Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known

The highly rearranged mitochondrial genomes of the crabs Maja crispata and Maja squinado (Majidae) and gene order evolution in Brachyura

Abstract We sequenced the mitochondrial genomes of the spider crabs Maja crispata and Maja squinado (Majidae, Brachyura). Both genomes contain the whole set of 37 genes characteristic of Bilaterian genomes, encoded on both \u3b1- and \u3b2-strands. Both species exhibit the same gene order, which is unique among known animal genomes. In particular, all the genes located on the \u3b2-strand form a single block. This gene order was analysed together with the other nine gene orders known for the Brachyura. Our study confirms that the most widespread gene order (BraGO) represents the plesiomorphic condition for Brachyura and was established at the onset of this clade. All other gene orders are the result of transformational pathways originating from BraGO. The different gene orders exhibit variable levels of genes rearrangements, which involve only tRNAs or all types of genes. Local homoplastic arrangements were identified, while complete gene orders remain unique and represent signatures that can have a diagnostic value. Brachyura appear to be a hot-spot of gene order diversity within the phylum Arthropoda. Our analysis, allowed to track, for the first time, the fully evolutionary pathways producing the Brachyuran gene orders. This goal was achieved by coupling sophisticated bioinformatic tools with phylogenetic analysis

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

The complete sequences and gene organisation of the mitochondrial genomes of the heterodont bivalves Acanthocardia tuberculata and Hiatella arctica – and the first record for a putative Atpase subunit 8 gene in marine bivalves

BACKGROUND: Mitochondrial (mt) gene arrangement is highly variable among molluscs and especially among bivalves. Of the 30 complete molluscan mt-genomes published to date, only one is of a heterodont bivalve, although this is the most diverse taxon in terms of species numbers. We determined the complete sequence of the mitochondrial genomes of Acanthocardia tuberculata and Hiatella arctica, (Mollusca, Bivalvia, Heterodonta) and describe their gene contents and genome organisations to assess the variability of these features among the Bivalvia and their value for phylogenetic inference. RESULTS: The size of the mt-genome in Acanthocardia tuberculata is 16.104 basepairs (bp), and in Hiatella arctica 18.244 bp. The Acanthocardia mt-genome contains 12 of the typical protein coding genes, lacking the Atpase subunit 8 (atp8) gene, as all published marine bivalves. In contrast, a complete atp8 gene is present in Hiatella arctica. In addition, we found a putative truncated atp8 gene when re-annotating the mt-genome of Venerupis philippinarum. Both mt-genomes reported here encode all genes on the same strand and have an additional trnM. In Acanthocardia several large non-coding regions are present. One of these contains 3.5 nearly identical copies of a 167 bp motive. In Hiatella, the 3' end of the NADH dehydrogenase subunit (nad)6 gene is duplicated together with the adjacent non-coding region. The gene arrangement of Hiatella is markedly different from all other known molluscan mt-genomes, that of Acanthocardia shows few identities with the Venerupis philippinarum. Phylogenetic analyses on amino acid and nucleotide levels robustly support the Heterodonta and the sister group relationship of Acanthocardia and Venerupis. Monophyletic Bivalvia are resolved only by a Bayesian inference of the nucleotide data set. In all other analyses the two unionid species, being to only ones with genes located on both strands, do not group with the remaining bivalves. CONCLUSION: The two mt-genomes reported here add to and underline the high variability of gene order and presence of duplications in bivalve and molluscan taxa. Some genomic traits like the loss of the atp8 gene or the encoding of all genes on the same strand are homoplastic among the Bivalvia. These characters, gene order, and the nucleotide sequence data show considerable potential of resolving phylogenetic patterns at lower taxonomic levels

A framework for orthology assignment from gene rearrangement data

Abstract. Gene rearrangements have successfully been used in phylogenetic reconstruction and comparative genomics, but usually under the assumption that all genomes have the same gene content and that no gene is duplicated. While these assumptions allow one to work with organellar genomes, they are too restrictive when comparing nuclear genomes. The main challenge is how to deal with gene families, specifically, how to identify orthologs. While searching for orthologies is a common task in computational biology, it is usually done using sequence data. We approach that problem using gene rearrangement data, provide an optimization framework in which to phrase the problem, and present some preliminary theoretical results.

The Complete Mitochondrial Genomes of Six Heterodont Bivalves (Tellinoidea and Solenoidea): Variable Gene Arrangements and Phylogenetic Implications

