Models of Quantitative Variation of Flux in Metabolic Pathways

As a model of variation in a quantitative character, enzyme activity variation segregating in a population is assumed to affect the flux in simple metabolic pathways. The genetic variation of flux is partitioned into additive and nonadditive components. An interaction component of flux variance is present because the effect of an allelic substitution is modified by other substitutions which change the concentrations of shared metabolites. In a haploid population, the the proportion of interaction variance is a function of the gene frequencies at the loci contributing to the flux variation, enzyme activities of mutant and wild type at variable loci and activities at nonvariable loci. The proportion of interaction variance is inversely related to the ratio of mutant to wild-type activities at the loci controlling the enzyme activities. The interaction component as a function of gene frequencies is at a maximum with high mutant allele frequencies. In contrast, the dominance component which would apply to a diploid population is maximal as a proportion of the total when mutant alleles are at low frequencies. Unless there are many loci with large differences in activity between the alleles, the interaction component is a small proportion of the total variance. Data on enzyme activity variation from natural and artificial populations suggest that such variation generates little nonadditive variance despite the highly interactive nature of the underlying biochemical system.