Models of pattern formation applied to plant development

Plants are the beautiful results of a chain of complex pattern forming events. Pattern formation—the generation of regular differences in space—occurs at several levels of organization. For example, a particular group of cells at the shoot apex may receive a signal to form a leaf. The leaf will get a polarity, developing an upper and a lower side. Some cells of the leaf may develop into stomata, while chains of other cells may form vascular strands. Individual cells may become polar. All these patterns must ultimately arise from similar mechanisms although they do not act at the same structural level. In this chapter we would like to discuss basic signalling systems among cells that allow to generate different cell types in a defined spatial arrangement and apply them to plant development. We will further show that a linkage of several such pattern forming systems allows the reproducible generation of complex patterns. Models for the generation of the primary shoot-root axis and for the generation of leaf primordia around the meristem will be elaborated. These models are certainly not complete. For instance, shape changes of a tissue (see Gierer, 1977a) or the tissue-specific control of cell proliferation will not be discussed. Comparisons with pattern formation in the freshwater polyp Hydra, with the formation of imaginal disks in insects or the patterning on the shells of some mollusks will reveal that in plants mechanisms are at work that are closely related to those in other systems that, at first sight, look very different from plants. In plants, as in most other higher organisms, the adult structure develops from a single cell. The final pattern cannot already be present in this cell in a hidden form. Regulatory phenomena observed after an experimental interference indicate that cells communicate with each other to achieve the translation from the genetic information into the three-dimensional structure. We assume that the formation of a given structure is initiated by a particular biochemical signal that may consist of a high concentration of one ore more substances. If mechanical forces are involved that bring a particular tissue into shape, it will be assumed that this is initiated by a preceding chemical signal that caused, for instance, a rearrangement of the cytoskeleton. These models are therefore different from models assuming pattern formation directly on a mechanical level (Green and Poething, 1982 ; Oster et al, 1983).