Mathematical Models of Plant Morphogenesis

Abstract

Analyses are presented of the structure and the development of several biological entities, ranging in level of organization from the molecular to the organismal. Classical methods of analysis which have been used in the physical sciences have proved appropriate, showing the applicability of physical principles to biological structure and morphogenesis. At the ultrastructural level, bacterial flagella, microtubules and similar objects exhibit regularities of packing of their constituent protein subunits, which can be analyzed in crystallographic terms. The growth of a plant cell wall is shown to depend on the physical properties of the wall itself, and its susceptibility to strain hardening and metabolic softening. In multicellular tissues and organs, the growth deformations which lead to mature structures can be described and analyzed appropriately using concepts and principles drawn from fluid dynamics. In some cases growth is steady, that is the growth pattern is invariant with time over some period. A structure such as a meristem, may maintain its form, while the elements or cells of which it consists are continually changing. It is suggested that plants exploit the physical properties of their constituent materials, and physical forces such as turgor stress, in their morphogenesis.