Morphogenesis of lines and nets.

Complex linear appearing structures and networks (e.g. blood vessels, leaf veins, nerves) are formed reproducibly during the development of nearly every organism, but the molecular mechanism leading to such patterns is still unknown. A model is proposed in which a few simple coupled biochemical reactions are able to generate such structures. Among undifferentiated cells, a local peak of differentiation-inducing substance (activator) is formed by autocatalysis and lateral inhibition. The activator peak triggers the differentiation of the cell at that location. Due to changes in metabolism, the differentiated cell repels the activator peak and drives it to a neighbouring cell which then also differentiates. The repulsion between the activator peak and the already differentiated cells forces the activator peak to move ahead of the tip of the extending filament. Long filaments of differentiated cells may be formed, which can split, branch laterally, reconnect with each other and grow towards specific target cells. Partial differential equations describing the mutual interaction of the substances involved were presented and solved with a computer. The resulting patterns show self-regulating properties and other features found in the leaf vascular system, the pattern of tracheae in insect epidermis, and other biological networks.