Model of haplotype and phenotype in the evolution of a duplicated autoregulatory activator

Gene duplication is believed to play a major role in the evolution of genomic complexity. The presence of a duplicate frees a gene from the constraint of natural selection, leading to its loss of function or the gain of a novel one. Alternately, a pleiotropic gene might partition its functions among its duplicates, thus preserving both copies. Such arguments invoking duplication for novelty or specialisation are not qualitatively true of diploid genotypes, but only of haplotypes. In this paper, we study the consequences of regulatory interactions in diploid genotypes and explore how the context of allelic interactions gives rise to dynamical phenotypes that enable duplicate genes to spread in a population. The regulatory network we study is that of a single autoregulatory activator gene, and the two copies of the gene diverge either as alleles in a diploid species or as duplicates in haploids. These differences are in their transcriptional ability-either via alterations to its activating domain, or to its cis-regulatory binding repertoire. When cis-regulatory changes are introduced that partition multiple regulatory triggers among the duplicates, it is shown that mutually exclusive expression states of the duplicates that emerge are accompanied by a back-up facility: when a highly expressed gene is deleted, the previously unexpressed duplicate copy compensates for it. The diploid version of the regulatory network model can account for allele-specific expression variants, and a model of inheritance of the haplotype network enables us to trace the evolutionary consequence of heterozygous phenotypes. This is modelled for the variations in the activating domain of one copy, whereby stable as well as transiently bursting oscillations ensue in single cells. The evolutionary model shows that these phenotypic states accessible to a diploid, heterozygous genotype enable the spread of a duplicated haplotype.