Evolution of gene networks by gene duplications: a mathematical model and its implications on genome organization

Networks of transcriptional regulators have key roles in metazoan development. Important forces in the evolution of these networks are gene duplications and gene deletions, events that may change the spatiotemporal expression pattern of network genes. A measure for the probability of such changes after gene-duplication events is proposed. This measure is based on a simple mathematical model that describes such networks as dynamical systems and on properties of ensembles of these dynamical systems. It is predicted that this probability depends only on the fraction of genes duplicated in a single event and that it is largest if approximately 40% of the genes in a network are duplicated. This property is robust with respect to variations in model parameters. On these grounds, it is argued that (i) evolution of gene networks should preferentially occur either by duplication of single genes or by duplication of all genes involved in a network, and that (ii) tight linkage ("clustering") or strong dispersal are the two evolutionarily most favorable forms of genomic organization of genes forming such networks.