Endosomes are dynamic vesicular structures which transport cargo molecules internalized into the cell via endocytosis. Endosomal trafficking of cargo involves a large number of individual endosomes that regularly interact with each other via fusion and fission and thus form a dynamic network wherein endocytosed cargo is sorted and transported to various other intracellular compartments. In this study we present a general theoretical framework that takes into account individual endosomes and several key microscopic interaction processes among them. By combining theory with quantitative experiments, we seek to address the fundamental question of how the behaviour of the endosomal network emerges from the interactions among many individual endosomes of different sizes and cargo contents. Our theory is based on distributions of endosomes of various sizes and cargo amount. We compare our theory to experimental time course distributions of LDL, a degradative cargo, in a population of early endosomes. Early endosomes display a broad distribution of cargo with a characteristic power law, which we show is a consequence of stochastic fusion events of cargo carrying early endosomes. A simple model can quantitatively describe time-dependent statistics of LDL distributions in individual early endosomes. From fits of the theory to experimental data we can determine key parameters of endosomal trafficking such as the endosome fusion rate and the fluxes of cargo into and out of the network. Our theory predicts several experimentally confirmed scaling behaviours, which arise as a result of endosome fusion. Our theory provides a link between the dynamics at individual endosome level and average properties of the endosomal network. We show from our theory that some features of the endosomal distributions, which arise from interactions among individual endosomes, are sensitive to alterations in chosen parameters. This provides a direct means to study perturbation experiments wherein the cargo distribution can vary in response to changes of the endocytic system. Our analysis provides a powerful tool for the study of genetic and chemical perturbations that may alter specific systems properties and for extracting various kinetic rates involved in endosomal trafficking from only still images at different points.

Im Mittelpunkt dieser Arbeit steht die Untersuchung der kollektiven Dynamik des binaeren Systems Rb-Sb im fluessigen Zustand. Die dynamische Struktur wurde fuer zwei Zusammensetzungen durch inelastische Neutronenstreuung bestimmt. Die daraus ermittelten Dispersionsrelationen geben Aufschluss ueber die kollektiven Anregungen im System. Um kuenftig noch bessere Experimente durchfuehren zu koennen, wurden die Parameter eines neues Neutronen Brillouin Spektrometers mittels Monte-Carlo Simulation optimiert. / In the first part of this report the collective atomic dynamics of liquid Rb-Sb is discussed. The dynamic structure factors were measured by inelastic neutron scattering. The resulting dispersion relations show how the dynamics of this system alters with the change in the interatomic potential. To improve the experimental part the setup of a new neutron Brillouin spectrometer was optimized by a Monte-Carlo simulation. These results are presented in the second part.

Im Mittelpunkt dieser Arbeit steht die Untersuchung der kollektiven Dynamik des binaeren Systems Rb-Sb im fluessigen Zustand. Die dynamische Struktur wurde fuer zwei Zusammensetzungen durch inelastische Neutronenstreuung bestimmt. Die daraus ermittelten Dispersionsrelationen geben Aufschluss ueber die kollektiven Anregungen im System. Um kuenftig noch bessere Experimente durchfuehren zu koennen, wurden die Parameter eines neues Neutronen Brillouin Spektrometers mittels Monte-Carlo Simulation optimiert. / In the first part of this report the collective atomic dynamics of liquid Rb-Sb is discussed. The dynamic structure factors were measured by inelastic neutron scattering. The resulting dispersion relations show how the dynamics of this system alters with the change in the interatomic potential. To improve the experimental part the setup of a new neutron Brillouin spectrometer was optimized by a Monte-Carlo simulation. These results are presented in the second part.

Endosomes are dynamic vesicular structures which transport cargo molecules internalized into the cell via endocytosis. Endosomal trafficking of cargo involves a large number of individual endosomes that regularly interact with each other via fusion and fission and thus form a dynamic network wherein endocytosed cargo is sorted and transported to various other intracellular compartments. In this study we present a general theoretical framework that takes into account individual endosomes and several key microscopic interaction processes among them. By combining theory with quantitative experiments, we seek to address the fundamental question of how the behaviour of the endosomal network emerges from the interactions among many individual endosomes of different sizes and cargo contents. Our theory is based on distributions of endosomes of various sizes and cargo amount. We compare our theory to experimental time course distributions of LDL, a degradative cargo, in a population of early endosomes. Early endosomes display a broad distribution of cargo with a characteristic power law, which we show is a consequence of stochastic fusion events of cargo carrying early endosomes. A simple model can quantitatively describe time-dependent statistics of LDL distributions in individual early endosomes. From fits of the theory to experimental data we can determine key parameters of endosomal trafficking such as the endosome fusion rate and the fluxes of cargo into and out of the network. Our theory predicts several experimentally confirmed scaling behaviours, which arise as a result of endosome fusion. Our theory provides a link between the dynamics at individual endosome level and average properties of the endosomal network. We show from our theory that some features of the endosomal distributions, which arise from interactions among individual endosomes, are sensitive to alterations in chosen parameters. This provides a direct means to study perturbation experiments wherein the cargo distribution can vary in response to changes of the endocytic system. Our analysis provides a powerful tool for the study of genetic and chemical perturbations that may alter specific systems properties and for extracting various kinetic rates involved in endosomal trafficking from only still images at different points.

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.