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.

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.

During the development of multicellular organisms, organs grow to well-defined shapes and sizes. The proper size and patterning of tissues are ensured by signaling molecules as e.g. morphogens. Secreted from a restricted source, morphogens spread into the adjacent target tissue where they form a graded concentration profile. Upon binding of the morphogens to receptors on the cell surfaces, the morphogenetic signal is transduced inside the cell via the phosphorylation of transcription factors, which subsequently regulate the expression of different target genes. Thus, cell fates are determined by the local concentration of such morphogens. In this work, we investigate three key aspects of morphogenetic signaling processes in growing tissues. First, we study the mechanics of tissue growth via cell division and cell death. We examine the rearrangements of cells on large scales and times by developing a continuum theory which describes the growing tissue as an active complex fluid. In our description we include anisotropic stresses generated by oriented cell division, and we show that average cellular trajectories exhibit anisotropic scaling behaviors. Our description is used to study experimentally measured shape changes of the developing wing disk of the fruit fly Drosophila melanogaster. Second, we focus on the spreading of morphogens in growing tissues. We show that the flow field of cell movements due to oriented cell division and cell death causes a drift term in the morphogen transport equation, which captures the stretching and dilution of the concentration profile. Comparing our theoretical results to recent experiments in the Drosophila wing disk, we find that the transport of the morphogen Dpp is mainly intracellular. We moreover show that the decay length of the Dpp gradient increases during development as a result of changing degradation rate and diffusion coefficient, whereas the drift of molecules due to growth is negligible. Thus growth does not affect the decay length of the gradient, but the decay length of the gradient might affect the tissue growth rate as discussed in this work. Finally, we develop a microscopic theoretical description of the intracellular transduction machinery of morphogenetic signals within an individual cell. Our description captures the kinetics of the trafficking of proteins between different cellular compartments in response to receptor-bound signaling molecules. Analyzing experimental data at the Drosophila neuromuscular junction, we show that the morphogenetic signaling is modulated by synaptic signaling via neuronal action potentials.

Biological cells consist of many subunits that form distinct compartments and work together to allow for life. These compartments are clearly separated from each other and their sizes are often strongly correlated with cell size. Examples for those structures are centrosomes, which we consider in this thesis. Centrosomes are essential for many processes inside cells, most importantly for organizing cell division, and they provide an interesting example of cellular compartments without a membrane. Experiments suggest that such compartments can be described as liquid-like droplets. In this thesis, we suggest a theoretical description of the growth phase of centrosomes. We identify a possible mechanism based on phase separation by which the centrosome may be organized. Specifically, we propose that the centrosome material exists in a soluble and in a phase separating form. Chemical reactions controlling the transitions between these forms then determine the temporal evolution of the system. We investigate various possible reaction schemes and generally find that droplet sizes and nucleation properties deviate from the known equilibrium results. Additionally, the non-equilibrium effects of the chemical reactions can stabilize multiple droplets and thus counteract the destabilizing effect of surface tension. Interestingly, only a reaction scheme with autocatalytic growth can account for the experimental data of centrosomes. Here, it is important that the centrioles found at the center of all centrosomes also catalyze the production of droplet material. This catalytic activity allows the centrioles to control the onset of centrosome growth, to stabilize multiple centrosomes, and to center themselves inside the centrosome. We also investigate a stochastic version of the model, where we find that the autocatalytic growth amplifies noise. Our theory explains the growth dynamics of the centrosomes of the round worm Caenorhabditis elegans for all embryonic cells down to the eight-cell stage. It also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with disturbed centrioles. Our example thus suggests a general picture of the organization of membrane-less organelles. / Biologische Zellen bestehen aus vielen Unterstrukturen, die zusammen arbeiten um Leben zu ermöglichen. Die Größe dieser meist klar voneinander abgegrenzten Strukturen korreliert oft mit der Zellgröße. In der vorliegenden Arbeit werden als Beispiel für solche Strukturen Zentrosomen untersucht. Zentrosomen sind für viele Prozesse innerhalb der Zelle, insbesondere für die Zellteilung, unverzichtbar und sie besitzen keine Membran, welche ihnen eine feste Struktur verleihen könnte. Experimentelle Untersuchungen legen nahe, dass solche membranlose Strukturen als Flüssigkeitstropfen beschrieben werden können. In dieser Arbeit wird eine theoretische Beschreibung der Wachstumsphase von Zentrosomen hergeleitet, welche auf Phasenseparation beruht. Im Modell wird angenommen, dass das Zentrosomenmaterial in einer löslichen und einer phasenseparierenden Form existiert, wobei der Übergang zwischen diesen Formen durch chemische Reaktionen gesteuert wird. Die drei verschiedenen in dieser Arbeit untersuchten Reaktionen führen unter anderem zu Tropfengrößen und Nukleationseigenschaften, welche von den bekannten Ergebnissen im thermodynamischen Gleichgewicht abweichen. Insbesondere verursachen die chemischen Reaktionen ein thermisches Nichtgleichgewicht, in dem mehrere Tropfen stabil sein können und der destabilisierende Effekt der Oberflächenspannung unterdrückt wird. Konkret kann die Wachstumsdynamik der Zentrosomen nur durch eine selbstverstärkende Produktion der phasenseparierenden Form des Zentrosomenmaterials erklärt werden. Hierbei ist zusätzlich wichtig, dass die Zentriolen, die im Inneren jedes Zentrosoms vorhanden sind, ebenfalls diese Produktion katalysieren. Dadurch können die Zentriolen den Beginn des Zentrosomwachstums kontrollieren, mehrere Zentrosomen stabilisieren und sich selbst im Zentrosom zentrieren. Des Weiteren führt das selbstverstärkende Wachstum zu einer Verstärkung von Fluktuationen der Zentrosomgröße. Unsere Theorie erklärt die Wachstumsdynamik der Zentrosomen des Fadenwurms Caenorhabditis elegans für alle Embryonalzellen bis zum Achtzellstadium und deckt dabei auch Fälle mit anormaler Zentrosomenanzahl und veränderter Zellgröße ab. Das Modell kann auch Situationen mit unterschiedlich großen Zentrosomen erklären, welche auftreten, wenn die Struktur der Zentriolen verändert wird. Unser Beispiel beschreibt damit eine generelle Möglichkeit, wie membranlose Zellstrukturen organisiert sein können.