Dosage, deletions and dominance: simple models of the evolution of gene expression

Dominance of the wild-type allele over spontaneous null mutations, such as deletions, can be explained in terms of the effects of changes in enzyme dose on the flux of metabolic pathways. If ever increasing levels of enzyme activity have ever decreasing effects on the flux of the biochemical pathway, then halving of dosage will always have a lesser effect on flux than half the effect of complete removal of gene activity. Furthermore, if gene expression rates are high, then halving of dose can have a negligible effect on flux and dominance will be strong. Given that strong dominance appears to be common, this leaves open the issue of why enzyme activity levels are so high that a halving of expression rates is of minimal effect. Why produce so much surplus enzyme? One explanation, suggested by Haldane, is that selection favoured high expression levels as a defence against mutation. We model this scenario formally and show that protection from mutation is an extremely weak force determining expression levels. The selective coefficients are only of the order of the mutation rate. However, if we suppose a linear mapping of flux with fitness and a monotonic cost to increased gene expression, it follows simply that here exists an optimal level of gene expression. By contrast to the mutational model, doubling of gene expression rates when the system is distant from the optimum is associated with extremely high selective coefficients (orders of magnitude higher than the mutation rate). When the cost of gene expression is slight the optimal rate of expression is such that strong dominance will follow.