Canards in stiction: on solutions of a friction oscillator by regularization

We study the solutions of a friction oscillator subject to stiction. This discontinuous model is non-Filippov, and the concept of Filippov solution cannot be used. Furthermore some Carath\'eodory solutions are unphysical. Therefore we introduce the concept of stiction solutions: these are the Carath\'eodory solutions that are physically relevant, i.e. the ones that follow the stiction law. However, we find that some of the stiction solutions are forward non-unique in subregions of the slip onset. We call these solutions singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We identify a repelling slow manifold that separates the forward slipping to forward sticking solutions, leading to a high sensitivity to the initial conditions. On this slow manifold we find canard trajectories, that have the physical interpretation of delaying the slip onset. We show with numerics that the regularized problem has a family of periodic orbits interacting with the canards. We observe that this family has a saddle stability and that it connects, in the rigid body limit, the two regular, slip-stick branches of the discontinuous problem, that were otherwise disconnected.Comment: Submitted to: SIADS. 28 pages, 12 figure

Development of simple sequence repeat markers specific for the Lr34 resistance region of wheat using sequence information from rice and Aegilops tauschii

Hexaploid wheat (Triticum aestivum L.) originated about 8,000years ago from the hybridization of tetraploid wheat with diploid Aegilops tauschii Coss. containing the D-genome. Thus, the bread wheat D-genome is evolutionary young and shows a low degree of polymorphism in the bread wheat gene pool. To increase marker density around the durable leaf rust resistance gene Lr34 located on chromosome 7DS, we used molecular information from the orthologous region in rice. Wheat expressed sequence tags (wESTs) were identified by homology with the rice genes in the interval of interest, but were monomorphic in the ‘Arina'בForno' mapping population. To derive new polymorphic markers, bacterial artificial chromosome (BAC) clones representing a total physical size of ∼1Mb and belonging to four contigs were isolated from Ae. tauschii by hybridization screening with wheat ESTs. Several BAC clones were low-pass sequenced, resulting in a total of ∼560kb of sequence. Ten microsatellite sequences were found, and three of them were polymorphic in our population and were genetically mapped close to Lr34. Comparative analysis of marker order revealed a large inversion between the rice genome and the wheat D-genome. The SWM10 microsatellite is closely linked to Lr34 and has the same allele in the three independent sources of Lr34: ‘Frontana', ‘Chinese Spring', and ‘Forno', as well in most of the genotypes containing Lr34. Therefore, SWM10 is a highly useful marker to assist selection for Lr34 in breeding programs worldwid

A novel bioinformatics pipeline to discover genes related to arbuscular mycorrhizal symbiosis based on their evolutionary conservation pattern among higher plants

Genes involved in arbuscular mycorrhizal (AM) symbiosis have been identified primarily by mutant screens, followed by identification of the mutated genes (forward genetics). In addition, a number of AM-related genes has been identified by their AM-related expression patterns, and their function has subsequently been elucidated by knock-down or knock-out approaches (reverse genetics). However, genes that are members of functionally redundant gene families, or genes that have a vital function and therefore result in lethal mutant phenotypes, are difficult to identify. If such genes are constitutively expressed and therefore escape differential expression analyses, they remain elusive. The goal of this study was to systematically search for AM-related genes with a bioinformatics strategy that is insensitive to these problems. The central element of our approach is based on the fact that many AM-related genes are conserved only among AM-competent species.Results: Our approach involves genome-wide comparisons at the proteome level of AM-competent host species with non-mycorrhizal species. Using a clustering method we first established orthologous/paralogous relationships and subsequently identified protein clusters that contain members only of the AM-competent species. Proteins of these clusters were then analyzed in an extended set of 16 plant species and ranked based on their relatedness among AM-competent monocot and dicot species, relative to non-mycorrhizal species. In addition, we combined the information on the protein-coding sequence with gene expression data and with promoter analysis. As a result we present a list of yet uncharacterized proteins that show a strongly AM-related pattern of sequence conservation, indicating that the respective genes may have been under selection for a function in AM. Among the top candidates are three genes that encode a small family of similar receptor-like kinases that are related to the S-locus receptor kinases involved in sporophytic self-incompatibility.Conclusions: We present a new systematic strategy of gene discovery based on conservation of the protein-coding sequence that complements classical forward and reverse genetics. This strategy can be applied to diverse other biological phenomena if species with established genome sequences fall into distinguished groups that differ in a defined functional trait of interest

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

Gene flow and diversification in a species complex of Alcantarea inselberg bromeliads

Inselberg-adapted species of bromeliads (Bromeliaceae) have been suggested as model systems for understanding the evolutionary genetics of species complexes and radiations in terrestrial, island-like environments. Bromeliads are particularly suitable for addressing the potential roles of interspecific gene exchange during plant speciation and radiation. We have studied populations of five narrowly endemic Alcantarea species adapted to high-elevation inselbergs of the Atlantic Rainforest of Brazil with nuclear and plastid DNA markers, estimated outcrossing rates in the giant bromeliad A. imperialis using progeny arrays and carried out a pilot study on the use of next generation sequencing-based genotyping in this group. Our results suggest widespread and asymmetric interspecific gene flow in the studied species complex, which visibly affects patterns of genetic diversity in the phenotypically variable mixed outcrosser A. imperialis. Our data support the hypothesis that gene flow has contributed to the origin of phenotypic forms in the A. imperialis s.l. species complex. We discuss potential conflicts between our neutral marker data and previous taxonomic work and suggest how these might be resolved. We close with a brief outlook on the potential of genomic tools to uncover the hidden links between genotypes, phenotypes and niches in bromeliads and other plant radiations

