A model for pattern formation of hypostome, tentacles, and foot in hydra: how to form structures close to each other, how to form them at a distance.

A model for head, tentacle, and foot formation in Hydra is proposed. The model shows that systems which suggest a positional information scheme may be realized by a set of hierarchically coupled pattern forming systems: a structure generates the precondition for a second structure but excludes this structure locally. In this way, a well-regulated neighborhood of structures is enforced. According to the model, head, tentacle, and foot formation are under the control of separate activator-inhibitor systems. These systems are coupled via the source density. The head activator increases the source density and the activation takes place preferentially in regions of highest source density. The foot activation has the opposite behavior. It appears at the lowest source density and lowers the effective source density further. Therefore, head and foot activation appear preferentially at opposite positions of the field. Tentacle activation occurs in the region of highest source density that is not occupied by a primary head activation. Tentacle activation requires a certain threshold level of the source density. As shown by computer simulations, the model accounts for many so far unexplained observations, such as during regeneration the tissue obtains tentacle-like properties until the newly formed hypostome displaces the tentacles into a subhypostomal region. Since no direct inhibition between head and foot is involved, both structures can appear close to each other in experimental situations. The dramatic effects of treatment with diacylglycerol, such as the formation of new tentacles preceding the formation of additional hypostomes, become understandable under the simple assumption that the agent increases the source density. Budding is regarded as a trigger of a second head activator maximum. Budding can occur only beyond a minimum distance from the head due to the head inhibitor and beyond a minimum distance from the foot since the source density would be too low there. The model accounts for the periodic spacing of secondary structures around a primary organizing region such as that found in the arrangement of leaves and flower elements in plants around the primary meristem. Similarities to the vulva development of Caenorhabditis elegans and to the segmentation of insects are discussed.