Phylogeny of Parasitic Parabasalia and Free-Living Relatives Inferred from Conventional Markers vs. Rpb1, a Single-Copy Gene

Parabasalia are single-celled eukaryotes (protists) that are mainly comprised of endosymbionts of termites and wood roaches, intestinal commensals, human or veterinary parasites, and free-living species. Phylogenetic comparisons of parabasalids are typically based upon morphological characters and 18S ribosomal RNA gene sequence data (rDNA), while biochemical or molecular studies of parabasalids are limited to a few axenically cultivable parasites. These previous analyses and other studies based on PCR amplification of duplicated protein-coding genes are unable to fully resolve the evolutionary relationships of parabasalids. As a result, genetic studies of Parabasalia lag behind other organisms.Comparing parabasalid EF1α, α-tubulin, enolase and MDH protein-coding genes with information from the Trichomonas vaginalis genome reveals difficulty in resolving the history of species or isolates apart from duplicated genes. A conserved single-copy gene encodes the largest subunit of RNA polymerase II (Rpb1) in T. vaginalis and other eukaryotes. Here we directly sequenced Rpb1 degenerate PCR products from 10 parabasalid genera, including several T. vaginalis isolates and avian isolates, and compared these data by phylogenetic analyses. Rpb1 genes from parabasalids, diplomonads, Parabodo, Diplonema and Percolomonas were all intronless, unlike intron-rich homologs in Naegleria, Jakoba and Malawimonas.The phylogeny of Rpb1 from parasitic and free-living parabasalids, and conserved Rpb1 insertions, support Trichomonadea, Tritrichomonadea, and Hypotrichomonadea as monophyletic groups. These results are consistent with prior analyses of rDNA and GAPDH sequences and ultrastructural data. The Rpb1 phylogenetic tree also resolves species- and isolate-level relationships. These findings, together with the relative ease of Rpb1 isolation, make it an attractive tool for evaluating more extensive relationships within Parabasalia

Asymptotics of the frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer

A two-dimensional statement of the scattering problem for an oblique incident surface wave by an obstacle in the form of a submerged barrier is considered. If the barrier is vertical, the discrete spectrum of the problem is shown to be empty, but for an inclined barrier an eigenvalue appears below the threshold of the continuous spectrum and the corresponding trapped mode decays exponentially in the direction perpendicular to the obstacle. The behaviour of the eigenvalue is analyzed for small values of the angle of inclination from the vertica