Dynamic balance of segregation distortion and selection maintains normal allele sizes at the myotonic dystrophy locus

Myotonic dystrophy (DM), an autosomal dominant neurological disorder, is caused by CTG-repeat expansions at the DMPK locus, with affected individuals having ≤50 repeats of this trinucleotide. Reduced reproductive fitness of affected individuals and decreased viability of congenital DM have been noted. Expanded CTG-repeat alleles are highly unstable, predominantly yielding even higher repeat sizes. Preferential transmission of longer alleles from heterozygous mothers within the normal size range of alleles also is observed. In view of these observations, it is worth examining how DM has been maintained in human populations for hundreds of generations. We present an analysis of the dynamic properties of a model of joint effects of segregation distortion and selection (intensity of which increases with allele sizes of an individual's genotype). Our mathematical formulation and numerical analyses demonstrate that a weak segregation distortion during female meiosis, together with selection of comparable intensity (within the normal allele size range), can maintain an equilibrium distribution of allele frequencies. Genetic drift, acting in conjunction with the occasional contraction of alleles by mutation, can contribute to the balance of segregation distortion and mutation, in the sense that even weaker selection can explain the observed allele frequencies. The model is applied to CTG- repeat size distributions at the DMPK locus, observed in normal individuals from world populations.