According to the model proposed, filaments appear like traces behind local signals that wander over the field. In the simulation above, it is assumed that local signals are generated by an activator (red) - inhibitor system. When these signals are above a certain threshold, the exposed cells to differentiate into members of the filament system. Differentiated cells repel the signal, causing in this way their shift into a neighboring region. These cells also differentiate and the filament becomes elongated, and so on. To orient the elongation into a region not supplied by filaments, all cells are supposed to produce a substance (green) that is removed by the differentiated cells. The substrate concentration is a measure of how urgently the cells need the in growth of veins, for instance, in order to remove an oxygen deficiency. Due to the activator-inhibitor mechanism, there is a competition along the filament and those regions will win and become elongated the that are exposed to the highest substrate concentration. This is usually the tip region of a filament. A repetition of this process - differentiation, shift of the signal, differentiation - leads to a long strand of differentiated cells behind a wandering activator maximum (Meinhardt
; the essence of the model is also available in a commented PowerPoint presentation [PPT
]). For tracheae in insects, most of the predicted ingredients have been found (see [1,2]. The addition of newly differentiated cells is one possible realization. In nerves and tracheae, for instance, the elongation of the filaments occurs essentially by the local elongation of individual cells.
Branches are formed whenever activator maxima become sufficiently remote from each other during elongation of filaments. Then, the inhibitor concentration can become locally so low that a new activator maximum is triggered along an existing filament due to a small baseline activator production of the differentiated cells. Whether a branch is formed towards the one side or the other depends on minute fluctuations. However, if a branch has been formed, let us say, to the right, the next branch will probably point to the left due to the substrate removal by the first branch. Such alternation in the branching direction can be seen in many leaves. If the details of a pattern depend on fluctuations but each step has a strong influence on forthcoming decisions, the actual pattern will be unpredictable. Indeed, the venation of two leaves on the same tree are never identical although they are certainly formed under control of the same positional information.