Visualization of the development of multicellular structures

This dissertation presents simulation-based methods for visualizing the development of multicellular structures in two and three dimensions. The goal is to develop methods that can be used to explore the fundamental mechanisms responsible for the development of complex forms found in living organisms, namely lineage and interaction. In the case of two-dimensional cell layers, the formalism of map L-systems is used to express the neighborhood relations between the cells, or topology of the structure. The production rules which determine topology operate on cell walls, and are based solely on cell lineage. Cell shapes (geometry of the structure) result from mechanical cell interactions. Two types of forces are considered: the osmotic pressure within cells, and the tension of cell walls. Developmental sequences can be animated by considering periods of continuous expansion delimited by synchronous cell divisions. This method is used to model the development of the fern gametophytes Microsorium linguaeforme and Dryopteris thelypteris, and is valuable in analyzing the effect of cell division patterns on global shape. A simple extension of the two-dimensional method to one operating on a spherical surface allows for the modeling of the early developmental stages of animal embryos. In order to model three-dimensional cellular structures, map L-systems are extended to cellwork L-systems. Cellwork L-systems operate on a set of enclosed volumes (cellworks) rather than regions (as in map L-systems), requiring modifications to both the previous formalism and to the dynamic model for cell shape. The major drawbacks of the map L-system-based approaches are the tedious task involved in expressing cell division patterns using cell walls, and the limitation to models that only capture cell lineage and do not consider interaction. A formalism called cell systems is introduced whose rules express division and differentiation at the cell level, and capture the communication between cells. Positions of division walls are specified with respect to an underlying vector field, and can be influenced by the concentrations of morphogens which diffuse throughout a growing structure. Thus, cell systems offer a highly intuitive method of describing development using both fundamental mechanism of control (lineage and interaction). It is important to note that the models considered in this dissertation do not capture the motion of cells relative to each other, for example cell migration in animal tissues. Therefore, the methods presented are applicable only to plants, and to some very early stages of animal development. The methods are illustrated using examples based on biological data.