Common pattern formation, modularity and phase transitions in a gene network model of morphogenesis

A model of biological morphogenesis is presented. The model is based on a gene network cell description and the interaction among the nearest cells. Here interactions between cells are due to diffusion-like mechanisms and also due to inductive, cell-to-cell interactions. An extensive analysis shows that (a) a small number of basic patterns are present, linked to a set of minimal gene nets (modules) with a small number of units and (b) spatial patterns are common in both types of interaction, but are much more common in the inductive case. These results support the idea (early conjectured by S. Kauffman) that evolution does not need to fine-tune through a high-dimensional parameter space, since spatial patterning is already a robust property of spatially extended gene networks displaying modular organization.