The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu

Hierarchies and Ranks for Persistence Pairs

We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial relationships between features in persistence diagrams, leading to a limited expressive power. We build upon a recently-introduced hierarchy of pairs in persistence diagrams that augments the pairing stored in persistence diagrams with information about which components merge. Our proposed hierarchy captures differences in branching structure. Moreover, we show how to use our hierarchy to measure the spatial stability of a pairing and we define a rank function for persistence pairs and demonstrate different applications.Comment: Topology-based Methods in Visualization 201

The GC-Rich Mitochondrial and Plastid Genomes of the Green Alga Coccomyxa Give Insight into the Evolution of Organelle DNA Nucleotide Landscape

Most of the available mitochondrial and plastid genome sequences are biased towards adenine and thymine (AT) over guanine and cytosine (GC). Examples of GC-rich organelle DNAs are limited to a small but eclectic list of species, including certain green algae. Here, to gain insight in the evolution of organelle nucleotide landscape, we present the GC-rich mitochondrial and plastid DNAs from the trebouxiophyte green alga Coccomyxa sp. C-169. We compare these sequences with other GC-rich organelle DNAs and argue that the forces biasing them towards G and C are nonadaptive and linked to the metabolic and/or life history features of this species. The Coccomyxa organelle genomes are also used for phylogenetic analyses, which highlight the complexities in trying to resolve the interrelationships among the core chlorophyte green algae, but ultimately favour a sister relationship between the Ulvophyceae and Chlorophyceae, with the Trebouxiophyceae branching at the base of the chlorophyte crown

The Plastid Genome of Eutreptiella Provides a Window into the Process of Secondary Endosymbiosis of Plastid in Euglenids

Euglenids are a group of protists that comprises species with diverse feeding modes. One distinct and diversified clade of euglenids is photoautotrophic, and its members bear green secondary plastids. In this paper we present the plastid genome of the euglenid Eutreptiella, which we assembled from 454 sequencing of Eutreptiella gDNA. Comparison of this genome and the only other available plastid genomes of photosynthetic euglenid, Euglena gracilis, revealed that they contain a virtually identical set of 57 protein coding genes, 24 genes fewer than the genome of Pyramimonas parkeae, the closest extant algal relative of the euglenid plastid. Searching within the transcriptomes of Euglena and Eutreptiella showed that 6 of the missing genes were transferred to the nucleus of the euglenid host while 18 have been probably lost completely. Euglena and Eutreptiella represent the deepest bifurcation in the photosynthetic clade, and therefore all these gene transfers and losses must have happened before the last common ancestor of all known photosynthetic euglenids. After the split of Euglena and Eutreptiella only one additional gene loss took place. The conservation of gene content in the two lineages of euglenids is in contrast to the variability of gene order and intron counts, which diversified dramatically. Our results show that the early secondary plastid of euglenids was much more susceptible to gene losses and endosymbiotic gene transfers than the established plastid, which is surprisingly resistant to changes in gene content

Biparental inheritance of plastidial and mitochondrial DNA and hybrid variegation in Pelargonium

Plastidial (pt) and mitochondrial (mt) genes usually show maternal inheritance. Non-Mendelian, biparental inheritance of plastids was first described by Baur (Z Indukt Abstamm Vererbungslehre 1:330–351, 1909) for crosses between Pelargonium cultivars. We have analyzed the inheritance of pt and mtDNA by examining the progeny from reciprocal crosses of Pelargoniumzonale and P. inquinans using nucleotide sequence polymorphisms of selected pt and mt genes. Sequence analysis of the progeny revealed biparental inheritance of both pt and mtDNA. Hybrid plants exhibited variegation: our data demonstrate that the inquinans chloroplasts, but not the zonale chloroplasts bleach out, presumably due to incompatibility of the former with the hybrid nuclear genome. Different distribution of maternal and paternal sequences could be observed in different sectors of the same leaf, in different leaves of the same plant, and in different plants indicating random segregation and sorting-out of maternal and paternal plastids and mitochondria in the hybrids. The substantial transmission of both maternal and paternal mitochondria to the progeny turns Pelargonium into a particular interesting subject for studies on the inheritance, segregation and recombination of mt genes

The evolution of the plastid chromosome in land plants: gene content, gene order, gene function

This review bridges functional and evolutionary aspects of plastid chromosome architecture in land plants and their putative ancestors. We provide an overview on the structure and composition of the plastid genome of land plants as well as the functions of its genes in an explicit phylogenetic and evolutionary context. We will discuss the architecture of land plant plastid chromosomes, including gene content and synteny across land plants. Moreover, we will explore the functions and roles of plastid encoded genes in metabolism and their evolutionary importance regarding gene retention and conservation. We suggest that the slow mode at which the plastome typically evolves is likely to be influenced by a combination of different molecular mechanisms. These include the organization of plastid genes in operons, the usually uniparental mode of plastid inheritance, the activity of highly effective repair mechanisms as well as the rarity of plastid fusion. Nevertheless, structurally rearranged plastomes can be found in several unrelated lineages (e.g. ferns, Pinaceae, multiple angiosperm families). Rearrangements and gene losses seem to correlate with an unusual mode of plastid transmission, abundance of repeats, or a heterotrophic lifestyle (parasites or myco-heterotrophs). While only a few functional gene gains and more frequent gene losses have been inferred for land plants, the plastid Ndh complex is one example of multiple independent gene losses and will be discussed in detail. Patterns of ndh-gene loss and functional analyses indicate that these losses are usually found in plant groups with a certain degree of heterotrophy, might rendering plastid encoded Ndh1 subunits dispensable

Evolutionary Diversification of Plant Shikimate Kinase Gene Duplicates

Shikimate kinase (SK; EC 2.7.1.71) catalyzes the fifth reaction of the shikimate pathway, which directs carbon from the central metabolism pool to a broad range of secondary metabolites involved in plant development, growth, and stress responses. In this study, we demonstrate the role of plant SK gene duplicate evolution in the diversification of metabolic regulation and the acquisition of novel and physiologically essential function. Phylogenetic analysis of plant SK homologs resolves an orthologous cluster of plant SKs and two functionally distinct orthologous clusters. These previously undescribed genes, shikimate kinase-like 1 (SKL1) and -2 (SKL2), do not encode SK activity, are present in all major plant lineages, and apparently evolved under positive selection following SK gene duplication over 400 MYA. This is supported by functional assays using recombinant SK, SKL1, and SKL2 from Arabidopsis thaliana (At) and evolutionary analyses of the diversification of SK-catalytic and -substrate binding sites based on theoretical structure models. AtSKL1 mutants yield albino and novel variegated phenotypes, which indicate SKL1 is required for chloroplast biogenesis. Extant SKL2 sequences show a strong genetic signature of positive selection, which is enriched in a protein–protein interaction module not found in other SK homologs. We also report the first kinetic characterization of plant SKs and show that gene expression diversification among the AtSK inparalogs is correlated with developmental processes and stress responses. This study examines the functional diversification of ancient and recent plant SK gene duplicates and highlights the utility of SKs as scaffolds for functional innovation

Mechanisms of metastasis

Metastasis is an enormously complex process that remains to be a major problem in the management of cancer. The fact that cancer patients might develop metastasis after years or even decades from diagnosis of the primary tumor makes the metastatic process even more complex. Over the years many hypotheses were developed to try to explain the inefficiency of the metastatic process, but none of these theories completely explains the current biological and clinical observations. In this review we summarize some of the proposed models that were developed in attempt to understand the mechanisms of tumor dissemination and colonization as well as metastatic progression

Vitamin C and infectious diseases

Non peer reviewe