Gene Space Dynamics During the Evolution of Aegilops tauschii, Brachypodium distachyon, Oryza sativa, and Sorghum bicolor Genomes

Nine different regions totaling 9.7 Mb of the 4.02 Gb Aegilops tauschii genome were sequenced using the Sanger sequencing technology and compared with orthologous Brachypodium distachyon, Oryza sativa (rice), and Sorghum bicolor (sorghum) genomic sequences. The ancestral gene content in these regions was inferred and used to estimate gene deletion and gene duplication rates along each branch of the phylogenetic tree relating the four species. The total gene number in the extant Ae. tauschii genome was estimated to be 36,371. The gene deletion and gene duplication rates and total gene numbers in the four genomes were used to estimate the total gene number in each node of the phylogenetic tree. The common ancestor of the Brachypodieae and Triticeae lineages was estimated to have had 28,558 genes, and the common ancestor of the Panicoideae, Ehrhartoideae, and Pooideae subfamilies was estimated to have had 27,152 or 28,350 genes, depending on the ancestral gene scenario. Relative to the Brachypodieae and Triticeae common ancestor, the gene number was reduced in B. distachyon by 3,026 genes and increased in Ae. tauschii by 7,813 genes. The sum of gene deletion and gene duplication rates, which reflects the rate of gene synteny loss, was correlated with the rate of structural chromosome rearrangements and was highest in the Ae. tauschii lineage and lowest in the rice lineage. The high rate of gene space evolution in the Ae. tauschii lineage accounts for the fact that, contrary to the expectations, the level of synteny between the phylogenetically more related Ae. tauschii and B. distachyon genomes is similar to the level of synteny between the Ae. tauschii genome and the genomes of the less related rice and sorghum. The ratio of gene duplication to gene deletion rates in these four grass species closely parallels both the total number of genes in a species and the overall genome size. Because the overall genome size is to a large extent a function of the repeated sequence content in a genome, we suggest that the amount and activity of repeated sequences are important factors determining the number of genes in a genome

Control of flowering time and spike development in cereals: the earliness per se Eps-1 region in wheat, rice, and Brachypodium

The earliness per se gene Eps-Am1 from diploid wheat Triticum monococcum affects heading time, spike development, and spikelet number. In this study, the Eps1 orthologous regions from rice, Aegilops tauschii, and Brachypodium distachyon were compared as part of current efforts to clone this gene. A single Brachypodium BAC clone spanned the Eps-Am1 region, but a gap was detected in the A. tauschii physical map. Sequencing of the Brachypodium and A. tauschii BAC clones revealed three genes shared by the three species, which showed higher identity between wheat and Brachypodium than between them and rice. However, most of the structural changes were detected in the wheat lineage. These included an inversion encompassing the wg241-VatpC region and the presence of six unique genes. In contrast, only one unique gene (and one pseudogene) was found in Brachypodium and none in rice. Three genes were present in both Brachypodium and wheat but were absent in rice. Two of these genes, Mot1 and FtsH4, were completely linked to the earliness per se phenotype in the T. monococcum high-density genetic map and are candidates for Eps-Am1. Both genes were expressed in apices and developing spikes, as expected for Eps-Am1 candidates. The predicted MOT1 protein showed amino acid differences between the parental T. monococcum lines, but its effect is difficult to predict. Future steps to clone the Eps-Am1 gene include the generation of mot1 and ftsh4 mutants and the completion of the T. monococcum physical map to test for the presence of additional candidate genes

Origin and Diversification of Land Plant CC-Type Glutaredoxins

Glutaredoxins (GRXs) are ubiquitous glutathione-dependent oxidoreductase enzymes implicated in redox homeostasis, particularly oxidative stress response. Three major classes of GRX genes exist, the CPYC, CGFS classes are present in all pro- and eukaryote species, whereas the CC-type class GRXs are specific to land plants. In the basal land plant Physcomitrella patens, only two CC-type GRXs are present, compared with 21 in Arabidopsis. In contrast, sizes of the CPYC and CGFS classes remained rather similar throughout plant evolution, raising the interesting question as to when the CC-type GRXs first originated and how and why they expanded during land plant evolution. Recent evidence suggests that CC-type GRXs may have been recruited during evolution into diverse plant-specific functions of flower development (ROXY1, ROXY2) and pathogenesis response (ROXY19/GRX480). In the present study, GRX genes from the genomes of a range of green algae and evolutionarily diverse land plant species were identified; Ostreococcus, Micromonas, Volvox, Selaginella, Vitis, Sorghum, and Brachypodium. Previously identified sequences from Chlamydomonas, Physcomitrella, Oryza, Arabidopsis, and Populus were integrated to generate a more comprehensive understanding of the forces behind the evolution of various GRX classes. The analysis indicates that the CC-type GRXs probably arose by diversification from the CPYC class, at a time coinciding with colonization of land by plants. This strong differential expansion of the CC-type class occurred exclusively in the angiosperms, mainly through paleopolyploidy duplication events shortly after the monocot–eudicot split, and more recently through multiple tandem duplications that occurred independently in five investigated angiosperm lineages. The presented data suggest that following duplications, subfunctionalization, and subsequent neofunctionalization likely facilitated the sequestration of land plant-specific CC-type GRXs into novel functions such as development and pathogenesis response