Phenotypic and dynamical transitions in model genetic networks. I. Emergence of patterns and genotype-phenotype relationships.

Genotype-phenotype interactions during the evolution of form in multicellular organisms is a complex problem but one that can be aided by computational approaches. We present here a framework within which developmental patterns and their underlying genetic networks can be simulated. Gene networks were chosen to reflect realistic regulatory circuits, including positive and negative feedback control, and the exchange of a subset of gene products between cells, or within a syncytium. Some of these networks generate stable spatial patterns of a subset of their molecular constituents, and can be assigned to categories (e.g., "emergent" or "hierarchic") based on the topology of molecular circuitry. These categories roughly correspond to what has been discussed in the literature as "self-organizing" and "programmed" processes of development. The capability of such networks to form patterns of repeating stripes was studied in network ensembles in which parameters of gene-gene interaction were caused to vary in a manner analogous to genetic mutation. The evolution under mutational change of individual representative networks of each category was also simulated. We have found that patterns with few stripes (< or =3) are most likely to originate in the form of a hierarchic network, whereas those with greater numbers of stripes (> or =4) originate most readily as emergent networks. However, regardless of how many stripes it contains, once a pattern is established, there appears to be an evolutionary tendency for emergent mechanisms to be replaced by hierarchic mechanisms. These results have potential significance for the understanding of genotype-phenotype relationships in the evolution of metazoan form.