Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

The Salmonella pathogenicity island (SPI)-2 and SPI-1 type III secretion systems allow Salmonella serovar typhimurium to trigger colitis via MyD88-dependent and MyD88-independent mechanisms.

Salmonella typhimurium can colonize the gut, invade intestinal tissues, and cause enterocolitis. In vitro studies suggest different mechanisms leading to mucosal inflammation, including 1) direct modulation of proinflammatory signaling by bacterial type III effector proteins and 2) disruption or penetration of the intestinal epithelium so that penetrating bacteria or bacterial products can trigger innate immunity (i.e., TLR signaling). We studied these mechanisms in vivo using streptomycin-pretreated wild-type and knockout mice including MyD88(-/-) animals lacking an adaptor molecule required for signaling via most TLRs. The Salmonella SPI-1 and the SPI-2 type III secretion systems (TTSS) contributed to inflammation. Mutants that retain only a functional SPI-1 (M556; sseD::aphT) or a SPI-2 TTSS (SB161; DeltainvG) caused attenuated colitis, which reflected distinct aspects of the colitis caused by wild-type S. typhimurium: M556 caused diffuse cecal inflammation that did not require MyD88 signaling. In contrast, SB161 induced focal mucosal inflammation requiring MyD88. M556 but not SB161 was found in intestinal epithelial cells. In the lamina propria, M556 and SB161 appeared to reside in different leukocyte cell populations as indicated by differential CD11c staining. Only the SPI-2-dependent inflammatory pathway required aroA-dependent intracellular growth. Thus, S. typhimurium can use two independent mechanisms to elicit colitis in vivo: SPI-1-dependent and MyD88-independent signaling to epithelial cells and SPI-2-dependent intracellular proliferation in the lamina propria triggering MyD88-dependent innate immune responses.

Differential inflammatory response of dental pulp explants and fibroblasts to saliva

Abstract AIM: To investigate the inflammatory response of dental pulp fibroblasts and the respective explants to whole saliva. METHODOLOGY: Explants from human and porcine dental pulp tissue and isolated dental pulp fibroblasts were used to investigate the inflammatory response to sterile saliva. Cytokine and chemokine expression was assessed by RT-PCR. Western blot analysis and pharmacologic inhibitors were used to determine the involvement of signalling pathways. RESULTS: Dental pulp explants of human and porcine origin exposed to human saliva exhibited no major changes of IL-6 and IL-8 mRNA expression (P > 0.05). In contrast, isolated porcine and human dental pulp fibroblasts, when stimulated with human saliva, exhibited a vastly increased expression of IL-6 and IL-8 mRNA (P < 0.05). In pulp fibroblasts, saliva also increased the expression of other cytokines and chemokines via activation of NFkappaB, ERK and p38 signalling. Notably, a significantly reduced inflammatory response was elicited when pulp fibroblasts were transiently exposed to saliva. CONCLUSIONS: Saliva has a potential impact on inflammation of dental pulp fibroblasts in vitro but not when cells are embedded in the intrinsic extracellular matrix of the explant tissue.

Evaluation of cell responses toward adhesives with different photoinitiating systems

OBJECTIVES The photoinitiator diphenyl-(2,4,6-trimethylbenzoyl)phosphine oxide (TPO) is more reactive than a camphorquinone/amine (CQ) system, and TPO-based adhesives obtained a higher degree of conversion (DC) with fewer leached monomers. The hypothesis tested here is that a TPO-based adhesive is less toxic than a CQ-based adhesive. METHODS A CQ-based adhesive (SBU-CQ) (Scotchbond Universal, 3M ESPE) and its experimental counterpart with TPO (SBU-TPO) were tested for cytotoxicity in human pulp-derived cells (tHPC). Oxidative stress was analyzed by the generation of reactive oxygen species (ROS) and by the expression of antioxidant enzymes. A dentin barrier test (DBT) was used to evaluate cell viability in simulated clinical circumstances. RESULTS Unpolymerized SBU-TPO was significantly more toxic than SBU-CQ after a 24h exposure, and TPO alone (EC50=0.06mM) was more cytotoxic than CQ (EC50=0.88mM), EDMAB (EC50=0.68mM) or CQ/EDMAB (EC50=0.50mM). Cultures preincubated with BSO (l-buthionine sulfoximine), an inhibitor of glutathione synthesis, indicated a minor role of glutathione in cytotoxic responses toward the adhesives. Although the generation of ROS was not detected, a differential expression of enzymatic antioxidants revealed that cells exposed to unpolymerized SBU-TPO or SBU-CQ are subject to oxidative stress. Polymerized SBU-TPO was more cytotoxic than SBU-CQ under specific experimental conditions only, but no cytotoxicity was detected in a DBT with a 200μm dentin barrier. SIGNIFICANCE Not only DC and monomer-release determine the biocompatibility of adhesives, but also the cytotoxicity of the (photo-)initiator should be taken into account. Addition of TPO rendered a universal adhesive more toxic compared to CQ; however, this effect could be annulled by a thin dentin barrier.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.