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According to Tzouvaras, a set is nontypical in the Russell sense if it belongs to a countable ordinal definable set. The class \mathbf {HNT} of all hereditarily nontypical sets satisfies all axioms of \mathbf {ZF} and the double inclusion \mathbf {HOD}\subseteq \mathbf {HNT}\subseteq \mathbf {V} holds. Several questions about the nature of such sets, recently proposed by Tzouvaras, are solved in this paper. In particular, a model of \mathbf {ZFC} is presented in which \mathbf {HOD}\subsetneqq \mathbf {HNT}\subsetneqq \mathbf {V}, and another model of \mathbf {ZFC} in which \mathbf {HNT} does not satisfy the axiom of choice. [ABSTRACT FROM AUTHOR]

The paper solves the problem of constructing an evolutionary tree and the evolution of structures along it. This problem has long been posed and extensively researched; it is formulated and discussed below. As a result, we construct an exact cubic-time algorithm which outputs a tree with the minimum cost of embedding into it and of embedding it into a given network (Theorem 1). We construct an algorithm that outputs a minimum embedding of a tree into a network, taking into account incomplete linear sorting; the algorithm depends linearly on the number of nodes in the network and is exact if the sorting cost is not less than the sum of the duplication cost and the loss cost (Theorem 3). We construct an exact approximately quadratic-time algorithm which, for arbitrary costs of SCJ operations, solves the problem of reconstruction of given structures on any two-star tree (Theorem 4). We construct an exact algorithm which reduced the problem of DCJ reconstruction of given structures on any star to a logarithmic-length sequence of SAT problems, each of them being of approximately quadratic size (Theorem 5). The theorems have rigorous and complete proofs of correctness and complexity of the algorithms, and are accompanied by numerical examples and numerous explanatory illustrations, including flowcharts. [ABSTRACT FROM AUTHOR]

Parasitic life-strategies in the phylum Nematoda (roundworms) are remarkably diverse and intricate in terms of evolution and taxonomy. By analysing novel rDNA data obtained on rare host-associated groups with unusual biology, we reveal paraphyly of the last major taxon with uncertain higher-rank classification that united solely parasitic nematodes (Marimermithida) to show that primarily marine parasitism only emerged independently and repeatedly in a few free-living lineages. We report secondary seaward ingression of land-based parasites (Mermithida) via invading hosts in the subtidal zone to illustrate the host-borne scenario of oceanic fish and mammal colonization by primarily terrestrial parasites (Spiruria). We also present the first molecular data on marine nematodes from unicellular hosts (foraminiferan protozoans) to demonstrate the independent origins of exploitative nematode associations at a microscopic scale. We argue that, in contrast with primarily intestinal associations arising from saprotrophy and commensalism, non-intestinal host capture (colonization of host body cavity or internal organs) is likely to be a primary route of transition to truly exploitative parasitism in roundworms. Predispositions to host capture in nematode morphology, ecology and life cycles imply its evolution as part of innate pre-adaptations to crossing environmental boundaries to enable multiple successful transitions to parasitism in the phylum history. [ABSTRACT FROM AUTHOR]

Abstract Background A long recognized problem is the inference of the supertree S that amalgamates a given set {Gj} of trees Gj, with leaves in each Gj being assigned homologous elements. We ground on an approach to find the tree S by minimizing the total cost of mappings αj of individual gene trees Gj into S. Traditionally, this cost is defined basically as a sum of duplications and gaps in each αj. The classical problem is to minimize the total cost, where S runs over the set of all trees that contain an exhaustive non-redundant set of species from all input Gj. Results We suggest a reformulation of the classical NP-hard problem of building a supertree in terms of the global minimization of the same cost functional but only over species trees S that consist of clades belonging to a fixed set P (e.g., an exhaustive set of clades in all Gj). We developed a deterministic solving algorithm with a low degree polynomial (typically cubic) time complexity with respect to the size of input data. We define an extensive set of elementary evolutionary events and suggest an original definition of mapping β of tree G into tree S. We introduce the cost functional c(G, S, f ) and define the mapping β as the global minimum of this functional with respect to the variable f, in which sense it is a generalization of classical mapping α. We suggest a reformulation of the classical NP-hard mapping (reconciliation) problem by introducing time slices into the species tree S and present a cubic time solving algorithm to compute the mapping β. We introduce two novel definitions of the evolutionary scenario based on mapping β or a random process of gene evolution along a species tree. Conclusions Developed algorithms are mathematically proved, which justifies the following statements. The supertree building algorithm finds exactly the global minimum of the total cost if only gene duplications and losses are allowed and the given sets of gene trees satisfies a certain condition. The mapping algorithm finds exactly the minimal mapping β, the minimal total cost and the evolutionary scenario as a minimum over all possible distributions of elementary evolutionary events along the edges of tree S. The algorithms and their effective software implementations provide useful tools in many biological studies. They facilitate processing of voluminous tree data in acceptable time still largely avoiding heuristics. Performance of the tools is tested with artificial and prokaryotic tree data. Reviewers This article was reviewed by Prof. Anthony Almudevar, Prof. Alexander Bolshoy (nominated by Prof. Peter Olofsson), and Prof. Marek Kimmel.

