The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability ρ as a function of recombination θ, effective population size N, linear systematic pressure v, and time t, predicting both ρrt, the decrease of association from founders and ρct, the increase by genetic drift, with ρt = ρrt + ρct. These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that ρ is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for ρ. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of ρ are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the ρ metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

Nonlinearity in genetic decoding: Homologous DNA replicase genes use alternatives of transcriptional slippage or translational frameshifting

The τ and γ subunits of DNA polymerase III are both encoded by a single gene in Escherichia coli and Thermus thermophilus. γ is two-thirds the size of τ and shares virtually all its amino acid sequence with τ. E. coli and T. thermophilus have evolved very different mechanisms for setting the approximate 1:1 ratio between τ and γ. Both mechanisms put ribosomes into alternate reading frames so that stop codons in the new frame serve to make the smaller γ protein. In E. coli, ≈50% of initiating ribosomes translate the dnaX mRNA conventionally to give τ, but the other 50% shift into the −1 reading frame at a specific site (A AAA AAG) in the mRNA to produce γ. In T. thermophilus ribosomal frameshifting is not required: the dnaX mRNA is a heterogeneous population of molecules with different numbers of A residues arising from transcriptional slippage on a run of nine T residues in the DNA template. Translation of the subpopulation containing nine As (or +/− multiples of three As) yields τ. The rest of the population of mRNAs (containing nine +/− nonmultiples of three As) puts ribosomes into the alternate reading frames to produce the γ protein(s). It is surprising that two rather similar dnaX sequences in E. coli and T. thermophilus lead to very different mechanisms of expression.