The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

Discovery of nucleotide polymorphisms in the Musa gene pool by Ecotilling

Musa (banana and plantain) is an important genus for the global export market and in local markets where it provides staple food for approximately 400 million people. Hybridization and polyploidization of several (sub)species, combined with vegetative propagation and human selection have produced a complex genetic history. We describe the application of the Ecotilling method for the discovery and characterization of nucleotide polymorphisms in diploid and polyploid accessions of Musa. We discovered over 800 novel alleles in 80 accessions. Sequencing and band evaluation shows Ecotilling to be a robust and accurate platform for the discovery of polymorphisms in homologous and homeologous gene targets. In the process of validating the method, we identified two single nucleotide polymorphisms that may be deleterious for the function of a gene putatively important for phototropism. Evaluation of heterozygous polymorphism and haplotype blocks revealed a high level of nucleotide diversity in Musa accessions. We further applied a strategy for the simultaneous discovery of heterozygous and homozygous polymorphisms in diploid accessions to rapidly evaluate nucleotide diversity in accessions of the same genome type. This strategy can be used to develop hypotheses for inheritance patterns of nucleotide polymorphisms within and between genome types. We conclude that Ecotilling is suitable for diversity studies in Musa, that it can be considered for functional genomics studies and as tool in selecting germplasm for traditional and mutation breeding approaches

Classification of Plant Associated Bacteria Using RIF, a Computationally Derived DNA Marker

A DNA marker that distinguishes plant associated bacteria at the species level and below was derived by comparing six sequenced genomes of Xanthomonas, a genus that contains many important phytopathogens. This DNA marker comprises a portion of the dnaA replication initiation factor (RIF). Unlike the rRNA genes, dnaA is a single copy gene in the vast majority of sequenced bacterial genomes, and amplification of RIF requires genus-specific primers. In silico analysis revealed that RIF has equal or greater ability to differentiate closely related species of Xanthomonas than the widely used ribosomal intergenic spacer region (ITS). Furthermore, in a set of 263 Xanthomonas, Ralstonia and Clavibacter strains, the RIF marker was directly sequenced in both directions with a success rate approximately 16% higher than that for ITS. RIF frameworks for Xanthomonas, Ralstonia and Clavibacter were constructed using 682 reference strains representing different species, subspecies, pathovars, races, hosts and geographic regions, and contain a total of 109 different RIF sequences. RIF sequences showed subspecific groupings but did not place strains of X. campestris or X. axonopodis into currently named pathovars nor R. solanacearum strains into their respective races, confirming previous conclusions that pathovar and race designations do not necessarily reflect genetic relationships. The RIF marker also was sequenced for 24 reference strains from three genera in the Enterobacteriaceae: Pectobacterium, Pantoea and Dickeya. RIF sequences of 70 previously uncharacterized strains of Ralstonia, Clavibacter, Pectobacterium and Dickeya matched, or were similar to, those of known reference strains, illustrating the utility of the frameworks to classify bacteria below the species level and rapidly match unknown isolates to reference strains. The RIF sequence frameworks are available at the online RIF database, RIFdb, and can be queried for diagnostic purposes with RIF sequences obtained from unknown strains in both chromatogram and FASTA format

Purinergic signalling and immune cells

This review article provides a historical perspective on the role of purinergic signalling in the regulation of various subsets of immune cells from early discoveries to current understanding. It is now recognised that adenosine 5'-triphosphate (ATP) and other nucleotides are released from cells following stress or injury. They can act on virtually all subsets of immune cells through a spectrum of P2X ligand-gated ion channels and G protein-coupled P2Y receptors. Furthermore, ATP is rapidly degraded into adenosine by ectonucleotidases such as CD39 and CD73, and adenosine exerts additional regulatory effects through its own receptors. The resulting effect ranges from stimulation to tolerance depending on the amount and time courses of nucleotides released, and the balance between ATP and adenosine. This review identifies the various receptors involved in the different subsets of immune cells and their effects on the function of these cells