Abstract
Microtubules are highly dynamic polymers and components of the cellular cytoskeleton of all eukaryotic organisms. Microtubules are important for many cellular processes, as they play an active role in mechanisms such as gene expression, cell migration, and chromosome segregation during the mitosis, among others. Furthermore, microtubules are involved in the morphogenesis and the maintenance of the structure of the cell and, therefore, of the entire organisms. The aim of this thesis is to understand how the dynamics of cytoskeletal components influences the spatial organization of the cytoskeleton. We focus on two different systems: the cortical microtubule array, and an idealized cell consisting of diffusing actin filaments and dynamic microtubules. In the first part of the thesis we study the spatial reorganization of the cortical microtubule array, a highly ordered assembly of microtubules close to the plasma membrane of plant cells. Recent in vivo experiments have revealed that the cortical array of dark-grown hypocotyl cells undergoes a striking severing-driven reorientation from a direction transverse to the growth direction of the cell to a longitudinal, upon exposure to blue light. By developing a stochastic model of dynamic microtubules, and by using a combination of analytical calculations and computer simulations, we first identify the factors that enable the reorientation, and then we make theoretical predictions about how the new orientation is maintained. In the second part of the thesis, we extend the study of microtubule systems by developing a new model in which microtubules interact with diffusing actin filaments in a three-dimensional confinement. Indeed, although microtubules and actin have been extensively studied independently from each other, so far, no comprehensive research that considers the interaction between different cytoskeletal components has been performed. Here, we assess to what extent it is possible to regulate the spatial organization of actin by acting on the dynamic parameters of the model. In particular, we analytically identified the key parameters that regulate the localization of actin in the cell. We hope that this model can be used as a starting point for theoretically studying the interaction between different cytoskeletal components.
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