The recent popularization of machine learning as a new paradigm in computer science provides interesting opportunities for explaining phenomena of collective motion in living systems, as for...Show moreThe recent popularization of machine learning as a new paradigm in computer science provides interesting opportunities for explaining phenomena of collective motion in living systems, as for example flocks of birds or schools of fish. In this thesis we develop a model for collective motion using multi-agent reinforcement learning with orientation-based rewards, a new type of reward system that has not yet been found in literature. While the developed model is in principle generally applicable to all forms of collective motion observed in nature, we use the language of the flocking behaviour of birds as a particular example to frame our model. The birds have the option to either fly into an instinctive direction or act based on a Viscek-type of interaction with their neighbors, and are rewarded maximally when the resulting direction of movement is some predetermined prefered direction. The model distinghuishes between leaders that instinctively move towards this direction and followers that do not. We show that collective motion into this prefered direction emerges from this model, but only with a minimum of 1.23 encounters with neighbours on average, of which a minimal fraction of 0.2 should be leaders, which on average roughly corresponds to at least one encounter with a leader every four timesteps. These lower bounds are rudimentary estimates, as the present study serves mainly as a proof of concept that collective motion can emerge from this new type of model. Additionally it is suggested that, using deep reinforcement learning, this model can be viewed as a reinforcement learning extension of the Vicsek model.Show less
The cytoskeleton gives a cell its main structure and rigidity. It plays a significant role during many (force sensitive) mechanical cues from outside the cell. The anisotropy of the cytoskeleton...Show moreThe cytoskeleton gives a cell its main structure and rigidity. It plays a significant role during many (force sensitive) mechanical cues from outside the cell. The anisotropy of the cytoskeleton has been shown to control the geometry and forces of adherent cells. Bases on the the shape of curved cell edge segments of single cells, the size of internal stresses and traction forces can be calculated. However, such methods have not yet been applied to clusters of cells. Here we introduce two methods to describe the mechanical equilibrium of cell doublets. Either in a discontinuous way, where both cells are treated separately, or continuous, where we do not differentiate between the cells and treat it as a single cell.Show less
The protein tubulin has the ability to assemble in a multitude of two-dimensional shapes, among which the surprisingly rigid cylindrical microtubules. We attempt to understand this behaviour by...Show moreThe protein tubulin has the ability to assemble in a multitude of two-dimensional shapes, among which the surprisingly rigid cylindrical microtubules. We attempt to understand this behaviour by modelling the tubulin as a crystalline membrane upon which we study a form of elastic energy which includes intrinsic mean curvature and intrinsic deviatoric curvature. We study analytical work about this energy, and create a numerical method for obtaining the equilibrium shapes, which we explore for various boundary conditions and parameters. Although we cannot fully explain the polymorphism, we do find a possible explanation for microtubule stability and collapse.Show less
In this thesis, we investigate the mechanical interplay between a cell’s shape and its actin cytoskeleton organisation. We combine theoretical work with numerical simulations and experimental data...Show moreIn this thesis, we investigate the mechanical interplay between a cell’s shape and its actin cytoskeleton organisation. We combine theoretical work with numerical simulations and experimental data to investigate this behaviour. The actin cytoskeleton is modelled using a liquid crystal framework and is combined with a model for the cell contour that has stress fibers apply a directed stress on the edge. We describe a feedback mechanism where the orientation of stress fibers is a competition between alignment with the cell edge and with one another, and where the shape of the cell edge is dependent on the contractile force exerted along the direction of the nearby stress fibers. We show that we can accurately reproduce the shape and anisotropic actin cytoskeleton structure of cells on micropillar arrays, as well as the emergence of topological defects.Show less
The Vicsek model offers a phenomonologically rich set of behaviours while maintaining simple rules of interaction. By introducing a convex hull as a means of providing cohesion within the system,...Show moreThe Vicsek model offers a phenomonologically rich set of behaviours while maintaining simple rules of interaction. By introducing a convex hull as a means of providing cohesion within the system, we have been able to probe the behaviour of this model as it is moved off of the usual periodic boundary conditions, to the infinite plane. We present the findings of 4 different schemes that introduce this cohesive effect by way of deflecting Boids on the convex hull back into the bulk. In one such scheme, a new phase transition is found, between a state wherein the flock has a constant direction of motion, and a state where this direction precesses. The rate of precession is found to be dependent on both the noise level and the deflection coupling.Show less
A recent paper [DeCamp et al 2015] reported dynamical effects of defect orientation in experiments with planar nematic liquid crystals. The numerical determination of defect orientations was...Show moreA recent paper [DeCamp et al 2015] reported dynamical effects of defect orientation in experiments with planar nematic liquid crystals. The numerical determination of defect orientations was complicated by the absence of a rigorous definition of defect orientation in the paper. In this thesis I will introduce rigorously a defect orientation which can be easily determined numerically. I will show that defect orientation is a significant factor in the dynamics of defect annihilations with most notably an orthogonal velocity component not documented in the literature.Show less
