THE RELATIONSHIP BETWEEN CELL-DIVISION PATTERN AND GLOBAL SHAPE OF YOUNG FERN GAMETOPHYTES .1. A MODEL STUDY

We have investigated the relationship between cell division and shape in mathematical models of fern gametophyte development. In particular, we attempted to infer what properties of cell division patterns are responsible for the development of heart-shaped thalli. We focused on those types of gametophytes that develop from an initial cell, splitting off segments alternately to the left and to the right. Computer simulations showed that a heart shape developed when the ratio between the rates of anticlinal and periclinal divisions in segments (the division ratio) was below a certain threshold. In the computer simulations we used map L-systems for the generation of cell division patterns and a center-of-gravity algorithm for the computation of cell shapes. The division ratio provided a quantitative characterization of the tendency of the cell division pattern to develop a heart shape. Together with map DOL-systems it can be applied to real gametophytes to investigate their morphogenesis.