Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure

Domain architecture evolution of pattern-recognition receptors

In animals, the innate immune system is the first line of defense against invading microorganisms, and the pattern-recognition receptors (PRRs) are the key components of this system, detecting microbial invasion and initiating innate immune defenses. Two families of PRRs, the intracellular NOD-like receptors (NLRs) and the transmembrane Toll-like receptors (TLRs), are of particular interest because of their roles in a number of diseases. Understanding the evolutionary history of these families and their pattern of evolutionary changes may lead to new insights into the functioning of this critical system. We found that the evolution of both NLR and TLR families included massive species-specific expansions and domain shuffling in various lineages, which resulted in the same domain architectures evolving independently within different lineages in a process that fits the definition of parallel evolution. This observation illustrates both the dynamics of the innate immune system and the effects of “combinatorially constrained” evolution, where existence of the limited numbers of functionally relevant domains constrains the choices of domain architectures for new members in the family, resulting in the emergence of independently evolved proteins with identical domain architectures, often mistaken for orthologs

The Whereabouts of an Ancient Wanderer: Global Phylogeography of the Solitary Ascidian Styela plicata

Genetic tools have greatly aided in tracing the sources and colonization history of introduced species. However, recurrent introductions and repeated shuffling of populations may have blurred some of the genetic signals left by ancient introductions. Styela plicata is a solitary ascidian distributed worldwide. Although its origin remains unclear, this species is believed to have spread worldwide by travelling on ship's hulls. The goals of this study were to infer the genetic structure and global phylogeography of S. plicata and to look for present-day and historical genetic patterns. Two genetic markers were used: a fragment of the mitochondrial gene Cytochrome Oxidase subunit I (COI) and a fragment of the nuclear gene Adenine Nucleotide Transporter/ADP-ATP Translocase (ANT). A total of 368 individuals for COI and 315 for ANT were sequenced from 17 locations worldwide. The levels of gene diversity were moderate for COI to high for ANT. The Mediterranean populations showed the least diversity and allelic richness for both markers, while the Indian, Atlantic and Pacific Oceans had the highest gene and nucleotide diversities. Network and phylogenetic analyses with COI and ANT revealed two groups of alleles separated by 15 and 4 mutational steps, respectively. The existence of different lineages suggested an ancient population split. However, the geographic distributions of these groups did not show any consistent pattern, indicating different phylogeographic histories for each gene. Genetic divergence was significant for many population-pairs irrespective of the geographic distance among them. Stochastic introduction events are reflected in the uneven distribution of COI and ANT allele frequencies and groups among many populations. Our results confirmed that S. plicata has been present in all studied oceans for a long time, and that recurrent colonization events and occasional shuffling among populations have determined the actual genetic structure of this species

Can the understory affect the Hymenoptera parasitoids in a Eucalyptus plantation?

The understory in forest plantations can increase richness and diversity of natural enemies due to greater plant species richness. The objective of this study was to test the hypothesis that the presence of the understory and climatic season in the region (wet or dry) can increase the richness and abundance of Hymenoptera parasitoids in Eucalyptus plantations, in the municipality of Belo Oriente, Minas Gerais State, Brazil. In each eucalyptus cultivation (five areas of cultivation) ten Malaise traps were installed, five with the understory and five without it. A total of 9,639 individuals from 30 families of the Hymenoptera parasitoids were collected, with Mymaridae, Scelionidae, Encyrtidae and Braconidae being the most collected ones with 4,934, 1,212, 619 and 612 individuals, respectively. The eucalyptus stands with and without the understory showed percentage of individuals 45.65% and 54.35% collected, respectively. The understory did not represent a positive effect on the overall abundance of the individuals Hymenoptera in the E. grandis stands, but rather exerted a positive effect on the specific families of the parasitoids of this order

Rickettsia Phylogenomics: Unwinding the Intricacies of Obligate Intracellular Life

