Identification and Phylogenetic Analysis of Tityus pachyurus and Tityus obscurus Novel Putative Na+-Channel Scorpion Toxins

Background: Colombia and Brazil are affected by severe cases of scorpionism. In Colombia the most dangerous accidents are caused by Tityus pachyurus that is widely distributed around this country. In the Brazilian Amazonian region scorpion stings are a common event caused by Tityus obscurus. The main objective of this work was to perform the molecular cloning of the putative Na+-channel scorpion toxins (NaScTxs) from T. pachyurus and T. obscurus venom glands and to analyze their phylogenetic relationship with other known NaScTxs from Tityus species. Methodology/Principal Findings: cDNA libraries from venom glands of these two species were constructed and five nucleotide sequences from T. pachyurus were identified as putative modulators of Na+-channels, and were named Tpa4, Tpa5, Tpa6, Tpa7 and Tpa8; the latter being the first anti-insect excitatory b-class NaScTx in Tityus scorpion venom to be described. Fifteen sequences from T. obscurus were identified as putative NaScTxs, among which three had been previously described, and the others were named To4 to To15. The peptides Tpa4, Tpa5, Tpa6, To6, To7, To9, To10 and To14 are closely related to the a-class NaScTxs, whereas Tpa7, Tpa8, To4, To8, To12 and To15 sequences are more related to the b-class NaScTxs. To5 is possibly an arthropod specific toxin. To11 and To13 share sequence similarities with both a and b NaScTxs. By means of phylogenetic analysis using the Maximum Parsimony method and the known NaScTxs from Tityus species, these toxins were clustered into 14 distinct groups. Conclusions/Significance: This communication describes new putative NaScTxs from T. pachyurus and T. obscurus and their phylogenetic analysis. The results indicate clear geographic separation between scorpions of Tityus genus inhabiting the Amazonian and Mountain Andes regions and those distributed over the Southern of the Amazonian rainforest. Based on the consensus sequences for the different clusters, a new nomenclature for the NaScTxs is proposed

Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms

We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop an algorithm to check whether the invariant measure of a given random walk is a sum of geometric terms. We also provide the explicit form of the invariant measure if it is a sum of geometric terms. Secondly, for random walks of which the invariant measure is not a sum of geometric terms, we provide an approximation scheme to obtain error bounds for the performance measures. Finally, some numerical examples are provided