Modelling the development of phyllotactic patterns at the shoot apical meristem of Arabidopsis thaliana

The study of phyllotactic patterns have a long history, but the bulk of our detailed understanding of developmental processes in plants comes from research conducted in the last thirty or forty years. New modern techniques have made it possible to study plants in ways that previously was not possible. Using confocal microscopy it is possible to generate three-dimensional stacks of images of a plant, and series of stacks makes it possible to follow the development in time. In combination with biological markers, gene and protein expression patterns can be followed both in time and space. This new type of data plays an important role in the modern development of mathematical and computational models of developmental processes in plants. In this thesis we study different aspects of the development of phyllotactic patterns at the shoot apical meristem of Arabidopsis thaliana; the self-regulating feedback network of the WUSCHEL and CLAVATA genes, anisotropic growth of plant cells, cell division in the epidermal layer of the meristem, and intercellular transport of the plant hormone auxin. A systems biology approach is taken to make models from experimental data. All models are represented mathematically by ordinary differential equations and a toolbox of both analytical, numerical, and statistical methods is used to analyse the models. Using computer simulations and the following data analysis we provide predictions that can be tested in experiments