| Biological cells and tissue move and rearrange under the influence of mechanical, locally applied forces. One open question is how such local forces combine together to create large scale motions in cells and tissues for biological functions. This thesis addresses this question in the context of how forces between molecular components lead to polarization and motility for a single cell, and in the context of how forces at the whole-cell level lead to morphogenesis of tissues.;In Chapter 2, we present a mathematical description for the crawling motion of a single cell. This motion arises from the self-organized behavior of molecular components pushing on a cell membrane, which may be thought of as a flexible boundary that responds to contact forces. The molecular components themselves consist of many filaments and motors, coarse grained such that they are described by continuum concentration profiles. This system is intrinsically driven out of thermodynamic equilibrium by active forces that include filament treadmilling and attractive forces generated by motors. However, steady state configurations still exist in which the modeled cell, coupled through a friction coefficient with the outside environment, moves persistently in a single direction. This symmetry broken, moving state results from instabilities of the filament density distribution and in particular regions of parameter space, coexists with symmetric, stationary states, thus making the system capable of spontaneous polarization and bistable in certain regimes.;In Chapter 3, we consider a larger length scale. Specifically, we discuss a different model based on mechanical forces existing at a cellular level and the organization of tissue that results from the application of these forces. The biological system under investigation is the sheet of epithelial cells covering the egg chamber of Drosophila from which two breathing tubes are eventually molded. We adapt a model previously employed in foam and Drosophila wing disc research, use it to model out-of-plane deformations of a sheet of cells, and show that specific patterns of line tension within the sheet, combined with discrete topological rearrangement rules typical of such models, can lead to the formation of tubes. We show that the model supports recent experimental results on this system and that the novel mechanism of tube formation proposed by the experiments can be driven by simple line tension patterning within a sheet. |