Abstract Background In previous work, we introduced a concept, a mathematical model and its computer realization that describe the interaction between bacterial and phage type RNA polymerases, protein factors, DNA and RNA secondary structures during transcription, including transcription initiation and termination. The model accurately reproduces changes of gene transcription level observed in polymerase sigma-subunit knockout and heat shock experiments in plant plastids. The corresponding computer program and a user guide are available at http://lab6.iitp.ru/en/rivals. Here we apply the model to the analysis of transcription and (partially) translation processes in the mitochondria of frog, rat and human. Notably, mitochondria possess only phage-type polymerases. We consider the entire mitochondrial genome so that our model allows RNA polymerases to complete more than one circle on the DNA strand. Results Our model of RNA polymerase interaction during transcription initiation and elongation accurately reproduces experimental data obtained for plastids. Moreover, it also reproduces evidence on bulk RNA concentrations and RNA half-lives in the mitochondria of frog, human with or without the MELAS mutation, and rat with normal (euthyroid) or hyposecretion of thyroid hormone (hypothyroid). The transcription characteristics predicted by the model include: (i) the fraction of polymerases terminating at a protein-dependent terminator in both directions (the terminator polarization), (ii) the binding intensities of the regulatory protein factor (mTERF) with the termination site and, (iii) the transcription initiation intensities (initiation frequencies) of all promoters in all five conditions (frog, healthy human, human with MELAS syndrome, healthy rat, and hypothyroid rat with aberrant mtDNA methylation). Using the model, absolute levels of all gene transcription can be inferred from an arbitrary array of the three transcription characteristics, whereas, for selected genes only relative RNA concentrations have been experimentally determined. Conversely, these characteristics and absolute transcription levels can be obtained using relative RNA concentrations and RNA half-lives known from various experimental studies. In this case, the “inverse problem” is solved with multi-objective optimization. Conclusions In this study, we demonstrate that our model accurately reproduces all relevant experimental data available for plant plastids, as well as the mitochondria of chordates. Using experimental data, the model is applied to estimate binding intensities of phage-type RNA polymerases to their promoters as well as predicting terminator characteristics, including polarization. In addition, one can predict characteristics of phage-type RNA polymerases and the transcription process that are difficult to measure directly, e.g., the association between the promoter’s nucleotide composition and the intensity of polymerase binding. To illustrate the application of our model in functional predictions, we propose a possible mechanism for MELAS syndrome development in human involving a decrease of Phe-tRNA, Val-tRNA and rRNA concentrations in the cell. In addition, we describe how changes in methylation patterns of the mTERF binding site and three promoters in hypothyroid rat correlate with changes in intensities of the mTERF binding and transcription initiations. Finally, we introduce an auxiliary model to describe the interaction between polysomal mRNA and ribonucleases.

