of the cell and simultaneous preferential dissolution on the opposite side. It is also shown that this behavior is linked to the concentration gradient of the protein Mex-5 along the anterio-posterior axis of the cell, which is necessary to induce the preferential growth of P granules. From this experimental data, a theoretical model for the preferential growth of P granules is developed, where the localization of P granules occurs by phase separa- tion. That is, P granules separate from the bulk cytoplasm by a process described by a first order liquid-liquid phase transitition, where a liquid droplet granule phase nucleates and then grows out of the bulk liquid cytoplasmic phase. In this model, a spatial gradient is imposed on the saturation point, the boundary point between the single phase state consisting only of the cytoplasm, and a metastable state which includes both a P granule and cytoplasm phase. This gradient mimics the properties of the Mex-5 gradient and is sufficient in explaining P granule localization. Using numerical simulations, the theoretical model is studied. It is found suffi- cient to both successfully describe P granule localizaion, and to describe interesting behavior in a system with assymetric growth due to a spatial gradient. From a purely theoretical standpoint, we observe cyclical non-equilibrium steady states, where material is cycled back and forth along the gradient. From the biological side, experimental properties of the system, such as the diffusion coefficient of P granules and P granule growth rates are determined through both simulation and image analysis of data. In addition, the possiblility of different types of growth behavior at later cell stages, and a method of long range intracellular signalling are suggested from the theoretical model.

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