A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

Degradation of [D-Leu]-Microcystin-LR by solar heterogeneous photocatalysis (TiO2)

The present study investigates the use of solar heterogeneous photocatalyis (TiO2) for the destruction of [D-Leu]-Microcystin-LR, powerful toxin of widespread occurrence within cyanobacteria blooms. We extracted [D-Leu]-Microcystin-LR from a culture of Microcystis spp. and used a flat plate glass reactor coated with TiO2 (Degussa, P25) for the degradation studies. The irradiance was measured during the experiments with the aid of a spectroradiometer. After the degradation experiments, toxin concentrations were determined by HPLC and mineralization by TOC analyses. Acute and chronic toxicities were, quantified using mice and phosphatase inhibition in vitro assays, respectively. According to the performed experiments, 150 min were necessary to reduce the toxin concentration to the WHO's guideline for drinking water (from 10 to 1 mu g L-1) and to mineralize 90% of the initial carbon content. Another important finding is that solar heterogeneous photocatalysis was a destructive process indeed, not only for the toxin, but also for the other extract components and degradation products generated. Moreover, toxicity tests using mice have shown that the acute effect caused by the initial sample was removed. However, tests using the phosphatase enzyme indicated that it may be formed products capable of inducing chronic effects on mammals. The performed experiments indicate the feasibility of using solar heterogeneous photocatalysis for treating contaminated water with [D-Leu]-Microcystin-LR, not only due to its destruction, but also to the significant removal of organic matter and acute toxicity that can be achieved. (C) 2012 Elsevier Ltd. All rights reserved.

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Convergent evolution of [D-Leucine1] microcystin-LR in taxonomically disparate cyanobacteria

Abstract Background Many important toxins and antibiotics are produced by non-ribosomal biosynthetic pathways. Microcystins are a chemically diverse family of potent peptide toxins and the end-products of a hybrid NRPS and PKS secondary metabolic pathway. They are produced by a variety of cyanobacteria and are responsible for the poisoning of humans as well as the deaths of wild and domestic animals around the world. The chemical diversity of the microcystin family is attributed to a number of genetic events that have resulted in the diversification of the pathway for microcystin assembly. Results Here, we show that independent evolutionary events affecting the substrate specificity of the microcystin biosynthetic pathway have resulted in convergence on a rare [D-Leu1] microcystin-LR chemical variant. We detected this rare microcystin variant from strains of the distantly related genera Microcystis, Nostoc, and Phormidium. Phylogenetic analysis performed using sequences of the catalytic domains within the mcy gene cluster demonstrated a clear recombination pattern in the adenylation domain phylogenetic tree. We found evidence for conversion of the gene encoding the McyA2 adenylation domain in strains of the genera Nostoc and Phormidium. However, point mutations affecting the substrate-binding sequence motifs of the McyA2 adenylation domain were associated with the change in substrate specificity in two strains of Microcystis. In addition to the main [D-Leu1] microcystin-LR variant, these two strains produced a new microcystin that was identified as [Met1] microcystin-LR. Conclusions Phylogenetic analysis demonstrated that both point mutations and gene conversion result in functional mcy gene clusters that produce the same rare [D-Leu1] variant of microcystin in strains of the genera Microcystis, Nostoc, and Phormidium. Engineering pathways to produce recombinant non-ribosomal peptides could provide new natural products or increase the activity of known compounds. Our results suggest that the replacement of entire adenylation domains could be a more successful strategy to obtain higher specificity in the modification of the non-ribosomal peptides than point mutations.