Biochemical and genetic properties of oligomeric structures: a general approach.

The oligomers constituted by association of different subunits can exist under multiple forms. In the case of the genetically variable proteins, such a multiplicity leads to numerous questions (i) on the enumerations: what is the number of active forms when a given subunit can make the oligomer inactive, or when the subunits are encoded by s alleles; (ii) on the subunit effects on biochemical properties: how to estimate these effects, are they equal, are there interactions between subunits, etc. Theoretical methods for the study of such oligomeric structures are developed, which mainly rely on linear model techniques. Peculiar properties examined are Vmax and Km, but also the quantities of the various oligomers, which depend on their association law. This approach is extended to the oligomers composed of different sets of subunits, as are for example some enzymes. These aspects are discussed from numerous bibliographic examples, with special reference to molecular interactions (protein complementation or molecular heterosis). Otherwise the genetic application of this theoretical approach is presented: it is possible to consider a genotype as an oligomer of alleles, and thus to study their effects and their interactions, in the one-locus case as well as in the several-loci case. The relevance of this generalization is discussed in connection with two other concepts, the "sequence space" used in molecular evolution and the regression of the genotypic values on the number of alleles used in quantitative genetics.