Genes of cathepsin L-like proteases in Trypanosoma rangeli isolates: Markers for diagnosis, genotyping and phylogenetic relationships

We have sequenced genes encoding cathepsin L-like (CatL-like) cysteine proteases from isolates of Trypanosoma rangeli from humans, wild mammals and Rhodnius species of Central and South America. Phylogenetic trees of sequences encoding mature CatL-like enzymes of T rangeli and homologous genes from other trypanosomes, Leishmania spp. and bodonids positioned sequences of T rangeli (rangelipain) closest to T cruzi (cruzipain). Phylogenetic tree of kinetoplastids based on sequences of CatL-like was totally congruent with those derived from SSU rRNA and gGAPDH genes. Analysis of sequences from the CatL-like catalytic domains of 17 isolates representative of the overall phylogenetic diversity and geographical range of T rangeli supported all the lineages (A-D) previously defined using ribosomal and spliced leader genes. Comparison of the proteolytic activities of T rangeli isolates revealed heterogeneous banding profiles of cysteine proteases in gelatin gels, with differences even among isolates of the same lineage. CatL-like sequences proved to be excellent targets for diagnosis and genotyping of T rangeli by PCR. Data from CatL-like encoding genes agreed with results from previous studies of kDNA markers, and ribosomal and spliced leader genes, thereby corroborating clonal evolution, independent transmission cycles and the divergence of T rangeli lineages associated with sympatric species of Rhodnius. (c) 2009 Elsevier B.V. All rights reserved.

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.