Derivation of a macroscopic model for Brownian hard needles

We study the role of anisotropic steric interactions in a system of hard Brownian needles. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system, we use the method of matched asymptotic expansions and conformal mapping to systematically derive a nonlinear nonlocal partial differential equation for the evolution of the population density in position and orientation. We consider the regime of high rotational diffusion, resulting in an equation for the spatial density that allows us to compare the effective excluded volume of a hard-needles system with that of a hard-spheres system. We further consider spatially homogeneous solutions and find an isotropic to nematic transition as density increases, consistent with Onsager's theory

On a novel gradient flow structure for the aggregation equation

The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous inelastic Boltzmann equation, a formal Taylor expansion reveals a link between this equation and the aggregation equation with an appropriately chosen interaction potential. Inspired by this formal link and the fact that the associated aggregation equation also dissipates the kinetic energy, we present a novel way of interpreting the aggregation equation as a gradient flow, in the sense of curves of maximal slope, of the kinetic energy, rather than the usual interaction energy, with respect to an appropriately constructed transportation metric on the space of probability measures

On a novel gradient flow structure for the aggregation equation

The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous inelastic Boltzmann equation, a formal Taylor expansion reveals a link between this equation and the aggregation equation with an appropriately chosen interaction potential. Inspired by this formal link and the fact that the associated aggregation equation also dissipates the kinetic energy, we present a novel way of interpreting the aggregation equation as a gradient flow, in the sense of curves of maximal slope, of the kinetic energy, rather than the usual interaction energy, with respect to an appropriately constructed transportation metric on the space of probability measures.Comment: 37 pages. Restructured version. Comments welcom

Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table

Randomly Evolving Idiotypic Networks: Modular Mean Field Theory

We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular architectures, the building principles of which are known. The nodes of the network can be classified into groups of nodes, the modules, which share statistical properties. Each node experiences only the mean influence of the groups to which it is linked. Given the size of the groups and linking between them the statistical properties such as mean occupation, mean life time, and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations. For a pattern which consists of pairs of occupied nodes correlations are taken into account.Comment: 14 pages, 8 figures, 4 table

Thrombin and Plasmin Alter the Proteome of Neutrophil Extracellular Traps

Neutrophil extracellular traps (NETs) consist of a decondensed DNA scaffold decorated with neutrophil-derived proteins. The proteome of NETs, or “NETome,” has been largely elucidated in vitro. However, components such as plasma and extracellular matrix proteins may affect the NETome under physiological conditions. Here, using a reductionistic approach, we explored the effects of two proteases active during injury and wounding, human thrombin and plasmin, on the NETome. Using high-resolution mass spectrometry, we identified a total of 164 proteins, including those previously not described in NETs. The serine proteases, particularly thrombin, were also found to interact with DNA and bound to NETs in vitro. Among the most abundant proteins were those identified previously, including histones, neutrophil elastase, and antimicrobial proteins. We observed reduced histone (H2B, H3, and H4) and neutrophil elastase levels upon the addition of the two proteases. Analyses of NET-derived tryptic peptides identified subtle changes upon protease treatments. Our results provide evidence that exogenous proteases, present during wounding and inflammation, influence the NETome. Taken together, regulation of NETs and their proteins under different physiological conditions may affect their roles in infection, inflammation, and the host response

A major population of mucosal memory CD4⁺ T cells, coexpressing IL-18Rα and DR3, display innate lymphocyte functionality

Mucosal tissues contain large numbers of memory CD4(+) T cells that, through T-cell receptor-dependent interactions with antigen-presenting cells, are believed to have a key role in barrier defense and maintenance of tissue integrity. Here we identify a major subset of memory CD4(+) T cells at barrier surfaces that coexpress interleukin-18 receptor alpha (IL-18Rα) and death receptor-3 (DR3), and display innate lymphocyte functionality. The cytokines IL-15 or the DR3 ligand tumor necrosis factor (TNF)-like cytokine 1A (TL1a) induced memory IL-18Rα(+)DR3(+)CD4(+) T cells to produce interferon-γ, TNF-α, IL-6, IL-5, IL-13, granulocyte-macrophage colony-stimulating factor (GM-CSF), and IL-22 in the presence of IL-12/IL-18. TL1a synergized with IL-15 to enhance this response, while suppressing IL-15-induced IL-10 production. TL1a- and IL-15-mediated cytokine induction required the presence of IL-18, whereas induction of IL-5, IL-13, GM-CSF, and IL-22 was IL-12 independent. IL-18Rα(+)DR3(+)CD4(+) T cells with similar functionality were present in human skin, nasal polyps, and, in particular, the intestine, where in chronic inflammation they localized with IL-18-producing cells in lymphoid aggregates. Collectively, these results suggest that human memory IL-18Rα(+)DR3(+) CD4(+) T cells may contribute to antigen-independent innate responses at barrier surfaces.Mucosal Immunology advance online publication, 1 October 2014; doi:10.1038/mi.2014.87

Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions

We prove global-in-time existence and uniqueness of measure solutions of a nonlocal interaction system of two species in one spatial dimension. For initial data including atomic parts we provide a notion of gradient-flow solutions in terms of the pseudo-inverses of the corresponding cumulative distribution functions, for which the system can be stated as a gradient flow on the Hilbert space L 2 ( 0 , 1 ) 2 according to the classical theory by Brézis. For absolutely continuous initial data we construct solutions using a minimising movement scheme in the set of probability measures. In addition we show that the scheme preserves finiteness of the L m -norms for all m ∈ [ 1 , + ∞ ] and of the second moments. We then provide a characterisation of equilibria and prove that they are achieved (up to time subsequences) in the large time asymptotics. We conclude the paper constructing two examples of non-uniqueness of measure solutions emanating from the same (atomic) initial datum, showing that the notion of gradient flow solution is necessary to single out a unique measure solution

Protein C Inhibitor—A Novel Antimicrobial Agent

Protein C inhibitor (PCI) is a heparin-binding serine proteinase inhibitor belonging to the family of serpin proteins. Here we describe that PCI exerts broad antimicrobial activity against bacterial pathogens. This ability is mediated by the interaction of PCI with lipid membranes, which subsequently leads to their permeabilization. As shown by negative staining electron microscopy, treatment of Escherichia coli or Streptococcus pyogenes bacteria with PCI triggers membrane disruption followed by the efflux of bacterial cytosolic contents and bacterial killing. The antimicrobial activity of PCI is located to the heparin-binding site of the protein and a peptide spanning this region was found to mimic the antimicrobial activity of PCI, without causing lysis or membrane destruction of eukaryotic cells. Finally, we show that platelets can assemble PCI on their surface upon activation. As platelets are recruited to the site of a bacterial infection, these results may explain our finding that PCI levels are increased in tissue biopsies from patients suffering from necrotizing fasciitis caused by S. pyogenes. Taken together, our data describe a new function for PCI in innate immunity

Highly Selective End-Tagged Antimicrobial Peptides Derived from PRELP

Background: Antimicrobial peptides (AMPs) are receiving increasing attention due to resistance development against conventional antibiotics. Pseudomonas aeruginosa and Staphylococcus aureus are two major pathogens involved in an array of infections such as ocular infections, cystic fibrosis, wound and post-surgery infections, and sepsis. The goal of the study was to design novel AMPs against these pathogens. Methodology and Principal Findings: Antibacterial activity was determined by radial diffusion, viable count, and minimal inhibitory concentration assays, while toxicity was evaluated by hemolysis and effects on human epithelial cells. Liposome and fluorescence studies provided mechanistic information. Protease sensitivity was evaluated after subjection to human leukocyte elastase, staphylococcal aureolysin and V8 proteinase, as well as P. aeruginosa elastase. Highly active peptides were evaluated in ex vivo skin infection models. C-terminal end-tagging by W and F amino acid residues increased antimicrobial potency of the peptide sequences GRRPRPRPRP and RRPRPRPRP, derived from proline arginine-rich and leucine-rich repeat protein (PRELP). The optimized peptides were antimicrobial against a range of Gram-positive S. aureus and Gram-negative P. aeruginosa clinical isolates, also in the presence of human plasma and blood. Simultaneously, they showed low toxicity against mammalian cells. Particularly W-tagged peptides displayed stability against P. aeruginosa elastase, and S. aureus V8 proteinase and aureolysin, and the peptide RRPRPRPRPWWWW-NH2 was effective against various "superbugs'' including vancomycin-resistant enterococci, multi-drug resistant P. aeruginosa, and methicillin-resistant S. aureus, as well as demonstrated efficiency in an ex vivo skin wound model of S. aureus and P. aeruginosa infection. Conclusions/Significance: Hydrophobic C-terminal end-tagging of the cationic sequence RRPRPRPRP generates highly selective AMPs with potent activity against multiresistant bacteria and efficiency in ex vivo wound infection models. A precise "tuning'' of toxicity and proteolytic stability may be achieved by changing tag-length and adding W-or F-amino acid tags