Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Vagaries of the molecular clock

The hypothesis of the molecular evolutionary clock asserts that informational macromolecules (i.e., proteins and nucleic acids) evolve at rates that are constant through time and for different lineages. The clock hypothesis has been extremely powerful for determining evolutionary events of the remote past for which the fossil and other evidence is lacking or insufficient. I review the evolution of two genes, Gpdh and Sod. In fruit flies, the encoded glycerol-3-phosphate dehydrogenase (GPDH) protein evolves at a rate of 1.1 × 10−10 amino acid replacements per site per year when Drosophila species are compared that diverged within the last 55 million years (My), but a much faster rate of ≈4.5 × 10−10 replacements per site per year when comparisons are made between mammals (≈70 My) or Dipteran families (≈100 My), animal phyla (≈650 My), or multicellular kingdoms (≈1100 My). The rate of superoxide dismutase (SOD) evolution is very fast between Drosophila species (16.2 × 10−10 replacements per site per year) and remains the same between mammals (17.2) or Dipteran families (15.9), but it becomes much slower between animal phyla (5.3) and still slower between the three kingdoms (3.3). If we assume a molecular clock and use the Drosophila rate for estimating the divergence of remote organisms, GPDH yields estimates of 2,500 My for the divergence between the animal phyla (occurred ≈650 My) and 3,990 My for the divergence of the kingdoms (occurred ≈1,100 My). At the other extreme, SOD yields divergence times of 211 My and 224 My for the animal phyla and the kingdoms, respectively. It remains unsettled how often proteins evolve in such erratic fashion as GPDH and SOD.