BACKGROUND: Completed genome sequences are rapidly increasing for Rickettsia, obligate intracellular alpha-proteobacteria responsible for various human diseases, including epidemic typhus and Rocky Mountain spotted fever. In light of phylogeny, the establishment of orthologous groups (OGs) of open reading frames (ORFs) will distinguish the core rickettsial genes and other group specific genes (class 1 OGs or C1OGs) from those distributed indiscriminately throughout the rickettsial tree (class 2 OG or C2OGs). METHODOLOGY/PRINCIPAL FINDINGS: We present 1823 representative (no gene duplications) and 259 non-representative (at least one gene duplication) rickettsial OGs. While the highly reductive (approximately 1.2 MB) Rickettsia genomes range in predicted ORFs from 872 to 1512, a core of 752 OGs was identified, depicting the essential Rickettsia genes. Unsurprisingly, this core lacks many metabolic genes, reflecting the dependence on host resources for growth and survival. Additionally, we bolster our recent reclassification of Rickettsia by identifying OGs that define the AG (ancestral group), TG (typhus group), TRG (transitional group), and SFG (spotted fever group) rickettsiae. OGs for insect-associated species, tick-associated species and species that harbor plasmids were also predicted. Through superimposition of all OGs over robust phylogeny estimation, we discern between C1OGs and C2OGs, the latter depicting genes either decaying from the conserved C1OGs or acquired laterally. Finally, scrutiny of non-representative OGs revealed high levels of split genes versus gene duplications, with both phenomena confounding gene orthology assignment. Interestingly, non-representative OGs, as well as OGs comprised of several gene families typically involved in microbial pathogenicity and/or the acquisition of virulence factors, fall predominantly within C2OG distributions. CONCLUSION/SIGNIFICANCE: Collectively, we determined the relative conservation and distribution of 14354 predicted ORFs from 10 rickettsial genomes across robust phylogeny estimation. The data, available at PATRIC (PathoSystems Resource Integration Center), provide novel information for unwinding the intricacies associated with Rickettsia pathogenesis, expanding the range of potential diagnostic, vaccine and therapeutic targets

An Anomalous Type IV Secretion System in Rickettsia Is Evolutionarily Conserved

Bacterial type IV secretion systems (T4SSs) comprise a diverse transporter family functioning in conjugation, competence, and effector molecule (DNA and/or protein) translocation. Thirteen genome sequences from Rickettsia, obligate intracellular symbionts/pathogens of a wide range of eukaryotes, have revealed a reduced T4SS relative to the Agrobacterium tumefaciens archetype (vir). However, the Rickettsia T4SS has not been functionally characterized for its role in symbiosis/virulence, and none of its substrates are known.Superimposition of T4SS structural/functional information over previously identified Rickettsia components implicate a functional Rickettsia T4SS. virB4, virB8 and virB9 are duplicated, yet only one copy of each has the conserved features of similar genes in other T4SSs. An extraordinarily duplicated VirB6 gene encodes five hydrophobic proteins conserved only in a short region known to be involved in DNA transfer in A. tumefaciens. virB1, virB2 and virB7 are newly identified, revealing a Rickettsia T4SS lacking only virB5 relative to the vir archetype. Phylogeny estimation suggests vertical inheritance of all components, despite gene rearrangements into an archipelago of five islets. Similarities of Rickettsia VirB7/VirB9 to ComB7/ComB9 proteins of epsilon-proteobacteria, as well as phylogenetic affinities to the Legionella lvh T4SS, imply the Rickettsiales ancestor acquired a vir-like locus from distantly related bacteria, perhaps while residing in a protozoan host. Modern modifications of these systems likely reflect diversification with various eukaryotic host cells.We present the rvh (Rickettsiales vir homolog) T4SS, an evolutionary conserved transporter with an unknown role in rickettsial biology. This work lays the foundation for future laboratory characterization of this system, and also identifies the Legionella lvh T4SS as a suitable genetic model

Between a Rock and a Hard Place: Habitat Selection in Female-Calf Humpback Whale (Megaptera novaeangliae) Pairs on the Hawaiian Breeding Grounds

The Au'au Channel between the islands of Maui and Lanai, Hawaii comprises critical breeding habitat for humpback whales (Megaptera novaeangliae) of the Central North Pacific stock. However, like many regions where marine mega-fauna gather, these waters are also the focus of a flourishing local eco-tourism and whale watching industry. Our aim was to establish current trends in habitat preference in female-calf humpback whale pairs within this region, focusing specifically on the busy, eastern portions of the channel. We used an equally-spaced zigzag transect survey design, compiled our results in a GIS model to identify spatial trends and calculated Neu's Indices to quantify levels of habitat use. Our study revealed that while mysticete female-calf pairs on breeding grounds typically favor shallow, inshore waters, female-calf pairs in the Au'au Channel avoided shallow waters (<20 m) and regions within 2 km of the shoreline. Preferred regions for female-calf pairs comprised water depths between 40–60 m, regions of rugged bottom topography and regions that lay between 4 and 6 km from a small boat harbor (Lahaina Harbor) that fell within the study area. In contrast to other humpback whale breeding grounds, there was only minimal evidence of typical patterns of stratification or segregation according to group composition. A review of habitat use by maternal females across Hawaiian waters indicates that maternal habitat choice varies between localities within the Hawaiian Islands, suggesting that maternal females alter their use of habitat according to locally varying pressures. This ability to respond to varying environments may be the key that allows wildlife species to persist in regions where human activity and critical habitat overlap