Theoretical implications of the application of polymorphic protein systems to gene location on a trisomic chromosome, and its application to the haptoglobin phenotype frequencies in Down's syndrome

Abstract

In this, the first of a series of communications on the application of the study of polymorphic enzyme and protein systems to gene location on a trisomic chromosome, the theoretical implications are considered. Mathematical models for the expected phenotype shift have been examined, and have been expanded to include a three‐allele locus and a three‐allele locus with one allele being of the ‘silent’ variety. Some modifications in the existing mathematical models were necessary due to possible failure of electrophoretic and immuno‐electrophoretic separations to differentiate between some heterozygote forms. The mathematical models have been applied to a series of hi‐allelic polymorphic systems and one tri‐allelic system to determine the minimum number of subjets with trisomy that would be required to establish the presence or absence of a phenotype shift. The additional use of the techniques for estimating the position of the gene with respect to the centromere, and estimating the timing of the non‐disjunction are discussed. The application of Haldane's log ratio test (1956) involving the combining of the homozygous Corms is considered and applied to the phenotype data on the serum haptoglobins of 254 subjects with Down's syndrome and 853 mentally retarded control subjects.

Red cell polymorphisms in Down's syndrome. Gene frequencies and phenotype associations

“…Increasing information on study of, and normal data the methods of on larger numbers of, protein polymorphisms in general and enzymes in particular (for example, Harris & Hopkinson (1972) list 71 different loci) have already inspired several investigators to adopt this approach in studying gene location on trisomic chromosomes and the mechanisms involved in the maintenance of heterozygote advantage in disease (Rundle & Atkin 1971, Rundle et al 1972, Hsia et al 1969, Ball et al 1972). As we have shown elsewhere (Rundle 1973), the use of phenotype shift for gene location is extremely limited, as factors such as the distance from the centromere, frequency of 1st meiotic division non-disjunction and frequency of part-fertilisation non-disjunction will affect the degree of such a shift, and increase the number of subjects necessary for any significant conclusions to be drawn.…”