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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.