Phase Transitions in a Gene Network Model of Morphogenesis

A model of biological morphogenesis is presented. The model is based in a gene-network cell description plus the interaction among cells. Here interactions between nearest cells are due to diffusion-like mechanisms and also to inductive, cell-to-cell interactions. The gene network properties are studied and their relationship with previous abstract graph-based analogies are explored, showing they are robust. An extensive analysis of random gene networks shows that spatial patterns are common in both types of interaction but are much more common in the inductive case. These results support the idea 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.