Abstract Background Modeling of a complex biological process can explain the results of experimental studies and help predict its characteristics. Among such processes is transcription in the presence of competing RNA polymerases. This process involves RNA polymerases collision followed by transcription termination. Results A mathematical and computer simulation model is developed to describe the competition of RNA polymerases during genes transcription on complementary DNA strands. E.g., in the barley Hordeum vulgare the polymerase competition occurs in the locus containing plastome genes psbA, rpl23, rpl2 and four bacterial type promoters. In heat shock experiments on isolated chloroplasts, a twofold decrease of psbA transcripts and even larger increase of rpl23-rpl2 transcripts were observed, which is well reproduced in the model. The model predictions are in good agreement with virtually all relevant experimental data (knockout, heat shock, chromatogram data, etc.). The model allows to hypothesize a mechanism of cell response to knockout and heat shock, as well as a mechanism of gene expression regulation in presence of RNA polymerase competition. The model is implemented for multiprocessor platforms with MPI and supported on Linux and MS Windows. The source code written in C++ is available under the GNU General Public License from the laboratory website. A user-friendly GUI version is also provided at http://lab6.iitp.ru/en/rivals. Conclusions The developed model is in good agreement with virtually all relevant experimental data. The model can be applied to estimate intensities of binding of the holoenzyme and phage type RNA polymerase to their promoters using data on gene transcription levels, as well as to predict characteristics of RNA polymerases and the transcription process that are difficult to measure directly, e.g., the intensity (frequency) of holoenzyme binding to the promoter in correlation to its nucleotide composition and the type of σ-subunit, the amount of transcription initiation aborts, etc. The model can be used to make functional predictions, e.g., heat shock response in isolated chloroplasts and changes of gene transcription levels under knockout of different σ-subunits or RNA polymerases or due to gene expression regulation. Reviewers This article was reviewed by Dr. Anthony Almudevar, Dr. Aniko Szabo, Dr. Yuri Wolf (nominated by Dr. Peter Olofsson) and Prof. Marek Kimmel.

Abstract We demonstrate the scarcity of conserved bacterial-type promoters in plastids of Streptophyta and report widely conserved promoters only for genes psaA, psbA, psbB, psbE, rbcL. Among the reasonable explanations are: evolutionary changes of sigma subunit paralogs and phage-type RNA polymerases possibly entailing the loss of corresponding nuclear genes, de novo emergence of the promoters, their loss together with plastome genes; functional substitution of the promoter boxes by transcription activation factor binding sites. Reviewers This article was reviewed by Dr. Arcady Mushegian, and by Dr. Alexander Bolshoy and Dr. Yuri Wolf (both nominated by Dr. Purificación López-García).

Abstract Background Formation of alternative structures in mRNA in response to external stimuli, either direct or mediated by proteins or other RNAs, is a major mechanism of regulation of gene expression in bacteria. This mechanism has been studied in detail using experimental and computational approaches in proteobacteria and Firmicutes, but not in other groups of bacteria. Results Comparative analysis of amino acid biosynthesis operons in Actinobacteria resulted in identification of conserved regions upstream of several operons. Classical attenuators were predicted upstream of trp operons in Corynebacterium spp. and Streptomyces spp., and trpS and leuS genes in some Streptomyces spp. Candidate leader peptides with terminators were observed upstream of ilvB genes in Corynebacterium spp., Mycobacterium spp. and Streptomyces spp. Candidate leader peptides without obvious terminators were found upstream of cys operons in Mycobacterium spp. and several other species. A conserved pseudoknot (named LEU element) was identified upstream of leuA operons in most Actinobacteria. Finally, T-boxes likely involved in the regulation of translation initiation were observed upstream of ileS genes from several Actinobacteria. Conclusion The metabolism of tryptophan, cysteine and leucine in Actinobacteria seems to be regulated on the RNA level. In some cases the mechanism is classical attenuation, but in many cases some components of attenuators are missing. The most interesting case seems to be the leuA operon preceded by the LEU element that may fold into a conserved pseudoknot or an alternative structure. A LEU element has been observed in a transposase gene from Bifidobacterium longum, but it is not conserved in genes encoding closely related transposases despite a very high level of protein similarity. One possibility is that the regulatory region of the leuA has been co-opted from some element involved in transposition. Analysis of phylogenetic patterns allowed for identification of ML1624 of M. leprae and its orthologs as the candidate regulatory proteins that may bind to the LEU element. T-boxes upstream of the ileS genes are unusual, as their regulatory mechanism seems to be inhibition of translation initiation via a hairpin sequestering the Shine-Dalgarno box.

It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of OD elements. [ABSTRACT FROM AUTHOR]