BACKGROUND: Taxonomy and phylogeny of subclass Heterodonta including Tellinoidea are long-debated issues and a complete agreement has not been reached yet. Mitochondrial (mt) genomes have been proved to be a powerful tool in resolving phylogenetic relationship. However, to date, only ten complete mitochondrial genomes of Heterodonta, which is by far the most diverse major group of Bivalvia, have been determined. In this paper, we newly sequenced the complete mt genomes of six species belonging to Heterodonta in order to resolve some problematical relationships among this subclass. PRINCIPAL FINDINGS: The complete mt genomes of six species vary in size from 16,352 bp to 18,182. Hairpin-like secondary structures are found in the largest non-coding regions of six freshly sequenced mt genomes, five of which contain tandem repeats. It is noteworthy that two species belonging to the same genus show different gene arrangements with three translocations. The phylogenetic analysis of Heterodonta indicates that Sinonovacula constricta, distant from the Solecurtidae belonging to Tellinoidea, is as a sister group with Solen grandis of family Solenidae. Besides, all five species of Tellinoidea cluster together, while Sanguinolaria diphos has closer relationship with Solecurtus divaricatus, Moerella iridescens and Semele scaba rather than with Sanguinolaria olivacea. CONCLUSIONS/SIGNIFICANCE: By comparative study of gene order rearrangements and phylogenetic relationships of the five species belonging to Tellinoidea, our results support that comparisons of mt gene order rearrangements, to some extent, are a useful tool for phylogenetic studies. Based on phylogenetic analyses of multiple protein-coding genes, we prefer classifying the genus Sinonovacula within the superfamily Solenoidea and not the superfamily Tellinoidea. Besides, both gene order and sequence data agree that Sanguinolaria (Psammobiidae) is not monophyletic. Nevertheless, more studies based on more mt genomes via combination of gene order and phylogenetic analysis are needed to further understand the phylogenetic relationships in subclass Heterodonta

The Mechanisms of Codon Reassignments in Mitochondrial Genetic Codes

Many cases of non-standard genetic codes are known in mitochondrial genomes. We carry out analysis of phylogeny and codon usage of organisms for which the complete mitochondrial genome is available, and we determine the most likely mechanism for codon reassignment in each case. Reassignment events can be classified according to the gain-loss framework. The gain represents the appearance of a new tRNA for the reassigned codon or the change of an existing tRNA such that it gains the ability to pair with the codon. The loss represents the deletion of a tRNA or the change in a tRNA so that it no longer translates the codon. One possible mechanism is Codon Disappearance, where the codon disappears from the genome prior to the gain and loss events. In the alternative mechanisms the codon does not disappear. In the Unassigned Codon mechanism, the loss occurs first, whereas in the Ambiguous Intermediate mechanism, the gain occurs first. Codon usage analysis gives clear evidence of cases where the codon disappeared at the point of the reassignment and also cases where it did not disappear. Codon disappearance is the probable explanation for stop to sense reassignments and a small number of reassignments of sense codons. However, the majority of sense to sense reassignments cannot be explained by codon disappearance. In the latter cases, by analysis of the presence or absence of tRNAs in the genome and of the changes in tRNA sequences, it is sometimes possible to distinguish between the Unassigned Codon and Ambiguous Intermediate mechanisms. We emphasize that not all reassignments follow the same scenario and that it is necessary to consider the details of each case carefully.Comment: 53 pages (45 pages, including 4 figures + 8 pages of supplementary information). To appear in J.Mol.Evo

The mitochondrial genome of Sinentomon erythranum (Arthropoda: Hexapoda: Protura): an example of highly divergent evolution

<p>Abstract</p> <p>Background</p> <p>The phylogenetic position of the Protura, traditionally considered the most basal hexapod group, is disputed because it has many unique morphological characters compared with other hexapods. Although mitochondrial genome information has been used extensively in phylogenetic studies, such information is not available for the Protura. This has impeded phylogenetic studies on this taxon, as well as the evolution of the arthropod mitochondrial genome.</p> <p>Results</p> <p>In this study, the mitochondrial genome of <it>Sinentomon erythranum </it>was sequenced, as the first proturan species to be reported. The genome contains a number of special features that differ from those of other hexapods and arthropods. As a very small arthropod mitochondrial genome, its 14,491 nucleotides encode 37 typical mitochondrial genes. Compared with other metazoan mtDNA, it has the most biased nucleotide composition with T = 52.4%, an extreme and reversed AT-skew of -0.351 and a GC-skew of 0.350. Two tandemly repeated regions occur in the A+T-rich region, and both could form stable stem-loop structures. Eighteen of the 22 tRNAs are greatly reduced in size with truncated secondary structures. The gene order is novel among available arthropod mitochondrial genomes. Rearrangements have involved in not only small tRNA genes, but also PCGs (protein-coding genes) and ribosome RNA genes. A large block of genes has experienced inversion and another nearby block has been reshuffled, which can be explained by the tandem duplication and random loss model. The most remarkable finding is that <it>trnL2(UUR) </it>is not located between <it>cox1 </it>and <it>cox2 </it>as observed in most hexapod and crustacean groups, but is between <it>rrnL </it>and <it>nad1 </it>as in the ancestral arthropod ground pattern. The "<it>cox1</it>-<it>cox2</it>" pattern was further confirmed in three more representative proturan species. The phylogenetic analyses based on the amino acid sequences of 13 mitochondrial PCGs suggest <it>S</it>. <it>erythranum </it>failed to group with other hexapod groups.</p> <p>Conclusions</p> <p>The mitochondrial genome of <it>S. erythranum </it>shows many different features from other hexapod and arthropod mitochondrial genomes. It underwent highly divergent evolution. The "<it>cox1</it>-<it>cox2</it>" pattern probably represents the ancestral state for all proturan mitogenomes, and suggests a long evolutionary history for the Protura.</p