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A reaction–diffusion model, known as the Sel'kov–Schnakenberg model, is considered. The nonlinear stability of the constant steady state is studied by using a special Liapunov functional and a maximum principle for regular solutions. [ABSTRACT FROM AUTHOR]

The final value value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed for quadratic and cubic types of Forchheimer nonlinearity. The main term in the Forchheimer equations is allowed to be fully anisotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in L 3. The technique employed avoids the use of a specialist method for an improperly posed problem such as logarithmic convexity. [ABSTRACT FROM AUTHOR]

The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights: A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction. [ABSTRACT FROM AUTHOR]

Mechanistic target of rapamycin (mTOR) enhances immunity in addition to orchestrating metabolism. Here we show that mTOR coordinates immunometabolic reconfiguration of marginal zone (MZ) B cells, a pre-activated lymphocyte subset that mounts antibody responses to T-cell-independent antigens through a Toll-like receptor (TLR)-amplified pathway involving transmembrane activator and CAML interactor (TACI). This receptor interacts with mTOR via the TLR adapter MyD88. The resulting mTOR activation instigates MZ B-cell proliferation, immunoglobulin G (IgG) class switching, and plasmablast differentiation through a rapamycin-sensitive pathway that integrates metabolic and antibody-inducing transcription programs, including NF-κB. Disruption of TACI–mTOR interaction by rapamycin, truncation of the MyD88-binding domain of TACI, or B-cell-conditional mTOR deficiency interrupts TACI signaling via NF-κB and cooperation with TLRs, thereby hampering IgG production to T-cell-independent antigens but not B-cell survival. Thus, mTOR drives innate-like antibody responses by linking proximal TACI signaling events with distal immunometabolic transcription programs. [ABSTRACT FROM AUTHOR]

Innate lymphoid cells (ILCs) regulate stromal cells, epithelial cells and cells of the immune system, but their effect on B cells remains unclear. Here we identified RORγt+ ILCs near the marginal zone (MZ), a splenic compartment that contains innate-like B cells highly responsive to circulating T cell-independent (TI) antigens. Splenic ILCs established bidirectional crosstalk with MAdCAM-1+ marginal reticular cells by providing tumor-necrosis factor (TNF) and lymphotoxin, and they stimulated MZ B cells via B cell-activation factor (BAFF), the ligand of the costimulatory receptor CD40 (CD40L) and the Notch ligand Delta-like 1 (DLL1). Splenic ILCs further helped MZ B cells and their plasma-cell progeny by coopting neutrophils through release of the cytokine GM-CSF. Consequently, depletion of ILCs impaired both pre- and post-immune TI antibody responses. Thus, ILCs integrate stromal and myeloid signals to orchestrate innate-like antibody production at the interface between the immune system and circulatory system. [ABSTRACT FROM AUTHOR]

Neutrophils use immunoglobulins to clear antigen, but their role in immunoglobulin production is unknown. Here we identified neutrophils around the marginal zone (MZ) of the spleen, a B cell area specialized in T cell-independent immunoglobulin responses to circulating antigen. Neutrophils colonized peri-MZ areas after postnatal mucosal colonization by microbes and enhanced their B cell-helper function after receiving reprogramming signals, including interleukin 10 (IL-10), from splenic sinusoidal endothelial cells. Splenic neutrophils induced immunoglobulin class switching, somatic hypermutation and antibody production by activating MZ B cells through a mechanism that involved the cytokines BAFF, APRIL and IL-21. Neutropenic patients had fewer and hypomutated MZ B cells and a lower abundance of preimmune immunoglobulins to T cell-independent antigens, which indicates that neutrophils generate an innate layer of antimicrobial immunoglobulin defense by interacting with MZ B cells. [ABSTRACT FROM AUTHOR]

Linear and nonlinear stability analyses of vertical throughflow in a fluid layer, where the density is quadratic in temperature, are studied. To avoid the loss of key terms a weighted functional is used in the energy analysis. Both conditional and unconditional thresholds are derived. When the throughflow is ascending the linear and nonlinear boundaries show substantial agreement. The linear boundary remains close to the conditional nonlinear boundary for descending throughflow, whilst the unconditional threshold begins to diverge. [ABSTRACT FROM AUTHOR]