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Abstract
Gene duplication is believed to play a major role in the evolution of genomic complexity.
The presence of a duplicate removes the constraint of natural selection upon the gene,
leading to its likely loss of function or, occasionally, the gain of a novel one.
Alternately, a pleiotropic gene might partition its functions among its duplicates,
thus preserving both copies. Duplicate genes is not a novelty for diploid genotypes,
but only for 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.